TSTP Solution File: ALG136+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG136+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:36:58 EDT 2023
% Result : Unsatisfiable 12.55s 2.44s
% Output : Proof 118.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG136+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon Aug 28 05:02:41 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.34/1.39 Prover 1: Preprocessing ...
% 4.34/1.39 Prover 4: Preprocessing ...
% 5.01/1.42 Prover 0: Preprocessing ...
% 5.01/1.42 Prover 2: Preprocessing ...
% 5.01/1.42 Prover 6: Preprocessing ...
% 5.01/1.43 Prover 5: Preprocessing ...
% 5.01/1.43 Prover 3: Preprocessing ...
% 8.27/1.84 Prover 2: Constructing countermodel ...
% 8.27/1.85 Prover 3: Constructing countermodel ...
% 8.70/1.93 Prover 6: Constructing countermodel ...
% 8.70/1.93 Prover 1: Constructing countermodel ...
% 8.70/1.93 Prover 4: Constructing countermodel ...
% 8.70/1.94 Prover 0: Constructing countermodel ...
% 9.85/2.14 Prover 5: Constructing countermodel ...
% 12.55/2.44 Prover 0: proved (1806ms)
% 12.55/2.44
% 12.55/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.55/2.44
% 12.55/2.44 Prover 6: stopped
% 12.55/2.45 Prover 2: stopped
% 12.55/2.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.55/2.45 Prover 3: stopped
% 12.55/2.46 Prover 5: stopped
% 12.97/2.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.97/2.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.97/2.48 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.97/2.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.34/2.66 Prover 10: Preprocessing ...
% 14.34/2.68 Prover 8: Preprocessing ...
% 14.34/2.68 Prover 13: Preprocessing ...
% 14.34/2.69 Prover 7: Preprocessing ...
% 14.34/2.69 Prover 11: Preprocessing ...
% 15.28/2.80 Prover 8: Constructing countermodel ...
% 15.98/2.92 Prover 11: Constructing countermodel ...
% 15.98/2.92 Prover 13: Constructing countermodel ...
% 15.98/2.95 Prover 10: Constructing countermodel ...
% 15.98/2.96 Prover 7: Constructing countermodel ...
% 61.85/8.93 Prover 13: stopped
% 61.85/8.93 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 62.44/9.02 Prover 16: Preprocessing ...
% 64.13/9.21 Prover 16: Constructing countermodel ...
% 104.17/14.48 Prover 8: Found proof (size 245087)
% 104.17/14.49 Prover 8: proved (11958ms)
% 104.17/14.49 Prover 16: stopped
% 104.17/14.49 Prover 11: stopped
% 104.17/14.49 Prover 7: stopped
% 104.17/14.49 Prover 10: stopped
% 104.17/14.49 Prover 4: stopped
% 104.74/14.50 Prover 1: stopped
% 104.74/14.50
% 104.74/14.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 104.74/14.50
% 106.23/15.19 % SZS output start Proof for theBenchmark
% 106.23/15.23 Assumptions after simplification:
% 106.23/15.23 ---------------------------------
% 106.23/15.23
% 106.23/15.23 (ax1)
% 106.49/15.28 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.28 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 106.49/15.28 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 106.49/15.28 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 106.49/15.28 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 106.49/15.28 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 106.49/15.28 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 106.49/15.28 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 106.49/15.28 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 106.49/15.28 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 106.49/15.28 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 106.49/15.28 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 106.49/15.28 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 106.49/15.28 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 106.49/15.28 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 106.49/15.28 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 106.49/15.28 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 106.49/15.28 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 106.49/15.28 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 106.49/15.28
% 106.49/15.28 (ax10)
% 106.49/15.28 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.28 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e3)))
% 106.49/15.29
% 106.49/15.29 (ax11)
% 106.49/15.29 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.29 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e3)))
% 106.49/15.29
% 106.49/15.29 (ax12)
% 106.49/15.29 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.29 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e0)))
% 106.49/15.29
% 106.49/15.29 (ax13)
% 106.49/15.29 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.29 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e0)))
% 106.49/15.29
% 106.49/15.29 (ax14)
% 106.49/15.29 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.29 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e2)))
% 106.49/15.29
% 106.49/15.29 (ax15)
% 106.49/15.29 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.29 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.29 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e2)))
% 106.49/15.29
% 106.49/15.29 (ax16)
% 106.49/15.30 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.30 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.49/15.30 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e3)))
% 106.49/15.30
% 106.49/15.30 (ax17)
% 106.49/15.30 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.30 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.30 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e3)))
% 106.49/15.30
% 106.49/15.30 (ax18)
% 106.49/15.30 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.30 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.49/15.30 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e0)))
% 106.49/15.30
% 106.49/15.30 (ax19)
% 106.49/15.30 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.30 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.49/15.30 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e0)))
% 106.49/15.30
% 106.49/15.30 (ax2)
% 106.49/15.31 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.31 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 106.49/15.31 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 106.49/15.31 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 106.49/15.31 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 106.49/15.31 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 106.49/15.31 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 106.49/15.31 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 106.49/15.31 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 106.49/15.31 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 =
% 106.49/15.31 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 |
% 106.49/15.31 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 =
% 106.49/15.31 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3
% 106.49/15.31 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0
% 106.49/15.31 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 =
% 106.49/15.31 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 =
% 106.49/15.31 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 106.49/15.31 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 =
% 106.49/15.31 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5
% 106.49/15.31 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 |
% 106.49/15.31 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0
% 106.49/15.31 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3)
% 106.49/15.31 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 106.49/15.31 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 |
% 106.49/15.31 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 |
% 106.49/15.31 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) &
% 106.49/15.31 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 106.49/15.31 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 |
% 106.49/15.31 v1 = e0))))
% 106.49/15.31
% 106.49/15.31 (ax20)
% 106.49/15.31 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.31 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.49/15.31 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e1)))
% 106.49/15.31
% 106.49/15.31 (ax21)
% 106.49/15.31 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.31 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.31 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e1)))
% 106.49/15.31
% 106.49/15.31 (ax22)
% 106.49/15.31 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.31 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.49/15.31 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e3)))
% 106.49/15.31
% 106.49/15.31 (ax23)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e3)))
% 106.49/15.32
% 106.49/15.32 (ax24)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e0)))
% 106.49/15.32
% 106.49/15.32 (ax25)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e0)))
% 106.49/15.32
% 106.49/15.32 (ax26)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e1)))
% 106.49/15.32
% 106.49/15.32 (ax27)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e1)))
% 106.49/15.32
% 106.49/15.32 (ax28)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e2)))
% 106.49/15.32
% 106.49/15.32 (ax29)
% 106.49/15.32 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.32 (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 106.49/15.32 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e2)))
% 106.49/15.32
% 106.49/15.32 (ax3)
% 106.49/15.33 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.49/15.33 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 106.49/15.33 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 106.49/15.33 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 106.49/15.33 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 106.49/15.33 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 106.49/15.33 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 106.49/15.33 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 106.49/15.33 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 106.49/15.33 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 106.49/15.33 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 106.49/15.33 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 106.49/15.33 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 106.49/15.33 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 106.49/15.33 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 106.49/15.33 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 106.49/15.33 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 106.49/15.33 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 106.49/15.33 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 106.49/15.33 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 106.49/15.33
% 106.49/15.33 (ax4)
% 106.49/15.33 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 106.49/15.33 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 106.49/15.33
% 106.49/15.33 (ax5)
% 106.86/15.34 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.86/15.34 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 106.86/15.34 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 106.86/15.34 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v3 = e3) & ~ (v2 = e2) & ~ (v1 =
% 106.86/15.34 e1) & ~ (v0 = e0) & op(e3, e3) = v3 & op(e3, e2) = v15 & op(e3, e1) = v14
% 106.86/15.34 & op(e3, e0) = v13 & op(e2, e3) = v12 & op(e2, e2) = v2 & op(e2, e1) = v11 &
% 106.86/15.34 op(e2, e0) = v10 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1, e1) = v1 &
% 106.86/15.34 op(e1, e0) = v7 & op(e0, e3) = v6 & op(e0, e2) = v5 & op(e0, e1) = v4 &
% 106.86/15.34 op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10)
% 106.86/15.34 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 106.86/15.34 $i(v1) & $i(v0) & ( ~ (v15 = e3) | ~ (v3 = e2)) & ( ~ (v15 = e3) | ~ (v1 =
% 106.86/15.34 e2)) & ( ~ (v15 = e3) | ~ (v0 = e2)) & ( ~ (v14 = e3) | ~ (v3 = e1)) &
% 106.86/15.34 ( ~ (v14 = e3) | ~ (v2 = e1)) & ( ~ (v14 = e3) | ~ (v0 = e1)) & ( ~ (v13 =
% 106.86/15.34 e3) | ~ (v3 = e0)) & ( ~ (v13 = e3) | ~ (v2 = e0)) & ( ~ (v13 = e3) |
% 106.86/15.34 ~ (v1 = e0)) & ( ~ (v12 = e2) | ~ (v2 = e3)) & ( ~ (v12 = e2) | ~ (v1 =
% 106.86/15.34 e3)) & ( ~ (v12 = e2) | ~ (v0 = e3)) & ( ~ (v11 = e2) | ~ (v3 = e1)) &
% 106.86/15.34 ( ~ (v11 = e2) | ~ (v2 = e1)) & ( ~ (v11 = e2) | ~ (v0 = e1)) & ( ~ (v10 =
% 106.86/15.34 e2) | ~ (v3 = e0)) & ( ~ (v10 = e2) | ~ (v2 = e0)) & ( ~ (v10 = e2) |
% 106.86/15.34 ~ (v1 = e0)) & ( ~ (v9 = e1) | ~ (v2 = e3)) & ( ~ (v9 = e1) | ~ (v1 =
% 106.86/15.34 e3)) & ( ~ (v9 = e1) | ~ (v0 = e3)) & ( ~ (v8 = e1) | ~ (v3 = e2)) & (
% 106.86/15.34 ~ (v8 = e1) | ~ (v1 = e2)) & ( ~ (v8 = e1) | ~ (v0 = e2)) & ( ~ (v7 =
% 106.86/15.34 e1) | ~ (v3 = e0)) & ( ~ (v7 = e1) | ~ (v2 = e0)) & ( ~ (v7 = e1) | ~
% 106.86/15.34 (v1 = e0)) & ( ~ (v6 = e0) | ~ (v2 = e3)) & ( ~ (v6 = e0) | ~ (v1 = e3))
% 106.86/15.34 & ( ~ (v6 = e0) | ~ (v0 = e3)) & ( ~ (v5 = e0) | ~ (v3 = e2)) & ( ~ (v5 =
% 106.86/15.34 e0) | ~ (v1 = e2)) & ( ~ (v5 = e0) | ~ (v0 = e2)) & ( ~ (v4 = e0) | ~
% 106.86/15.34 (v3 = e1)) & ( ~ (v4 = e0) | ~ (v2 = e1)) & ( ~ (v4 = e0) | ~ (v0 =
% 106.86/15.34 e1)))
% 106.86/15.34
% 106.86/15.34 (ax6)
% 106.86/15.34 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.86/15.34 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.86/15.34 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e1)))
% 106.86/15.34
% 106.86/15.34 (ax7)
% 106.86/15.34 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.86/15.34 (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 106.86/15.34 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e1)))
% 106.86/15.34
% 106.86/15.34 (ax8)
% 106.86/15.34 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.86/15.34 (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 106.86/15.34 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e2)))
% 106.86/15.34
% 106.86/15.34 (ax9)
% 106.86/15.34 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 106.86/15.34 (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 106.86/15.34 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e2)))
% 106.86/15.35
% 106.86/15.35 (function-axioms)
% 106.86/15.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 106.86/15.35 v2) = v1) | ~ (op(v3, v2) = v0))
% 106.86/15.35
% 106.86/15.35 Those formulas are unsatisfiable:
% 106.86/15.35 ---------------------------------
% 106.86/15.35
% 106.86/15.35 Begin of proof
% 106.86/15.35 |
% 106.86/15.35 | ALPHA: (ax1) implies:
% 106.86/15.36 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 106.86/15.36 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 106.86/15.36 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 106.86/15.36 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 106.86/15.36 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 106.86/15.36 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 106.86/15.36 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 106.86/15.36 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 106.86/15.36 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 106.86/15.36 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 106.86/15.36 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 106.86/15.36 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 106.86/15.37 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 106.86/15.37 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 106.86/15.37 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 106.86/15.37 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 106.86/15.37 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 106.86/15.37 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 106.86/15.37 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 106.86/15.37 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 106.86/15.37 | = e0))
% 106.86/15.37 |
% 106.86/15.37 | ALPHA: (ax2) implies:
% 107.04/15.38 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.04/15.38 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.04/15.38 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.04/15.38 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11
% 107.04/15.38 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1)
% 107.04/15.38 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1,
% 107.04/15.38 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 107.04/15.38 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 107.04/15.38 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 107.04/15.38 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 107.04/15.38 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 =
% 107.04/15.38 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13
% 107.04/15.38 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 =
% 107.04/15.38 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 =
% 107.04/15.39 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 =
% 107.04/15.39 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 =
% 107.04/15.39 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1)
% 107.04/15.39 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 107.04/15.39 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) &
% 107.04/15.39 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 107.04/15.39 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) &
% 107.04/15.39 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7
% 107.04/15.39 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 =
% 107.04/15.39 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 107.04/15.39 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8
% 107.04/15.39 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3)
% 107.04/15.39 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 107.04/15.39 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2
% 107.04/15.39 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 107.04/15.39 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 =
% 107.04/15.39 | e0 | v1 = e0))))
% 107.04/15.39 |
% 107.04/15.39 | ALPHA: (ax3) implies:
% 107.04/15.39 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.04/15.39 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 107.04/15.39 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 107.04/15.39 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 107.04/15.39 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 107.04/15.39 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 107.04/15.39 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 107.04/15.40 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 107.04/15.40 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 107.04/15.40 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 107.04/15.40 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 107.04/15.40 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 107.04/15.40 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 107.04/15.40 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 107.04/15.40 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 107.04/15.40 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 107.04/15.40 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 107.04/15.40 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 107.04/15.40 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 107.04/15.40 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 107.04/15.40 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 107.04/15.40 |
% 107.04/15.40 | ALPHA: (ax4) implies:
% 107.04/15.40 | (4) ~ (e1 = e0)
% 107.04/15.40 | (5) ~ (e2 = e0)
% 107.04/15.40 | (6) ~ (e2 = e1)
% 107.04/15.40 | (7) ~ (e3 = e0)
% 107.04/15.40 | (8) ~ (e3 = e1)
% 107.04/15.40 | (9) ~ (e3 = e2)
% 107.04/15.40 |
% 107.04/15.40 | ALPHA: (ax5) implies:
% 107.04/15.41 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 107.04/15.41 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 107.04/15.41 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 107.04/15.41 | $i] : ? [v15: $i] : ( ~ (v3 = e3) & ~ (v2 = e2) & ~ (v1 = e1) &
% 107.04/15.41 | ~ (v0 = e0) & op(e3, e3) = v3 & op(e3, e2) = v15 & op(e3, e1) = v14
% 107.04/15.41 | & op(e3, e0) = v13 & op(e2, e3) = v12 & op(e2, e2) = v2 & op(e2, e1)
% 107.04/15.41 | = v11 & op(e2, e0) = v10 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 107.04/15.41 | op(e1, e1) = v1 & op(e1, e0) = v7 & op(e0, e3) = v6 & op(e0, e2) =
% 107.04/15.41 | v5 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13)
% 107.04/15.41 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 107.04/15.41 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v15 = e3)
% 107.04/15.41 | | ~ (v3 = e2)) & ( ~ (v15 = e3) | ~ (v1 = e2)) & ( ~ (v15 = e3)
% 107.04/15.41 | | ~ (v0 = e2)) & ( ~ (v14 = e3) | ~ (v3 = e1)) & ( ~ (v14 = e3)
% 107.04/15.41 | | ~ (v2 = e1)) & ( ~ (v14 = e3) | ~ (v0 = e1)) & ( ~ (v13 = e3)
% 107.04/15.41 | | ~ (v3 = e0)) & ( ~ (v13 = e3) | ~ (v2 = e0)) & ( ~ (v13 = e3)
% 107.04/15.41 | | ~ (v1 = e0)) & ( ~ (v12 = e2) | ~ (v2 = e3)) & ( ~ (v12 = e2)
% 107.04/15.41 | | ~ (v1 = e3)) & ( ~ (v12 = e2) | ~ (v0 = e3)) & ( ~ (v11 = e2)
% 107.04/15.41 | | ~ (v3 = e1)) & ( ~ (v11 = e2) | ~ (v2 = e1)) & ( ~ (v11 = e2)
% 107.04/15.41 | | ~ (v0 = e1)) & ( ~ (v10 = e2) | ~ (v3 = e0)) & ( ~ (v10 = e2)
% 107.04/15.41 | | ~ (v2 = e0)) & ( ~ (v10 = e2) | ~ (v1 = e0)) & ( ~ (v9 = e1) |
% 107.04/15.41 | ~ (v2 = e3)) & ( ~ (v9 = e1) | ~ (v1 = e3)) & ( ~ (v9 = e1) | ~
% 107.04/15.41 | (v0 = e3)) & ( ~ (v8 = e1) | ~ (v3 = e2)) & ( ~ (v8 = e1) | ~
% 107.04/15.41 | (v1 = e2)) & ( ~ (v8 = e1) | ~ (v0 = e2)) & ( ~ (v7 = e1) | ~
% 107.04/15.41 | (v3 = e0)) & ( ~ (v7 = e1) | ~ (v2 = e0)) & ( ~ (v7 = e1) | ~
% 107.04/15.41 | (v1 = e0)) & ( ~ (v6 = e0) | ~ (v2 = e3)) & ( ~ (v6 = e0) | ~
% 107.04/15.41 | (v1 = e3)) & ( ~ (v6 = e0) | ~ (v0 = e3)) & ( ~ (v5 = e0) | ~
% 107.04/15.41 | (v3 = e2)) & ( ~ (v5 = e0) | ~ (v1 = e2)) & ( ~ (v5 = e0) | ~
% 107.04/15.41 | (v0 = e2)) & ( ~ (v4 = e0) | ~ (v3 = e1)) & ( ~ (v4 = e0) | ~
% 107.04/15.41 | (v2 = e1)) & ( ~ (v4 = e0) | ~ (v0 = e1)))
% 107.04/15.41 |
% 107.04/15.41 | ALPHA: (ax6) implies:
% 107.04/15.41 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.41 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.41 | e2) | ~ (v1 = e0) | ~ (v0 = e1)))
% 107.04/15.41 |
% 107.04/15.41 | ALPHA: (ax7) implies:
% 107.04/15.41 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.04/15.41 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.41 | e3) | ~ (v1 = e0) | ~ (v0 = e1)))
% 107.04/15.41 |
% 107.04/15.41 | ALPHA: (ax8) implies:
% 107.04/15.42 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.42 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e1) | ~ (v1 = e0) | ~ (v0 = e2)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax9) implies:
% 107.04/15.42 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.04/15.42 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e3) | ~ (v1 = e0) | ~ (v0 = e2)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax10) implies:
% 107.04/15.42 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.04/15.42 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e1) | ~ (v1 = e0) | ~ (v0 = e3)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax11) implies:
% 107.04/15.42 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.04/15.42 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e2) | ~ (v1 = e0) | ~ (v0 = e3)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax12) implies:
% 107.04/15.42 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.42 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e2) | ~ (v1 = e1) | ~ (v0 = e0)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax13) implies:
% 107.04/15.42 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.04/15.42 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e3) | ~ (v1 = e1) | ~ (v0 = e0)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax14) implies:
% 107.04/15.42 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.42 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e0) | ~ (v1 = e1) | ~ (v0 = e2)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax15) implies:
% 107.04/15.42 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.04/15.42 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e3) | ~ (v1 = e1) | ~ (v0 = e2)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax16) implies:
% 107.04/15.42 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.04/15.42 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.42 | e0) | ~ (v1 = e1) | ~ (v0 = e3)))
% 107.04/15.42 |
% 107.04/15.42 | ALPHA: (ax17) implies:
% 107.04/15.43 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.04/15.43 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e2) | ~ (v1 = e1) | ~ (v0 = e3)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax18) implies:
% 107.04/15.43 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.43 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e1) | ~ (v1 = e2) | ~ (v0 = e0)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax19) implies:
% 107.04/15.43 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.04/15.43 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e3) | ~ (v1 = e2) | ~ (v0 = e0)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax20) implies:
% 107.04/15.43 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 107.04/15.43 | v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e0) | ~ (v1 = e2) | ~ (v0 = e1)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax21) implies:
% 107.04/15.43 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.04/15.43 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e3) | ~ (v1 = e2) | ~ (v0 = e1)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax22) implies:
% 107.04/15.43 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.04/15.43 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e0) | ~ (v1 = e2) | ~ (v0 = e3)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax23) implies:
% 107.04/15.43 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.04/15.43 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.04/15.43 | e1) | ~ (v1 = e2) | ~ (v0 = e3)))
% 107.04/15.43 |
% 107.04/15.43 | ALPHA: (ax24) implies:
% 107.04/15.43 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.32/15.43 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.43 | e1) | ~ (v1 = e3) | ~ (v0 = e0)))
% 107.32/15.43 |
% 107.32/15.43 | ALPHA: (ax25) implies:
% 107.32/15.44 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.32/15.44 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.44 | e2) | ~ (v1 = e3) | ~ (v0 = e0)))
% 107.32/15.44 |
% 107.32/15.44 | ALPHA: (ax26) implies:
% 107.32/15.44 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 107.32/15.44 | v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.44 | e0) | ~ (v1 = e3) | ~ (v0 = e1)))
% 107.32/15.44 |
% 107.32/15.44 | ALPHA: (ax27) implies:
% 107.32/15.44 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.32/15.44 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.44 | e2) | ~ (v1 = e3) | ~ (v0 = e1)))
% 107.32/15.44 |
% 107.32/15.44 | ALPHA: (ax28) implies:
% 107.32/15.44 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 107.32/15.44 | v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.44 | e0) | ~ (v1 = e3) | ~ (v0 = e2)))
% 107.32/15.44 |
% 107.32/15.44 | ALPHA: (ax29) implies:
% 107.32/15.44 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 107.32/15.44 | v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 107.32/15.44 | e1) | ~ (v1 = e3) | ~ (v0 = e2)))
% 107.32/15.44 |
% 107.32/15.44 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 107.32/15.44 | (35) op(all_4_1, all_4_2) = all_4_0 & op(e0, all_4_2) = all_4_1 & op(e0,
% 107.32/15.44 | e0) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~
% 107.32/15.44 | (all_4_0 = e3) | ~ (all_4_1 = e1) | ~ (all_4_2 = e2))
% 107.32/15.44 |
% 107.32/15.44 | ALPHA: (35) implies:
% 107.32/15.44 | (36) op(e0, e0) = all_4_2
% 107.32/15.44 | (37) op(e0, all_4_2) = all_4_1
% 107.32/15.44 | (38) op(all_4_1, all_4_2) = all_4_0
% 107.32/15.44 | (39) ~ (all_4_0 = e3) | ~ (all_4_1 = e1) | ~ (all_4_2 = e2)
% 107.32/15.44 |
% 107.32/15.44 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 107.32/15.45 | (40) op(all_6_1, all_6_2) = all_6_0 & op(e1, all_6_2) = all_6_1 & op(e1,
% 107.32/15.45 | e1) = all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~
% 107.32/15.45 | (all_6_0 = e0) | ~ (all_6_1 = e2) | ~ (all_6_2 = e3))
% 107.32/15.45 |
% 107.32/15.45 | ALPHA: (40) implies:
% 107.32/15.45 | (41) op(e1, e1) = all_6_2
% 107.32/15.45 | (42) op(e1, all_6_2) = all_6_1
% 107.32/15.45 | (43) op(all_6_1, all_6_2) = all_6_0
% 107.32/15.45 | (44) ~ (all_6_0 = e0) | ~ (all_6_1 = e2) | ~ (all_6_2 = e3)
% 107.32/15.45 |
% 107.32/15.45 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 107.32/15.45 | (45) op(all_8_1, all_8_2) = all_8_0 & op(e2, all_8_2) = all_8_1 & op(e2,
% 107.32/15.45 | e2) = all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~
% 107.32/15.45 | (all_8_0 = e0) | ~ (all_8_1 = e1) | ~ (all_8_2 = e3))
% 107.32/15.45 |
% 107.32/15.45 | ALPHA: (45) implies:
% 107.32/15.45 | (46) op(e2, e2) = all_8_2
% 107.32/15.45 | (47) op(e2, all_8_2) = all_8_1
% 107.32/15.45 | (48) op(all_8_1, all_8_2) = all_8_0
% 107.32/15.45 | (49) ~ (all_8_0 = e0) | ~ (all_8_1 = e1) | ~ (all_8_2 = e3)
% 107.32/15.45 |
% 107.32/15.45 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 107.32/15.45 | gives:
% 107.32/15.45 | (50) op(all_10_1, all_10_2) = all_10_0 & op(e3, all_10_2) = all_10_1 &
% 107.32/15.45 | op(e3, e3) = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & (
% 107.32/15.45 | ~ (all_10_0 = e2) | ~ (all_10_1 = e0) | ~ (all_10_2 = e1))
% 107.32/15.45 |
% 107.32/15.45 | ALPHA: (50) implies:
% 107.32/15.45 | (51) op(e3, e3) = all_10_2
% 107.32/15.45 | (52) op(e3, all_10_2) = all_10_1
% 107.32/15.45 | (53) op(all_10_1, all_10_2) = all_10_0
% 107.32/15.45 | (54) ~ (all_10_0 = e2) | ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 107.32/15.45 |
% 107.32/15.45 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 107.32/15.45 | gives:
% 107.32/15.45 | (55) op(all_12_1, all_12_2) = all_12_0 & op(e0, all_12_2) = all_12_1 &
% 107.32/15.45 | op(e0, e0) = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & (
% 107.32/15.45 | ~ (all_12_0 = e2) | ~ (all_12_1 = e1) | ~ (all_12_2 = e3))
% 107.32/15.45 |
% 107.32/15.45 | ALPHA: (55) implies:
% 107.32/15.45 | (56) op(e0, e0) = all_12_2
% 107.32/15.45 | (57) op(e0, all_12_2) = all_12_1
% 107.32/15.45 | (58) op(all_12_1, all_12_2) = all_12_0
% 107.32/15.45 |
% 107.32/15.45 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 107.32/15.45 | gives:
% 107.32/15.45 | (59) op(all_14_1, all_14_2) = all_14_0 & op(e2, all_14_2) = all_14_1 &
% 107.32/15.45 | op(e2, e2) = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & (
% 107.32/15.45 | ~ (all_14_0 = e1) | ~ (all_14_1 = e3) | ~ (all_14_2 = e0))
% 107.32/15.45 |
% 107.32/15.45 | ALPHA: (59) implies:
% 107.32/15.46 | (60) op(e2, e2) = all_14_2
% 107.32/15.46 | (61) op(e2, all_14_2) = all_14_1
% 107.32/15.46 | (62) op(all_14_1, all_14_2) = all_14_0
% 107.32/15.46 | (63) ~ (all_14_0 = e1) | ~ (all_14_1 = e3) | ~ (all_14_2 = e0)
% 107.32/15.46 |
% 107.32/15.46 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 107.32/15.46 | gives:
% 107.32/15.46 | (64) op(all_16_1, all_16_2) = all_16_0 & op(e3, all_16_2) = all_16_1 &
% 107.32/15.46 | op(e3, e3) = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & (
% 107.32/15.46 | ~ (all_16_0 = e1) | ~ (all_16_1 = e2) | ~ (all_16_2 = e0))
% 107.32/15.46 |
% 107.32/15.46 | ALPHA: (64) implies:
% 107.32/15.46 | (65) op(e3, e3) = all_16_2
% 107.32/15.46 | (66) op(e3, all_16_2) = all_16_1
% 107.32/15.46 | (67) op(all_16_1, all_16_2) = all_16_0
% 107.43/15.46 | (68) ~ (all_16_0 = e1) | ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 107.43/15.46 |
% 107.43/15.46 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 107.43/15.46 | gives:
% 107.43/15.46 | (69) op(all_18_1, all_18_2) = all_18_0 & op(e1, all_18_2) = all_18_1 &
% 107.43/15.46 | op(e1, e1) = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & (
% 107.43/15.46 | ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0))
% 107.43/15.46 |
% 107.43/15.46 | ALPHA: (69) implies:
% 107.43/15.46 | (70) op(e1, e1) = all_18_2
% 107.43/15.46 | (71) op(e1, all_18_2) = all_18_1
% 107.43/15.46 | (72) op(all_18_1, all_18_2) = all_18_0
% 107.43/15.46 | (73) ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 107.43/15.46 |
% 107.43/15.46 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 107.43/15.46 | gives:
% 107.43/15.46 | (74) op(all_20_1, all_20_2) = all_20_0 & op(e0, all_20_2) = all_20_1 &
% 107.43/15.46 | op(e0, e0) = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & (
% 107.43/15.46 | ~ (all_20_0 = e3) | ~ (all_20_1 = e2) | ~ (all_20_2 = e1))
% 107.43/15.46 |
% 107.43/15.46 | ALPHA: (74) implies:
% 107.43/15.46 | (75) op(e0, e0) = all_20_2
% 107.43/15.46 | (76) op(e0, all_20_2) = all_20_1
% 107.43/15.46 | (77) op(all_20_1, all_20_2) = all_20_0
% 107.43/15.46 | (78) ~ (all_20_0 = e3) | ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 107.43/15.46 |
% 107.43/15.46 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 107.43/15.46 | gives:
% 107.43/15.46 | (79) op(all_22_1, all_22_2) = all_22_0 & op(e2, all_22_2) = all_22_1 &
% 107.43/15.46 | op(e2, e2) = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & (
% 107.43/15.46 | ~ (all_22_0 = e0) | ~ (all_22_1 = e3) | ~ (all_22_2 = e1))
% 107.43/15.46 |
% 107.43/15.46 | ALPHA: (79) implies:
% 107.43/15.46 | (80) op(e2, e2) = all_22_2
% 107.43/15.46 | (81) op(e2, all_22_2) = all_22_1
% 107.43/15.47 | (82) op(all_22_1, all_22_2) = all_22_0
% 107.43/15.47 | (83) ~ (all_22_0 = e0) | ~ (all_22_1 = e3) | ~ (all_22_2 = e1)
% 107.43/15.47 |
% 107.43/15.47 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 107.43/15.47 | gives:
% 107.43/15.47 | (84) op(all_24_1, all_24_2) = all_24_0 & op(e3, all_24_2) = all_24_1 &
% 107.43/15.47 | op(e3, e3) = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & (
% 107.43/15.47 | ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2))
% 107.43/15.47 |
% 107.43/15.47 | ALPHA: (84) implies:
% 107.43/15.47 | (85) op(e3, e3) = all_24_2
% 107.43/15.47 | (86) op(e3, all_24_2) = all_24_1
% 107.43/15.47 | (87) op(all_24_1, all_24_2) = all_24_0
% 107.43/15.47 | (88) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 107.43/15.47 |
% 107.43/15.47 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 107.43/15.47 | gives:
% 107.43/15.47 | (89) op(all_26_1, all_26_2) = all_26_0 & op(e0, all_26_2) = all_26_1 &
% 107.43/15.47 | op(e0, e0) = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & (
% 107.43/15.47 | ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3))
% 107.43/15.47 |
% 107.43/15.47 | ALPHA: (89) implies:
% 107.43/15.47 | (90) op(e0, e0) = all_26_2
% 107.43/15.47 | (91) op(e0, all_26_2) = all_26_1
% 107.43/15.47 | (92) op(all_26_1, all_26_2) = all_26_0
% 107.43/15.47 | (93) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 107.43/15.47 |
% 107.43/15.47 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 107.43/15.47 | gives:
% 107.43/15.47 | (94) op(all_28_1, all_28_2) = all_28_0 & op(e1, all_28_2) = all_28_1 &
% 107.43/15.47 | op(e1, e1) = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & (
% 107.43/15.47 | ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0))
% 107.43/15.47 |
% 107.43/15.47 | ALPHA: (94) implies:
% 107.43/15.47 | (95) op(e1, e1) = all_28_2
% 107.43/15.47 | (96) op(e1, all_28_2) = all_28_1
% 107.43/15.47 | (97) op(all_28_1, all_28_2) = all_28_0
% 107.43/15.47 | (98) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 107.43/15.47 |
% 107.43/15.47 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 107.43/15.47 | gives:
% 107.43/15.47 | (99) op(all_30_1, all_30_2) = all_30_0 & op(e2, all_30_2) = all_30_1 &
% 107.43/15.47 | op(e2, e2) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & (
% 107.43/15.47 | ~ (all_30_0 = e3) | ~ (all_30_1 = e0) | ~ (all_30_2 = e1))
% 107.43/15.47 |
% 107.43/15.47 | ALPHA: (99) implies:
% 107.43/15.47 | (100) op(e2, e2) = all_30_2
% 107.43/15.47 | (101) op(e2, all_30_2) = all_30_1
% 107.43/15.47 | (102) op(all_30_1, all_30_2) = all_30_0
% 107.43/15.47 |
% 107.43/15.47 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 107.43/15.47 | gives:
% 107.43/15.48 | (103) op(all_32_1, all_32_2) = all_32_0 & op(e3, all_32_2) = all_32_1 &
% 107.43/15.48 | op(e3, e3) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) &
% 107.43/15.48 | ( ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2))
% 107.43/15.48 |
% 107.43/15.48 | ALPHA: (103) implies:
% 107.43/15.48 | (104) op(e3, e3) = all_32_2
% 107.43/15.48 | (105) op(e3, all_32_2) = all_32_1
% 107.43/15.48 | (106) op(all_32_1, all_32_2) = all_32_0
% 107.43/15.48 | (107) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 107.43/15.48 |
% 107.43/15.48 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 107.43/15.48 | gives:
% 107.43/15.48 | (108) op(all_34_1, all_34_2) = all_34_0 & op(e0, all_34_2) = all_34_1 &
% 107.43/15.48 | op(e0, e0) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) &
% 107.43/15.48 | ( ~ (all_34_0 = e2) | ~ (all_34_1 = e3) | ~ (all_34_2 = e1))
% 107.43/15.48 |
% 107.43/15.48 | ALPHA: (108) implies:
% 107.43/15.48 | (109) op(e0, e0) = all_34_2
% 107.43/15.48 | (110) op(e0, all_34_2) = all_34_1
% 107.43/15.48 | (111) op(all_34_1, all_34_2) = all_34_0
% 107.43/15.48 |
% 107.43/15.48 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 107.43/15.48 | gives:
% 107.43/15.48 | (112) op(all_36_1, all_36_2) = all_36_0 & op(e1, all_36_2) = all_36_1 &
% 107.43/15.48 | op(e1, e1) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) &
% 107.43/15.48 | ( ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2))
% 107.43/15.48 |
% 107.43/15.48 | ALPHA: (112) implies:
% 107.43/15.48 | (113) op(e1, e1) = all_36_2
% 107.43/15.48 | (114) op(e1, all_36_2) = all_36_1
% 107.43/15.48 | (115) op(all_36_1, all_36_2) = all_36_0
% 107.43/15.48 | (116) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 107.43/15.48 |
% 107.43/15.48 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 107.43/15.48 | gives:
% 107.43/15.48 | (117) op(all_38_1, all_38_2) = all_38_0 & op(e3, all_38_2) = all_38_1 &
% 107.43/15.48 | op(e3, e3) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) &
% 107.43/15.48 | ( ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1))
% 107.43/15.48 |
% 107.43/15.48 | ALPHA: (117) implies:
% 107.43/15.48 | (118) op(e3, e3) = all_38_2
% 107.43/15.48 | (119) op(e3, all_38_2) = all_38_1
% 107.43/15.48 | (120) op(all_38_1, all_38_2) = all_38_0
% 107.43/15.48 | (121) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 107.43/15.48 |
% 107.43/15.48 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 107.43/15.48 | gives:
% 107.43/15.48 | (122) op(all_40_1, all_40_2) = all_40_0 & op(e1, all_40_2) = all_40_1 &
% 107.43/15.48 | op(e1, e1) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) &
% 107.43/15.48 | ( ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2))
% 107.43/15.48 |
% 107.43/15.48 | ALPHA: (122) implies:
% 107.43/15.48 | (123) op(e1, e1) = all_40_2
% 107.43/15.48 | (124) op(e1, all_40_2) = all_40_1
% 107.43/15.49 | (125) op(all_40_1, all_40_2) = all_40_0
% 107.43/15.49 | (126) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 107.43/15.49 |
% 107.43/15.49 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 107.43/15.49 | gives:
% 107.43/15.49 | (127) op(all_42_1, all_42_2) = all_42_0 & op(e2, all_42_2) = all_42_1 &
% 107.43/15.49 | op(e2, e2) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) &
% 107.43/15.49 | ( ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3))
% 107.43/15.49 |
% 107.43/15.49 | ALPHA: (127) implies:
% 107.43/15.49 | (128) op(e2, e2) = all_42_2
% 107.43/15.49 | (129) op(e2, all_42_2) = all_42_1
% 107.43/15.49 | (130) op(all_42_1, all_42_2) = all_42_0
% 107.43/15.49 | (131) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 107.43/15.49 |
% 107.43/15.49 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 107.43/15.49 | gives:
% 107.43/15.49 | (132) op(all_44_1, all_44_2) = all_44_0 & op(e0, all_44_2) = all_44_1 &
% 107.43/15.49 | op(e0, e0) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) &
% 107.43/15.49 | ( ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2))
% 107.43/15.49 |
% 107.43/15.49 | ALPHA: (132) implies:
% 107.43/15.49 | (133) op(e0, e0) = all_44_2
% 107.43/15.49 | (134) op(e0, all_44_2) = all_44_1
% 107.43/15.49 | (135) op(all_44_1, all_44_2) = all_44_0
% 107.43/15.49 | (136) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 107.43/15.49 |
% 107.43/15.49 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 107.43/15.49 | gives:
% 107.43/15.49 | (137) op(all_46_1, all_46_2) = all_46_0 & op(e1, all_46_2) = all_46_1 &
% 107.43/15.49 | op(e1, e1) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) &
% 107.43/15.49 | ( ~ (all_46_0 = e2) | ~ (all_46_1 = e0) | ~ (all_46_2 = e3))
% 107.43/15.49 |
% 107.43/15.49 | ALPHA: (137) implies:
% 107.43/15.49 | (138) op(e1, e1) = all_46_2
% 107.43/15.49 | (139) op(e1, all_46_2) = all_46_1
% 107.43/15.49 | (140) op(all_46_1, all_46_2) = all_46_0
% 107.43/15.49 |
% 107.43/15.49 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 107.43/15.49 | gives:
% 107.43/15.49 | (141) op(all_48_1, all_48_2) = all_48_0 & op(e2, all_48_2) = all_48_1 &
% 107.43/15.49 | op(e2, e2) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 107.43/15.49 | ( ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0))
% 107.43/15.49 |
% 107.43/15.49 | ALPHA: (141) implies:
% 107.43/15.49 | (142) op(e2, e2) = all_48_2
% 107.43/15.49 | (143) op(e2, all_48_2) = all_48_1
% 107.43/15.49 | (144) op(all_48_1, all_48_2) = all_48_0
% 107.43/15.50 | (145) ~ (all_48_0 = e3) | ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 107.43/15.50 |
% 107.43/15.50 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 107.43/15.50 | gives:
% 107.43/15.50 | (146) op(all_50_1, all_50_2) = all_50_0 & op(e3, all_50_2) = all_50_1 &
% 107.43/15.50 | op(e3, e3) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) &
% 107.43/15.50 | ( ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0))
% 107.43/15.50 |
% 107.43/15.50 | ALPHA: (146) implies:
% 107.43/15.50 | (147) op(e3, e3) = all_50_2
% 107.43/15.50 | (148) op(e3, all_50_2) = all_50_1
% 107.43/15.50 | (149) op(all_50_1, all_50_2) = all_50_0
% 107.43/15.50 | (150) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 107.43/15.50 |
% 107.43/15.50 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 107.43/15.50 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 107.43/15.50 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 107.43/15.50 | (151) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 107.43/15.50 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) &
% 107.43/15.50 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 107.43/15.50 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) &
% 107.43/15.50 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 107.43/15.50 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 107.43/15.50 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 107.43/15.50 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 107.43/15.50 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 107.43/15.50 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 107.43/15.50 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 107.43/15.50 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 107.43/15.50 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8
% 107.43/15.50 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11)
% 107.43/15.50 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~
% 107.43/15.50 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 =
% 107.43/15.50 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 =
% 107.43/15.50 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 =
% 107.43/15.50 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 =
% 107.43/15.50 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 =
% 107.43/15.50 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 107.43/15.50 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 107.43/15.50 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 107.43/15.50 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 107.43/15.50 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 107.43/15.50 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 107.43/15.50 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 107.43/15.50 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 107.43/15.50 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 107.43/15.50 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 107.43/15.50 |
% 107.43/15.50 | ALPHA: (151) implies:
% 107.43/15.50 | (152) ~ (all_52_14 = all_52_15)
% 107.43/15.50 | (153) ~ (all_52_13 = all_52_15)
% 107.43/15.51 | (154) ~ (all_52_13 = all_52_14)
% 107.43/15.51 | (155) ~ (all_52_12 = all_52_15)
% 107.43/15.51 | (156) ~ (all_52_12 = all_52_14)
% 107.43/15.51 | (157) ~ (all_52_12 = all_52_13)
% 107.43/15.51 | (158) ~ (all_52_11 = all_52_15)
% 107.43/15.51 | (159) ~ (all_52_10 = all_52_14)
% 107.43/15.51 | (160) ~ (all_52_10 = all_52_11)
% 107.43/15.51 | (161) ~ (all_52_9 = all_52_13)
% 107.43/15.51 | (162) ~ (all_52_9 = all_52_11)
% 107.43/15.51 | (163) ~ (all_52_9 = all_52_10)
% 107.43/15.51 | (164) ~ (all_52_8 = all_52_12)
% 107.43/15.51 | (165) ~ (all_52_8 = all_52_11)
% 107.43/15.51 | (166) ~ (all_52_8 = all_52_10)
% 107.43/15.51 | (167) ~ (all_52_8 = all_52_9)
% 107.43/15.51 | (168) ~ (all_52_7 = all_52_15)
% 107.43/15.51 | (169) ~ (all_52_7 = all_52_11)
% 107.43/15.51 | (170) ~ (all_52_6 = all_52_14)
% 107.43/15.51 | (171) ~ (all_52_6 = all_52_10)
% 107.43/15.51 | (172) ~ (all_52_6 = all_52_7)
% 107.43/15.51 | (173) ~ (all_52_5 = all_52_13)
% 107.43/15.51 | (174) ~ (all_52_5 = all_52_9)
% 107.43/15.51 | (175) ~ (all_52_5 = all_52_7)
% 107.43/15.51 | (176) ~ (all_52_5 = all_52_6)
% 107.43/15.51 | (177) ~ (all_52_4 = all_52_12)
% 107.43/15.51 | (178) ~ (all_52_4 = all_52_8)
% 107.43/15.51 | (179) ~ (all_52_4 = all_52_7)
% 107.43/15.51 | (180) ~ (all_52_4 = all_52_6)
% 107.43/15.51 | (181) ~ (all_52_4 = all_52_5)
% 107.43/15.51 | (182) ~ (all_52_3 = all_52_15)
% 107.43/15.51 | (183) ~ (all_52_3 = all_52_11)
% 107.43/15.51 | (184) ~ (all_52_3 = all_52_7)
% 107.43/15.51 | (185) ~ (all_52_2 = all_52_14)
% 107.43/15.51 | (186) ~ (all_52_2 = all_52_10)
% 107.43/15.51 | (187) ~ (all_52_2 = all_52_6)
% 107.43/15.51 | (188) ~ (all_52_2 = all_52_3)
% 107.43/15.51 | (189) ~ (all_52_1 = all_52_13)
% 107.43/15.51 | (190) ~ (all_52_1 = all_52_9)
% 107.43/15.51 | (191) ~ (all_52_1 = all_52_5)
% 107.43/15.51 | (192) ~ (all_52_1 = all_52_3)
% 107.43/15.51 | (193) ~ (all_52_1 = all_52_2)
% 107.43/15.51 | (194) ~ (all_52_0 = all_52_12)
% 107.43/15.51 | (195) ~ (all_52_0 = all_52_8)
% 107.43/15.51 | (196) ~ (all_52_0 = all_52_4)
% 107.43/15.51 | (197) ~ (all_52_0 = all_52_3)
% 107.43/15.51 | (198) ~ (all_52_0 = all_52_2)
% 107.43/15.51 | (199) ~ (all_52_0 = all_52_1)
% 107.43/15.51 | (200) op(e0, e0) = all_52_15
% 107.43/15.51 | (201) op(e0, e1) = all_52_11
% 107.43/15.51 | (202) op(e0, e2) = all_52_7
% 107.43/15.51 | (203) op(e0, e3) = all_52_3
% 107.43/15.51 | (204) op(e1, e0) = all_52_14
% 107.43/15.51 | (205) op(e1, e1) = all_52_10
% 107.43/15.51 | (206) op(e1, e2) = all_52_6
% 107.43/15.51 | (207) op(e1, e3) = all_52_2
% 107.43/15.51 | (208) op(e2, e0) = all_52_13
% 107.43/15.51 | (209) op(e2, e1) = all_52_9
% 107.43/15.51 | (210) op(e2, e2) = all_52_5
% 107.43/15.51 | (211) op(e2, e3) = all_52_1
% 107.43/15.51 | (212) op(e3, e0) = all_52_12
% 107.43/15.51 | (213) op(e3, e1) = all_52_8
% 107.43/15.51 | (214) op(e3, e2) = all_52_4
% 107.43/15.51 | (215) op(e3, e3) = all_52_0
% 107.43/15.51 |
% 107.43/15.51 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 107.43/15.51 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 107.43/15.51 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 107.69/15.52 | (216) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 107.69/15.52 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 107.69/15.52 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 107.69/15.52 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 107.69/15.52 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 107.69/15.52 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 107.69/15.52 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 107.69/15.52 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 107.69/15.52 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 107.69/15.52 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 107.69/15.52 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 107.69/15.52 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 107.69/15.52 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 107.69/15.52 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 107.69/15.52 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 107.69/15.52 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 107.69/15.52 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 107.69/15.52 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 107.69/15.52 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 107.69/15.52 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 107.69/15.52 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 107.69/15.52 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 107.69/15.52 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 107.69/15.52 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 107.69/15.52 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 107.69/15.52 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 107.69/15.52 |
% 107.69/15.52 | ALPHA: (216) implies:
% 107.69/15.52 | (217) op(e0, e0) = all_54_15
% 107.69/15.52 | (218) op(e0, e1) = all_54_14
% 107.69/15.52 | (219) op(e0, e2) = all_54_13
% 107.69/15.52 | (220) op(e0, e3) = all_54_12
% 107.69/15.52 | (221) op(e1, e0) = all_54_11
% 107.69/15.52 | (222) op(e1, e1) = all_54_10
% 107.69/15.52 | (223) op(e1, e2) = all_54_9
% 107.69/15.52 | (224) op(e1, e3) = all_54_8
% 107.69/15.52 | (225) op(e2, e0) = all_54_7
% 107.69/15.52 | (226) op(e2, e1) = all_54_6
% 107.69/15.52 | (227) op(e2, e2) = all_54_5
% 107.69/15.52 | (228) op(e2, e3) = all_54_4
% 107.69/15.52 | (229) op(e3, e0) = all_54_3
% 107.69/15.52 | (230) op(e3, e1) = all_54_2
% 107.69/15.52 | (231) op(e3, e2) = all_54_1
% 107.69/15.52 | (232) op(e3, e3) = all_54_0
% 107.69/15.52 | (233) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 107.69/15.52 | (234) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 107.69/15.53 | (235) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 107.69/15.53 | (236) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 107.69/15.53 | (237) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 107.69/15.53 | (238) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 107.69/15.53 | (239) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 107.69/15.53 | (240) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 107.69/15.53 | (241) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 107.69/15.53 | (242) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 107.69/15.53 | (243) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 107.69/15.53 | (244) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 107.69/15.53 | (245) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 107.69/15.53 | (246) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 107.69/15.53 | (247) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 107.69/15.53 | (248) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 107.69/15.53 |
% 107.69/15.53 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 107.69/15.53 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 107.69/15.53 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 107.69/15.54 | (249) ~ (all_56_12 = e3) & ~ (all_56_13 = e2) & ~ (all_56_14 = e1) & ~
% 107.69/15.54 | (all_56_15 = e0) & op(e3, e3) = all_56_12 & op(e3, e2) = all_56_0 &
% 107.69/15.54 | op(e3, e1) = all_56_1 & op(e3, e0) = all_56_2 & op(e2, e3) = all_56_3
% 107.69/15.54 | & op(e2, e2) = all_56_13 & op(e2, e1) = all_56_4 & op(e2, e0) =
% 107.69/15.54 | all_56_5 & op(e1, e3) = all_56_6 & op(e1, e2) = all_56_7 & op(e1, e1)
% 107.69/15.54 | = all_56_14 & op(e1, e0) = all_56_8 & op(e0, e3) = all_56_9 & op(e0,
% 107.69/15.54 | e2) = all_56_10 & op(e0, e1) = all_56_11 & op(e0, e0) = all_56_15 &
% 107.69/15.54 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) &
% 107.69/15.54 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) &
% 107.69/15.54 | $i(all_56_8) & $i(all_56_9) & $i(all_56_10) & $i(all_56_11) &
% 107.69/15.54 | $i(all_56_12) & $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & ( ~
% 107.69/15.54 | (all_56_0 = e3) | ~ (all_56_12 = e2)) & ( ~ (all_56_0 = e3) | ~
% 107.69/15.54 | (all_56_14 = e2)) & ( ~ (all_56_0 = e3) | ~ (all_56_15 = e2)) & (
% 107.69/15.54 | ~ (all_56_1 = e3) | ~ (all_56_12 = e1)) & ( ~ (all_56_1 = e3) | ~
% 107.69/15.54 | (all_56_13 = e1)) & ( ~ (all_56_1 = e3) | ~ (all_56_15 = e1)) & (
% 107.69/15.54 | ~ (all_56_2 = e3) | ~ (all_56_12 = e0)) & ( ~ (all_56_2 = e3) | ~
% 107.69/15.54 | (all_56_13 = e0)) & ( ~ (all_56_2 = e3) | ~ (all_56_14 = e0)) & (
% 107.69/15.54 | ~ (all_56_3 = e2) | ~ (all_56_13 = e3)) & ( ~ (all_56_3 = e2) | ~
% 107.69/15.54 | (all_56_14 = e3)) & ( ~ (all_56_3 = e2) | ~ (all_56_15 = e3)) & (
% 107.69/15.54 | ~ (all_56_4 = e2) | ~ (all_56_12 = e1)) & ( ~ (all_56_4 = e2) | ~
% 107.69/15.54 | (all_56_13 = e1)) & ( ~ (all_56_4 = e2) | ~ (all_56_15 = e1)) & (
% 107.69/15.54 | ~ (all_56_5 = e2) | ~ (all_56_12 = e0)) & ( ~ (all_56_5 = e2) | ~
% 107.69/15.54 | (all_56_13 = e0)) & ( ~ (all_56_5 = e2) | ~ (all_56_14 = e0)) & (
% 107.69/15.54 | ~ (all_56_6 = e1) | ~ (all_56_13 = e3)) & ( ~ (all_56_6 = e1) | ~
% 107.69/15.54 | (all_56_14 = e3)) & ( ~ (all_56_6 = e1) | ~ (all_56_15 = e3)) & (
% 107.69/15.54 | ~ (all_56_7 = e1) | ~ (all_56_12 = e2)) & ( ~ (all_56_7 = e1) | ~
% 107.69/15.54 | (all_56_14 = e2)) & ( ~ (all_56_7 = e1) | ~ (all_56_15 = e2)) & (
% 107.69/15.54 | ~ (all_56_8 = e1) | ~ (all_56_12 = e0)) & ( ~ (all_56_8 = e1) | ~
% 107.69/15.54 | (all_56_13 = e0)) & ( ~ (all_56_8 = e1) | ~ (all_56_14 = e0)) & (
% 107.69/15.54 | ~ (all_56_9 = e0) | ~ (all_56_13 = e3)) & ( ~ (all_56_9 = e0) | ~
% 107.69/15.54 | (all_56_14 = e3)) & ( ~ (all_56_9 = e0) | ~ (all_56_15 = e3)) & (
% 107.69/15.54 | ~ (all_56_10 = e0) | ~ (all_56_12 = e2)) & ( ~ (all_56_10 = e0) |
% 107.69/15.54 | ~ (all_56_14 = e2)) & ( ~ (all_56_10 = e0) | ~ (all_56_15 = e2)) &
% 107.69/15.54 | ( ~ (all_56_11 = e0) | ~ (all_56_12 = e1)) & ( ~ (all_56_11 = e0) |
% 107.69/15.54 | ~ (all_56_13 = e1)) & ( ~ (all_56_11 = e0) | ~ (all_56_15 = e1))
% 107.69/15.54 |
% 107.69/15.54 | ALPHA: (249) implies:
% 107.69/15.54 | (250) ~ (all_56_15 = e0)
% 107.69/15.54 | (251) ~ (all_56_14 = e1)
% 107.69/15.54 | (252) ~ (all_56_13 = e2)
% 107.69/15.54 | (253) ~ (all_56_12 = e3)
% 107.69/15.54 | (254) op(e0, e0) = all_56_15
% 107.69/15.54 | (255) op(e0, e1) = all_56_11
% 107.69/15.54 | (256) op(e0, e2) = all_56_10
% 107.69/15.54 | (257) op(e0, e3) = all_56_9
% 107.69/15.54 | (258) op(e1, e0) = all_56_8
% 107.69/15.54 | (259) op(e1, e1) = all_56_14
% 107.69/15.54 | (260) op(e1, e2) = all_56_7
% 107.69/15.54 | (261) op(e1, e3) = all_56_6
% 107.69/15.54 | (262) op(e2, e0) = all_56_5
% 107.69/15.54 | (263) op(e2, e1) = all_56_4
% 107.69/15.54 | (264) op(e2, e2) = all_56_13
% 107.69/15.54 | (265) op(e2, e3) = all_56_3
% 107.69/15.54 | (266) op(e3, e0) = all_56_2
% 107.69/15.54 | (267) op(e3, e1) = all_56_1
% 107.69/15.54 | (268) op(e3, e2) = all_56_0
% 107.69/15.54 | (269) op(e3, e3) = all_56_12
% 107.69/15.54 | (270) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 107.69/15.54 | (271) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 107.69/15.54 | (272) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 107.69/15.54 | (273) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 107.69/15.54 | (274) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 107.69/15.54 | (275) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 107.69/15.54 | (276) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 107.69/15.54 | (277) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 107.69/15.54 | (278) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 107.69/15.55 | (279) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 107.69/15.55 | (280) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 107.69/15.55 | (281) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 107.69/15.55 | (282) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 107.69/15.55 | (283) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 107.69/15.55 | (284) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 107.69/15.55 | (285) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 107.69/15.55 | (286) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 107.69/15.55 | (287) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 107.69/15.55 | (288) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 107.69/15.55 | (289) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 107.69/15.55 | (290) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 107.69/15.55 | (291) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 107.69/15.55 | (292) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 107.69/15.55 | (293) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 107.69/15.55 | (294) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 107.69/15.55 | (295) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 107.69/15.55 | (296) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 107.69/15.55 | (297) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 107.69/15.55 | (298) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 107.69/15.55 | (299) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 107.69/15.55 | (300) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 107.69/15.55 | (301) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 107.69/15.55 | (302) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 107.69/15.55 | (303) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 107.69/15.55 | (304) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 107.69/15.55 | (305) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 107.69/15.55 |
% 107.69/15.55 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 107.69/15.55 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 107.69/15.55 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 107.85/15.56 | (306) op(e3, e3) = all_58_0 & op(e3, e2) = all_58_1 & op(e3, e1) = all_58_4
% 107.85/15.56 | & op(e3, e0) = all_58_9 & op(e2, e3) = all_58_2 & op(e2, e2) =
% 107.85/15.56 | all_58_3 & op(e2, e1) = all_58_5 & op(e2, e0) = all_58_10 & op(e1,
% 107.85/15.56 | e3) = all_58_6 & op(e1, e2) = all_58_7 & op(e1, e1) = all_58_8 &
% 107.85/15.56 | op(e1, e0) = all_58_11 & op(e0, e3) = all_58_12 & op(e0, e2) =
% 107.85/15.56 | all_58_13 & op(e0, e1) = all_58_14 & op(e0, e0) = all_58_15 &
% 107.85/15.56 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) &
% 107.85/15.56 | $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) &
% 107.85/15.56 | $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) &
% 107.85/15.56 | $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) &
% 107.85/15.56 | (all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3) &
% 107.85/15.56 | (all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3) &
% 107.85/15.56 | (all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2) &
% 107.85/15.56 | (all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2) &
% 107.85/15.56 | (all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1) &
% 107.85/15.56 | (all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1) &
% 107.85/15.56 | (all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0) &
% 107.85/15.56 | (all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0) &
% 107.85/15.56 | (all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3) &
% 107.85/15.56 | (all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2) &
% 107.85/15.56 | (all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1) &
% 107.85/15.56 | (all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0) &
% 107.85/15.56 | (all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3) &
% 107.85/15.56 | (all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2) &
% 107.85/15.56 | (all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1) &
% 107.85/15.56 | (all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0) &
% 107.85/15.56 | (all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3) &
% 107.85/15.56 | (all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2) &
% 107.85/15.56 | (all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1) &
% 107.85/15.56 | (all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0) &
% 107.85/15.56 | (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3) &
% 107.85/15.56 | (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2) &
% 107.85/15.56 | (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1) &
% 107.85/15.56 | (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0) &
% 107.85/15.56 | (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3) &
% 107.85/15.56 | (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2) &
% 107.85/15.56 | (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1) &
% 107.85/15.56 | (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) &
% 107.85/15.56 | (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) &
% 107.85/15.56 | (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) &
% 107.85/15.56 | (all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 107.85/15.56 | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)))
% 107.85/15.56 |
% 107.85/15.56 | ALPHA: (306) implies:
% 107.85/15.56 | (307) op(e0, e0) = all_58_15
% 107.85/15.56 | (308) op(e0, e1) = all_58_14
% 107.85/15.56 | (309) op(e0, e2) = all_58_13
% 107.85/15.56 | (310) op(e0, e3) = all_58_12
% 107.85/15.56 | (311) op(e1, e0) = all_58_11
% 107.85/15.56 | (312) op(e1, e1) = all_58_8
% 107.85/15.56 | (313) op(e1, e2) = all_58_7
% 107.85/15.56 | (314) op(e1, e3) = all_58_6
% 107.85/15.56 | (315) op(e2, e0) = all_58_10
% 107.85/15.56 | (316) op(e2, e1) = all_58_5
% 107.85/15.56 | (317) op(e2, e2) = all_58_3
% 107.85/15.56 | (318) op(e2, e3) = all_58_2
% 107.85/15.56 | (319) op(e3, e0) = all_58_9
% 107.85/15.56 | (320) op(e3, e1) = all_58_4
% 107.85/15.56 | (321) op(e3, e2) = all_58_1
% 107.85/15.56 | (322) op(e3, e3) = all_58_0
% 107.85/15.56 | (323) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 107.85/15.56 | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 107.85/15.56 | (324) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 107.85/15.56 | (325) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 107.85/15.56 | (326) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 107.85/15.56 | (327) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 107.85/15.56 | (328) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 107.85/15.56 | (329) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 107.85/15.57 | (330) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 107.85/15.57 | (331) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 107.85/15.57 | (332) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 107.85/15.57 | (333) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 107.85/15.57 | (334) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 107.85/15.57 | (335) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 107.85/15.57 | (336) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 107.85/15.57 | (337) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 107.85/15.57 | (338) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 107.85/15.57 | (339) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 107.85/15.57 | (340) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 107.85/15.57 | (341) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 107.85/15.57 | (342) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 107.85/15.57 | (343) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 107.85/15.57 | (344) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 107.85/15.57 | (345) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 107.85/15.57 | (346) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 107.85/15.57 | (347) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 107.85/15.57 | (348) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 107.85/15.57 | (349) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 107.85/15.57 | (350) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 107.85/15.57 | (351) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 107.85/15.57 | (352) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 107.85/15.57 |
% 107.85/15.57 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_34_2, e0, e0,
% 107.85/15.57 | simplifying with (90), (109) gives:
% 107.85/15.57 | (353) all_34_2 = all_26_2
% 107.85/15.57 |
% 107.85/15.57 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0,
% 107.85/15.57 | simplifying with (133), (200) gives:
% 107.85/15.57 | (354) all_52_15 = all_44_2
% 107.85/15.57 |
% 107.85/15.57 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_15, e0, e0,
% 107.85/15.57 | simplifying with (109), (200) gives:
% 107.85/15.57 | (355) all_52_15 = all_34_2
% 107.85/15.57 |
% 107.85/15.57 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_54_15, e0, e0,
% 107.85/15.57 | simplifying with (36), (217) gives:
% 107.85/15.57 | (356) all_54_15 = all_4_2
% 107.85/15.57 |
% 107.85/15.57 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0,
% 107.85/15.57 | e0, simplifying with (217), (254) gives:
% 107.85/15.57 | (357) all_56_15 = all_54_15
% 107.85/15.57 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_56_15, e0, e0,
% 107.85/15.58 | simplifying with (90), (254) gives:
% 107.85/15.58 | (358) all_56_15 = all_26_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_56_15, e0, e0,
% 107.85/15.58 | simplifying with (75), (254) gives:
% 107.85/15.58 | (359) all_56_15 = all_20_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_58_15, e0,
% 107.85/15.58 | e0, simplifying with (200), (307) gives:
% 107.85/15.58 | (360) all_58_15 = all_52_15
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_58_15, e0, e0,
% 107.85/15.58 | simplifying with (56), (307) gives:
% 107.85/15.58 | (361) all_58_15 = all_12_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_56_11, e1,
% 107.85/15.58 | e0, simplifying with (201), (255) gives:
% 107.85/15.58 | (362) all_56_11 = all_52_11
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_14, e1,
% 107.85/15.58 | e0, simplifying with (255), (308) gives:
% 107.85/15.58 | (363) all_58_14 = all_56_11
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_58_14, e1,
% 107.85/15.58 | e0, simplifying with (218), (308) gives:
% 107.85/15.58 | (364) all_58_14 = all_54_14
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_56_10, e2, e0,
% 107.85/15.58 | simplifying with (202), (256) gives:
% 107.85/15.58 | (365) all_56_10 = all_52_7
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_10, all_58_13, e2,
% 107.85/15.58 | e0, simplifying with (256), (309) gives:
% 107.85/15.58 | (366) all_58_13 = all_56_10
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_58_13, e2,
% 107.85/15.58 | e0, simplifying with (219), (309) gives:
% 107.85/15.58 | (367) all_58_13 = all_54_13
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_56_9, e3, e0,
% 107.85/15.58 | simplifying with (220), (257) gives:
% 107.85/15.58 | (368) all_56_9 = all_54_12
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_12, e3, e0,
% 107.85/15.58 | simplifying with (257), (310) gives:
% 107.85/15.58 | (369) all_58_12 = all_56_9
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_58_12, e3, e0,
% 107.85/15.58 | simplifying with (203), (310) gives:
% 107.85/15.58 | (370) all_58_12 = all_52_3
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_56_8, e0, e1,
% 107.85/15.58 | simplifying with (204), (258) gives:
% 107.85/15.58 | (371) all_56_8 = all_52_14
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_11, e0, e1,
% 107.85/15.58 | simplifying with (258), (311) gives:
% 107.85/15.58 | (372) all_58_11 = all_56_8
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_11, all_58_11, e0,
% 107.85/15.58 | e1, simplifying with (221), (311) gives:
% 107.85/15.58 | (373) all_58_11 = all_54_11
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_40_2, e1, e1,
% 107.85/15.58 | simplifying with (113), (123) gives:
% 107.85/15.58 | (374) all_40_2 = all_36_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_40_2, e1, e1,
% 107.85/15.58 | simplifying with (41), (123) gives:
% 107.85/15.58 | (375) all_40_2 = all_6_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_46_2, e1, e1,
% 107.85/15.58 | simplifying with (113), (138) gives:
% 107.85/15.58 | (376) all_46_2 = all_36_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1,
% 107.85/15.58 | simplifying with (70), (222) gives:
% 107.85/15.58 | (377) all_54_10 = all_18_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_14, e1,
% 107.85/15.58 | e1, simplifying with (222), (259) gives:
% 107.85/15.58 | (378) all_56_14 = all_54_10
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_56_14, e1,
% 107.85/15.58 | e1, simplifying with (205), (259) gives:
% 107.85/15.58 | (379) all_56_14 = all_52_10
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_56_14, e1, e1,
% 107.85/15.58 | simplifying with (138), (259) gives:
% 107.85/15.58 | (380) all_56_14 = all_46_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_58_8, e1, e1,
% 107.85/15.58 | simplifying with (123), (312) gives:
% 107.85/15.58 | (381) all_58_8 = all_40_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_58_8, e1, e1,
% 107.85/15.58 | simplifying with (95), (312) gives:
% 107.85/15.58 | (382) all_58_8 = all_28_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_7, e2, e1,
% 107.85/15.58 | simplifying with (223), (260) gives:
% 107.85/15.58 | (383) all_56_7 = all_54_9
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_7, e2, e1,
% 107.85/15.58 | simplifying with (260), (313) gives:
% 107.85/15.58 | (384) all_58_7 = all_56_7
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_58_7, e2, e1,
% 107.85/15.58 | simplifying with (206), (313) gives:
% 107.85/15.58 | (385) all_58_7 = all_52_6
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_56_6, e3, e1,
% 107.85/15.58 | simplifying with (207), (261) gives:
% 107.85/15.58 | (386) all_56_6 = all_52_2
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_6, e3, e1,
% 107.85/15.58 | simplifying with (261), (314) gives:
% 107.85/15.58 | (387) all_58_6 = all_56_6
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_58_6, e3, e1,
% 107.85/15.58 | simplifying with (224), (314) gives:
% 107.85/15.58 | (388) all_58_6 = all_54_8
% 107.85/15.58 |
% 107.85/15.58 | GROUND_INST: instantiating (function-axioms) with all_54_7, all_56_5, e0, e2,
% 107.85/15.58 | simplifying with (225), (262) gives:
% 107.85/15.58 | (389) all_56_5 = all_54_7
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_5, all_58_10, e0, e2,
% 107.85/15.59 | simplifying with (262), (315) gives:
% 107.85/15.59 | (390) all_58_10 = all_56_5
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_10, e0,
% 107.85/15.59 | e2, simplifying with (208), (315) gives:
% 107.85/15.59 | (391) all_58_10 = all_52_13
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_4, e1, e2,
% 107.85/15.59 | simplifying with (226), (263) gives:
% 107.85/15.59 | (392) all_56_4 = all_54_6
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_5, e1, e2,
% 107.85/15.59 | simplifying with (263), (316) gives:
% 107.85/15.59 | (393) all_58_5 = all_56_4
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_58_5, e1, e2,
% 107.85/15.59 | simplifying with (209), (316) gives:
% 107.85/15.59 | (394) all_58_5 = all_52_9
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_5, e2, e2,
% 107.85/15.59 | simplifying with (80), (210) gives:
% 107.85/15.59 | (395) all_52_5 = all_22_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_52_5, e2, e2,
% 107.85/15.59 | simplifying with (46), (210) gives:
% 107.85/15.59 | (396) all_52_5 = all_8_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_5, e2, e2,
% 107.85/15.59 | simplifying with (60), (227) gives:
% 107.85/15.59 | (397) all_54_5 = all_14_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_56_13, e2, e2,
% 107.85/15.59 | simplifying with (227), (264) gives:
% 107.85/15.59 | (398) all_56_13 = all_54_5
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_13, e2, e2,
% 107.85/15.59 | simplifying with (128), (264) gives:
% 107.85/15.59 | (399) all_56_13 = all_42_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_56_13, e2, e2,
% 107.85/15.59 | simplifying with (100), (264) gives:
% 107.85/15.59 | (400) all_56_13 = all_30_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_56_13, e2, e2,
% 107.85/15.59 | simplifying with (80), (264) gives:
% 107.85/15.59 | (401) all_56_13 = all_22_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_5, all_58_3, e2, e2,
% 107.85/15.59 | simplifying with (227), (317) gives:
% 107.85/15.59 | (402) all_58_3 = all_54_5
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_58_3, e2, e2,
% 107.85/15.59 | simplifying with (142), (317) gives:
% 107.85/15.59 | (403) all_58_3 = all_48_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_56_3, e3, e2,
% 107.85/15.59 | simplifying with (228), (265) gives:
% 107.85/15.59 | (404) all_56_3 = all_54_4
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_2, e3, e2,
% 107.85/15.59 | simplifying with (265), (318) gives:
% 107.85/15.59 | (405) all_58_2 = all_56_3
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_2, e3, e2,
% 107.85/15.59 | simplifying with (211), (318) gives:
% 107.85/15.59 | (406) all_58_2 = all_52_1
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_56_2, e0, e3,
% 107.85/15.59 | simplifying with (212), (266) gives:
% 107.85/15.59 | (407) all_56_2 = all_52_12
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_9, e0, e3,
% 107.85/15.59 | simplifying with (266), (319) gives:
% 107.85/15.59 | (408) all_58_9 = all_56_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_58_9, e0, e3,
% 107.85/15.59 | simplifying with (229), (319) gives:
% 107.85/15.59 | (409) all_58_9 = all_54_3
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_56_1, e1, e3,
% 107.85/15.59 | simplifying with (230), (267) gives:
% 107.85/15.59 | (410) all_56_1 = all_54_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_4, e1, e3,
% 107.85/15.59 | simplifying with (267), (320) gives:
% 107.85/15.59 | (411) all_58_4 = all_56_1
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_58_4, e1, e3,
% 107.85/15.59 | simplifying with (213), (320) gives:
% 107.85/15.59 | (412) all_58_4 = all_52_8
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_56_0, e2, e3,
% 107.85/15.59 | simplifying with (214), (268) gives:
% 107.85/15.59 | (413) all_56_0 = all_52_4
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_56_0, all_58_1, e2, e3,
% 107.85/15.59 | simplifying with (268), (321) gives:
% 107.85/15.59 | (414) all_58_1 = all_56_0
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_58_1, e2, e3,
% 107.85/15.59 | simplifying with (231), (321) gives:
% 107.85/15.59 | (415) all_58_1 = all_54_1
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3,
% 107.85/15.59 | simplifying with (118), (147) gives:
% 107.85/15.59 | (416) all_50_2 = all_38_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_50_2, e3, e3,
% 107.85/15.59 | simplifying with (104), (147) gives:
% 107.85/15.59 | (417) all_50_2 = all_32_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_50_2, e3, e3,
% 107.85/15.59 | simplifying with (85), (147) gives:
% 107.85/15.59 | (418) all_50_2 = all_24_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_0, e3, e3,
% 107.85/15.59 | simplifying with (118), (215) gives:
% 107.85/15.59 | (419) all_52_0 = all_38_2
% 107.85/15.59 |
% 107.85/15.59 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_0, e3, e3,
% 107.85/15.59 | simplifying with (85), (232) gives:
% 107.85/15.60 | (420) all_54_0 = all_24_2
% 107.85/15.60 |
% 107.85/15.60 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_54_0, e3, e3,
% 107.85/15.60 | simplifying with (65), (232) gives:
% 107.85/15.60 | (421) all_54_0 = all_16_2
% 107.85/15.60 |
% 107.85/15.60 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_56_12, e3, e3,
% 107.85/15.60 | simplifying with (215), (269) gives:
% 107.85/15.60 | (422) all_56_12 = all_52_0
% 107.85/15.60 |
% 107.85/15.60 | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_0, e3, e3,
% 107.85/15.60 | simplifying with (269), (322) gives:
% 107.85/15.60 | (423) all_58_0 = all_56_12
% 107.85/15.60 |
% 107.85/15.60 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_58_0, e3, e3,
% 107.85/15.60 | simplifying with (51), (322) gives:
% 107.85/15.60 | (424) all_58_0 = all_10_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (423), (424) imply:
% 107.85/15.60 | (425) all_56_12 = all_10_2
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (425) implies:
% 107.85/15.60 | (426) all_56_12 = all_10_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (414), (415) imply:
% 107.85/15.60 | (427) all_56_0 = all_54_1
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (427) implies:
% 107.85/15.60 | (428) all_56_0 = all_54_1
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (405), (406) imply:
% 107.85/15.60 | (429) all_56_3 = all_52_1
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (429) implies:
% 107.85/15.60 | (430) all_56_3 = all_52_1
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (402), (403) imply:
% 107.85/15.60 | (431) all_54_5 = all_48_2
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (431) implies:
% 107.85/15.60 | (432) all_54_5 = all_48_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (411), (412) imply:
% 107.85/15.60 | (433) all_56_1 = all_52_8
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (433) implies:
% 107.85/15.60 | (434) all_56_1 = all_52_8
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (393), (394) imply:
% 107.85/15.60 | (435) all_56_4 = all_52_9
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (435) implies:
% 107.85/15.60 | (436) all_56_4 = all_52_9
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (387), (388) imply:
% 107.85/15.60 | (437) all_56_6 = all_54_8
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (437) implies:
% 107.85/15.60 | (438) all_56_6 = all_54_8
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (384), (385) imply:
% 107.85/15.60 | (439) all_56_7 = all_52_6
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (439) implies:
% 107.85/15.60 | (440) all_56_7 = all_52_6
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (381), (382) imply:
% 107.85/15.60 | (441) all_40_2 = all_28_2
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (441) implies:
% 107.85/15.60 | (442) all_40_2 = all_28_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (408), (409) imply:
% 107.85/15.60 | (443) all_56_2 = all_54_3
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (443) implies:
% 107.85/15.60 | (444) all_56_2 = all_54_3
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (390), (391) imply:
% 107.85/15.60 | (445) all_56_5 = all_52_13
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (445) implies:
% 107.85/15.60 | (446) all_56_5 = all_52_13
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (372), (373) imply:
% 107.85/15.60 | (447) all_56_8 = all_54_11
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (447) implies:
% 107.85/15.60 | (448) all_56_8 = all_54_11
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (369), (370) imply:
% 107.85/15.60 | (449) all_56_9 = all_52_3
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (449) implies:
% 107.85/15.60 | (450) all_56_9 = all_52_3
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (366), (367) imply:
% 107.85/15.60 | (451) all_56_10 = all_54_13
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (451) implies:
% 107.85/15.60 | (452) all_56_10 = all_54_13
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (363), (364) imply:
% 107.85/15.60 | (453) all_56_11 = all_54_14
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (453) implies:
% 107.85/15.60 | (454) all_56_11 = all_54_14
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (360), (361) imply:
% 107.85/15.60 | (455) all_52_15 = all_12_2
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (455) implies:
% 107.85/15.60 | (456) all_52_15 = all_12_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (413), (428) imply:
% 107.85/15.60 | (457) all_54_1 = all_52_4
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (457) implies:
% 107.85/15.60 | (458) all_54_1 = all_52_4
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (410), (434) imply:
% 107.85/15.60 | (459) all_54_2 = all_52_8
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (459) implies:
% 107.85/15.60 | (460) all_54_2 = all_52_8
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (407), (444) imply:
% 107.85/15.60 | (461) all_54_3 = all_52_12
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (461) implies:
% 107.85/15.60 | (462) all_54_3 = all_52_12
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (404), (430) imply:
% 107.85/15.60 | (463) all_54_4 = all_52_1
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (463) implies:
% 107.85/15.60 | (464) all_54_4 = all_52_1
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (392), (436) imply:
% 107.85/15.60 | (465) all_54_6 = all_52_9
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (465) implies:
% 107.85/15.60 | (466) all_54_6 = all_52_9
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (389), (446) imply:
% 107.85/15.60 | (467) all_54_7 = all_52_13
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (467) implies:
% 107.85/15.60 | (468) all_54_7 = all_52_13
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (386), (438) imply:
% 107.85/15.60 | (469) all_54_8 = all_52_2
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (469) implies:
% 107.85/15.60 | (470) all_54_8 = all_52_2
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (383), (440) imply:
% 107.85/15.60 | (471) all_54_9 = all_52_6
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (471) implies:
% 107.85/15.60 | (472) all_54_9 = all_52_6
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (371), (448) imply:
% 107.85/15.60 | (473) all_54_11 = all_52_14
% 107.85/15.60 |
% 107.85/15.60 | SIMP: (473) implies:
% 107.85/15.60 | (474) all_54_11 = all_52_14
% 107.85/15.60 |
% 107.85/15.60 | COMBINE_EQS: (368), (450) imply:
% 107.85/15.61 | (475) all_54_12 = all_52_3
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (365), (452) imply:
% 107.85/15.61 | (476) all_54_13 = all_52_7
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (476) implies:
% 107.85/15.61 | (477) all_54_13 = all_52_7
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (362), (454) imply:
% 107.85/15.61 | (478) all_54_14 = all_52_11
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (478) implies:
% 107.85/15.61 | (479) all_54_14 = all_52_11
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (422), (426) imply:
% 107.85/15.61 | (480) all_52_0 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (480) implies:
% 107.85/15.61 | (481) all_52_0 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (398), (399) imply:
% 107.85/15.61 | (482) all_54_5 = all_42_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (482) implies:
% 107.85/15.61 | (483) all_54_5 = all_42_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (399), (401) imply:
% 107.85/15.61 | (484) all_42_2 = all_22_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (399), (400) imply:
% 107.85/15.61 | (485) all_42_2 = all_30_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (379), (380) imply:
% 107.85/15.61 | (486) all_52_10 = all_46_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (378), (379) imply:
% 107.85/15.61 | (487) all_54_10 = all_52_10
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (487) implies:
% 107.85/15.61 | (488) all_54_10 = all_52_10
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (357), (359) imply:
% 107.85/15.61 | (489) all_54_15 = all_20_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (489) implies:
% 107.85/15.61 | (490) all_54_15 = all_20_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (358), (359) imply:
% 107.85/15.61 | (491) all_26_2 = all_20_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (491) implies:
% 107.85/15.61 | (492) all_26_2 = all_20_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (420), (421) imply:
% 107.85/15.61 | (493) all_24_2 = all_16_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (493) implies:
% 107.85/15.61 | (494) all_24_2 = all_16_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (432), (483) imply:
% 107.85/15.61 | (495) all_48_2 = all_42_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (397), (432) imply:
% 107.85/15.61 | (496) all_48_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (377), (488) imply:
% 107.85/15.61 | (497) all_52_10 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (497) implies:
% 107.85/15.61 | (498) all_52_10 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (356), (490) imply:
% 107.85/15.61 | (499) all_20_2 = all_4_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (499) implies:
% 107.85/15.61 | (500) all_20_2 = all_4_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (419), (481) imply:
% 107.85/15.61 | (501) all_38_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (501) implies:
% 107.85/15.61 | (502) all_38_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (395), (396) imply:
% 107.85/15.61 | (503) all_22_2 = all_8_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (503) implies:
% 107.85/15.61 | (504) all_22_2 = all_8_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (486), (498) imply:
% 107.85/15.61 | (505) all_46_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (505) implies:
% 107.85/15.61 | (506) all_46_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (354), (456) imply:
% 107.85/15.61 | (507) all_44_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (354), (355) imply:
% 107.85/15.61 | (508) all_44_2 = all_34_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (417), (418) imply:
% 107.85/15.61 | (509) all_32_2 = all_24_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (416), (417) imply:
% 107.85/15.61 | (510) all_38_2 = all_32_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (510) implies:
% 107.85/15.61 | (511) all_38_2 = all_32_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (495), (496) imply:
% 107.85/15.61 | (512) all_42_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (512) implies:
% 107.85/15.61 | (513) all_42_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (376), (506) imply:
% 107.85/15.61 | (514) all_36_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (514) implies:
% 107.85/15.61 | (515) all_36_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (507), (508) imply:
% 107.85/15.61 | (516) all_34_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (516) implies:
% 107.85/15.61 | (517) all_34_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (484), (485) imply:
% 107.85/15.61 | (518) all_30_2 = all_22_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (485), (513) imply:
% 107.85/15.61 | (519) all_30_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (374), (442) imply:
% 107.85/15.61 | (520) all_36_2 = all_28_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (520) implies:
% 107.85/15.61 | (521) all_36_2 = all_28_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (375), (442) imply:
% 107.85/15.61 | (522) all_28_2 = all_6_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (502), (511) imply:
% 107.85/15.61 | (523) all_32_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (523) implies:
% 107.85/15.61 | (524) all_32_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (515), (521) imply:
% 107.85/15.61 | (525) all_28_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (525) implies:
% 107.85/15.61 | (526) all_28_2 = all_18_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (353), (517) imply:
% 107.85/15.61 | (527) all_26_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (527) implies:
% 107.85/15.61 | (528) all_26_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (509), (524) imply:
% 107.85/15.61 | (529) all_24_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (529) implies:
% 107.85/15.61 | (530) all_24_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (518), (519) imply:
% 107.85/15.61 | (531) all_22_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (531) implies:
% 107.85/15.61 | (532) all_22_2 = all_14_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (522), (526) imply:
% 107.85/15.61 | (533) all_18_2 = all_6_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (492), (528) imply:
% 107.85/15.61 | (534) all_20_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (534) implies:
% 107.85/15.61 | (535) all_20_2 = all_12_2
% 107.85/15.61 |
% 107.85/15.61 | COMBINE_EQS: (494), (530) imply:
% 107.85/15.61 | (536) all_16_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.61 | SIMP: (536) implies:
% 107.85/15.61 | (537) all_16_2 = all_10_2
% 107.85/15.61 |
% 107.85/15.62 | COMBINE_EQS: (504), (532) imply:
% 107.85/15.62 | (538) all_14_2 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (500), (535) imply:
% 107.85/15.62 | (539) all_12_2 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (528), (539) imply:
% 107.85/15.62 | (540) all_26_2 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (519), (538) imply:
% 107.85/15.62 | (541) all_30_2 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (517), (539) imply:
% 107.85/15.62 | (542) all_34_2 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (515), (533) imply:
% 107.85/15.62 | (543) all_36_2 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (485), (541) imply:
% 107.85/15.62 | (544) all_42_2 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (507), (539) imply:
% 107.85/15.62 | (545) all_44_2 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (506), (533) imply:
% 107.85/15.62 | (546) all_46_2 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (496), (538) imply:
% 107.85/15.62 | (547) all_48_2 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (417), (524) imply:
% 107.85/15.62 | (548) all_50_2 = all_10_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (354), (545) imply:
% 107.85/15.62 | (549) all_52_15 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (498), (533) imply:
% 107.85/15.62 | (550) all_52_10 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (377), (533) imply:
% 107.85/15.62 | (551) all_54_10 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (432), (547) imply:
% 107.85/15.62 | (552) all_54_5 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (421), (537) imply:
% 107.85/15.62 | (553) all_54_0 = all_10_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (359), (500) imply:
% 107.85/15.62 | (554) all_56_15 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (379), (550) imply:
% 107.85/15.62 | (555) all_56_14 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (399), (544) imply:
% 107.85/15.62 | (556) all_56_13 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (361), (539) imply:
% 107.85/15.62 | (557) all_58_15 = all_4_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (364), (479) imply:
% 107.85/15.62 | (558) all_58_14 = all_52_11
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (367), (477) imply:
% 107.85/15.62 | (559) all_58_13 = all_52_7
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (373), (474) imply:
% 107.85/15.62 | (560) all_58_11 = all_52_14
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (409), (462) imply:
% 107.85/15.62 | (561) all_58_9 = all_52_12
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (382), (522) imply:
% 107.85/15.62 | (562) all_58_8 = all_6_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (388), (470) imply:
% 107.85/15.62 | (563) all_58_6 = all_52_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (403), (547) imply:
% 107.85/15.62 | (564) all_58_3 = all_8_2
% 107.85/15.62 |
% 107.85/15.62 | COMBINE_EQS: (415), (458) imply:
% 107.85/15.62 | (565) all_58_1 = all_52_4
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (253), (426) imply:
% 107.85/15.62 | (566) ~ (all_10_2 = e3)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (252), (556) imply:
% 107.85/15.62 | (567) ~ (all_8_2 = e2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (251), (555) imply:
% 107.85/15.62 | (568) ~ (all_6_2 = e1)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (250), (554) imply:
% 107.85/15.62 | (569) ~ (all_4_2 = e0)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (199), (481) imply:
% 107.85/15.62 | (570) ~ (all_52_1 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (570) implies:
% 107.85/15.62 | (571) ~ (all_52_1 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (198), (481) imply:
% 107.85/15.62 | (572) ~ (all_52_2 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (572) implies:
% 107.85/15.62 | (573) ~ (all_52_2 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (197), (481) imply:
% 107.85/15.62 | (574) ~ (all_52_3 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (574) implies:
% 107.85/15.62 | (575) ~ (all_52_3 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (196), (481) imply:
% 107.85/15.62 | (576) ~ (all_52_4 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (576) implies:
% 107.85/15.62 | (577) ~ (all_52_4 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (195), (481) imply:
% 107.85/15.62 | (578) ~ (all_52_8 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (578) implies:
% 107.85/15.62 | (579) ~ (all_52_8 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (194), (481) imply:
% 107.85/15.62 | (580) ~ (all_52_12 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (580) implies:
% 107.85/15.62 | (581) ~ (all_52_12 = all_10_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (191), (396) imply:
% 107.85/15.62 | (582) ~ (all_52_1 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (186), (550) imply:
% 107.85/15.62 | (583) ~ (all_52_2 = all_6_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (182), (549) imply:
% 107.85/15.62 | (584) ~ (all_52_3 = all_4_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (181), (396) imply:
% 107.85/15.62 | (585) ~ (all_52_4 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (176), (396) imply:
% 107.85/15.62 | (586) ~ (all_52_6 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (586) implies:
% 107.85/15.62 | (587) ~ (all_52_6 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (175), (396) imply:
% 107.85/15.62 | (588) ~ (all_52_7 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (588) implies:
% 107.85/15.62 | (589) ~ (all_52_7 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (174), (396) imply:
% 107.85/15.62 | (590) ~ (all_52_9 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (590) implies:
% 107.85/15.62 | (591) ~ (all_52_9 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (173), (396) imply:
% 107.85/15.62 | (592) ~ (all_52_13 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | SIMP: (592) implies:
% 107.85/15.62 | (593) ~ (all_52_13 = all_8_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (171), (550) imply:
% 107.85/15.62 | (594) ~ (all_52_6 = all_6_2)
% 107.85/15.62 |
% 107.85/15.62 | REDUCE: (168), (549) imply:
% 107.85/15.63 | (595) ~ (all_52_7 = all_4_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (166), (550) imply:
% 107.85/15.63 | (596) ~ (all_52_8 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (163), (550) imply:
% 107.85/15.63 | (597) ~ (all_52_9 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (160), (550) imply:
% 107.85/15.63 | (598) ~ (all_52_11 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | SIMP: (598) implies:
% 107.85/15.63 | (599) ~ (all_52_11 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (159), (550) imply:
% 107.85/15.63 | (600) ~ (all_52_14 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | SIMP: (600) implies:
% 107.85/15.63 | (601) ~ (all_52_14 = all_6_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (158), (549) imply:
% 107.85/15.63 | (602) ~ (all_52_11 = all_4_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (155), (549) imply:
% 107.85/15.63 | (603) ~ (all_52_12 = all_4_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (153), (549) imply:
% 107.85/15.63 | (604) ~ (all_52_13 = all_4_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (152), (549) imply:
% 107.85/15.63 | (605) ~ (all_52_14 = all_4_2)
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (149), (548) imply:
% 107.85/15.63 | (606) op(all_50_1, all_10_2) = all_50_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (144), (547) imply:
% 107.85/15.63 | (607) op(all_48_1, all_8_2) = all_48_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (140), (546) imply:
% 107.85/15.63 | (608) op(all_46_1, all_6_2) = all_46_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (135), (545) imply:
% 107.85/15.63 | (609) op(all_44_1, all_4_2) = all_44_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (130), (544) imply:
% 107.85/15.63 | (610) op(all_42_1, all_8_2) = all_42_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (125), (375) imply:
% 107.85/15.63 | (611) op(all_40_1, all_6_2) = all_40_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (120), (502) imply:
% 107.85/15.63 | (612) op(all_38_1, all_10_2) = all_38_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (115), (543) imply:
% 107.85/15.63 | (613) op(all_36_1, all_6_2) = all_36_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (111), (542) imply:
% 107.85/15.63 | (614) op(all_34_1, all_4_2) = all_34_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (106), (524) imply:
% 107.85/15.63 | (615) op(all_32_1, all_10_2) = all_32_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (102), (541) imply:
% 107.85/15.63 | (616) op(all_30_1, all_8_2) = all_30_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (97), (522) imply:
% 107.85/15.63 | (617) op(all_28_1, all_6_2) = all_28_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (92), (540) imply:
% 107.85/15.63 | (618) op(all_26_1, all_4_2) = all_26_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (87), (530) imply:
% 107.85/15.63 | (619) op(all_24_1, all_10_2) = all_24_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (82), (504) imply:
% 107.85/15.63 | (620) op(all_22_1, all_8_2) = all_22_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (77), (500) imply:
% 107.85/15.63 | (621) op(all_20_1, all_4_2) = all_20_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (72), (533) imply:
% 107.85/15.63 | (622) op(all_18_1, all_6_2) = all_18_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (67), (537) imply:
% 107.85/15.63 | (623) op(all_16_1, all_10_2) = all_16_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (62), (538) imply:
% 107.85/15.63 | (624) op(all_14_1, all_8_2) = all_14_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (58), (539) imply:
% 107.85/15.63 | (625) op(all_12_1, all_4_2) = all_12_0
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (148), (548) imply:
% 107.85/15.63 | (626) op(e3, all_10_2) = all_50_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (119), (502) imply:
% 107.85/15.63 | (627) op(e3, all_10_2) = all_38_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (105), (524) imply:
% 107.85/15.63 | (628) op(e3, all_10_2) = all_32_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (86), (530) imply:
% 107.85/15.63 | (629) op(e3, all_10_2) = all_24_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (66), (537) imply:
% 107.85/15.63 | (630) op(e3, all_10_2) = all_16_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (143), (547) imply:
% 107.85/15.63 | (631) op(e2, all_8_2) = all_48_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (129), (544) imply:
% 107.85/15.63 | (632) op(e2, all_8_2) = all_42_1
% 107.85/15.63 |
% 107.85/15.63 | REDUCE: (101), (541) imply:
% 108.19/15.63 | (633) op(e2, all_8_2) = all_30_1
% 108.19/15.63 |
% 108.19/15.63 | REDUCE: (81), (504) imply:
% 108.19/15.63 | (634) op(e2, all_8_2) = all_22_1
% 108.19/15.63 |
% 108.19/15.63 | REDUCE: (61), (538) imply:
% 108.19/15.63 | (635) op(e2, all_8_2) = all_14_1
% 108.19/15.63 |
% 108.19/15.63 | REDUCE: (139), (546) imply:
% 108.19/15.63 | (636) op(e1, all_6_2) = all_46_1
% 108.19/15.63 |
% 108.19/15.63 | REDUCE: (124), (375) imply:
% 108.19/15.64 | (637) op(e1, all_6_2) = all_40_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (114), (543) imply:
% 108.19/15.64 | (638) op(e1, all_6_2) = all_36_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (96), (522) imply:
% 108.19/15.64 | (639) op(e1, all_6_2) = all_28_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (71), (533) imply:
% 108.19/15.64 | (640) op(e1, all_6_2) = all_18_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (134), (545) imply:
% 108.19/15.64 | (641) op(e0, all_4_2) = all_44_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (110), (542) imply:
% 108.19/15.64 | (642) op(e0, all_4_2) = all_34_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (91), (540) imply:
% 108.19/15.64 | (643) op(e0, all_4_2) = all_26_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (76), (500) imply:
% 108.19/15.64 | (644) op(e0, all_4_2) = all_20_1
% 108.19/15.64 |
% 108.19/15.64 | REDUCE: (57), (539) imply:
% 108.19/15.64 | (645) op(e0, all_4_2) = all_12_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_34_1, all_4_2,
% 108.19/15.64 | e0, simplifying with (642), (643) gives:
% 108.19/15.64 | (646) all_34_1 = all_26_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_34_1, all_4_2,
% 108.19/15.64 | e0, simplifying with (642), (644) gives:
% 108.19/15.64 | (647) all_34_1 = all_20_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_34_1, all_4_2,
% 108.19/15.64 | e0, simplifying with (642), (645) gives:
% 108.19/15.64 | (648) all_34_1 = all_12_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_44_1, all_4_2,
% 108.19/15.64 | e0, simplifying with (37), (641) gives:
% 108.19/15.64 | (649) all_44_1 = all_4_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_44_1, all_4_2,
% 108.19/15.64 | e0, simplifying with (641), (643) gives:
% 108.19/15.64 | (650) all_44_1 = all_26_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_18_1, all_40_1, all_6_2,
% 108.19/15.64 | e1, simplifying with (637), (640) gives:
% 108.19/15.64 | (651) all_40_1 = all_18_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_46_1, all_6_2,
% 108.19/15.64 | e1, simplifying with (42), (636) gives:
% 108.19/15.64 | (652) all_46_1 = all_6_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_40_1, all_46_1, all_6_2,
% 108.19/15.64 | e1, simplifying with (636), (637) gives:
% 108.19/15.64 | (653) all_46_1 = all_40_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_36_1, all_46_1, all_6_2,
% 108.19/15.64 | e1, simplifying with (636), (638) gives:
% 108.19/15.64 | (654) all_46_1 = all_36_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_46_1, all_6_2,
% 108.19/15.64 | e1, simplifying with (636), (639) gives:
% 108.19/15.64 | (655) all_46_1 = all_28_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_22_1, all_8_2,
% 108.19/15.64 | e2, simplifying with (634), (635) gives:
% 108.19/15.64 | (656) all_22_1 = all_14_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_42_1, all_8_2,
% 108.19/15.64 | e2, simplifying with (47), (632) gives:
% 108.19/15.64 | (657) all_42_1 = all_8_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_42_1, all_8_2,
% 108.19/15.64 | e2, simplifying with (632), (634) gives:
% 108.19/15.64 | (658) all_42_1 = all_22_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_48_1, all_8_2,
% 108.19/15.64 | e2, simplifying with (631), (632) gives:
% 108.19/15.64 | (659) all_48_1 = all_42_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_48_1, all_8_2,
% 108.19/15.64 | e2, simplifying with (631), (633) gives:
% 108.19/15.64 | (660) all_48_1 = all_30_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_24_1,
% 108.19/15.64 | all_10_2, e3, simplifying with (52), (629) gives:
% 108.19/15.64 | (661) all_24_1 = all_10_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_32_1,
% 108.19/15.64 | all_10_2, e3, simplifying with (628), (629) gives:
% 108.19/15.64 | (662) all_32_1 = all_24_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_38_1,
% 108.19/15.64 | all_10_2, e3, simplifying with (627), (628) gives:
% 108.19/15.64 | (663) all_38_1 = all_32_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_38_1, all_50_1,
% 108.19/15.64 | all_10_2, e3, simplifying with (626), (627) gives:
% 108.19/15.64 | (664) all_50_1 = all_38_1
% 108.19/15.64 |
% 108.19/15.64 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_50_1,
% 108.19/15.64 | all_10_2, e3, simplifying with (626), (630) gives:
% 108.19/15.64 | (665) all_50_1 = all_16_1
% 108.19/15.64 |
% 108.19/15.65 | COMBINE_EQS: (664), (665) imply:
% 108.19/15.65 | (666) all_38_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (666) implies:
% 108.19/15.65 | (667) all_38_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (659), (660) imply:
% 108.19/15.65 | (668) all_42_1 = all_30_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (668) implies:
% 108.19/15.65 | (669) all_42_1 = all_30_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (652), (654) imply:
% 108.19/15.65 | (670) all_36_1 = all_6_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (653), (654) imply:
% 108.19/15.65 | (671) all_40_1 = all_36_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (671) implies:
% 108.19/15.65 | (672) all_40_1 = all_36_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (654), (655) imply:
% 108.19/15.65 | (673) all_36_1 = all_28_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (649), (650) imply:
% 108.19/15.65 | (674) all_26_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (674) implies:
% 108.19/15.65 | (675) all_26_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (657), (669) imply:
% 108.19/15.65 | (676) all_30_1 = all_8_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (658), (669) imply:
% 108.19/15.65 | (677) all_30_1 = all_22_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (651), (672) imply:
% 108.19/15.65 | (678) all_36_1 = all_18_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (678) implies:
% 108.19/15.65 | (679) all_36_1 = all_18_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (663), (667) imply:
% 108.19/15.65 | (680) all_32_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (680) implies:
% 108.19/15.65 | (681) all_32_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (673), (679) imply:
% 108.19/15.65 | (682) all_28_1 = all_18_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (670), (673) imply:
% 108.19/15.65 | (683) all_28_1 = all_6_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (646), (647) imply:
% 108.19/15.65 | (684) all_26_1 = all_20_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (684) implies:
% 108.19/15.65 | (685) all_26_1 = all_20_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (647), (648) imply:
% 108.19/15.65 | (686) all_20_1 = all_12_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (662), (681) imply:
% 108.19/15.65 | (687) all_24_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (687) implies:
% 108.19/15.65 | (688) all_24_1 = all_16_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (676), (677) imply:
% 108.19/15.65 | (689) all_22_1 = all_8_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (689) implies:
% 108.19/15.65 | (690) all_22_1 = all_8_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (682), (683) imply:
% 108.19/15.65 | (691) all_18_1 = all_6_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (691) implies:
% 108.19/15.65 | (692) all_18_1 = all_6_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (675), (685) imply:
% 108.19/15.65 | (693) all_20_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (693) implies:
% 108.19/15.65 | (694) all_20_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (661), (688) imply:
% 108.19/15.65 | (695) all_16_1 = all_10_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (656), (690) imply:
% 108.19/15.65 | (696) all_14_1 = all_8_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (696) implies:
% 108.19/15.65 | (697) all_14_1 = all_8_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (686), (694) imply:
% 108.19/15.65 | (698) all_12_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | SIMP: (698) implies:
% 108.19/15.65 | (699) all_12_1 = all_4_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (681), (695) imply:
% 108.19/15.65 | (700) all_32_1 = all_10_1
% 108.19/15.65 |
% 108.19/15.65 | COMBINE_EQS: (647), (694) imply:
% 108.19/15.66 | (701) all_34_1 = all_4_1
% 108.19/15.66 |
% 108.19/15.66 | COMBINE_EQS: (667), (695) imply:
% 108.19/15.66 | (702) all_38_1 = all_10_1
% 108.19/15.66 |
% 108.19/15.66 | COMBINE_EQS: (651), (692) imply:
% 108.19/15.66 | (703) all_40_1 = all_6_1
% 108.19/15.66 |
% 108.19/15.66 | COMBINE_EQS: (660), (676) imply:
% 108.19/15.66 | (704) all_48_1 = all_8_1
% 108.19/15.66 |
% 108.19/15.66 | COMBINE_EQS: (665), (695) imply:
% 108.19/15.66 | (705) all_50_1 = all_10_1
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (606), (705) imply:
% 108.19/15.66 | (706) op(all_10_1, all_10_2) = all_50_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (607), (704) imply:
% 108.19/15.66 | (707) op(all_8_1, all_8_2) = all_48_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (608), (652) imply:
% 108.19/15.66 | (708) op(all_6_1, all_6_2) = all_46_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (609), (649) imply:
% 108.19/15.66 | (709) op(all_4_1, all_4_2) = all_44_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (610), (657) imply:
% 108.19/15.66 | (710) op(all_8_1, all_8_2) = all_42_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (611), (703) imply:
% 108.19/15.66 | (711) op(all_6_1, all_6_2) = all_40_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (612), (702) imply:
% 108.19/15.66 | (712) op(all_10_1, all_10_2) = all_38_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (613), (670) imply:
% 108.19/15.66 | (713) op(all_6_1, all_6_2) = all_36_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (614), (701) imply:
% 108.19/15.66 | (714) op(all_4_1, all_4_2) = all_34_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (615), (700) imply:
% 108.19/15.66 | (715) op(all_10_1, all_10_2) = all_32_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (616), (676) imply:
% 108.19/15.66 | (716) op(all_8_1, all_8_2) = all_30_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (617), (683) imply:
% 108.19/15.66 | (717) op(all_6_1, all_6_2) = all_28_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (618), (675) imply:
% 108.19/15.66 | (718) op(all_4_1, all_4_2) = all_26_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (619), (661) imply:
% 108.19/15.66 | (719) op(all_10_1, all_10_2) = all_24_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (620), (690) imply:
% 108.19/15.66 | (720) op(all_8_1, all_8_2) = all_22_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (621), (694) imply:
% 108.19/15.66 | (721) op(all_4_1, all_4_2) = all_20_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (622), (692) imply:
% 108.19/15.66 | (722) op(all_6_1, all_6_2) = all_18_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (623), (695) imply:
% 108.19/15.66 | (723) op(all_10_1, all_10_2) = all_16_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (624), (697) imply:
% 108.19/15.66 | (724) op(all_8_1, all_8_2) = all_14_0
% 108.19/15.66 |
% 108.19/15.66 | REDUCE: (625), (699) imply:
% 108.19/15.66 | (725) op(all_4_1, all_4_2) = all_12_0
% 108.19/15.66 |
% 108.19/15.66 | GROUND_INST: instantiating (function-axioms) with all_12_0, all_26_0, all_4_2,
% 108.19/15.66 | all_4_1, simplifying with (718), (725) gives:
% 108.19/15.66 | (726) all_26_0 = all_12_0
% 108.19/15.66 |
% 108.19/15.66 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_44_0, all_4_2,
% 108.19/15.66 | all_4_1, simplifying with (38), (709) gives:
% 108.19/15.66 | (727) all_44_0 = all_4_0
% 108.19/15.66 |
% 108.19/15.66 | GROUND_INST: instantiating (function-axioms) with all_34_0, all_44_0, all_4_2,
% 108.19/15.66 | all_4_1, simplifying with (709), (714) gives:
% 108.19/15.66 | (728) all_44_0 = all_34_0
% 108.19/15.66 |
% 108.19/15.66 | GROUND_INST: instantiating (function-axioms) with all_26_0, all_44_0, all_4_2,
% 108.19/15.66 | all_4_1, simplifying with (709), (718) gives:
% 108.19/15.66 | (729) all_44_0 = all_26_0
% 108.19/15.66 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_20_0, all_44_0, all_4_2,
% 108.19/15.67 | all_4_1, simplifying with (709), (721) gives:
% 108.19/15.67 | (730) all_44_0 = all_20_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_40_0, all_6_2,
% 108.19/15.67 | all_6_1, simplifying with (43), (711) gives:
% 108.19/15.67 | (731) all_40_0 = all_6_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_40_0, all_6_2,
% 108.19/15.67 | all_6_1, simplifying with (711), (717) gives:
% 108.19/15.67 | (732) all_40_0 = all_28_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_36_0, all_46_0, all_6_2,
% 108.19/15.67 | all_6_1, simplifying with (708), (713) gives:
% 108.19/15.67 | (733) all_46_0 = all_36_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_46_0, all_6_2,
% 108.19/15.67 | all_6_1, simplifying with (708), (717) gives:
% 108.19/15.67 | (734) all_46_0 = all_28_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_18_0, all_46_0, all_6_2,
% 108.19/15.67 | all_6_1, simplifying with (708), (722) gives:
% 108.19/15.67 | (735) all_46_0 = all_18_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_30_0, all_8_2,
% 108.19/15.67 | all_8_1, simplifying with (48), (716) gives:
% 108.19/15.67 | (736) all_30_0 = all_8_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_14_0, all_30_0, all_8_2,
% 108.19/15.67 | all_8_1, simplifying with (716), (724) gives:
% 108.19/15.67 | (737) all_30_0 = all_14_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_42_0, all_48_0, all_8_2,
% 108.19/15.67 | all_8_1, simplifying with (707), (710) gives:
% 108.19/15.67 | (738) all_48_0 = all_42_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_30_0, all_48_0, all_8_2,
% 108.19/15.67 | all_8_1, simplifying with (707), (716) gives:
% 108.19/15.67 | (739) all_48_0 = all_30_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_48_0, all_8_2,
% 108.19/15.67 | all_8_1, simplifying with (707), (720) gives:
% 108.19/15.67 | (740) all_48_0 = all_22_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_10_0, all_38_0,
% 108.19/15.67 | all_10_2, all_10_1, simplifying with (53), (712) gives:
% 108.19/15.67 | (741) all_38_0 = all_10_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_38_0,
% 108.19/15.67 | all_10_2, all_10_1, simplifying with (712), (715) gives:
% 108.19/15.67 | (742) all_38_0 = all_32_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_38_0,
% 108.19/15.67 | all_10_2, all_10_1, simplifying with (712), (719) gives:
% 108.19/15.67 | (743) all_38_0 = all_24_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_32_0, all_50_0,
% 108.19/15.67 | all_10_2, all_10_1, simplifying with (706), (715) gives:
% 108.19/15.67 | (744) all_50_0 = all_32_0
% 108.19/15.67 |
% 108.19/15.67 | GROUND_INST: instantiating (function-axioms) with all_16_0, all_50_0,
% 108.19/15.67 | all_10_2, all_10_1, simplifying with (706), (723) gives:
% 108.19/15.67 | (745) all_50_0 = all_16_0
% 108.19/15.67 |
% 108.19/15.67 | COMBINE_EQS: (744), (745) imply:
% 108.19/15.67 | (746) all_32_0 = all_16_0
% 108.19/15.67 |
% 108.19/15.67 | SIMP: (746) implies:
% 108.19/15.67 | (747) all_32_0 = all_16_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (738), (740) imply:
% 108.37/15.67 | (748) all_42_0 = all_22_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (738), (739) imply:
% 108.37/15.67 | (749) all_42_0 = all_30_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (733), (735) imply:
% 108.37/15.67 | (750) all_36_0 = all_18_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (733), (734) imply:
% 108.37/15.67 | (751) all_36_0 = all_28_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (727), (728) imply:
% 108.37/15.67 | (752) all_34_0 = all_4_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (728), (729) imply:
% 108.37/15.67 | (753) all_34_0 = all_26_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (728), (730) imply:
% 108.37/15.67 | (754) all_34_0 = all_20_0
% 108.37/15.67 |
% 108.37/15.67 | COMBINE_EQS: (748), (749) imply:
% 108.37/15.67 | (755) all_30_0 = all_22_0
% 108.37/15.67 |
% 108.37/15.68 | SIMP: (755) implies:
% 108.37/15.68 | (756) all_30_0 = all_22_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (731), (732) imply:
% 108.37/15.68 | (757) all_28_0 = all_6_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (757) implies:
% 108.37/15.68 | (758) all_28_0 = all_6_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (741), (743) imply:
% 108.37/15.68 | (759) all_24_0 = all_10_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (742), (743) imply:
% 108.37/15.68 | (760) all_32_0 = all_24_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (760) implies:
% 108.37/15.68 | (761) all_32_0 = all_24_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (750), (751) imply:
% 108.37/15.68 | (762) all_28_0 = all_18_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (762) implies:
% 108.37/15.68 | (763) all_28_0 = all_18_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (752), (754) imply:
% 108.37/15.68 | (764) all_20_0 = all_4_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (753), (754) imply:
% 108.37/15.68 | (765) all_26_0 = all_20_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (765) implies:
% 108.37/15.68 | (766) all_26_0 = all_20_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (747), (761) imply:
% 108.37/15.68 | (767) all_24_0 = all_16_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (767) implies:
% 108.37/15.68 | (768) all_24_0 = all_16_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (737), (756) imply:
% 108.37/15.68 | (769) all_22_0 = all_14_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (736), (756) imply:
% 108.37/15.68 | (770) all_22_0 = all_8_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (758), (763) imply:
% 108.37/15.68 | (771) all_18_0 = all_6_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (726), (766) imply:
% 108.37/15.68 | (772) all_20_0 = all_12_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (772) implies:
% 108.37/15.68 | (773) all_20_0 = all_12_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (759), (768) imply:
% 108.37/15.68 | (774) all_16_0 = all_10_0
% 108.37/15.68 |
% 108.37/15.68 | SIMP: (774) implies:
% 108.37/15.68 | (775) all_16_0 = all_10_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (769), (770) imply:
% 108.37/15.68 | (776) all_14_0 = all_8_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (764), (773) imply:
% 108.37/15.68 | (777) all_12_0 = all_4_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (726), (777) imply:
% 108.37/15.68 | (778) all_26_0 = all_4_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (747), (775) imply:
% 108.37/15.68 | (779) all_32_0 = all_10_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (750), (771) imply:
% 108.37/15.68 | (780) all_36_0 = all_6_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (748), (770) imply:
% 108.37/15.68 | (781) all_42_0 = all_8_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (738), (781) imply:
% 108.37/15.68 | (782) all_48_0 = all_8_0
% 108.37/15.68 |
% 108.37/15.68 | COMBINE_EQS: (745), (775) imply:
% 108.37/15.68 | (783) all_50_0 = all_10_0
% 108.37/15.68 |
% 108.37/15.68 | BETA: splitting (39) gives:
% 108.37/15.68 |
% 108.37/15.68 | Case 1:
% 108.37/15.68 | |
% 108.37/15.68 | | (784) ~ (all_4_0 = e3)
% 108.37/15.68 | |
% 108.37/15.68 | | BETA: splitting (44) gives:
% 108.37/15.68 | |
% 108.37/15.68 | | Case 1:
% 108.37/15.68 | | |
% 108.37/15.68 | | | (785) ~ (all_6_1 = e2)
% 108.37/15.68 | | |
% 108.37/15.68 | | | BETA: splitting (49) gives:
% 108.37/15.68 | | |
% 108.37/15.68 | | | Case 1:
% 108.37/15.68 | | | |
% 108.37/15.68 | | | | (786) ~ (all_8_1 = e1)
% 108.37/15.68 | | | |
% 108.37/15.68 | | | | BETA: splitting (54) gives:
% 108.37/15.68 | | | |
% 108.37/15.68 | | | | Case 1:
% 108.37/15.68 | | | | |
% 108.37/15.68 | | | | | (787) ~ (all_10_0 = e2)
% 108.37/15.68 | | | | |
% 108.37/15.68 | | | | | BETA: splitting (63) gives:
% 108.37/15.68 | | | | |
% 108.37/15.68 | | | | | Case 1:
% 108.37/15.68 | | | | | |
% 108.37/15.68 | | | | | | (788) ~ (all_14_0 = e1)
% 108.37/15.68 | | | | | |
% 108.37/15.68 | | | | | | REDUCE: (776), (788) imply:
% 108.37/15.68 | | | | | | (789) ~ (all_8_0 = e1)
% 108.37/15.68 | | | | | |
% 108.37/15.68 | | | | | | BETA: splitting (68) gives:
% 108.37/15.68 | | | | | |
% 108.37/15.68 | | | | | | Case 1:
% 108.37/15.68 | | | | | | |
% 108.37/15.68 | | | | | | | (790) ~ (all_16_0 = e1)
% 108.37/15.68 | | | | | | |
% 108.37/15.68 | | | | | | | REDUCE: (775), (790) imply:
% 108.37/15.68 | | | | | | | (791) ~ (all_10_0 = e1)
% 108.37/15.68 | | | | | | |
% 108.37/15.68 | | | | | | | BETA: splitting (83) gives:
% 108.37/15.68 | | | | | | |
% 108.37/15.68 | | | | | | | Case 1:
% 108.37/15.68 | | | | | | | |
% 108.37/15.68 | | | | | | | | (792) ~ (all_22_1 = e3)
% 108.37/15.68 | | | | | | | |
% 108.37/15.68 | | | | | | | | REDUCE: (690), (792) imply:
% 108.37/15.68 | | | | | | | | (793) ~ (all_8_1 = e3)
% 108.37/15.68 | | | | | | | |
% 108.37/15.68 | | | | | | | | BETA: splitting (93) gives:
% 108.37/15.68 | | | | | | | |
% 108.37/15.68 | | | | | | | | Case 1:
% 108.37/15.68 | | | | | | | | |
% 108.37/15.68 | | | | | | | | | (794) ~ (all_26_0 = e1)
% 108.37/15.68 | | | | | | | | |
% 108.37/15.68 | | | | | | | | | REDUCE: (778), (794) imply:
% 108.37/15.68 | | | | | | | | | (795) ~ (all_4_0 = e1)
% 108.37/15.68 | | | | | | | | |
% 108.37/15.68 | | | | | | | | | BETA: splitting (98) gives:
% 108.37/15.68 | | | | | | | | |
% 108.37/15.68 | | | | | | | | | Case 1:
% 108.37/15.68 | | | | | | | | | |
% 108.37/15.68 | | | | | | | | | | (796) ~ (all_28_0 = e2)
% 108.37/15.68 | | | | | | | | | |
% 108.37/15.68 | | | | | | | | | | REDUCE: (758), (796) imply:
% 108.37/15.68 | | | | | | | | | | (797) ~ (all_6_0 = e2)
% 108.37/15.68 | | | | | | | | | |
% 108.37/15.69 | | | | | | | | | | REF_CLOSE: (6), (8), (37), (38), (42), (43), (52), (53),
% 108.37/15.69 | | | | | | | | | | (107), (116), (121), (126), (154), (157), (169),
% 108.37/15.69 | | | | | | | | | | (170), (172), (178), (179), (183), (184), (185),
% 108.37/15.69 | | | | | | | | | | (187), (202), (203), (204), (206), (207), (208),
% 108.37/15.69 | | | | | | | | | | (209), (211), (212), (213), (214), (233), (235),
% 108.37/15.69 | | | | | | | | | | (236), (237), (238), (239), (240), (241), (242),
% 108.37/15.69 | | | | | | | | | | (243), (244), (245), (247), (248), (270), (271),
% 108.37/15.69 | | | | | | | | | | (272), (273), (274), (275), (276), (277), (278),
% 108.37/15.69 | | | | | | | | | | (279), (281), (282), (283), (284), (285), (286),
% 108.37/15.69 | | | | | | | | | | (287), (288), (289), (290), (291), (292), (293),
% 108.37/15.69 | | | | | | | | | | (294), (295), (297), (298), (299), (300), (302),
% 108.37/15.69 | | | | | | | | | | (303), (304), (305), (323), (324), (327), (328),
% 108.37/15.69 | | | | | | | | | | (331), (332), (336), (340), (342), (343), (344),
% 108.37/15.69 | | | | | | | | | | (345), (347), (349), (351), (352), (356), (362),
% 108.37/15.69 | | | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.37/15.69 | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.37/15.69 | | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.37/15.69 | | | | | | | | | | (462), (464), (466), (468), (470), (472), (474),
% 108.37/15.69 | | | | | | | | | | (475), (477), (502), (524), (543), (551), (552),
% 108.37/15.69 | | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 108.37/15.69 | | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 108.37/15.69 | | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 108.37/15.69 | | | | | | | | | | (579), (581), (582), (583), (584), (585), (587),
% 108.37/15.69 | | | | | | | | | | (589), (594), (595), (596), (597), (599), (601),
% 108.37/15.69 | | | | | | | | | | (602), (603), (604), (605), (670), (700), (702),
% 108.37/15.69 | | | | | | | | | | (703), (731), (741), (779), (780), (784), (785),
% 108.37/15.69 | | | | | | | | | | (787), (791), (795), (797), (function-axioms) are
% 108.37/15.69 | | | | | | | | | | inconsistent by sub-proof #287.
% 108.37/15.69 | | | | | | | | | |
% 108.37/15.69 | | | | | | | | | Case 2:
% 108.37/15.69 | | | | | | | | | |
% 108.37/15.69 | | | | | | | | | | (798) all_28_0 = e2
% 108.37/15.69 | | | | | | | | | | (799) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 108.37/15.69 | | | | | | | | | |
% 108.37/15.69 | | | | | | | | | | COMBINE_EQS: (758), (798) imply:
% 108.37/15.69 | | | | | | | | | | (800) all_6_0 = e2
% 108.37/15.69 | | | | | | | | | |
% 108.37/15.69 | | | | | | | | | | SIMP: (800) implies:
% 108.37/15.69 | | | | | | | | | | (801) all_6_0 = e2
% 108.37/15.69 | | | | | | | | | |
% 108.37/15.70 | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (37), (42), (43), (47), (52),
% 108.37/15.70 | | | | | | | | | | (53), (107), (121), (154), (161), (162), (164),
% 108.37/15.70 | | | | | | | | | | (165), (167), (169), (170), (172), (177), (178),
% 108.37/15.70 | | | | | | | | | | (179), (180), (185), (187), (188), (193), (201),
% 108.37/15.70 | | | | | | | | | | (202), (204), (206), (207), (208), (209), (212),
% 108.37/15.70 | | | | | | | | | | (213), (214), (233), (234), (235), (237), (238),
% 108.37/15.70 | | | | | | | | | | (239), (240), (242), (243), (245), (246), (247),
% 108.37/15.70 | | | | | | | | | | (248), (270), (271), (272), (273), (274), (275),
% 108.37/15.70 | | | | | | | | | | (276), (277), (278), (279), (280), (281), (283),
% 108.37/15.70 | | | | | | | | | | (284), (285), (286), (287), (288), (289), (290),
% 108.37/15.70 | | | | | | | | | | (291), (292), (293), (294), (295), (296), (298),
% 108.37/15.70 | | | | | | | | | | (299), (300), (301), (302), (303), (304), (305),
% 108.37/15.70 | | | | | | | | | | (323), (325), (327), (329), (331), (332), (335),
% 108.37/15.70 | | | | | | | | | | (336), (340), (342), (343), (344), (345), (352),
% 108.37/15.70 | | | | | | | | | | (356), (362), (365), (370), (371), (385), (386),
% 108.37/15.70 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 108.37/15.70 | | | | | | | | | | (426), (430), (434), (436), (440), (446), (450),
% 108.37/15.70 | | | | | | | | | | (458), (460), (462), (466), (470), (472), (474),
% 108.37/15.70 | | | | | | | | | | (477), (479), (502), (522), (524), (551), (552),
% 108.37/15.70 | | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 108.37/15.70 | | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 108.37/15.70 | | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 108.37/15.70 | | | | | | | | | | (579), (581), (582), (583), (585), (587), (589),
% 108.37/15.70 | | | | | | | | | | (591), (593), (594), (595), (596), (597), (599),
% 108.37/15.70 | | | | | | | | | | (601), (602), (603), (604), (605), (683), (700),
% 108.37/15.70 | | | | | | | | | | (702), (741), (779), (785), (787), (791), (793),
% 108.37/15.70 | | | | | | | | | | (799), (801), (function-axioms) are inconsistent
% 108.37/15.70 | | | | | | | | | | by sub-proof #240.
% 108.37/15.70 | | | | | | | | | |
% 108.37/15.70 | | | | | | | | | End of split
% 108.37/15.70 | | | | | | | | |
% 108.37/15.70 | | | | | | | | Case 2:
% 108.37/15.70 | | | | | | | | |
% 108.37/15.70 | | | | | | | | | (802) all_26_0 = e1
% 108.37/15.70 | | | | | | | | | (803) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 108.37/15.70 | | | | | | | | |
% 108.37/15.70 | | | | | | | | | COMBINE_EQS: (778), (802) imply:
% 108.37/15.70 | | | | | | | | | (804) all_4_0 = e1
% 108.37/15.70 | | | | | | | | |
% 108.37/15.70 | | | | | | | | | SIMP: (804) implies:
% 108.37/15.70 | | | | | | | | | (805) all_4_0 = e1
% 108.37/15.70 | | | | | | | | |
% 108.37/15.70 | | | | | | | | | REF_CLOSE: (37), (38), (42), (43), (98), (116), (126), (136),
% 108.37/15.70 | | | | | | | | | (154), (157), (161), (170), (172), (179), (185),
% 108.37/15.70 | | | | | | | | | (188), (202), (203), (204), (206), (207), (212),
% 108.37/15.70 | | | | | | | | | (214), (233), (235), (236), (237), (238), (239),
% 108.37/15.70 | | | | | | | | | (240), (241), (243), (245), (247), (248), (270),
% 108.37/15.70 | | | | | | | | | (273), (274), (276), (279), (283), (286), (287),
% 108.37/15.70 | | | | | | | | | (288), (289), (290), (291), (294), (295), (297),
% 108.37/15.70 | | | | | | | | | (298), (300), (304), (323), (325), (331), (332),
% 108.37/15.70 | | | | | | | | | (340), (342), (344), (345), (352), (356), (362),
% 108.37/15.70 | | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.37/15.70 | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.37/15.70 | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.37/15.70 | | | | | | | | | (462), (468), (470), (472), (474), (475), (477),
% 108.37/15.70 | | | | | | | | | (522), (540), (543), (545), (551), (552), (553),
% 108.37/15.70 | | | | | | | | | (554), (555), (556), (557), (558), (559), (560),
% 108.37/15.70 | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 108.37/15.70 | | | | | | | | | (568), (569), (571), (573), (575), (577), (583),
% 108.37/15.70 | | | | | | | | | (584), (585), (587), (589), (593), (594), (595),
% 108.37/15.70 | | | | | | | | | (597), (601), (603), (604), (605), (649), (670),
% 108.37/15.70 | | | | | | | | | (675), (683), (703), (727), (731), (758), (780),
% 108.37/15.70 | | | | | | | | | (785), (803), (805), (function-axioms) are
% 108.37/15.70 | | | | | | | | | inconsistent by sub-proof #225.
% 108.37/15.70 | | | | | | | | |
% 108.37/15.71 | | | | | | | | End of split
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | Case 2:
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | (806) all_22_1 = e3
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | COMBINE_EQS: (690), (806) imply:
% 108.37/15.71 | | | | | | | | (807) all_8_1 = e3
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | REDUCE: (48), (807) imply:
% 108.37/15.71 | | | | | | | | (808) op(e3, all_8_2) = all_8_0
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | REDUCE: (47), (807) imply:
% 108.37/15.71 | | | | | | | | (809) op(e2, all_8_2) = e3
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | BETA: splitting (93) gives:
% 108.37/15.71 | | | | | | | |
% 108.37/15.71 | | | | | | | | Case 1:
% 108.37/15.71 | | | | | | | | |
% 108.37/15.71 | | | | | | | | | (810) ~ (all_26_0 = e1)
% 108.37/15.71 | | | | | | | | |
% 108.37/15.71 | | | | | | | | | REDUCE: (778), (810) imply:
% 108.37/15.71 | | | | | | | | | (811) ~ (all_4_0 = e1)
% 108.37/15.71 | | | | | | | | |
% 108.37/15.71 | | | | | | | | | BETA: splitting (98) gives:
% 108.37/15.71 | | | | | | | | |
% 108.37/15.71 | | | | | | | | | Case 1:
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | (812) ~ (all_28_0 = e2)
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | REDUCE: (758), (812) imply:
% 108.37/15.71 | | | | | | | | | | (813) ~ (all_6_0 = e2)
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | REF_CLOSE: (6), (8), (37), (38), (42), (43), (52), (53),
% 108.37/15.71 | | | | | | | | | | (107), (116), (121), (126), (154), (157), (169),
% 108.37/15.71 | | | | | | | | | | (170), (172), (178), (179), (183), (184), (185),
% 108.37/15.71 | | | | | | | | | | (187), (202), (203), (204), (206), (207), (208),
% 108.37/15.71 | | | | | | | | | | (209), (211), (212), (213), (214), (233), (235),
% 108.37/15.71 | | | | | | | | | | (236), (237), (238), (239), (240), (241), (242),
% 108.37/15.71 | | | | | | | | | | (243), (244), (245), (247), (248), (270), (271),
% 108.37/15.71 | | | | | | | | | | (272), (273), (274), (275), (276), (277), (278),
% 108.37/15.71 | | | | | | | | | | (279), (281), (282), (283), (284), (285), (286),
% 108.37/15.71 | | | | | | | | | | (287), (288), (289), (290), (291), (292), (293),
% 108.37/15.71 | | | | | | | | | | (294), (295), (297), (298), (299), (300), (302),
% 108.37/15.71 | | | | | | | | | | (303), (304), (305), (323), (324), (327), (328),
% 108.37/15.71 | | | | | | | | | | (331), (332), (336), (340), (342), (343), (344),
% 108.37/15.71 | | | | | | | | | | (345), (347), (349), (351), (352), (356), (362),
% 108.37/15.71 | | | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.37/15.71 | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.37/15.71 | | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.37/15.71 | | | | | | | | | | (462), (464), (466), (468), (470), (472), (474),
% 108.37/15.71 | | | | | | | | | | (475), (477), (502), (524), (543), (551), (552),
% 108.37/15.71 | | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 108.37/15.71 | | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 108.37/15.71 | | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 108.37/15.71 | | | | | | | | | | (579), (581), (582), (583), (584), (585), (587),
% 108.37/15.71 | | | | | | | | | | (589), (594), (595), (596), (597), (599), (601),
% 108.37/15.71 | | | | | | | | | | (602), (603), (604), (605), (670), (700), (702),
% 108.37/15.71 | | | | | | | | | | (703), (731), (741), (779), (780), (784), (785),
% 108.37/15.71 | | | | | | | | | | (787), (791), (811), (813), (function-axioms) are
% 108.37/15.71 | | | | | | | | | | inconsistent by sub-proof #287.
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | Case 2:
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | (814) all_28_0 = e2
% 108.37/15.71 | | | | | | | | | | (815) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | COMBINE_EQS: (758), (814) imply:
% 108.37/15.71 | | | | | | | | | | (816) all_6_0 = e2
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | SIMP: (816) implies:
% 108.37/15.71 | | | | | | | | | | (817) all_6_0 = e2
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.71 | | | | | | | | | | REDUCE: (43), (817) imply:
% 108.37/15.71 | | | | | | | | | | (818) op(all_6_1, all_6_2) = e2
% 108.37/15.71 | | | | | | | | | |
% 108.37/15.72 | | | | | | | | | | REF_CLOSE: (5), (8), (9), (37), (42), (52), (53), (107),
% 108.37/15.72 | | | | | | | | | | (121), (154), (161), (162), (164), (165), (167),
% 108.37/15.72 | | | | | | | | | | (169), (170), (172), (178), (179), (180), (184),
% 108.37/15.72 | | | | | | | | | | (185), (187), (188), (193), (201), (202), (204),
% 108.37/15.72 | | | | | | | | | | (206), (207), (208), (209), (211), (212), (213),
% 108.37/15.72 | | | | | | | | | | (214), (233), (234), (235), (237), (238), (239),
% 108.37/15.72 | | | | | | | | | | (240), (242), (243), (245), (246), (247), (248),
% 108.37/15.72 | | | | | | | | | | (270), (271), (272), (273), (274), (275), (276),
% 108.37/15.72 | | | | | | | | | | (277), (278), (279), (280), (281), (283), (284),
% 108.37/15.72 | | | | | | | | | | (285), (286), (287), (288), (289), (290), (291),
% 108.37/15.72 | | | | | | | | | | (292), (293), (294), (295), (296), (298), (299),
% 108.37/15.72 | | | | | | | | | | (300), (301), (302), (303), (304), (305), (323),
% 108.37/15.72 | | | | | | | | | | (325), (327), (331), (332), (335), (336), (337),
% 108.37/15.72 | | | | | | | | | | (340), (342), (343), (344), (345), (346), (349),
% 108.37/15.72 | | | | | | | | | | (352), (356), (362), (365), (370), (371), (385),
% 108.37/15.72 | | | | | | | | | | (386), (391), (394), (406), (407), (412), (413),
% 108.37/15.72 | | | | | | | | | | (424), (426), (430), (434), (436), (440), (446),
% 108.37/15.72 | | | | | | | | | | (450), (458), (460), (462), (466), (470), (472),
% 108.37/15.72 | | | | | | | | | | (474), (477), (479), (502), (522), (524), (551),
% 108.37/15.72 | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 108.37/15.72 | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 108.37/15.72 | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 108.37/15.72 | | | | | | | | | | (577), (579), (581), (582), (583), (584), (585),
% 108.37/15.72 | | | | | | | | | | (587), (589), (591), (593), (594), (595), (596),
% 108.37/15.72 | | | | | | | | | | (597), (599), (601), (602), (603), (604), (605),
% 108.37/15.72 | | | | | | | | | | (683), (700), (702), (741), (779), (785), (787),
% 108.37/15.72 | | | | | | | | | | (789), (791), (808), (809), (815), (818),
% 108.37/15.72 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.37/15.72 | | | | | | | | | | #216.
% 108.37/15.72 | | | | | | | | | |
% 108.37/15.72 | | | | | | | | | End of split
% 108.37/15.72 | | | | | | | | |
% 108.37/15.72 | | | | | | | | Case 2:
% 108.37/15.72 | | | | | | | | |
% 108.37/15.72 | | | | | | | | | (819) all_26_0 = e1
% 108.37/15.72 | | | | | | | | | (820) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 108.37/15.72 | | | | | | | | |
% 108.37/15.72 | | | | | | | | | COMBINE_EQS: (778), (819) imply:
% 108.37/15.72 | | | | | | | | | (821) all_4_0 = e1
% 108.37/15.72 | | | | | | | | |
% 108.37/15.72 | | | | | | | | | SIMP: (821) implies:
% 108.37/15.72 | | | | | | | | | (822) all_4_0 = e1
% 108.37/15.72 | | | | | | | | |
% 108.37/15.73 | | | | | | | | | REF_CLOSE: (37), (38), (42), (43), (98), (116), (126), (136),
% 108.37/15.73 | | | | | | | | | (154), (157), (161), (170), (172), (179), (185),
% 108.37/15.73 | | | | | | | | | (188), (202), (203), (204), (206), (207), (212),
% 108.37/15.73 | | | | | | | | | (214), (233), (235), (236), (237), (238), (239),
% 108.37/15.73 | | | | | | | | | (240), (241), (243), (245), (247), (248), (270),
% 108.37/15.73 | | | | | | | | | (273), (274), (276), (279), (283), (286), (287),
% 108.37/15.73 | | | | | | | | | (288), (289), (290), (291), (294), (295), (297),
% 108.37/15.73 | | | | | | | | | (298), (300), (304), (323), (325), (331), (332),
% 108.37/15.73 | | | | | | | | | (340), (342), (344), (345), (352), (356), (362),
% 108.37/15.73 | | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.37/15.73 | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.37/15.73 | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.37/15.73 | | | | | | | | | (462), (468), (470), (472), (474), (475), (477),
% 108.37/15.73 | | | | | | | | | (522), (540), (543), (545), (551), (552), (553),
% 108.37/15.73 | | | | | | | | | (554), (555), (556), (557), (558), (559), (560),
% 108.37/15.73 | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 108.37/15.73 | | | | | | | | | (568), (569), (571), (573), (575), (577), (583),
% 108.37/15.73 | | | | | | | | | (584), (585), (587), (589), (593), (594), (595),
% 108.37/15.73 | | | | | | | | | (597), (601), (603), (604), (605), (649), (670),
% 108.37/15.73 | | | | | | | | | (675), (683), (703), (727), (731), (758), (780),
% 108.37/15.73 | | | | | | | | | (785), (820), (822), (function-axioms) are
% 108.37/15.73 | | | | | | | | | inconsistent by sub-proof #225.
% 108.37/15.73 | | | | | | | | |
% 108.37/15.73 | | | | | | | | End of split
% 108.37/15.73 | | | | | | | |
% 108.37/15.73 | | | | | | | End of split
% 108.37/15.73 | | | | | | |
% 108.37/15.73 | | | | | | Case 2:
% 108.37/15.73 | | | | | | |
% 108.37/15.73 | | | | | | | (823) all_16_0 = e1
% 108.37/15.73 | | | | | | | (824) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 108.37/15.73 | | | | | | |
% 108.63/15.74 | | | | | | | REF_CLOSE: (8), (37), (38), (42), (43), (52), (53), (88), (93),
% 108.63/15.74 | | | | | | | (98), (116), (126), (136), (154), (156), (157), (161),
% 108.63/15.74 | | | | | | | (164), (165), (167), (170), (172), (177), (178), (179),
% 108.63/15.74 | | | | | | | (180), (183), (185), (187), (188), (189), (190), (202),
% 108.63/15.74 | | | | | | | (203), (204), (206), (207), (211), (212), (214), (233),
% 108.63/15.74 | | | | | | | (235), (236), (237), (238), (239), (240), (241), (242),
% 108.63/15.74 | | | | | | | (243), (244), (245), (246), (247), (248), (270), (271),
% 108.63/15.74 | | | | | | | (272), (273), (274), (275), (276), (277), (278), (279),
% 108.63/15.74 | | | | | | | (281), (282), (283), (285), (286), (287), (288), (289),
% 108.63/15.74 | | | | | | | (290), (291), (292), (293), (294), (295), (296), (297),
% 108.63/15.74 | | | | | | | (298), (299), (300), (302), (304), (305), (323), (325),
% 108.63/15.74 | | | | | | | (328), (329), (330), (331), (332), (335), (336), (340),
% 108.63/15.74 | | | | | | | (342), (343), (344), (345), (349), (350), (351), (352),
% 108.63/15.74 | | | | | | | (356), (362), (365), (370), (371), (375), (385), (386),
% 108.63/15.74 | | | | | | | (391), (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.74 | | | | | | | (430), (434), (436), (440), (446), (450), (458), (460),
% 108.63/15.74 | | | | | | | (462), (464), (466), (468), (470), (472), (474), (475),
% 108.63/15.74 | | | | | | | (477), (522), (530), (537), (540), (543), (545), (551),
% 108.63/15.74 | | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 108.63/15.74 | | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.74 | | | | | | | (568), (569), (571), (573), (575), (577), (579), (581),
% 108.63/15.74 | | | | | | | (582), (583), (584), (585), (587), (589), (591), (593),
% 108.63/15.74 | | | | | | | (594), (595), (596), (597), (599), (601), (602), (603),
% 108.63/15.74 | | | | | | | (604), (605), (649), (661), (670), (675), (683), (695),
% 108.63/15.74 | | | | | | | (703), (727), (731), (758), (759), (775), (778), (780),
% 108.63/15.74 | | | | | | | (784), (785), (787), (823), (824), (function-axioms)
% 108.63/15.74 | | | | | | | are inconsistent by sub-proof #176.
% 108.63/15.74 | | | | | | |
% 108.63/15.74 | | | | | | End of split
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | Case 2:
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | (825) all_14_0 = e1
% 108.63/15.74 | | | | | | (826) ~ (all_14_1 = e3) | ~ (all_14_2 = e0)
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | COMBINE_EQS: (776), (825) imply:
% 108.63/15.74 | | | | | | (827) all_8_0 = e1
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | SIMP: (827) implies:
% 108.63/15.74 | | | | | | (828) all_8_0 = e1
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | COMBINE_EQS: (781), (828) imply:
% 108.63/15.74 | | | | | | (829) all_42_0 = e1
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | BETA: splitting (68) gives:
% 108.63/15.74 | | | | | |
% 108.63/15.74 | | | | | | Case 1:
% 108.63/15.74 | | | | | | |
% 108.63/15.74 | | | | | | | (830) ~ (all_16_0 = e1)
% 108.63/15.74 | | | | | | |
% 108.63/15.74 | | | | | | | REDUCE: (775), (830) imply:
% 108.63/15.74 | | | | | | | (831) ~ (all_10_0 = e1)
% 108.63/15.74 | | | | | | |
% 108.63/15.74 | | | | | | | BETA: splitting (93) gives:
% 108.63/15.74 | | | | | | |
% 108.63/15.74 | | | | | | | Case 1:
% 108.63/15.74 | | | | | | | |
% 108.63/15.74 | | | | | | | | (832) ~ (all_26_0 = e1)
% 108.63/15.74 | | | | | | | |
% 108.63/15.74 | | | | | | | | REDUCE: (778), (832) imply:
% 108.63/15.74 | | | | | | | | (833) ~ (all_4_0 = e1)
% 108.63/15.74 | | | | | | | |
% 108.63/15.74 | | | | | | | | BETA: splitting (98) gives:
% 108.63/15.74 | | | | | | | |
% 108.63/15.74 | | | | | | | | Case 1:
% 108.63/15.74 | | | | | | | | |
% 108.63/15.74 | | | | | | | | | (834) ~ (all_28_0 = e2)
% 108.63/15.74 | | | | | | | | |
% 108.63/15.74 | | | | | | | | | REDUCE: (758), (834) imply:
% 108.63/15.74 | | | | | | | | | (835) ~ (all_6_0 = e2)
% 108.63/15.74 | | | | | | | | |
% 108.63/15.75 | | | | | | | | | REF_CLOSE: (6), (8), (37), (38), (42), (43), (52), (53),
% 108.63/15.75 | | | | | | | | | (107), (116), (121), (126), (154), (157), (169),
% 108.63/15.75 | | | | | | | | | (170), (172), (178), (179), (183), (184), (185),
% 108.63/15.75 | | | | | | | | | (187), (202), (203), (204), (206), (207), (208),
% 108.63/15.75 | | | | | | | | | (209), (211), (212), (213), (214), (233), (235),
% 108.63/15.75 | | | | | | | | | (236), (237), (238), (239), (240), (241), (242),
% 108.63/15.75 | | | | | | | | | (243), (244), (245), (247), (248), (270), (271),
% 108.63/15.75 | | | | | | | | | (272), (273), (274), (275), (276), (277), (278),
% 108.63/15.75 | | | | | | | | | (279), (281), (282), (283), (284), (285), (286),
% 108.63/15.75 | | | | | | | | | (287), (288), (289), (290), (291), (292), (293),
% 108.63/15.75 | | | | | | | | | (294), (295), (297), (298), (299), (300), (302),
% 108.63/15.75 | | | | | | | | | (303), (304), (305), (323), (324), (327), (328),
% 108.63/15.75 | | | | | | | | | (331), (332), (336), (340), (342), (343), (344),
% 108.63/15.75 | | | | | | | | | (345), (347), (349), (351), (352), (356), (362),
% 108.63/15.75 | | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.63/15.75 | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.75 | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.63/15.75 | | | | | | | | | (462), (464), (466), (468), (470), (472), (474),
% 108.63/15.75 | | | | | | | | | (475), (477), (502), (524), (543), (551), (552),
% 108.63/15.75 | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 108.63/15.75 | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 108.63/15.75 | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 108.63/15.75 | | | | | | | | | (579), (581), (582), (583), (584), (585), (587),
% 108.63/15.75 | | | | | | | | | (589), (594), (595), (596), (597), (599), (601),
% 108.63/15.75 | | | | | | | | | (602), (603), (604), (605), (670), (700), (702),
% 108.63/15.75 | | | | | | | | | (703), (731), (741), (779), (780), (784), (785),
% 108.63/15.75 | | | | | | | | | (787), (831), (833), (835), (function-axioms) are
% 108.63/15.75 | | | | | | | | | inconsistent by sub-proof #287.
% 108.63/15.75 | | | | | | | | |
% 108.63/15.75 | | | | | | | | Case 2:
% 108.63/15.75 | | | | | | | | |
% 108.63/15.75 | | | | | | | | | (836) all_28_0 = e2
% 108.63/15.75 | | | | | | | | | (837) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 108.63/15.75 | | | | | | | | |
% 108.63/15.75 | | | | | | | | | REF_CLOSE: (5), (7), (9), (37), (42), (43), (47), (52), (53),
% 108.63/15.75 | | | | | | | | | (107), (121), (131), (154), (161), (162), (164),
% 108.63/15.75 | | | | | | | | | (165), (167), (169), (170), (172), (179), (180),
% 108.63/15.75 | | | | | | | | | (185), (187), (188), (193), (201), (202), (204),
% 108.63/15.75 | | | | | | | | | (206), (207), (208), (209), (211), (212), (213),
% 108.63/15.75 | | | | | | | | | (214), (233), (234), (235), (237), (238), (239),
% 108.63/15.75 | | | | | | | | | (240), (242), (243), (245), (246), (247), (248),
% 108.63/15.75 | | | | | | | | | (270), (271), (272), (273), (274), (275), (277),
% 108.63/15.75 | | | | | | | | | (278), (279), (280), (281), (283), (284), (285),
% 108.63/15.75 | | | | | | | | | (286), (287), (288), (289), (290), (291), (292),
% 108.63/15.75 | | | | | | | | | (293), (294), (295), (296), (298), (299), (300),
% 108.63/15.75 | | | | | | | | | (301), (302), (303), (304), (305), (323), (325),
% 108.63/15.75 | | | | | | | | | (327), (331), (332), (335), (336), (338), (340),
% 108.63/15.75 | | | | | | | | | (341), (343), (344), (345), (352), (356), (362),
% 108.63/15.75 | | | | | | | | | (365), (370), (371), (385), (386), (391), (394),
% 108.63/15.75 | | | | | | | | | (406), (407), (412), (413), (424), (426), (430),
% 108.63/15.75 | | | | | | | | | (434), (436), (440), (446), (450), (458), (460),
% 108.63/15.75 | | | | | | | | | (462), (466), (470), (472), (474), (477), (479),
% 108.63/15.75 | | | | | | | | | (502), (522), (524), (538), (544), (551), (552),
% 108.63/15.75 | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 108.63/15.75 | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 108.63/15.75 | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 108.63/15.75 | | | | | | | | | (579), (581), (582), (583), (585), (587), (589),
% 108.63/15.75 | | | | | | | | | (591), (593), (594), (595), (596), (597), (599),
% 108.63/15.75 | | | | | | | | | (601), (602), (603), (604), (605), (657), (683),
% 108.63/15.75 | | | | | | | | | (697), (700), (702), (741), (758), (779), (785),
% 108.63/15.75 | | | | | | | | | (787), (826), (829), (831), (836), (837),
% 108.63/15.75 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.75 | | | | | | | | | #171.
% 108.63/15.75 | | | | | | | | |
% 108.63/15.75 | | | | | | | | End of split
% 108.63/15.75 | | | | | | | |
% 108.63/15.75 | | | | | | | Case 2:
% 108.63/15.75 | | | | | | | |
% 108.63/15.75 | | | | | | | | (838) all_26_0 = e1
% 108.63/15.75 | | | | | | | | (839) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 108.63/15.75 | | | | | | | |
% 108.63/15.75 | | | | | | | | COMBINE_EQS: (778), (838) imply:
% 108.63/15.75 | | | | | | | | (840) all_4_0 = e1
% 108.63/15.75 | | | | | | | |
% 108.63/15.77 | | | | | | | | REF_CLOSE: (37), (38), (42), (43), (98), (116), (126), (136),
% 108.63/15.77 | | | | | | | | (154), (157), (161), (170), (172), (179), (185),
% 108.63/15.77 | | | | | | | | (188), (202), (203), (204), (206), (207), (212),
% 108.63/15.77 | | | | | | | | (214), (233), (235), (236), (237), (238), (239),
% 108.63/15.77 | | | | | | | | (240), (241), (243), (245), (247), (248), (270),
% 108.63/15.77 | | | | | | | | (273), (274), (276), (279), (283), (286), (287),
% 108.63/15.77 | | | | | | | | (288), (289), (290), (291), (294), (295), (297),
% 108.63/15.77 | | | | | | | | (298), (300), (304), (323), (325), (331), (332),
% 108.63/15.77 | | | | | | | | (340), (342), (344), (345), (352), (356), (362),
% 108.63/15.77 | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 108.63/15.77 | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.77 | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 108.63/15.77 | | | | | | | | (462), (468), (470), (472), (474), (475), (477),
% 108.63/15.77 | | | | | | | | (522), (540), (543), (545), (551), (552), (553),
% 108.63/15.77 | | | | | | | | (554), (555), (556), (557), (558), (559), (560),
% 108.63/15.77 | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.77 | | | | | | | | (568), (569), (571), (573), (575), (577), (583),
% 108.63/15.77 | | | | | | | | (584), (585), (587), (589), (593), (594), (595),
% 108.63/15.77 | | | | | | | | (597), (601), (603), (604), (605), (649), (670),
% 108.63/15.77 | | | | | | | | (675), (683), (703), (727), (731), (758), (780),
% 108.63/15.77 | | | | | | | | (785), (839), (840), (function-axioms) are
% 108.63/15.77 | | | | | | | | inconsistent by sub-proof #225.
% 108.63/15.77 | | | | | | | |
% 108.63/15.77 | | | | | | | End of split
% 108.63/15.77 | | | | | | |
% 108.63/15.77 | | | | | | Case 2:
% 108.63/15.77 | | | | | | |
% 108.63/15.77 | | | | | | | (841) all_16_0 = e1
% 108.63/15.77 | | | | | | | (842) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 108.63/15.77 | | | | | | |
% 108.63/15.78 | | | | | | | REF_CLOSE: (8), (37), (38), (42), (43), (52), (53), (88), (93),
% 108.63/15.78 | | | | | | | (98), (116), (126), (136), (154), (156), (157), (161),
% 108.63/15.78 | | | | | | | (164), (165), (167), (170), (172), (177), (178), (179),
% 108.63/15.78 | | | | | | | (180), (183), (185), (187), (188), (189), (190), (202),
% 108.63/15.78 | | | | | | | (203), (204), (206), (207), (211), (212), (214), (233),
% 108.63/15.78 | | | | | | | (235), (236), (237), (238), (239), (240), (241), (242),
% 108.63/15.78 | | | | | | | (243), (244), (245), (246), (247), (248), (270), (271),
% 108.63/15.78 | | | | | | | (272), (273), (274), (275), (276), (277), (278), (279),
% 108.63/15.78 | | | | | | | (281), (282), (283), (285), (286), (287), (288), (289),
% 108.63/15.78 | | | | | | | (290), (291), (292), (293), (294), (295), (296), (297),
% 108.63/15.78 | | | | | | | (298), (299), (300), (302), (304), (305), (323), (325),
% 108.63/15.78 | | | | | | | (328), (329), (330), (331), (332), (335), (336), (340),
% 108.63/15.78 | | | | | | | (342), (343), (344), (345), (349), (350), (351), (352),
% 108.63/15.78 | | | | | | | (356), (362), (365), (370), (371), (375), (385), (386),
% 108.63/15.78 | | | | | | | (391), (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.78 | | | | | | | (430), (434), (436), (440), (446), (450), (458), (460),
% 108.63/15.78 | | | | | | | (462), (464), (466), (468), (470), (472), (474), (475),
% 108.63/15.78 | | | | | | | (477), (522), (530), (537), (540), (543), (545), (551),
% 108.63/15.78 | | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 108.63/15.78 | | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.78 | | | | | | | (568), (569), (571), (573), (575), (577), (579), (581),
% 108.63/15.78 | | | | | | | (582), (583), (584), (585), (587), (589), (591), (593),
% 108.63/15.78 | | | | | | | (594), (595), (596), (597), (599), (601), (602), (603),
% 108.63/15.78 | | | | | | | (604), (605), (649), (661), (670), (675), (683), (695),
% 108.63/15.78 | | | | | | | (703), (727), (731), (758), (759), (775), (778), (780),
% 108.63/15.78 | | | | | | | (784), (785), (787), (841), (842), (function-axioms)
% 108.63/15.78 | | | | | | | are inconsistent by sub-proof #176.
% 108.63/15.78 | | | | | | |
% 108.63/15.78 | | | | | | End of split
% 108.63/15.78 | | | | | |
% 108.63/15.78 | | | | | End of split
% 108.63/15.78 | | | | |
% 108.63/15.78 | | | | Case 2:
% 108.63/15.78 | | | | |
% 108.63/15.78 | | | | | (843) all_10_0 = e2
% 108.63/15.78 | | | | | (844) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 108.63/15.78 | | | | |
% 108.63/15.79 | | | | | REF_CLOSE: (6), (8), (37), (38), (42), (43), (47), (52), (53), (93),
% 108.63/15.79 | | | | | (98), (116), (126), (136), (150), (154), (156), (157),
% 108.63/15.79 | | | | | (161), (164), (165), (167), (170), (172), (177), (178),
% 108.63/15.79 | | | | | (179), (180), (183), (184), (185), (187), (188), (192),
% 108.63/15.79 | | | | | (193), (201), (202), (203), (204), (206), (207), (208),
% 108.63/15.79 | | | | | (209), (211), (212), (213), (214), (233), (234), (235),
% 108.63/15.79 | | | | | (236), (237), (238), (239), (240), (241), (243), (244),
% 108.63/15.79 | | | | | (245), (246), (247), (248), (270), (271), (272), (273),
% 108.63/15.79 | | | | | (274), (275), (276), (277), (278), (279), (280), (281),
% 108.63/15.79 | | | | | (283), (284), (285), (286), (287), (288), (289), (290),
% 108.63/15.79 | | | | | (291), (292), (293), (294), (295), (297), (298), (299),
% 108.63/15.79 | | | | | (300), (301), (302), (304), (305), (323), (325), (326),
% 108.63/15.79 | | | | | (327), (328), (330), (331), (332), (333), (335), (336),
% 108.63/15.79 | | | | | (339), (340), (342), (343), (344), (345), (347), (351),
% 108.63/15.79 | | | | | (352), (356), (362), (365), (370), (371), (375), (385),
% 108.63/15.79 | | | | | (386), (391), (394), (406), (407), (412), (413), (424),
% 108.63/15.79 | | | | | (426), (430), (434), (436), (440), (446), (450), (458),
% 108.63/15.79 | | | | | (460), (462), (464), (468), (470), (472), (474), (475),
% 108.63/15.79 | | | | | (477), (479), (522), (540), (543), (545), (548), (551),
% 108.63/15.79 | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 108.63/15.79 | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.79 | | | | | (568), (569), (571), (573), (575), (577), (579), (581),
% 108.63/15.79 | | | | | (582), (583), (584), (585), (587), (589), (591), (593),
% 108.63/15.79 | | | | | (594), (595), (596), (597), (599), (601), (602), (603),
% 108.63/15.79 | | | | | (604), (605), (649), (670), (675), (683), (703), (705),
% 108.63/15.79 | | | | | (727), (731), (758), (778), (780), (783), (785), (786),
% 108.63/15.79 | | | | | (843), (844), (function-axioms) are inconsistent by
% 108.63/15.79 | | | | | sub-proof #137.
% 108.63/15.79 | | | | |
% 108.63/15.79 | | | | End of split
% 108.63/15.79 | | | |
% 108.63/15.79 | | | Case 2:
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | (845) all_8_1 = e1
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | COMBINE_EQS: (704), (845) imply:
% 108.63/15.79 | | | | (846) all_48_1 = e1
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | REDUCE: (48), (845) imply:
% 108.63/15.79 | | | | (847) op(e1, all_8_2) = all_8_0
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | REDUCE: (47), (845) imply:
% 108.63/15.79 | | | | (848) op(e2, all_8_2) = e1
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | BETA: splitting (54) gives:
% 108.63/15.79 | | | |
% 108.63/15.79 | | | | Case 1:
% 108.63/15.79 | | | | |
% 108.63/15.79 | | | | | (849) ~ (all_10_0 = e2)
% 108.63/15.79 | | | | |
% 108.63/15.79 | | | | | BETA: splitting (68) gives:
% 108.63/15.79 | | | | |
% 108.63/15.79 | | | | | Case 1:
% 108.63/15.79 | | | | | |
% 108.63/15.79 | | | | | | (850) ~ (all_16_0 = e1)
% 108.63/15.79 | | | | | |
% 108.63/15.79 | | | | | | REDUCE: (775), (850) imply:
% 108.63/15.79 | | | | | | (851) ~ (all_10_0 = e1)
% 108.63/15.79 | | | | | |
% 108.63/15.79 | | | | | | REF_CLOSE: (4), (8), (9), (37), (38), (41), (42), (52), (53), (93),
% 108.63/15.79 | | | | | | (107), (121), (154), (157), (162), (164), (165), (167),
% 108.63/15.79 | | | | | | (169), (172), (177), (178), (179), (180), (183), (184),
% 108.63/15.79 | | | | | | (185), (187), (188), (189), (190), (192), (193), (201),
% 108.63/15.79 | | | | | | (202), (203), (206), (207), (208), (209), (211), (212),
% 108.63/15.79 | | | | | | (213), (214), (233), (234), (235), (236), (238), (239),
% 108.63/15.79 | | | | | | (240), (241), (242), (243), (244), (245), (246), (247),
% 108.63/15.79 | | | | | | (248), (270), (271), (272), (273), (274), (275), (276),
% 108.63/15.79 | | | | | | (277), (278), (279), (280), (281), (282), (283), (284),
% 108.63/15.79 | | | | | | (285), (286), (287), (288), (289), (290), (291), (292),
% 108.63/15.79 | | | | | | (293), (294), (295), (296), (297), (298), (299), (300),
% 108.63/15.79 | | | | | | (301), (302), (304), (305), (323), (324), (329), (330),
% 108.63/15.79 | | | | | | (331), (332), (333), (334), (335), (336), (338), (339),
% 108.63/15.79 | | | | | | (340), (341), (343), (344), (348), (349), (350), (351),
% 108.63/15.79 | | | | | | (352), (356), (362), (365), (370), (371), (385), (386),
% 108.63/15.79 | | | | | | (391), (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.80 | | | | | | (430), (434), (436), (440), (446), (450), (458), (460),
% 108.63/15.80 | | | | | | (462), (464), (466), (468), (470), (472), (475), (477),
% 108.63/15.80 | | | | | | (479), (524), (540), (551), (552), (553), (554), (555),
% 108.63/15.80 | | | | | | (556), (557), (558), (559), (560), (561), (562), (563),
% 108.63/15.80 | | | | | | (564), (565), (566), (567), (568), (569), (571), (573),
% 108.63/15.80 | | | | | | (575), (577), (579), (581), (582), (583), (584), (585),
% 108.63/15.80 | | | | | | (587), (589), (591), (593), (594), (595), (596), (597),
% 108.63/15.80 | | | | | | (599), (601), (602), (603), (604), (605), (675), (700),
% 108.63/15.80 | | | | | | (702), (778), (779), (784), (848), (849), (851),
% 108.63/15.80 | | | | | | (function-axioms) are inconsistent by sub-proof #86.
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | Case 2:
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | | (852) all_16_0 = e1
% 108.63/15.80 | | | | | | (853) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | | COMBINE_EQS: (775), (852) imply:
% 108.63/15.80 | | | | | | (854) all_10_0 = e1
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | | COMBINE_EQS: (759), (854) imply:
% 108.63/15.80 | | | | | | (855) all_24_0 = e1
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | | BETA: splitting (88) gives:
% 108.63/15.80 | | | | | |
% 108.63/15.80 | | | | | | Case 1:
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | (856) ~ (all_24_0 = e1)
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | REDUCE: (855), (856) imply:
% 108.63/15.80 | | | | | | | (857) $false
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | CLOSE: (857) is inconsistent.
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | Case 2:
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | (858) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | BETA: splitting (93) gives:
% 108.63/15.80 | | | | | | |
% 108.63/15.80 | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | |
% 108.63/15.80 | | | | | | | | (859) ~ (all_26_0 = e1)
% 108.63/15.80 | | | | | | | |
% 108.63/15.80 | | | | | | | | REDUCE: (778), (859) imply:
% 108.63/15.80 | | | | | | | | (860) ~ (all_4_0 = e1)
% 108.63/15.80 | | | | | | | |
% 108.63/15.80 | | | | | | | | BETA: splitting (98) gives:
% 108.63/15.80 | | | | | | | |
% 108.63/15.80 | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | |
% 108.63/15.80 | | | | | | | | | (861) ~ (all_28_0 = e2)
% 108.63/15.80 | | | | | | | | |
% 108.63/15.80 | | | | | | | | | REDUCE: (758), (861) imply:
% 108.63/15.80 | | | | | | | | | (862) ~ (all_6_0 = e2)
% 108.63/15.80 | | | | | | | | |
% 108.63/15.80 | | | | | | | | | BETA: splitting (116) gives:
% 108.63/15.80 | | | | | | | | |
% 108.63/15.80 | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | (863) ~ (all_36_1 = e3)
% 108.63/15.80 | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | REDUCE: (670), (863) imply:
% 108.63/15.80 | | | | | | | | | | (864) ~ (all_6_1 = e3)
% 108.63/15.80 | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | BETA: splitting (270) gives:
% 108.63/15.80 | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | (865) ~ (all_56_15 = e1)
% 108.63/15.80 | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | REDUCE: (554), (865) imply:
% 108.63/15.80 | | | | | | | | | | | (866) ~ (all_4_2 = e1)
% 108.63/15.80 | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | BETA: splitting (272) gives:
% 108.63/15.80 | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | (867) ~ (all_56_12 = e1)
% 108.63/15.80 | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | REDUCE: (426), (867) imply:
% 108.63/15.80 | | | | | | | | | | | | (868) ~ (all_10_2 = e1)
% 108.63/15.80 | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | BETA: splitting (273) gives:
% 108.63/15.80 | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | (869) ~ (all_56_15 = e2)
% 108.63/15.80 | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | REDUCE: (554), (869) imply:
% 108.63/15.80 | | | | | | | | | | | | | (870) ~ (all_4_2 = e2)
% 108.63/15.80 | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | BETA: splitting (233) gives:
% 108.63/15.80 | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | (871) all_54_15 = e3
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | COMBINE_EQS: (356), (871) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (872) all_4_2 = e3
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | SIMP: (872) implies:
% 108.63/15.80 | | | | | | | | | | | | | | (873) all_4_2 = e3
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | COMBINE_EQS: (554), (873) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (874) all_56_15 = e3
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | REDUCE: (584), (873) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (875) ~ (all_52_3 = e3)
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | REDUCE: (603), (873) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (876) ~ (all_52_12 = e3)
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | REDUCE: (38), (873) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (877) op(all_4_1, e3) = all_4_0
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | REDUCE: (37), (873) imply:
% 108.63/15.80 | | | | | | | | | | | | | | (878) op(e0, e3) = all_4_1
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 108.63/15.80 | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | (879) ~ (all_56_3 = e2)
% 108.63/15.80 | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | REDUCE: (430), (879) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | (880) ~ (all_52_1 = e2)
% 108.63/15.80 | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 108.63/15.80 | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (878)
% 108.63/15.80 | | | | | | | | | | | | | | | gives:
% 108.63/15.80 | | | | | | | | | | | | | | | (881) all_52_3 = all_4_1
% 108.63/15.80 | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 108.63/15.80 | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | (882) ~ (all_56_0 = e3)
% 108.63/15.80 | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | REDUCE: (413), (882) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | (883) ~ (all_52_4 = e3)
% 108.63/15.80 | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 108.63/15.80 | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | (884) all_58_0 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (884) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | (885) all_10_2 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | REDUCE: (566), (885) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | (886) $false
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | CLOSE: (886) is inconsistent.
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | (887) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | BETA: splitting (887) gives:
% 108.63/15.80 | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | (888) all_58_1 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (888) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | (889) all_52_4 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | REDUCE: (883), (889) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | (890) $false
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | CLOSE: (890) is inconsistent.
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | (891) all_58_4 = e3 | all_58_9 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | BETA: splitting (891) gives:
% 108.63/15.80 | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | (892) all_58_4 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (892) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | (893) all_52_8 = e3
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | REDUCE: (579), (893) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | (894) ~ (all_10_2 = e3)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | REDUCE: (596), (893) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | (895) ~ (all_6_2 = e3)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | SIMP: (895) implies:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | (896) ~ (all_6_2 = e3)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (897) ~ (all_56_5 = e2)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (446), (897) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (898) ~ (all_52_13 = e2)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (238), (279), (340), (352),
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (371), (391), (394), (406), (424), (474), (551),
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (555), (564), (566), (567), (568), (597), (601),
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (785), (864), (880), (896), (898),
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | #85.
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (899) all_56_5 = e2
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (900) ~ (all_56_13 = e0)
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (899) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (901) all_52_13 = e2
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (900) imply:
% 108.63/15.80 | | | | | | | | | | | | | | | | | | | | (902) ~ (all_8_2 = e0)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (901) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | (903) ~ (all_8_2 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (904) ~ (all_56_5 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (899), (904) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (905) $false
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (905) is inconsistent.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (906) ~ (all_56_12 = e0)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (906) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (907) ~ (all_10_2 = e0)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (172), (179), (180), (187), (211), (214),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (235), (243), (247), (248), (275), (278), (305),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (342), (346), (365), (370), (385), (406), (413),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (424), (426), (450), (458), (477), (530), (552),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (553), (556), (559), (563), (564), (565), (566),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (567), (577), (585), (589), (661), (848), (858),
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (868), (902), (907), (function-axioms) are
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #80.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | (908) all_58_9 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (908) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | (909) all_52_12 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | REDUCE: (876), (909) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | (910) $false
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | CLOSE: (910) is inconsistent.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | End of split
% 108.63/15.81 | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | End of split
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | (911) all_56_0 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | (912) ~ (all_56_14 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (911) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | (913) all_52_4 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | REDUCE: (555), (912) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | (914) ~ (all_6_2 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | REDUCE: (179), (913) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | (915) ~ (all_52_7 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | SIMP: (915) implies:
% 108.63/15.81 | | | | | | | | | | | | | | | | (916) ~ (all_52_7 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | REDUCE: (177), (913) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | (917) ~ (all_52_12 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | REDUCE: (577), (913) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | (918) ~ (all_10_2 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | (919) ~ (all_56_6 = e1)
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | REDUCE: (386), (919) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | (920) ~ (all_52_2 = e1)
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (881) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | (921) all_58_12 = all_4_1
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | REDUCE: (875), (881) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | (922) ~ (all_4_1 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | (923) ~ (all_56_4 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | REDUCE: (436), (923) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | (924) ~ (all_52_9 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | (925) all_58_2 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (880), (925) are inconsistent by sub-proof
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | #335.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | (926) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (926) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (927) all_58_3 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (927) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (928) all_8_2 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (928) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (929) $false
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | CLOSE: (929) is inconsistent.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | (930) all_58_5 = e2 | all_58_10 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (930) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | (931) all_58_5 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (394), (924), (931) are inconsistent by sub-proof
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | #119.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | (932) all_58_10 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (932) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | (933) all_52_13 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (933) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | (934) all_56_5 = e2
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (933) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | (935) ~ (all_8_2 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | (936) ~ (all_56_5 = e2)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (934), (936) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | (937) $false
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (937) is inconsistent.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | (938) ~ (all_56_13 = e0)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (938) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | (939) ~ (all_8_2 = e0)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | (940) all_54_10 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (940) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | (941) all_6_2 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (941) implies:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | (942) all_6_2 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (942) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | (943) ~ (all_52_2 = e3)
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_58_0 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (944) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_10_2 = e3
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (945) imply:
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | (946) $false
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (946) is inconsistent.
% 108.63/15.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | (947) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (947) gives:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (948) all_58_2 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (948) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_52_1 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (949) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (950) ~ (all_8_2 = e3)
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (950) implies:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (951) ~ (all_8_2 = e3)
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (209), (243), (552), (567), (591), (848), (939),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (951), (function-axioms) are inconsistent by
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #79.
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_58_6 = e3 | all_58_12 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (952) gives:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_58_6 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (563), (943), (953) are inconsistent by sub-proof
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | #318.
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_58_12 = e3
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (921), (922), (954) are inconsistent by sub-proof
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | (955) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (279), (352), (371), (424),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | (474), (551), (555), (566), (568), (601), (785),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | (864), (914), (955), (function-axioms) are
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #414.
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (956) all_56_4 = e2
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (436), (956) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (957) all_52_9 = e2
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | REDUCE: (167), (957) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (958) ~ (all_52_8 = e2)
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | REDUCE: (597), (957) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (959) ~ (all_6_2 = e2)
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (52), (164), (172), (177), (178), (179),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (204), (211), (212), (235), (237), (238), (243),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (244), (245), (246), (247), (248), (275), (279),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (281), (305), (331), (349), (350), (351), (352),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (371), (385), (406), (412), (413), (424), (426),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (458), (460), (462), (464), (474), (477), (537),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (551), (552), (553), (555), (560), (561), (562),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (563), (565), (566), (568), (571), (577), (579),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (581), (582), (585), (587), (589), (596), (601),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (695), (785), (853), (860), (864), (868), (876),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (877), (880), (914), (916), (920), (921), (922),
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | (958), (function-axioms) are inconsistent by
% 108.63/15.82 | | | | | | | | | | | | | | | | | | | sub-proof #203.
% 108.63/15.82 | | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | (960) ~ (all_56_15 = e3)
% 108.63/15.82 | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | REDUCE: (874), (960) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | | (961) $false
% 108.63/15.82 | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | | CLOSE: (961) is inconsistent.
% 108.63/15.82 | | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | (962) ~ (all_56_15 = e3)
% 108.63/15.82 | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | REDUCE: (874), (962) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | | | (963) $false
% 108.63/15.82 | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | | CLOSE: (963) is inconsistent.
% 108.63/15.82 | | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | End of split
% 108.63/15.82 | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | Case 2:
% 108.63/15.82 | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | (964) ~ (all_56_15 = e3)
% 108.63/15.82 | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | REDUCE: (874), (964) imply:
% 108.63/15.82 | | | | | | | | | | | | | | | (965) $false
% 108.63/15.82 | | | | | | | | | | | | | | |
% 108.63/15.82 | | | | | | | | | | | | | | | CLOSE: (965) is inconsistent.
% 108.63/15.82 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | End of split
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | Case 2:
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | (966) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (866), (870), (966) are inconsistent
% 108.63/15.83 | | | | | | | | | | | | | | by sub-proof #417.
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | End of split
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | Case 2:
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | (967) all_56_15 = e2
% 108.63/15.83 | | | | | | | | | | | | | (968) ~ (all_56_10 = e0)
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | COMBINE_EQS: (554), (967) imply:
% 108.63/15.83 | | | | | | | | | | | | | (969) all_4_2 = e2
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | SIMP: (969) implies:
% 108.63/15.83 | | | | | | | | | | | | | (970) all_4_2 = e2
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | REDUCE: (365), (968) imply:
% 108.63/15.83 | | | | | | | | | | | | | (971) ~ (all_52_7 = e0)
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | REDUCE: (602), (970) imply:
% 108.63/15.83 | | | | | | | | | | | | | (972) ~ (all_52_11 = e2)
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | REDUCE: (604), (970) imply:
% 108.63/15.83 | | | | | | | | | | | | | (973) ~ (all_52_13 = e2)
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | BETA: splitting (303) gives:
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | Case 1:
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | (974) ~ (all_56_0 = e3)
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | REDUCE: (413), (974) imply:
% 108.63/15.83 | | | | | | | | | | | | | | (975) ~ (all_52_4 = e3)
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | Case 1:
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | | (976) ~ (all_56_2 = e3)
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | | REDUCE: (407), (976) imply:
% 108.63/15.83 | | | | | | | | | | | | | | | (977) ~ (all_52_12 = e3)
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (42), (162), (167), (178), (190), (204),
% 108.63/15.83 | | | | | | | | | | | | | | | (208), (209), (211), (233), (237), (238), (243),
% 108.63/15.83 | | | | | | | | | | | | | | | (271), (276), (278), (279), (289), (294), (296),
% 108.63/15.83 | | | | | | | | | | | | | | | (298), (300), (301), (323), (338), (340), (341),
% 108.63/15.83 | | | | | | | | | | | | | | | (352), (356), (362), (370), (371), (391), (394),
% 108.63/15.83 | | | | | | | | | | | | | | | (406), (407), (412), (424), (430), (434), (446),
% 108.63/15.83 | | | | | | | | | | | | | | | (450), (474), (551), (552), (554), (555), (556),
% 108.63/15.83 | | | | | | | | | | | | | | | (557), (558), (559), (561), (564), (565), (566),
% 108.63/15.83 | | | | | | | | | | | | | | | (567), (568), (569), (579), (582), (591), (593),
% 108.63/15.83 | | | | | | | | | | | | | | | (596), (597), (601), (604), (785), (848), (864),
% 108.63/15.83 | | | | | | | | | | | | | | | (971), (972), (973), (975), (977),
% 108.63/15.83 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.83 | | | | | | | | | | | | | | | #78.
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | Case 2:
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | | (978) all_56_2 = e3
% 108.63/15.83 | | | | | | | | | | | | | | | (979) ~ (all_56_12 = e0)
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | | REF_CLOSE: (52), (172), (179), (180), (187), (211), (214),
% 108.63/15.83 | | | | | | | | | | | | | | | (235), (243), (247), (248), (278), (298), (305),
% 108.63/15.83 | | | | | | | | | | | | | | | (342), (346), (370), (385), (406), (407), (413),
% 108.63/15.83 | | | | | | | | | | | | | | | (424), (426), (450), (458), (477), (530), (552),
% 108.63/15.83 | | | | | | | | | | | | | | | (553), (556), (559), (563), (564), (565), (567),
% 108.63/15.83 | | | | | | | | | | | | | | | (577), (581), (585), (589), (661), (848), (858),
% 108.63/15.83 | | | | | | | | | | | | | | | (868), (971), (978), (979), (function-axioms) are
% 108.63/15.83 | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 108.63/15.83 | | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | End of split
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | Case 2:
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | (980) ~ (all_56_15 = e2)
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | REDUCE: (967), (980) imply:
% 108.63/15.83 | | | | | | | | | | | | | | (981) $false
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | | CLOSE: (981) is inconsistent.
% 108.63/15.83 | | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | | End of split
% 108.63/15.83 | | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | End of split
% 108.63/15.83 | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | Case 2:
% 108.63/15.83 | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | (982) all_56_12 = e1
% 108.63/15.83 | | | | | | | | | | | | (983) ~ (all_56_11 = e0)
% 108.63/15.83 | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | COMBINE_EQS: (426), (982) imply:
% 108.63/15.83 | | | | | | | | | | | | (984) all_10_2 = e1
% 108.63/15.83 | | | | | | | | | | | |
% 108.63/15.83 | | | | | | | | | | | | SIMP: (984) implies:
% 108.63/15.83 | | | | | | | | | | | | (985) all_10_2 = e1
% 108.63/15.83 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 108.63/15.84 | | | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 108.63/15.84 | | | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 108.63/15.84 | | | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 108.63/15.84 | | | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 108.63/15.84 | | | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 108.63/15.84 | | | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 108.63/15.84 | | | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 108.63/15.84 | | | | | | | | | | | | (589), (591), (593), (602), (603), (604), (848),
% 108.63/15.84 | | | | | | | | | | | | (866), (982), (983), (985), (function-axioms) are
% 108.63/15.84 | | | | | | | | | | | | inconsistent by sub-proof #74.
% 108.63/15.84 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | End of split
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | Case 2:
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | (986) all_56_15 = e1
% 108.63/15.84 | | | | | | | | | | | (987) ~ (all_56_11 = e0)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | COMBINE_EQS: (554), (986) imply:
% 108.63/15.84 | | | | | | | | | | | (988) all_4_2 = e1
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | SIMP: (988) implies:
% 108.63/15.84 | | | | | | | | | | | (989) all_4_2 = e1
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | COMBINE_EQS: (557), (989) imply:
% 108.63/15.84 | | | | | | | | | | | (990) all_58_15 = e1
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | REDUCE: (362), (987) imply:
% 108.63/15.84 | | | | | | | | | | | (991) ~ (all_52_11 = e0)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | REDUCE: (602), (989) imply:
% 108.63/15.84 | | | | | | | | | | | (992) ~ (all_52_11 = e1)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | REDUCE: (605), (989) imply:
% 108.63/15.84 | | | | | | | | | | | (993) ~ (all_52_14 = e1)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | REF_CLOSE: (4), (42), (189), (190), (204), (209), (211),
% 108.63/15.84 | | | | | | | | | | | (237), (238), (243), (244), (248), (274), (278),
% 108.63/15.84 | | | | | | | | | | | (284), (286), (288), (289), (290), (291), (295),
% 108.63/15.84 | | | | | | | | | | | (298), (300), (304), (323), (331), (335), (338),
% 108.63/15.84 | | | | | | | | | | | (340), (352), (365), (370), (385), (386), (391),
% 108.63/15.84 | | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.84 | | | | | | | | | | | (430), (434), (436), (440), (446), (450), (464),
% 108.63/15.84 | | | | | | | | | | | (474), (551), (552), (553), (555), (556), (558),
% 108.63/15.84 | | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 108.63/15.84 | | | | | | | | | | | (566), (567), (568), (571), (579), (582), (591),
% 108.63/15.84 | | | | | | | | | | | (593), (601), (785), (848), (864), (986), (990),
% 108.63/15.84 | | | | | | | | | | | (991), (992), (993), (function-axioms) are
% 108.63/15.84 | | | | | | | | | | | inconsistent by sub-proof #70.
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | End of split
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | Case 2:
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | (994) all_36_1 = e3
% 108.63/15.84 | | | | | | | | | | (995) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | COMBINE_EQS: (670), (994) imply:
% 108.63/15.84 | | | | | | | | | | (996) all_6_1 = e3
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | SIMP: (996) implies:
% 108.63/15.84 | | | | | | | | | | (997) all_6_1 = e3
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | REDUCE: (43), (997) imply:
% 108.63/15.84 | | | | | | | | | | (998) op(e3, all_6_2) = all_6_0
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | REDUCE: (42), (997) imply:
% 108.63/15.84 | | | | | | | | | | (999) op(e1, all_6_2) = e3
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | BETA: splitting (145) gives:
% 108.63/15.84 | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | (1000) ~ (all_48_0 = e3)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | REDUCE: (782), (1000) imply:
% 108.63/15.84 | | | | | | | | | | | (1001) ~ (all_8_0 = e3)
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | BETA: splitting (270) gives:
% 108.63/15.84 | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | (1002) ~ (all_56_15 = e1)
% 108.63/15.84 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | REDUCE: (554), (1002) imply:
% 108.63/15.84 | | | | | | | | | | | | (1003) ~ (all_4_2 = e1)
% 108.63/15.84 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | BETA: splitting (272) gives:
% 108.63/15.84 | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | (1004) ~ (all_56_12 = e1)
% 108.63/15.84 | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | REDUCE: (426), (1004) imply:
% 108.63/15.84 | | | | | | | | | | | | | (1005) ~ (all_10_2 = e1)
% 108.63/15.84 | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | BETA: splitting (273) gives:
% 108.63/15.84 | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | (1006) ~ (all_56_15 = e2)
% 108.63/15.84 | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | REDUCE: (554), (1006) imply:
% 108.63/15.84 | | | | | | | | | | | | | | (1007) ~ (all_4_2 = e2)
% 108.63/15.84 | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 108.63/15.84 | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | (1008) all_54_15 = e3
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (1008) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1009) all_4_2 = e3
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | SIMP: (1009) implies:
% 108.63/15.84 | | | | | | | | | | | | | | | (1010) all_4_2 = e3
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1011) all_56_15 = e3
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | COMBINE_EQS: (557), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1012) all_58_15 = e3
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | REDUCE: (584), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1013) ~ (all_52_3 = e3)
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | REDUCE: (595), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1014) ~ (all_52_7 = e3)
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | REDUCE: (603), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1015) ~ (all_52_12 = e3)
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | REDUCE: (38), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1016) op(all_4_1, e3) = all_4_0
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | REDUCE: (37), (1010) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | (1017) op(e0, e3) = all_4_1
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 108.63/15.84 | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | (1018) ~ (all_56_3 = e2)
% 108.63/15.84 | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | REDUCE: (430), (1018) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | | (1019) ~ (all_52_1 = e2)
% 108.63/15.84 | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 108.63/15.84 | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | (1020) ~ (all_56_15 = e3)
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | REDUCE: (1011), (1020) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | | | (1021) $false
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | CLOSE: (1021) is inconsistent.
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | (1022) ~ (all_56_9 = e0)
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | REDUCE: (450), (1022) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | | | (1023) ~ (all_52_3 = e0)
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 108.63/15.84 | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.84 | | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | | (1024) ~ (all_56_6 = e1)
% 108.63/15.84 | | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | | REDUCE: (386), (1024) imply:
% 108.63/15.84 | | | | | | | | | | | | | | | | | | (1025) ~ (all_52_2 = e1)
% 108.63/15.84 | | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 108.63/15.84 | | | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (1017)
% 108.63/15.84 | | | | | | | | | | | | | | | | | | gives:
% 108.63/15.84 | | | | | | | | | | | | | | | | | | (1026) all_52_3 = all_4_1
% 108.63/15.84 | | | | | | | | | | | | | | | | | |
% 108.63/15.84 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1026) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | (1027) all_58_12 = all_4_1
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | REDUCE: (184), (1026) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | (1028) ~ (all_52_7 = all_4_1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | SIMP: (1028) implies:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | (1029) ~ (all_52_7 = all_4_1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | REDUCE: (1013), (1026) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | (1030) ~ (all_4_1 = e3)
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | REDUCE: (1023), (1026) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | (1031) ~ (all_4_1 = e0)
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | (1032) ~ (all_56_5 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | REDUCE: (446), (1032) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | (1033) ~ (all_52_13 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | (1034) all_58_2 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (1034) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | (1035) all_52_1 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (1019), (1035) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | (1036) $false
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | CLOSE: (1036) is inconsistent.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | (1037) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1037) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | (1038) all_58_3 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (1038) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | (1039) all_8_2 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1039) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | (1040) $false
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1040) is inconsistent.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | (1041) all_58_5 = e2 | all_58_10 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1041) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | (1042) all_58_5 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1042) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | (1043) all_52_9 = e2
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (1043) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | (1044) ~ (all_8_2 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1043) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | (1045) ~ (all_6_2 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1045) implies:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | (1046) ~ (all_6_2 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1047) ~ (all_56_8 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1047) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1048) ~ (all_52_14 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1049) all_58_6 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (563), (1025), (1049) are inconsistent by
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #452.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_58_7 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (1051) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_52_6 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (1052) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1053) all_56_7 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (1052) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1054) ~ (all_52_7 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1054) implies:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1055) ~ (all_52_7 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (1052) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ (all_8_2 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1056) implies:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1057) ~ (all_8_2 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (1052) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1058) ~ (all_6_2 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) ~ (all_56_7 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1053), (1059) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) $false
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1060) is inconsistent.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) ~ (all_56_12 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1061) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) ~ (all_10_2 = e2)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (178), (179), (207), (211), (235), (238),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (248), (302), (323), (324), (345),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (347), (349), (351), (352), (406), (412), (424),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (434), (464), (477), (551), (552), (553),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (558), (559), (561), (563), (564), (565), (566),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (567), (568), (571), (579), (582), (583), (585),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (599), (860), (999), (1012), (1014),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1015), (1016), (1019), (1027), (1029), (1030),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (1031), (1046), (1055), (1057), (1062),
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #321.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_58_8 = e1 | all_58_11 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (560), (562), (568), (1048), (1063) are
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #445.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1064) all_56_8 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1065) ~ (all_56_13 = e0)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (1064) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1066) all_52_14 = e1
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (1065) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | (1067) ~ (all_8_2 = e0)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1068) ~ (all_56_8 = e1)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1064), (1068) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1069) $false
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1069) is inconsistent.
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1070) ~ (all_56_12 = e0)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1070) imply:
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | | (1071) ~ (all_10_2 = e0)
% 108.63/15.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (172), (179), (180), (187), (211), (214),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (235), (243), (247), (248), (275), (278), (305),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (342), (346), (365), (370), (385), (406), (413),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (424), (426), (450), (458), (477), (530), (552),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (553), (556), (559), (563), (564), (565), (566),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (567), (577), (585), (589), (661), (848), (858),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | (1005), (1067), (1071), (function-axioms) are
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #80.
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | (1072) all_58_10 = e2
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1072) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | (1073) all_52_13 = e2
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1033), (1073) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | (1074) $false
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1074) is inconsistent.
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | (1075) all_56_5 = e2
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | (1076) ~ (all_56_12 = e0)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1075) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | (1077) all_52_13 = e2
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1076) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | (1078) ~ (all_10_2 = e0)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | REDUCE: (593), (1077) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | (1079) ~ (all_8_2 = e2)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | (1080) all_54_0 = e3
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (1080) are inconsistent by sub-proof
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | #451.
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | (1081) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (1082) ~ (all_56_5 = e2)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1075), (1082) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (1083) $false
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1083) is inconsistent.
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (1084) ~ (all_56_13 = e0)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (1084) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (1085) ~ (all_8_2 = e0)
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (172), (179), (180), (187), (211), (214),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (235), (243), (247), (275), (278), (305), (342),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (346), (365), (370), (385), (406), (413), (424),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (426), (450), (458), (477), (530), (552), (553),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (556), (559), (563), (564), (565), (567), (577),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (585), (589), (661), (848), (858), (1005), (1078),
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | (1081), (1085), (function-axioms) are inconsistent
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | | by sub-proof #81.
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | (1086) ~ (all_56_15 = e3)
% 108.63/15.86 | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | REDUCE: (1011), (1086) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | | | (1087) $false
% 108.63/15.86 | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | | CLOSE: (1087) is inconsistent.
% 108.63/15.86 | | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | (1088) ~ (all_56_15 = e3)
% 108.63/15.86 | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | REDUCE: (1011), (1088) imply:
% 108.63/15.86 | | | | | | | | | | | | | | | | (1089) $false
% 108.63/15.86 | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | | CLOSE: (1089) is inconsistent.
% 108.63/15.86 | | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | (1090) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 108.63/15.86 | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (1003), (1007), (1090) are
% 108.63/15.86 | | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 108.63/15.86 | | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | End of split
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | Case 2:
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | (1091) all_56_15 = e2
% 108.63/15.86 | | | | | | | | | | | | | | (1092) ~ (all_56_10 = e0)
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | COMBINE_EQS: (554), (1091) imply:
% 108.63/15.86 | | | | | | | | | | | | | | (1093) all_4_2 = e2
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | SIMP: (1093) implies:
% 108.63/15.86 | | | | | | | | | | | | | | (1094) all_4_2 = e2
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | REDUCE: (365), (1092) imply:
% 108.63/15.86 | | | | | | | | | | | | | | (1095) ~ (all_52_7 = e0)
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | REDUCE: (604), (1094) imply:
% 108.63/15.86 | | | | | | | | | | | | | | (1096) ~ (all_52_13 = e2)
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.86 | | | | | | | | | | | | | | REDUCE: (605), (1094) imply:
% 108.63/15.86 | | | | | | | | | | | | | | (1097) ~ (all_52_14 = e2)
% 108.63/15.86 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (167), (172), (179), (180), (185),
% 108.63/15.87 | | | | | | | | | | | | | | (187), (204), (208), (211), (214), (235), (237),
% 108.63/15.87 | | | | | | | | | | | | | | (238), (242), (243), (247), (248), (275), (278),
% 108.63/15.87 | | | | | | | | | | | | | | (280), (281), (282), (287), (298), (299), (301),
% 108.63/15.87 | | | | | | | | | | | | | | (303), (305), (331), (340), (341), (342), (346),
% 108.63/15.87 | | | | | | | | | | | | | | (352), (365), (370), (371), (385), (386), (391),
% 108.63/15.87 | | | | | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.87 | | | | | | | | | | | | | | (434), (440), (450), (458), (466), (474), (477),
% 108.63/15.87 | | | | | | | | | | | | | | (530), (551), (552), (553), (556), (559), (560),
% 108.63/15.87 | | | | | | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.87 | | | | | | | | | | | | | | (568), (577), (579), (581), (582), (583), (585),
% 108.63/15.87 | | | | | | | | | | | | | | (589), (593), (596), (597), (601), (661), (847),
% 108.63/15.87 | | | | | | | | | | | | | | (848), (858), (1001), (1005), (1091), (1095),
% 108.63/15.87 | | | | | | | | | | | | | | (1096), (1097), (function-axioms) are inconsistent
% 108.63/15.87 | | | | | | | | | | | | | | by sub-proof #69.
% 108.63/15.87 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | End of split
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | Case 2:
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | (1098) all_56_12 = e1
% 108.63/15.87 | | | | | | | | | | | | | (1099) ~ (all_56_11 = e0)
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | COMBINE_EQS: (426), (1098) imply:
% 108.63/15.87 | | | | | | | | | | | | | (1100) all_10_2 = e1
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | SIMP: (1100) implies:
% 108.63/15.87 | | | | | | | | | | | | | (1101) all_10_2 = e1
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 108.63/15.87 | | | | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 108.63/15.87 | | | | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 108.63/15.87 | | | | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 108.63/15.87 | | | | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 108.63/15.87 | | | | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 108.63/15.87 | | | | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 108.63/15.87 | | | | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 108.63/15.87 | | | | | | | | | | | | | (589), (591), (593), (602), (603), (604), (848),
% 108.63/15.87 | | | | | | | | | | | | | (1003), (1098), (1099), (1101), (function-axioms)
% 108.63/15.87 | | | | | | | | | | | | | are inconsistent by sub-proof #74.
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | End of split
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | Case 2:
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | (1102) all_56_15 = e1
% 108.63/15.87 | | | | | | | | | | | | (1103) ~ (all_56_11 = e0)
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | COMBINE_EQS: (554), (1102) imply:
% 108.63/15.87 | | | | | | | | | | | | (1104) all_4_2 = e1
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | SIMP: (1104) implies:
% 108.63/15.87 | | | | | | | | | | | | (1105) all_4_2 = e1
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | COMBINE_EQS: (557), (1105) imply:
% 108.63/15.87 | | | | | | | | | | | | (1106) all_58_15 = e1
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | REDUCE: (362), (1103) imply:
% 108.63/15.87 | | | | | | | | | | | | (1107) ~ (all_52_11 = e0)
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | BETA: splitting (300) gives:
% 108.63/15.87 | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | Case 1:
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | (1108) ~ (all_56_1 = e3)
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | REDUCE: (434), (1108) imply:
% 108.63/15.87 | | | | | | | | | | | | | (1109) ~ (all_52_8 = e3)
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | BETA: splitting (274) gives:
% 108.63/15.87 | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | Case 1:
% 108.63/15.87 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | (1110) ~ (all_56_14 = e2)
% 108.63/15.87 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | REDUCE: (555), (1110) imply:
% 108.63/15.87 | | | | | | | | | | | | | | (1111) ~ (all_6_2 = e2)
% 108.63/15.87 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 108.63/15.87 | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | Case 1:
% 108.63/15.87 | | | | | | | | | | | | | | |
% 108.63/15.87 | | | | | | | | | | | | | | | (1112) ~ (all_56_12 = e2)
% 108.63/15.87 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (38), (41), (157), (165), (167), (169),
% 108.63/15.88 | | | | | | | | | | | | | | | (172), (178), (179), (180), (183), (184), (185),
% 108.63/15.88 | | | | | | | | | | | | | | | (187), (188), (189), (190), (192), (193), (203),
% 108.63/15.88 | | | | | | | | | | | | | | | (204), (207), (208), (209), (211), (233), (234),
% 108.63/15.88 | | | | | | | | | | | | | | | (235), (236), (238), (240), (241), (242), (243),
% 108.63/15.88 | | | | | | | | | | | | | | | (244), (246), (248), (270), (272), (273), (274),
% 108.63/15.88 | | | | | | | | | | | | | | | (276), (277), (279), (280), (281), (282), (285),
% 108.63/15.88 | | | | | | | | | | | | | | | (286), (287), (288), (289), (291), (292), (293),
% 108.63/15.88 | | | | | | | | | | | | | | | (294), (295), (297), (298), (299), (300), (302),
% 108.63/15.88 | | | | | | | | | | | | | | | (323), (324), (329), (331), (332), (334), (335),
% 108.63/15.88 | | | | | | | | | | | | | | | (338), (339), (340), (341), (345), (347), (349),
% 108.63/15.88 | | | | | | | | | | | | | | | (351), (352), (356), (362), (365), (370), (371),
% 108.63/15.88 | | | | | | | | | | | | | | | (385), (386), (391), (394), (406), (407), (412),
% 108.63/15.88 | | | | | | | | | | | | | | | (424), (426), (430), (434), (436), (440), (446),
% 108.63/15.88 | | | | | | | | | | | | | | | (450), (460), (464), (466), (468), (470), (475),
% 108.63/15.88 | | | | | | | | | | | | | | | (477), (479), (551), (552), (553), (554), (555),
% 108.63/15.88 | | | | | | | | | | | | | | | (556), (557), (558), (559), (560), (561), (562),
% 108.63/15.88 | | | | | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 108.63/15.88 | | | | | | | | | | | | | | | (571), (573), (575), (579), (581), (582), (583),
% 108.63/15.88 | | | | | | | | | | | | | | | (584), (585), (587), (589), (591), (593), (594),
% 108.63/15.88 | | | | | | | | | | | | | | | (595), (597), (599), (601), (602), (603), (605),
% 108.63/15.88 | | | | | | | | | | | | | | | (847), (848), (860), (999), (1111), (1112),
% 108.63/15.88 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.88 | | | | | | | | | | | | | | | #68.
% 108.63/15.88 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | | (1113) all_56_12 = e2
% 108.63/15.88 | | | | | | | | | | | | | | | (1114) ~ (all_56_10 = e0)
% 108.63/15.88 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | | REDUCE: (365), (1114) imply:
% 108.63/15.88 | | | | | | | | | | | | | | | (1115) ~ (all_52_7 = e0)
% 108.63/15.88 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | | REF_CLOSE: (4), (209), (243), (278), (298), (305), (323),
% 108.63/15.88 | | | | | | | | | | | | | | | (352), (370), (407), (412), (413), (424), (450),
% 108.63/15.88 | | | | | | | | | | | | | | | (552), (556), (558), (559), (561), (565), (566),
% 108.63/15.88 | | | | | | | | | | | | | | | (567), (591), (848), (1106), (1107), (1109),
% 108.63/15.88 | | | | | | | | | | | | | | | (1113), (1115), (function-axioms) are inconsistent
% 108.63/15.88 | | | | | | | | | | | | | | | by sub-proof #67.
% 108.63/15.88 | | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | End of split
% 108.63/15.88 | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | (1116) all_56_14 = e2
% 108.63/15.88 | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 108.63/15.88 | | | | | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 108.63/15.88 | | | | | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 108.63/15.88 | | | | | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 108.63/15.88 | | | | | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 108.63/15.88 | | | | | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 108.63/15.88 | | | | | | | | | | | | | | (589), (595), (597), (780), (862), (995), (998),
% 108.63/15.88 | | | | | | | | | | | | | | (999), (1116), (function-axioms) are inconsistent
% 108.63/15.88 | | | | | | | | | | | | | | by sub-proof #306.
% 108.63/15.88 | | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | End of split
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | (1117) ~ (all_56_15 = e1)
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | REDUCE: (1102), (1117) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1118) $false
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | CLOSE: (1118) is inconsistent.
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | End of split
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | End of split
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | (1119) all_48_0 = e3
% 108.63/15.88 | | | | | | | | | | | (1120) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | COMBINE_EQS: (782), (1119) imply:
% 108.63/15.88 | | | | | | | | | | | (1121) all_8_0 = e3
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | SIMP: (1121) implies:
% 108.63/15.88 | | | | | | | | | | | (1122) all_8_0 = e3
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | REDUCE: (847), (1122) imply:
% 108.63/15.88 | | | | | | | | | | | (1123) op(e1, all_8_2) = e3
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | BETA: splitting (1120) gives:
% 108.63/15.88 | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | Case 1:
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | (1124) ~ (all_48_1 = e1)
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | REDUCE: (846), (1124) imply:
% 108.63/15.88 | | | | | | | | | | | | (1125) $false
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | CLOSE: (1125) is inconsistent.
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | (1126) ~ (all_48_2 = e0)
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | REDUCE: (547), (1126) imply:
% 108.63/15.88 | | | | | | | | | | | | (1127) ~ (all_8_2 = e0)
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | BETA: splitting (275) gives:
% 108.63/15.88 | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | Case 1:
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | (1128) ~ (all_56_12 = e2)
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | REF_CLOSE: (37), (38), (41), (154), (156), (161), (165),
% 108.63/15.88 | | | | | | | | | | | | | (167), (169), (183), (184), (185), (188), (189),
% 108.63/15.88 | | | | | | | | | | | | | (190), (192), (193), (203), (209), (211), (233),
% 108.63/15.88 | | | | | | | | | | | | | (234), (235), (236), (237), (238), (240), (242),
% 108.63/15.88 | | | | | | | | | | | | | (243), (244), (246), (248), (272), (274), (276),
% 108.63/15.88 | | | | | | | | | | | | | (278), (281), (282), (285), (287), (288), (290),
% 108.63/15.88 | | | | | | | | | | | | | (291), (292), (293), (294), (295), (296), (302),
% 108.63/15.88 | | | | | | | | | | | | | (323), (324), (329), (331), (334), (335), (338),
% 108.63/15.88 | | | | | | | | | | | | | (339), (340), (341), (349), (351), (356), (362),
% 108.63/15.88 | | | | | | | | | | | | | (365), (370), (371), (385), (386), (391), (394),
% 108.63/15.88 | | | | | | | | | | | | | (406), (412), (424), (426), (430), (434), (436),
% 108.63/15.88 | | | | | | | | | | | | | (440), (446), (450), (460), (464), (466), (470),
% 108.63/15.88 | | | | | | | | | | | | | (474), (475), (477), (479), (551), (552), (553),
% 108.63/15.88 | | | | | | | | | | | | | (554), (555), (556), (557), (558), (559), (560),
% 108.63/15.88 | | | | | | | | | | | | | (561), (562), (563), (564), (566), (567), (568),
% 108.63/15.88 | | | | | | | | | | | | | (569), (571), (573), (575), (579), (581), (582),
% 108.63/15.88 | | | | | | | | | | | | | (583), (584), (587), (589), (591), (593), (595),
% 108.63/15.88 | | | | | | | | | | | | | (597), (599), (601), (602), (604), (605), (848),
% 108.63/15.88 | | | | | | | | | | | | | (860), (1123), (1127), (1128), (function-axioms)
% 108.63/15.88 | | | | | | | | | | | | | are inconsistent by sub-proof #66.
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | Case 2:
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | (1129) all_56_12 = e2
% 108.63/15.88 | | | | | | | | | | | | | (1130) ~ (all_56_10 = e0)
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | COMBINE_EQS: (426), (1129) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1131) all_10_2 = e2
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | SIMP: (1131) implies:
% 108.63/15.88 | | | | | | | | | | | | | (1132) all_10_2 = e2
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | COMBINE_EQS: (530), (1132) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1133) all_24_2 = e2
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | COMBINE_EQS: (424), (1132) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1134) all_58_0 = e2
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | REDUCE: (365), (1130) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1135) ~ (all_52_7 = e0)
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | REDUCE: (577), (1132) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1136) ~ (all_52_4 = e2)
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.88 | | | | | | | | | | | | | REDUCE: (52), (1132) imply:
% 108.63/15.88 | | | | | | | | | | | | | (1137) op(e3, e2) = all_10_1
% 108.63/15.88 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | REF_CLOSE: (172), (179), (180), (187), (211), (214), (235),
% 108.63/15.89 | | | | | | | | | | | | | (243), (247), (278), (305), (342), (346), (370),
% 108.63/15.89 | | | | | | | | | | | | | (385), (406), (413), (450), (458), (477), (552),
% 108.63/15.89 | | | | | | | | | | | | | (556), (559), (563), (564), (565), (567), (585),
% 108.63/15.89 | | | | | | | | | | | | | (589), (661), (848), (858), (1127), (1129),
% 108.63/15.89 | | | | | | | | | | | | | (1133), (1134), (1135), (1136), (1137),
% 108.63/15.89 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.89 | | | | | | | | | | | | | #83.
% 108.63/15.89 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | End of split
% 108.63/15.89 | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | End of split
% 108.63/15.89 | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | End of split
% 108.63/15.89 | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | End of split
% 108.63/15.89 | | | | | | | | |
% 108.63/15.89 | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | |
% 108.63/15.89 | | | | | | | | | (1138) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 108.63/15.89 | | | | | | | | |
% 108.63/15.89 | | | | | | | | | BETA: splitting (274) gives:
% 108.63/15.89 | | | | | | | | |
% 108.63/15.89 | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | (1139) ~ (all_56_14 = e2)
% 108.63/15.89 | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | REDUCE: (555), (1139) imply:
% 108.63/15.89 | | | | | | | | | | (1140) ~ (all_6_2 = e2)
% 108.63/15.89 | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | BETA: splitting (270) gives:
% 108.63/15.89 | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | (1141) ~ (all_56_15 = e1)
% 108.63/15.89 | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | REDUCE: (554), (1141) imply:
% 108.63/15.89 | | | | | | | | | | | (1142) ~ (all_4_2 = e1)
% 108.63/15.89 | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | BETA: splitting (272) gives:
% 108.63/15.89 | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | (1143) ~ (all_56_12 = e1)
% 108.63/15.89 | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | REDUCE: (426), (1143) imply:
% 108.63/15.89 | | | | | | | | | | | | (1144) ~ (all_10_2 = e1)
% 108.63/15.89 | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | BETA: splitting (271) gives:
% 108.63/15.89 | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | (1145) ~ (all_56_13 = e1)
% 108.63/15.89 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | REDUCE: (556), (1145) imply:
% 108.63/15.89 | | | | | | | | | | | | | (1146) ~ (all_8_2 = e1)
% 108.63/15.89 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | BETA: splitting (273) gives:
% 108.63/15.89 | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | (1147) ~ (all_56_15 = e2)
% 108.63/15.89 | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | REDUCE: (554), (1147) imply:
% 108.63/15.89 | | | | | | | | | | | | | | (1148) ~ (all_4_2 = e2)
% 108.63/15.89 | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 108.63/15.89 | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | (1149) all_54_15 = e3
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (1149) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1150) all_4_2 = e3
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | SIMP: (1150) implies:
% 108.63/15.89 | | | | | | | | | | | | | | | (1151) all_4_2 = e3
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1152) all_56_15 = e3
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | REDUCE: (584), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1153) ~ (all_52_3 = e3)
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | REDUCE: (595), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1154) ~ (all_52_7 = e3)
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | REDUCE: (603), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1155) ~ (all_52_12 = e3)
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | REDUCE: (38), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1156) op(all_4_1, e3) = all_4_0
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | REDUCE: (37), (1151) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | (1157) op(e0, e3) = all_4_1
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 108.63/15.89 | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | (1158) ~ (all_56_6 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | REDUCE: (386), (1158) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | (1159) ~ (all_52_2 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | (1160) ~ (all_56_3 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | REDUCE: (430), (1160) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | (1161) ~ (all_52_1 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 108.63/15.89 | | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (1157)
% 108.63/15.89 | | | | | | | | | | | | | | | | | gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | (1162) all_52_3 = all_4_1
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1162) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | (1163) all_58_12 = all_4_1
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | REDUCE: (1153), (1162) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | (1164) ~ (all_4_1 = e3)
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | (1165) ~ (all_56_5 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | REDUCE: (446), (1165) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | (1166) ~ (all_52_13 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | (1167) all_58_2 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (1167) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | (1168) all_52_1 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | REDUCE: (1161), (1168) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | (1169) $false
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | CLOSE: (1169) is inconsistent.
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | (1170) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (1170) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | (1171) all_58_3 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (1171) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | (1172) all_8_2 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1172) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | (1173) $false
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | CLOSE: (1173) is inconsistent.
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | (1174) all_58_5 = e2 | all_58_10 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1174) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | (1175) all_58_5 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1175) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | (1176) all_52_9 = e2
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (1176) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | (1177) ~ (all_52_8 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (1176) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | (1178) ~ (all_8_2 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1176) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | (1179) ~ (all_6_2 = e2)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | (1180) ~ (all_56_7 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (440), (1180) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | (1181) ~ (all_52_6 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | (1182) all_58_6 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (563), (1159), (1182) are inconsistent by
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #452.
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | (1183) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1183) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | (1184) all_58_7 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (1184) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | (1185) all_52_6 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1181), (1185) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | (1186) $false
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1186) is inconsistent.
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_58_8 = e1 | all_58_11 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1187) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1188) all_58_8 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (562), (1188) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1189) all_6_2 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (1189) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1190) $false
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1190) is inconsistent.
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1191) all_58_11 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (560), (1191) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_52_14 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1192) implies:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_52_14 = e1
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (1193) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1194) ~ (all_52_13 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (601), (1193) imply:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | (1195) ~ (all_6_2 = e1)
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_54_5 = e3
% 108.63/15.89 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (238), (279), (352), (371),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (412), (424), (474), (522), (551), (552), (555),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (561), (565), (566), (568), (579), (585), (596),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (601), (683), (785), (1138), (1140), (1155),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1196), (function-axioms) are inconsistent by
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (208), (211), (241), (243), (289), (338), (391),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (394), (406), (446), (468), (552), (556), (564),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (567), (591), (593), (848), (1146), (1194),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1197), (function-axioms) are inconsistent by
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #129.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1198) all_56_7 = e1
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1199) ~ (all_56_12 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (1198) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1200) all_52_6 = e1
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1199) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1201) ~ (all_10_2 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (172), (1200) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1202) ~ (all_52_7 = e1)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1202) implies:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1203) ~ (all_52_7 = e1)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (1200) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | (1204) ~ (all_8_2 = e1)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | (1205) all_54_0 = e3
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (1205) are inconsistent by sub-proof
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | #451.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | (1206) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1206) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_54_0 = e2
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (1201), (1207) are inconsistent by
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #450.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | (1208) ~ (all_54_0 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | (1209) all_54_0 = e1 | all_54_0 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1209) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_54_0 = e1
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (1144), (1210) are inconsistent by
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #449.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_54_0 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1211) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_10_2 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1212) implies:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_10_2 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1214) all_16_2 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_58_0 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1216) ~ (all_52_1 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1217) ~ (all_52_4 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1218) ~ (all_52_8 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1219) ~ (all_52_12 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1201), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1220) ~ (e2 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1213) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | (1221) op(e3, e0) = all_10_1
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (853) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) ~ (all_16_1 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (695), (1222) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) ~ (all_10_1 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (177), (178), (179), (211), (212),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (243), (244), (245), (246), (247), (349),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (350), (351), (406), (458), (460), (462), (464),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (477), (552), (565), (582), (585), (589), (860),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1146), (1154), (1155), (1156), (1161), (1163),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1164), (1177), (1203), (1215), (1216), (1217),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1218), (1219), (1221), (1223), (function-axioms)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #205.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) ~ (all_16_2 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1214), (1224) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) $false
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1225) is inconsistent.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | (1226) all_58_10 = e2
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1226) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | (1227) all_52_13 = e2
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1166), (1227) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | (1228) $false
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1228) is inconsistent.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | (1229) all_56_5 = e2
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1229) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | (1230) all_52_13 = e2
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | REDUCE: (593), (1230) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | (1231) ~ (all_8_2 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | (1232) ~ (all_56_5 = e2)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | REDUCE: (1229), (1232) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | (1233) $false
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | CLOSE: (1233) is inconsistent.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | (1234) ~ (all_56_13 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | REDUCE: (556), (1234) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | (1235) ~ (all_8_2 = e0)
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (1236) all_54_5 = e3
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (238), (279), (352), (371),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (412), (424), (474), (522), (551), (552), (555),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (561), (565), (566), (568), (579), (585), (596),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (601), (683), (785), (1138), (1140), (1155),
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (1236), (function-axioms) are inconsistent by
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | (1237) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (552), (567), (1146), (1235), (1237) are
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #310.
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | (1238) ~ (all_56_15 = e3)
% 108.63/15.90 | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | REDUCE: (1152), (1238) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | | (1239) $false
% 108.63/15.90 | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | | CLOSE: (1239) is inconsistent.
% 108.63/15.90 | | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | End of split
% 108.63/15.90 | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | Case 2:
% 108.63/15.90 | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | (1240) ~ (all_56_15 = e3)
% 108.63/15.90 | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | REDUCE: (1152), (1240) imply:
% 108.63/15.90 | | | | | | | | | | | | | | | | (1241) $false
% 108.63/15.90 | | | | | | | | | | | | | | | |
% 108.63/15.90 | | | | | | | | | | | | | | | | CLOSE: (1241) is inconsistent.
% 108.63/15.90 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | End of split
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | (1242) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (1142), (1148), (1242) are
% 108.63/15.91 | | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | End of split
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | (1243) all_56_15 = e2
% 108.63/15.91 | | | | | | | | | | | | | | (1244) ~ (all_56_10 = e0)
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | COMBINE_EQS: (554), (1243) imply:
% 108.63/15.91 | | | | | | | | | | | | | | (1245) all_4_2 = e2
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | SIMP: (1245) implies:
% 108.63/15.91 | | | | | | | | | | | | | | (1246) all_4_2 = e2
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | REDUCE: (365), (1244) imply:
% 108.63/15.91 | | | | | | | | | | | | | | (1247) ~ (all_52_7 = e0)
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | REDUCE: (595), (1246) imply:
% 108.63/15.91 | | | | | | | | | | | | | | (1248) ~ (all_52_7 = e2)
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | REDUCE: (37), (1246) imply:
% 108.63/15.91 | | | | | | | | | | | | | | (1249) op(e0, e2) = all_4_1
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 108.63/15.91 | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | (1250) ~ (all_56_0 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REDUCE: (413), (1250) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1251) ~ (all_52_4 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 108.63/15.91 | | | | | | | | | | | | | | | all_4_1, e2, e0, simplifying with (202), (1249)
% 108.63/15.91 | | | | | | | | | | | | | | | gives:
% 108.63/15.91 | | | | | | | | | | | | | | | (1252) all_52_7 = all_4_1
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | COMBINE_EQS: (477), (1252) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1253) all_54_13 = all_4_1
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REDUCE: (169), (1252) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1254) ~ (all_52_11 = all_4_1)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | SIMP: (1254) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | (1255) ~ (all_52_11 = all_4_1)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REDUCE: (589), (1252) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1256) ~ (all_8_2 = all_4_1)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | SIMP: (1256) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | (1257) ~ (all_8_2 = all_4_1)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REDUCE: (1248), (1252) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1258) ~ (all_4_1 = e2)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | REDUCE: (1247), (1252) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | (1259) ~ (all_4_1 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 108.63/15.91 | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | (1260) ~ (all_56_2 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | REDUCE: (407), (1260) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | (1261) ~ (all_52_12 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (238), (279), (352), (371),
% 108.63/15.91 | | | | | | | | | | | | | | | | (412), (424), (474), (522), (551), (555), (561),
% 108.63/15.91 | | | | | | | | | | | | | | | | (565), (566), (568), (579), (596), (601), (683),
% 108.63/15.91 | | | | | | | | | | | | | | | | (785), (1138), (1140), (1251), (1261),
% 108.63/15.91 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.91 | | | | | | | | | | | | | | | | #251.
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | (1262) all_56_2 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | (1263) ~ (all_56_13 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1262) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | (1264) all_52_12 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | REDUCE: (556), (1263) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | (1265) ~ (all_8_2 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | REDUCE: (581), (1264) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | (1266) ~ (all_10_2 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | (1267) ~ (all_56_2 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | REDUCE: (1262), (1267) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | (1268) $false
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | CLOSE: (1268) is inconsistent.
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | (1269) ~ (all_56_12 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | REDUCE: (426), (1269) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | (1270) ~ (all_10_2 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | (1271) ~ (all_56_2 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | REDUCE: (1262), (1271) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | (1272) $false
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | CLOSE: (1272) is inconsistent.
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | (1273) ~ (all_56_14 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | REDUCE: (555), (1273) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | (1274) ~ (all_6_2 = e0)
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | (1275) all_54_10 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (551), (1275) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | (1276) all_6_2 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | SIMP: (1276) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | (1277) all_6_2 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1277) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | (1278) op(e1, e1) = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | (1279) all_54_0 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (1279) are inconsistent by sub-proof
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | #451.
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | (1280) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | (1281) ~ (all_56_3 = e2)
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (430), (1281) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | (1282) ~ (all_52_1 = e2)
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | (1283) all_54_5 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (1283) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | (1284) all_8_2 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1284) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | (1285) all_8_2 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1257), (1285) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | (1286) ~ (all_4_1 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1286) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | (1287) ~ (all_4_1 = e3)
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | (1288) all_54_13 = e3
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1253), (1287), (1288) are inconsistent by
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #235.
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | (1289) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | (1290) all_54_13 = e2
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1253), (1258), (1290) are inconsistent by
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #234.
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | (1291) all_54_13 = e1 | all_54_13 = e0
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1291) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | (1292) all_54_13 = e1
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1253), (1292) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | (1293) all_4_1 = e1
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1293) implies:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | (1294) all_4_1 = e1
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1255), (1294) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | (1295) ~ (all_52_11 = e1)
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1280) gives:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_54_0 = e2
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1296) imply:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_10_2 = e2
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (172), (179), (180), (187), (211), (214),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (243), (247), (278), (305), (342), (346),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (370), (385), (406), (413), (424), (426), (450),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (458), (477), (530), (552), (556), (559), (563),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (564), (565), (567), (577), (585), (589), (661),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (848), (858), (1247), (1265), (1297),
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | | #77.
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) all_54_0 = e1 | all_54_0 = e0
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (190), (211), (243), (244), (335), (338), (394),
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (406), (412), (464), (552), (553), (558), (562),
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (567), (568), (571), (579), (582), (591), (848),
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (1265), (1270), (1282), (1295), (1298),
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | | #125.
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_54_13 = e0
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1253), (1259), (1299) are inconsistent by
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #233.
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | (1300) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (298), (552), (556), (567), (1146), (1262), (1300)
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #286.
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | (1301) all_56_3 = e2
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (295), (555), (1278), (1301),
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | | #121.
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | (1302) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 108.63/15.92 | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (551), (568), (1140), (1274), (1302) are
% 108.63/15.92 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #435.
% 108.63/15.92 | | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | (1303) ~ (all_56_15 = e2)
% 108.63/15.92 | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | REDUCE: (1243), (1303) imply:
% 108.63/15.92 | | | | | | | | | | | | | | | (1304) $false
% 108.63/15.92 | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | | CLOSE: (1304) is inconsistent.
% 108.63/15.92 | | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | (1305) all_56_13 = e1
% 108.63/15.92 | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | COMBINE_EQS: (556), (1305) imply:
% 108.63/15.92 | | | | | | | | | | | | | (1306) all_8_2 = e1
% 108.63/15.92 | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | | REF_CLOSE: (209), (591), (848), (1306), (function-axioms) are
% 108.63/15.92 | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 108.63/15.92 | | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | (1307) all_56_12 = e1
% 108.63/15.92 | | | | | | | | | | | | (1308) ~ (all_56_11 = e0)
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | COMBINE_EQS: (426), (1307) imply:
% 108.63/15.92 | | | | | | | | | | | | (1309) all_10_2 = e1
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | SIMP: (1309) implies:
% 108.63/15.92 | | | | | | | | | | | | (1310) all_10_2 = e1
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | COMBINE_EQS: (424), (1310) imply:
% 108.63/15.92 | | | | | | | | | | | | (1311) all_58_0 = e1
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | REDUCE: (362), (1308) imply:
% 108.63/15.92 | | | | | | | | | | | | (1312) ~ (all_52_11 = e0)
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | REDUCE: (566), (1310) imply:
% 108.63/15.92 | | | | | | | | | | | | (1313) ~ (e3 = e1)
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | | REF_CLOSE: (4), (8), (162), (167), (208), (209), (211),
% 108.63/15.92 | | | | | | | | | | | | (233), (243), (271), (273), (276), (278), (289),
% 108.63/15.92 | | | | | | | | | | | | (293), (294), (296), (298), (300), (301), (302),
% 108.63/15.92 | | | | | | | | | | | | (303), (323), (338), (340), (341), (352), (356),
% 108.63/15.92 | | | | | | | | | | | | (362), (365), (370), (391), (394), (406), (407),
% 108.63/15.92 | | | | | | | | | | | | (412), (413), (424), (430), (434), (436), (446),
% 108.63/15.92 | | | | | | | | | | | | (450), (552), (554), (556), (557), (558), (559),
% 108.63/15.92 | | | | | | | | | | | | (561), (564), (565), (566), (567), (569), (582),
% 108.63/15.92 | | | | | | | | | | | | (585), (589), (591), (593), (602), (603), (604),
% 108.63/15.92 | | | | | | | | | | | | (848), (1142), (1307), (1311), (1312),
% 108.63/15.92 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.92 | | | | | | | | | | | | #75.
% 108.63/15.92 | | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | (1314) all_56_15 = e1
% 108.63/15.92 | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | | REF_CLOSE: (42), (189), (190), (204), (211), (237), (238),
% 108.63/15.92 | | | | | | | | | | | (243), (244), (248), (284), (286), (288), (289),
% 108.63/15.92 | | | | | | | | | | | (290), (291), (295), (331), (335), (338), (340),
% 108.63/15.92 | | | | | | | | | | | (352), (385), (386), (391), (394), (406), (412),
% 108.63/15.92 | | | | | | | | | | | (424), (426), (430), (436), (440), (446), (464),
% 108.63/15.92 | | | | | | | | | | | (474), (522), (551), (552), (553), (554), (555),
% 108.63/15.92 | | | | | | | | | | | (556), (558), (560), (562), (563), (564), (566),
% 108.63/15.92 | | | | | | | | | | | (567), (568), (571), (579), (582), (591), (593),
% 108.63/15.92 | | | | | | | | | | | (601), (602), (605), (683), (785), (848), (1138),
% 108.63/15.92 | | | | | | | | | | | (1140), (1314), (function-axioms) are inconsistent
% 108.63/15.92 | | | | | | | | | | | by sub-proof #64.
% 108.63/15.92 | | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | (1315) all_56_14 = e2
% 108.63/15.92 | | | | | | | | | | (1316) ~ (all_56_10 = e0)
% 108.63/15.92 | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | | REF_CLOSE: (4), (8), (162), (167), (208), (209), (211),
% 108.63/15.92 | | | | | | | | | | (233), (243), (271), (276), (278), (289), (294),
% 108.63/15.92 | | | | | | | | | | (296), (298), (300), (301), (304), (323), (338),
% 108.63/15.92 | | | | | | | | | | (340), (341), (352), (356), (362), (365), (370),
% 108.63/15.92 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 108.63/15.92 | | | | | | | | | | (430), (434), (446), (450), (552), (554), (555),
% 108.63/15.92 | | | | | | | | | | (556), (557), (558), (559), (561), (564), (565),
% 108.63/15.92 | | | | | | | | | | (566), (567), (569), (582), (591), (593), (597),
% 108.63/15.92 | | | | | | | | | | (599), (604), (848), (1315), (1316),
% 108.63/15.92 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.92 | | | | | | | | | | #104.
% 108.63/15.92 | | | | | | | | | |
% 108.63/15.92 | | | | | | | | | End of split
% 108.63/15.92 | | | | | | | | |
% 108.63/15.92 | | | | | | | | End of split
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | Case 2:
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | (1317) all_26_0 = e1
% 108.63/15.92 | | | | | | | | (1318) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | COMBINE_EQS: (778), (1317) imply:
% 108.63/15.92 | | | | | | | | (1319) all_4_0 = e1
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | REDUCE: (784), (1319) imply:
% 108.63/15.92 | | | | | | | | (1320) ~ (e3 = e1)
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | REDUCE: (38), (1319) imply:
% 108.63/15.92 | | | | | | | | (1321) op(all_4_1, all_4_2) = e1
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | BETA: splitting (145) gives:
% 108.63/15.92 | | | | | | | |
% 108.63/15.92 | | | | | | | | Case 1:
% 108.63/15.92 | | | | | | | | |
% 108.63/15.92 | | | | | | | | | (1322) ~ (all_48_0 = e3)
% 108.63/15.92 | | | | | | | | |
% 108.63/15.93 | | | | | | | | | REDUCE: (782), (1322) imply:
% 108.63/15.93 | | | | | | | | | (1323) ~ (all_8_0 = e3)
% 108.63/15.93 | | | | | | | | |
% 108.63/15.93 | | | | | | | | | BETA: splitting (270) gives:
% 108.63/15.93 | | | | | | | | |
% 108.63/15.93 | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | (1324) ~ (all_56_15 = e1)
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | REDUCE: (554), (1324) imply:
% 108.63/15.93 | | | | | | | | | | (1325) ~ (all_4_2 = e1)
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | BETA: splitting (272) gives:
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | (1326) ~ (all_56_12 = e1)
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | REDUCE: (426), (1326) imply:
% 108.63/15.93 | | | | | | | | | | | (1327) ~ (all_10_2 = e1)
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | BETA: splitting (273) gives:
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | (1328) ~ (all_56_15 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REDUCE: (554), (1328) imply:
% 108.63/15.93 | | | | | | | | | | | | (1329) ~ (all_4_2 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REF_CLOSE: (37), (188), (203), (207), (233), (236), (276),
% 108.63/15.93 | | | | | | | | | | | | (356), (450), (475), (540), (554), (569), (584),
% 108.63/15.93 | | | | | | | | | | | | (675), (1318), (1321), (1325), (1329),
% 108.63/15.93 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 108.63/15.93 | | | | | | | | | | | | #236.
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | (1330) all_56_15 = e2
% 108.63/15.93 | | | | | | | | | | | | (1331) ~ (all_56_10 = e0)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | COMBINE_EQS: (554), (1330) imply:
% 108.63/15.93 | | | | | | | | | | | | (1332) all_4_2 = e2
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | SIMP: (1332) implies:
% 108.63/15.93 | | | | | | | | | | | | (1333) all_4_2 = e2
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REDUCE: (365), (1331) imply:
% 108.63/15.93 | | | | | | | | | | | | (1334) ~ (all_52_7 = e0)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REDUCE: (604), (1333) imply:
% 108.63/15.93 | | | | | | | | | | | | (1335) ~ (all_52_13 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REDUCE: (605), (1333) imply:
% 108.63/15.93 | | | | | | | | | | | | (1336) ~ (all_52_14 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (167), (172), (179), (180), (185),
% 108.63/15.93 | | | | | | | | | | | | (187), (204), (208), (211), (214), (235), (237),
% 108.63/15.93 | | | | | | | | | | | | (238), (242), (243), (247), (248), (275), (278),
% 108.63/15.93 | | | | | | | | | | | | (280), (281), (282), (287), (298), (299), (301),
% 108.63/15.93 | | | | | | | | | | | | (303), (305), (331), (340), (341), (342), (346),
% 108.63/15.93 | | | | | | | | | | | | (352), (365), (370), (371), (385), (386), (391),
% 108.63/15.93 | | | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 108.63/15.93 | | | | | | | | | | | | (434), (440), (450), (458), (466), (474), (477),
% 108.63/15.93 | | | | | | | | | | | | (530), (551), (552), (553), (556), (559), (560),
% 108.63/15.93 | | | | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 108.63/15.93 | | | | | | | | | | | | (568), (577), (579), (581), (582), (583), (585),
% 108.63/15.93 | | | | | | | | | | | | (589), (593), (596), (597), (601), (661), (847),
% 108.63/15.93 | | | | | | | | | | | | (848), (858), (1323), (1327), (1330), (1334),
% 108.63/15.93 | | | | | | | | | | | | (1335), (1336), (function-axioms) are inconsistent
% 108.63/15.93 | | | | | | | | | | | | by sub-proof #69.
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | End of split
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | (1337) all_56_12 = e1
% 108.63/15.93 | | | | | | | | | | | (1338) ~ (all_56_11 = e0)
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | COMBINE_EQS: (426), (1337) imply:
% 108.63/15.93 | | | | | | | | | | | (1339) all_10_2 = e1
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 108.63/15.93 | | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 108.63/15.93 | | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 108.63/15.93 | | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 108.63/15.93 | | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 108.63/15.93 | | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 108.63/15.93 | | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 108.63/15.93 | | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 108.63/15.93 | | | | | | | | | | | (589), (591), (593), (602), (603), (604), (848),
% 108.63/15.93 | | | | | | | | | | | (1325), (1337), (1338), (1339), (function-axioms)
% 108.63/15.93 | | | | | | | | | | | are inconsistent by sub-proof #74.
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | End of split
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | (1340) all_56_15 = e1
% 108.63/15.93 | | | | | | | | | | (1341) ~ (all_56_11 = e0)
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | COMBINE_EQS: (554), (1340) imply:
% 108.63/15.93 | | | | | | | | | | (1342) all_4_2 = e1
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | SIMP: (1342) implies:
% 108.63/15.93 | | | | | | | | | | (1343) all_4_2 = e1
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | COMBINE_EQS: (557), (1343) imply:
% 108.63/15.93 | | | | | | | | | | (1344) all_58_15 = e1
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | REDUCE: (362), (1341) imply:
% 108.63/15.93 | | | | | | | | | | (1345) ~ (all_52_11 = e0)
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | REDUCE: (603), (1343) imply:
% 108.63/15.93 | | | | | | | | | | (1346) ~ (all_52_12 = e1)
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | BETA: splitting (300) gives:
% 108.63/15.93 | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | (1347) ~ (all_56_1 = e3)
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | REDUCE: (434), (1347) imply:
% 108.63/15.93 | | | | | | | | | | | (1348) ~ (all_52_8 = e3)
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | BETA: splitting (275) gives:
% 108.63/15.93 | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | (1349) ~ (all_56_12 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | REDUCE: (426), (1349) imply:
% 108.63/15.93 | | | | | | | | | | | | (1350) ~ (all_10_2 = e2)
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | BETA: splitting (304) gives:
% 108.63/15.93 | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | (1351) ~ (all_56_0 = e3)
% 108.63/15.93 | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | REDUCE: (413), (1351) imply:
% 108.63/15.93 | | | | | | | | | | | | | (1352) ~ (all_52_4 = e3)
% 108.63/15.93 | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | BETA: splitting (352) gives:
% 108.63/15.93 | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | (1353) all_58_0 = e3
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | COMBINE_EQS: (424), (1353) imply:
% 108.63/15.93 | | | | | | | | | | | | | | (1354) all_10_2 = e3
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | REDUCE: (566), (1354) imply:
% 108.63/15.93 | | | | | | | | | | | | | | (1355) $false
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | CLOSE: (1355) is inconsistent.
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | (1356) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | BETA: splitting (1356) gives:
% 108.63/15.93 | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | (1357) all_58_1 = e3
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | COMBINE_EQS: (565), (1357) imply:
% 108.63/15.93 | | | | | | | | | | | | | | | (1358) all_52_4 = e3
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | REDUCE: (1352), (1358) imply:
% 108.63/15.93 | | | | | | | | | | | | | | | (1359) $false
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | CLOSE: (1359) is inconsistent.
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | (1360) all_58_4 = e3 | all_58_9 = e3
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | BETA: splitting (1360) gives:
% 108.63/15.93 | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | Case 1:
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | (1361) all_58_4 = e3
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (1361) imply:
% 108.63/15.93 | | | | | | | | | | | | | | | | (1362) all_52_8 = e3
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | REDUCE: (1348), (1362) imply:
% 108.63/15.93 | | | | | | | | | | | | | | | | (1363) $false
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | CLOSE: (1363) is inconsistent.
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | Case 2:
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | (1364) all_58_9 = e3
% 108.63/15.93 | | | | | | | | | | | | | | | |
% 108.63/15.93 | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (1364) imply:
% 108.63/15.94 | | | | | | | | | | | | | | | | (1365) all_52_12 = e3
% 108.63/15.94 | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1365) imply:
% 108.63/15.94 | | | | | | | | | | | | | | | | (1366) all_56_2 = e3
% 108.63/15.94 | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | REDUCE: (581), (1365) imply:
% 108.63/15.94 | | | | | | | | | | | | | | | | (1367) ~ (all_10_2 = e3)
% 108.63/15.94 | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 108.63/15.94 | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | Case 1:
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | (1368) ~ (all_56_2 = e3)
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | REDUCE: (1366), (1368) imply:
% 108.63/15.94 | | | | | | | | | | | | | | | | | (1369) $false
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | CLOSE: (1369) is inconsistent.
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | Case 2:
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | (1370) ~ (all_56_13 = e0)
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | REDUCE: (556), (1370) imply:
% 108.63/15.94 | | | | | | | | | | | | | | | | | (1371) ~ (all_8_2 = e0)
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (37), (41), (42), (52), (162),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (167), (172), (179), (180), (183), (184), (187),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (188), (190), (192), (193), (203), (207), (208),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (209), (211), (214), (233), (234), (235), (236),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (238), (241), (242), (243), (244), (247), (248),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (271), (272), (273), (274), (275), (276), (277),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (278), (279), (281), (282), (286), (287), (288),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (289), (290), (292), (294), (295), (296), (297),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (298), (299), (300), (301), (304), (305), (323),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (324), (329), (331), (335), (338), (340), (341),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (342), (346), (349), (352), (356), (362), (365),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (407), (412), (413), (424), (426), (430), (434),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (436), (440), (446), (450), (458), (464), (466),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (468), (475), (477), (479), (530), (540), (551),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (577), (579), (581), (582), (584), (585), (587),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (589), (591), (593), (594), (597), (599), (601),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (602), (604), (605), (661), (675), (848), (858),
% 108.63/15.94 | | | | | | | | | | | | | | | | | (1318), (1321), (1371), (function-axioms) are
% 108.63/15.94 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63.
% 108.63/15.94 | | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | | End of split
% 108.63/15.94 | | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | | End of split
% 108.63/15.94 | | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | | End of split
% 108.63/15.94 | | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | End of split
% 108.63/15.94 | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | Case 2:
% 108.63/15.94 | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | (1372) all_56_0 = e3
% 108.63/15.94 | | | | | | | | | | | | | (1373) ~ (all_56_14 = e2)
% 108.63/15.94 | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | COMBINE_EQS: (413), (1372) imply:
% 108.63/15.94 | | | | | | | | | | | | | (1374) all_52_4 = e3
% 108.63/15.94 | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | REDUCE: (555), (1373) imply:
% 108.63/15.94 | | | | | | | | | | | | | (1375) ~ (all_6_2 = e2)
% 108.63/15.94 | | | | | | | | | | | | |
% 108.63/15.94 | | | | | | | | | | | | | REDUCE: (577), (1374) imply:
% 108.63/15.94 | | | | | | | | | | | | | (1376) ~ (all_10_2 = e3)
% 108.63/15.94 | | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | | | REF_CLOSE: (9), (37), (41), (42), (162), (183), (184), (188),
% 109.38/15.94 | | | | | | | | | | | | | (190), (192), (193), (203), (207), (208), (209),
% 109.38/15.94 | | | | | | | | | | | | | (211), (233), (234), (236), (238), (241), (242),
% 109.38/15.94 | | | | | | | | | | | | | (243), (244), (248), (272), (273), (276), (277),
% 109.38/15.94 | | | | | | | | | | | | | (279), (281), (282), (286), (287), (288), (289),
% 109.38/15.94 | | | | | | | | | | | | | (290), (292), (294), (295), (297), (298), (299),
% 109.38/15.94 | | | | | | | | | | | | | (300), (323), (324), (329), (331), (335), (338),
% 109.38/15.94 | | | | | | | | | | | | | (340), (341), (349), (352), (356), (362), (365),
% 109.38/15.94 | | | | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 109.38/15.94 | | | | | | | | | | | | | (407), (412), (424), (426), (430), (434), (436),
% 109.38/15.94 | | | | | | | | | | | | | (440), (446), (450), (464), (466), (468), (475),
% 109.38/15.94 | | | | | | | | | | | | | (479), (540), (551), (552), (553), (554), (555),
% 109.38/15.94 | | | | | | | | | | | | | (556), (557), (558), (559), (560), (561), (562),
% 109.38/15.94 | | | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 109.38/15.94 | | | | | | | | | | | | | (571), (573), (575), (579), (581), (582), (584),
% 109.38/15.94 | | | | | | | | | | | | | (585), (587), (589), (591), (593), (594), (597),
% 109.38/15.94 | | | | | | | | | | | | | (599), (601), (602), (604), (605), (675), (848),
% 109.38/15.94 | | | | | | | | | | | | | (1318), (1321), (1350), (1375), (function-axioms)
% 109.38/15.94 | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 109.38/15.94 | | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | | End of split
% 109.38/15.94 | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | Case 2:
% 109.38/15.94 | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | | (1377) all_56_12 = e2
% 109.38/15.94 | | | | | | | | | | | | (1378) ~ (all_56_10 = e0)
% 109.38/15.94 | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | | REDUCE: (365), (1378) imply:
% 109.38/15.94 | | | | | | | | | | | | (1379) ~ (all_52_7 = e0)
% 109.38/15.94 | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | | REF_CLOSE: (4), (209), (243), (278), (298), (305), (323),
% 109.38/15.94 | | | | | | | | | | | | (352), (370), (407), (412), (413), (424), (450),
% 109.38/15.94 | | | | | | | | | | | | (552), (556), (558), (559), (561), (565), (566),
% 109.38/15.94 | | | | | | | | | | | | (567), (591), (848), (1344), (1345), (1348),
% 109.38/15.94 | | | | | | | | | | | | (1377), (1379), (function-axioms) are inconsistent
% 109.38/15.94 | | | | | | | | | | | | by sub-proof #67.
% 109.38/15.94 | | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | End of split
% 109.38/15.94 | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | Case 2:
% 109.38/15.94 | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | (1380) ~ (all_56_15 = e1)
% 109.38/15.94 | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | REDUCE: (1340), (1380) imply:
% 109.38/15.94 | | | | | | | | | | | (1381) $false
% 109.38/15.94 | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | | CLOSE: (1381) is inconsistent.
% 109.38/15.94 | | | | | | | | | | |
% 109.38/15.94 | | | | | | | | | | End of split
% 109.38/15.94 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | End of split
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | Case 2:
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | (1382) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | BETA: splitting (1382) gives:
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | (1383) ~ (all_48_1 = e1)
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | REDUCE: (846), (1383) imply:
% 109.38/15.95 | | | | | | | | | | (1384) $false
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | CLOSE: (1384) is inconsistent.
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | Case 2:
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | (1385) ~ (all_48_2 = e0)
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | REDUCE: (547), (1385) imply:
% 109.38/15.95 | | | | | | | | | | (1386) ~ (all_8_2 = e0)
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | REF_CLOSE: (4), (8), (9), (37), (41), (42), (52), (162),
% 109.38/15.95 | | | | | | | | | | (167), (172), (179), (180), (183), (184), (187),
% 109.38/15.95 | | | | | | | | | | (188), (190), (192), (193), (203), (207), (208),
% 109.38/15.95 | | | | | | | | | | (209), (211), (214), (233), (234), (235), (236),
% 109.38/15.95 | | | | | | | | | | (238), (241), (242), (243), (244), (247), (248),
% 109.38/15.95 | | | | | | | | | | (271), (272), (273), (274), (275), (276), (277),
% 109.38/15.95 | | | | | | | | | | (278), (279), (281), (282), (286), (287), (288),
% 109.38/15.95 | | | | | | | | | | (289), (290), (292), (294), (295), (296), (297),
% 109.38/15.95 | | | | | | | | | | (298), (299), (300), (301), (304), (305), (323),
% 109.38/15.95 | | | | | | | | | | (324), (329), (331), (335), (338), (340), (341),
% 109.38/15.95 | | | | | | | | | | (342), (346), (349), (352), (356), (362), (365),
% 109.38/15.95 | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 109.38/15.95 | | | | | | | | | | (407), (412), (413), (424), (426), (430), (434),
% 109.38/15.95 | | | | | | | | | | (436), (440), (446), (450), (458), (464), (466),
% 109.38/15.95 | | | | | | | | | | (468), (475), (477), (479), (530), (540), (551),
% 109.38/15.95 | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 109.38/15.95 | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 109.38/15.95 | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 109.38/15.95 | | | | | | | | | | (577), (579), (581), (582), (584), (585), (587),
% 109.38/15.95 | | | | | | | | | | (589), (591), (593), (594), (597), (599), (601),
% 109.38/15.95 | | | | | | | | | | (602), (604), (605), (661), (675), (848), (858),
% 109.38/15.95 | | | | | | | | | | (1318), (1321), (1386), (function-axioms) are
% 109.38/15.95 | | | | | | | | | | inconsistent by sub-proof #63.
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | End of split
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | End of split
% 109.38/15.95 | | | | | | | |
% 109.38/15.95 | | | | | | | End of split
% 109.38/15.95 | | | | | | |
% 109.38/15.95 | | | | | | End of split
% 109.38/15.95 | | | | | |
% 109.38/15.95 | | | | | End of split
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | Case 2:
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | | (1387) all_10_0 = e2
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | | COMBINE_EQS: (783), (1387) imply:
% 109.38/15.95 | | | | | (1388) all_50_0 = e2
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | | REDUCE: (53), (1387) imply:
% 109.38/15.95 | | | | | (1389) op(all_10_1, all_10_2) = e2
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | | BETA: splitting (93) gives:
% 109.38/15.95 | | | | |
% 109.38/15.95 | | | | | Case 1:
% 109.38/15.95 | | | | | |
% 109.38/15.95 | | | | | | (1390) ~ (all_26_0 = e1)
% 109.38/15.95 | | | | | |
% 109.38/15.95 | | | | | | REDUCE: (778), (1390) imply:
% 109.38/15.95 | | | | | | (1391) ~ (all_4_0 = e1)
% 109.38/15.95 | | | | | |
% 109.38/15.95 | | | | | | BETA: splitting (98) gives:
% 109.38/15.95 | | | | | |
% 109.38/15.95 | | | | | | Case 1:
% 109.38/15.95 | | | | | | |
% 109.38/15.95 | | | | | | | (1392) ~ (all_28_0 = e2)
% 109.38/15.95 | | | | | | |
% 109.38/15.95 | | | | | | | REDUCE: (758), (1392) imply:
% 109.38/15.95 | | | | | | | (1393) ~ (all_6_0 = e2)
% 109.38/15.95 | | | | | | |
% 109.38/15.95 | | | | | | | BETA: splitting (116) gives:
% 109.38/15.95 | | | | | | |
% 109.38/15.95 | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | |
% 109.38/15.95 | | | | | | | | (1394) ~ (all_36_1 = e3)
% 109.38/15.95 | | | | | | | |
% 109.38/15.95 | | | | | | | | REDUCE: (670), (1394) imply:
% 109.38/15.95 | | | | | | | | (1395) ~ (all_6_1 = e3)
% 109.38/15.95 | | | | | | | |
% 109.38/15.95 | | | | | | | | BETA: splitting (150) gives:
% 109.38/15.95 | | | | | | | |
% 109.38/15.95 | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | (1396) ~ (all_50_0 = e2)
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | REDUCE: (1388), (1396) imply:
% 109.38/15.95 | | | | | | | | | (1397) $false
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | CLOSE: (1397) is inconsistent.
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | Case 2:
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | (1398) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | BETA: splitting (270) gives:
% 109.38/15.95 | | | | | | | | |
% 109.38/15.95 | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | (1399) ~ (all_56_15 = e1)
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | REDUCE: (554), (1399) imply:
% 109.38/15.95 | | | | | | | | | | (1400) ~ (all_4_2 = e1)
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | BETA: splitting (272) gives:
% 109.38/15.95 | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | (1401) ~ (all_56_12 = e1)
% 109.38/15.95 | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | REDUCE: (426), (1401) imply:
% 109.38/15.95 | | | | | | | | | | | (1402) ~ (all_10_2 = e1)
% 109.38/15.95 | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | BETA: splitting (271) gives:
% 109.38/15.95 | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | (1403) ~ (all_56_13 = e1)
% 109.38/15.95 | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | REDUCE: (556), (1403) imply:
% 109.38/15.95 | | | | | | | | | | | | (1404) ~ (all_8_2 = e1)
% 109.38/15.95 | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | BETA: splitting (273) gives:
% 109.38/15.95 | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | (1405) ~ (all_56_15 = e2)
% 109.38/15.95 | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | REDUCE: (554), (1405) imply:
% 109.38/15.95 | | | | | | | | | | | | | (1406) ~ (all_4_2 = e2)
% 109.38/15.95 | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | BETA: splitting (233) gives:
% 109.38/15.95 | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | (1407) all_54_15 = e3
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | COMBINE_EQS: (356), (1407) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1408) all_4_2 = e3
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | SIMP: (1408) implies:
% 109.38/15.95 | | | | | | | | | | | | | | (1409) all_4_2 = e3
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | COMBINE_EQS: (554), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1410) all_56_15 = e3
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | COMBINE_EQS: (557), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1411) all_58_15 = e3
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (584), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1412) ~ (all_52_3 = e3)
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (595), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1413) ~ (all_52_7 = e3)
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (602), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1414) ~ (all_52_11 = e3)
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (603), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1415) ~ (all_52_12 = e3)
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (38), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1416) op(all_4_1, e3) = all_4_0
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | REDUCE: (37), (1409) imply:
% 109.38/15.95 | | | | | | | | | | | | | | (1417) op(e0, e3) = all_4_1
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 109.38/15.95 | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | (1418) ~ (all_56_15 = e3)
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | REDUCE: (1410), (1418) imply:
% 109.38/15.95 | | | | | | | | | | | | | | | (1419) $false
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | CLOSE: (1419) is inconsistent.
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | Case 2:
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | (1420) ~ (all_56_9 = e0)
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | REDUCE: (450), (1420) imply:
% 109.38/15.95 | | | | | | | | | | | | | | | (1421) ~ (all_52_3 = e0)
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 109.38/15.95 | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | Case 1:
% 109.38/15.95 | | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | | (1422) ~ (all_56_3 = e2)
% 109.38/15.95 | | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | | REDUCE: (430), (1422) imply:
% 109.38/15.95 | | | | | | | | | | | | | | | | (1423) ~ (all_52_1 = e2)
% 109.38/15.95 | | | | | | | | | | | | | | | |
% 109.38/15.95 | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 109.38/15.95 | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1424) ~ (all_56_6 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | REDUCE: (386), (1424) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1425) ~ (all_52_2 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 109.38/15.96 | | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (1417)
% 109.38/15.96 | | | | | | | | | | | | | | | | | gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1426) all_52_3 = all_4_1
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1427) all_54_12 = all_4_1
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1428) all_58_12 = all_4_1
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | REDUCE: (192), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1429) ~ (all_52_1 = all_4_1)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | REDUCE: (575), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1430) ~ (all_10_2 = all_4_1)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | SIMP: (1430) implies:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1431) ~ (all_10_2 = all_4_1)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | REDUCE: (1412), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1432) ~ (all_4_1 = e3)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | REDUCE: (1421), (1426) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | (1433) ~ (all_4_1 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1434) ~ (all_56_7 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | REDUCE: (440), (1434) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1435) ~ (all_52_6 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (208), (211), (236), (241), (243), (244),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (248), (281), (289), (331), (338), (346), (371),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (385), (391), (394), (406), (424), (426), (446),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (464), (468), (552), (553), (556), (560), (562),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (563), (564), (566), (567), (568), (571), (582),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (591), (593), (848), (1402), (1404), (1425),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1427), (1429), (1431), (1432), (1433), (1435),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.38/15.96 | | | | | | | | | | | | | | | | | | #61.
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1436) all_56_7 = e1
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (440), (1436) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1437) all_52_6 = e1
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | REDUCE: (172), (1437) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1438) ~ (all_52_7 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | SIMP: (1438) implies:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1439) ~ (all_52_7 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | REDUCE: (594), (1437) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | (1440) ~ (all_6_2 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | (1441) ~ (all_56_7 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | REDUCE: (1436), (1441) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | (1442) $false
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | CLOSE: (1442) is inconsistent.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | (1443) ~ (all_56_14 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | REDUCE: (555), (1443) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | (1444) ~ (all_6_2 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | (1445) all_54_0 = e3
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (1445) are inconsistent by sub-proof
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | #451.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | (1446) ~ (all_54_0 = e3)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | (1447) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1447) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (1448) all_54_0 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (204), (237), (238), (279), (305), (352),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (371), (412), (413), (424), (426), (474), (551),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (553), (555), (561), (565), (566), (568), (579),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (596), (601), (785), (1395), (1415), (1444),
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (1448), (function-axioms) are inconsistent by
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | sub-proof #202.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (1449) ~ (all_54_0 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (1450) all_54_0 = e1 | all_54_0 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (1449) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | (1451) ~ (all_10_2 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1452) all_54_0 = e1
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (1402), (1452) are inconsistent by
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | sub-proof #449.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1453) all_54_0 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1453) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1454) all_10_2 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1454) implies:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1455) all_10_2 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (548), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1456) all_50_2 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1457) all_58_0 = e0
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1458) ~ (all_52_1 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1459) ~ (all_52_4 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1460) ~ (all_52_8 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1461) ~ (all_52_12 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1451), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1462) ~ (e2 = e0)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1389), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1463) op(all_10_1, e0) = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1455) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | (1464) op(e3, e0) = all_10_1
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | (1465) all_58_2 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (1423), (1465) are inconsistent by
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | (1466) ~ (all_58_2 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | (1467) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1398) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | (1468) ~ (all_50_1 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (705), (1468) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | (1469) ~ (all_10_1 = e1)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_58_3 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (1470) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_8_2 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1471) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1472) $false
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1472) is inconsistent.
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1473) ~ (all_58_3 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_58_5 = e2 | all_58_10 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1474) gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) all_58_5 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1475) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_52_9 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1476) implies:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_52_9 = e2
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (1477) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) ~ (all_52_8 = e2)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_1, e0, e3, simplifying with (212), (1464)
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) all_52_12 = all_10_1
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (462), (1479) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) all_54_3 = all_10_1
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (1479) imply:
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_58_9 = all_10_1
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (1479) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) ~ (all_52_4 = all_10_1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (1479) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) ~ (all_52_8 = all_10_1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (1479) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) ~ (all_52_13 = all_10_1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1484) implies:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) ~ (all_52_13 = all_10_1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1415), (1479) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) ~ (all_10_1 = e3)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1461), (1479) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) ~ (all_10_1 = e0)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_54_3 = e3
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1480), (1486), (1488) are inconsistent by
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #215.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) all_58_9 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1481), (1490) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_10_1 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1469), (1491) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) $false
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1492) is inconsistent.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1493) gives:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_58_10 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (1494) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_52_13 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1485), (1495) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) ~ (all_10_1 = e1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (1495) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) ~ (all_8_2 = e1)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (1495) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) op(e2, e0) = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1489) gives:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_54_3 = e2
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1480), (1499) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_10_1 = e2
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1500) implies:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_10_1 = e2
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1463), (1501) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) op(e2, e0) = e2
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1498), (1502), (function-axioms) are
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #170.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_54_3 = e1 | all_54_3 = e0
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (178), (179), (211), (235), (243), (244),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (349), (350), (351), (406), (458),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460), (464), (477), (552), (565), (582), (585),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589), (1391), (1404), (1413), (1416), (1423),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428), (1432), (1439), (1457), (1458), (1459),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460), (1478), (1480), (1482), (1483), (1487),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503), (function-axioms) are inconsistent by
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #206.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) all_58_11 = e1 | all_58_15 = e1
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (281), (371), (426), (553), (560), (1402),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411), (1447), (1451), (1504) are inconsistent by
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #369.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_58_10 = e2
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (167), (169), (183), (184), (188), (189),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (192), (193), (203), (209), (211), (234),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (238), (240), (243), (244), (246),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (272), (274), (281), (288), (289), (293),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (302), (331), (334), (338), (339), (340), (341),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (349), (351), (362), (365), (370), (371), (385),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (394), (406), (412), (424), (426), (434),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (436), (446), (460), (464), (470), (475), (477),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (479), (551), (552), (553), (555), (556), (560),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (562), (563), (564), (566), (567), (568), (571),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (573), (575), (582), (583), (587), (589), (591),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (593), (597), (599), (848), (1391), (1412),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1413), (1414), (1416), (1417), (1421), (1423),
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1425), (1451), (1505), (function-axioms) are
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | (1506) ~ (all_50_2 = e0)
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1456), (1506) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | (1507) $false
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1507) is inconsistent.
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | (1508) ~ (all_56_15 = e3)
% 109.38/15.97 | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | REDUCE: (1410), (1508) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | | (1509) $false
% 109.38/15.97 | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | | CLOSE: (1509) is inconsistent.
% 109.38/15.97 | | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | (1510) ~ (all_56_15 = e3)
% 109.38/15.97 | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | REDUCE: (1410), (1510) imply:
% 109.38/15.97 | | | | | | | | | | | | | | | | (1511) $false
% 109.38/15.97 | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | | CLOSE: (1511) is inconsistent.
% 109.38/15.97 | | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | (1512) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 109.38/15.97 | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (1400), (1406), (1512) are
% 109.38/15.97 | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 109.38/15.97 | | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | End of split
% 109.38/15.97 | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | Case 2:
% 109.38/15.97 | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | (1513) all_56_15 = e2
% 109.38/15.97 | | | | | | | | | | | | | (1514) ~ (all_56_10 = e0)
% 109.38/15.97 | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | COMBINE_EQS: (554), (1513) imply:
% 109.38/15.97 | | | | | | | | | | | | | (1515) all_4_2 = e2
% 109.38/15.97 | | | | | | | | | | | | |
% 109.38/15.97 | | | | | | | | | | | | | SIMP: (1515) implies:
% 109.38/15.98 | | | | | | | | | | | | | (1516) all_4_2 = e2
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | | REDUCE: (365), (1514) imply:
% 109.38/15.98 | | | | | | | | | | | | | (1517) ~ (all_52_7 = e0)
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | | REDUCE: (602), (1516) imply:
% 109.38/15.98 | | | | | | | | | | | | | (1518) ~ (all_52_11 = e2)
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | | REDUCE: (603), (1516) imply:
% 109.38/15.98 | | | | | | | | | | | | | (1519) ~ (all_52_12 = e2)
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | | REDUCE: (604), (1516) imply:
% 109.38/15.98 | | | | | | | | | | | | | (1520) ~ (all_52_13 = e2)
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (42), (52), (156), (162), (165),
% 109.38/15.98 | | | | | | | | | | | | | (167), (169), (170), (172), (177), (178), (179),
% 109.38/15.98 | | | | | | | | | | | | | (180), (185), (187), (188), (190), (192), (193),
% 109.38/15.98 | | | | | | | | | | | | | (202), (204), (208), (209), (211), (214), (233),
% 109.38/15.98 | | | | | | | | | | | | | (235), (236), (237), (238), (240), (243), (244),
% 109.38/15.98 | | | | | | | | | | | | | (245), (246), (247), (248), (270), (271), (276),
% 109.38/15.98 | | | | | | | | | | | | | (277), (278), (279), (282), (287), (288), (289),
% 109.38/15.98 | | | | | | | | | | | | | (292), (294), (296), (298), (299), (300), (301),
% 109.38/15.98 | | | | | | | | | | | | | (303), (305), (323), (324), (326), (327), (331),
% 109.38/15.98 | | | | | | | | | | | | | (332), (338), (339), (340), (341), (342), (344),
% 109.38/15.98 | | | | | | | | | | | | | (346), (347), (352), (356), (362), (370), (371),
% 109.38/15.98 | | | | | | | | | | | | | (385), (386), (391), (394), (406), (407), (412),
% 109.38/15.98 | | | | | | | | | | | | | (413), (424), (426), (430), (434), (436), (440),
% 109.38/15.98 | | | | | | | | | | | | | (446), (450), (458), (460), (462), (464), (470),
% 109.38/15.98 | | | | | | | | | | | | | (474), (475), (477), (551), (552), (553), (554),
% 109.38/15.98 | | | | | | | | | | | | | (555), (556), (557), (558), (559), (560), (561),
% 109.38/15.98 | | | | | | | | | | | | | (562), (563), (564), (565), (566), (567), (568),
% 109.38/15.98 | | | | | | | | | | | | | (569), (571), (573), (577), (579), (581), (582),
% 109.38/15.98 | | | | | | | | | | | | | (583), (584), (585), (589), (591), (593), (594),
% 109.38/15.98 | | | | | | | | | | | | | (596), (597), (601), (602), (603), (604), (605),
% 109.38/15.98 | | | | | | | | | | | | | (785), (848), (1389), (1395), (1402), (1513),
% 109.38/15.98 | | | | | | | | | | | | | (1517), (1518), (1519), (1520), (function-axioms)
% 109.38/15.98 | | | | | | | | | | | | | are inconsistent by sub-proof #55.
% 109.38/15.98 | | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | End of split
% 109.38/15.98 | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | Case 2:
% 109.38/15.98 | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | (1521) all_56_13 = e1
% 109.38/15.98 | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | COMBINE_EQS: (556), (1521) imply:
% 109.38/15.98 | | | | | | | | | | | | (1522) all_8_2 = e1
% 109.38/15.98 | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | | REF_CLOSE: (209), (591), (848), (1522), (function-axioms) are
% 109.38/15.98 | | | | | | | | | | | | inconsistent by sub-proof #109.
% 109.38/15.98 | | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | End of split
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | Case 2:
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | (1523) all_56_12 = e1
% 109.38/15.98 | | | | | | | | | | | (1524) ~ (all_56_11 = e0)
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | COMBINE_EQS: (426), (1523) imply:
% 109.38/15.98 | | | | | | | | | | | (1525) all_10_2 = e1
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | SIMP: (1525) implies:
% 109.38/15.98 | | | | | | | | | | | (1526) all_10_2 = e1
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 109.38/15.98 | | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 109.38/15.98 | | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 109.38/15.98 | | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 109.38/15.98 | | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 109.38/15.98 | | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 109.38/15.98 | | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 109.38/15.98 | | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 109.38/15.98 | | | | | | | | | | | (589), (591), (593), (602), (603), (604), (848),
% 109.38/15.98 | | | | | | | | | | | (1400), (1523), (1524), (1526), (function-axioms)
% 109.38/15.98 | | | | | | | | | | | are inconsistent by sub-proof #74.
% 109.38/15.98 | | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | End of split
% 109.38/15.98 | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | Case 2:
% 109.38/15.98 | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | (1527) all_56_15 = e1
% 109.38/15.98 | | | | | | | | | | (1528) ~ (all_56_11 = e0)
% 109.38/15.98 | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | | REF_CLOSE: (42), (189), (190), (204), (209), (211), (237),
% 109.38/15.98 | | | | | | | | | | (238), (243), (244), (248), (274), (278), (284),
% 109.38/15.98 | | | | | | | | | | (286), (288), (289), (290), (291), (295), (298),
% 109.38/15.98 | | | | | | | | | | (300), (304), (323), (331), (335), (338), (340),
% 109.38/15.98 | | | | | | | | | | (352), (362), (365), (370), (385), (386), (391),
% 109.38/15.98 | | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 109.38/15.98 | | | | | | | | | | (430), (434), (436), (440), (446), (450), (464),
% 109.38/15.98 | | | | | | | | | | (474), (551), (552), (553), (554), (555), (556),
% 109.38/15.98 | | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 109.38/15.98 | | | | | | | | | | (564), (565), (566), (567), (568), (569), (571),
% 109.38/15.98 | | | | | | | | | | (579), (582), (591), (593), (601), (602), (605),
% 109.38/15.98 | | | | | | | | | | (785), (848), (1395), (1527), (1528),
% 109.38/15.98 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.38/15.98 | | | | | | | | | | #54.
% 109.38/15.98 | | | | | | | | | |
% 109.38/15.98 | | | | | | | | | End of split
% 109.38/15.98 | | | | | | | | |
% 109.38/15.98 | | | | | | | | End of split
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | Case 2:
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | (1529) all_36_1 = e3
% 109.38/15.98 | | | | | | | | (1530) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | COMBINE_EQS: (670), (1529) imply:
% 109.38/15.98 | | | | | | | | (1531) all_6_1 = e3
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | SIMP: (1531) implies:
% 109.38/15.98 | | | | | | | | (1532) all_6_1 = e3
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | REDUCE: (43), (1532) imply:
% 109.38/15.98 | | | | | | | | (1533) op(e3, all_6_2) = all_6_0
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | REDUCE: (42), (1532) imply:
% 109.38/15.98 | | | | | | | | (1534) op(e1, all_6_2) = e3
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | BETA: splitting (145) gives:
% 109.38/15.98 | | | | | | | |
% 109.38/15.98 | | | | | | | | Case 1:
% 109.38/15.98 | | | | | | | | |
% 109.38/15.98 | | | | | | | | | (1535) ~ (all_48_0 = e3)
% 109.38/15.98 | | | | | | | | |
% 109.38/15.98 | | | | | | | | | REDUCE: (782), (1535) imply:
% 109.38/15.98 | | | | | | | | | (1536) ~ (all_8_0 = e3)
% 109.38/15.98 | | | | | | | | |
% 109.38/15.99 | | | | | | | | | BETA: splitting (274) gives:
% 109.38/15.99 | | | | | | | | |
% 109.38/15.99 | | | | | | | | | Case 1:
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | (1537) ~ (all_56_14 = e2)
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | REDUCE: (555), (1537) imply:
% 109.38/15.99 | | | | | | | | | | (1538) ~ (all_6_2 = e2)
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | BETA: splitting (275) gives:
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | Case 1:
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | (1539) ~ (all_56_12 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REF_CLOSE: (9), (37), (38), (41), (157), (165), (167), (169),
% 109.38/15.99 | | | | | | | | | | | (172), (178), (179), (180), (183), (184), (185),
% 109.38/15.99 | | | | | | | | | | | (187), (188), (189), (190), (192), (193), (203),
% 109.38/15.99 | | | | | | | | | | | (204), (207), (208), (209), (211), (233), (234),
% 109.38/15.99 | | | | | | | | | | | (235), (236), (238), (240), (241), (242), (243),
% 109.38/15.99 | | | | | | | | | | | (244), (246), (248), (270), (272), (273), (274),
% 109.38/15.99 | | | | | | | | | | | (276), (277), (279), (280), (281), (282), (285),
% 109.38/15.99 | | | | | | | | | | | (286), (287), (288), (289), (291), (292), (293),
% 109.38/15.99 | | | | | | | | | | | (294), (295), (297), (298), (299), (300), (302),
% 109.38/15.99 | | | | | | | | | | | (323), (324), (329), (331), (332), (334), (335),
% 109.38/15.99 | | | | | | | | | | | (338), (339), (340), (341), (345), (347), (349),
% 109.38/15.99 | | | | | | | | | | | (351), (352), (356), (362), (365), (370), (371),
% 109.38/15.99 | | | | | | | | | | | (385), (386), (391), (394), (406), (407), (412),
% 109.38/15.99 | | | | | | | | | | | (424), (426), (430), (434), (436), (440), (446),
% 109.38/15.99 | | | | | | | | | | | (450), (460), (464), (466), (468), (470), (475),
% 109.38/15.99 | | | | | | | | | | | (477), (479), (551), (552), (553), (554), (555),
% 109.38/15.99 | | | | | | | | | | | (556), (557), (558), (559), (560), (561), (562),
% 109.38/15.99 | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 109.38/15.99 | | | | | | | | | | | (571), (573), (575), (579), (581), (582), (583),
% 109.38/15.99 | | | | | | | | | | | (584), (585), (587), (589), (591), (593), (594),
% 109.38/15.99 | | | | | | | | | | | (595), (597), (599), (601), (602), (603), (605),
% 109.38/15.99 | | | | | | | | | | | (847), (848), (1391), (1534), (1538), (1539),
% 109.38/15.99 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.38/15.99 | | | | | | | | | | | #68.
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | Case 2:
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | (1540) all_56_12 = e2
% 109.38/15.99 | | | | | | | | | | | (1541) ~ (all_56_10 = e0)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | COMBINE_EQS: (426), (1540) imply:
% 109.38/15.99 | | | | | | | | | | | (1542) all_10_2 = e2
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | SIMP: (1542) implies:
% 109.38/15.99 | | | | | | | | | | | (1543) all_10_2 = e2
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | COMBINE_EQS: (424), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1544) all_58_0 = e2
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (365), (1541) imply:
% 109.38/15.99 | | | | | | | | | | | (1545) ~ (all_52_7 = e0)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (571), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1546) ~ (all_52_1 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (573), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1547) ~ (all_52_2 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (577), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1548) ~ (all_52_4 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (579), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1549) ~ (all_52_8 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (566), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1550) ~ (e3 = e2)
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (1389), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1551) op(all_10_1, e2) = e2
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REDUCE: (52), (1543) imply:
% 109.38/15.99 | | | | | | | | | | | (1552) op(e3, e2) = all_10_1
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (165), (169), (170), (172), (179),
% 109.38/15.99 | | | | | | | | | | | (184), (185), (187), (188), (190), (192), (193),
% 109.38/15.99 | | | | | | | | | | | (202), (209), (214), (233), (236), (238), (240),
% 109.38/15.99 | | | | | | | | | | | (243), (244), (246), (270), (271), (277), (278),
% 109.38/15.99 | | | | | | | | | | | (280), (284), (285), (286), (287), (288), (291),
% 109.38/15.99 | | | | | | | | | | | (292), (298), (305), (323), (324), (326), (327),
% 109.38/15.99 | | | | | | | | | | | (331), (332), (339), (340), (342), (343), (344),
% 109.38/15.99 | | | | | | | | | | | (347), (352), (356), (362), (370), (371), (385),
% 109.38/15.99 | | | | | | | | | | | (386), (391), (394), (406), (407), (412), (413),
% 109.38/15.99 | | | | | | | | | | | (436), (440), (446), (450), (460), (464), (470),
% 109.38/15.99 | | | | | | | | | | | (475), (551), (552), (554), (555), (556), (557),
% 109.38/15.99 | | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 109.38/15.99 | | | | | | | | | | | (565), (567), (568), (569), (582), (583), (584),
% 109.38/15.99 | | | | | | | | | | | (585), (587), (591), (594), (595), (596), (599),
% 109.38/15.99 | | | | | | | | | | | (602), (603), (604), (605), (847), (848), (1534),
% 109.38/15.99 | | | | | | | | | | | (1536), (1538), (1540), (1544), (1545), (1546),
% 109.38/15.99 | | | | | | | | | | | (1547), (1548), (1549), (1551), (1552),
% 109.38/15.99 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.38/15.99 | | | | | | | | | | | #49.
% 109.38/15.99 | | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | End of split
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | Case 2:
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | (1553) all_56_14 = e2
% 109.38/15.99 | | | | | | | | | |
% 109.38/15.99 | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 109.38/15.99 | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 109.38/15.99 | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 109.38/15.99 | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 109.38/16.00 | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 109.38/16.00 | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 109.38/16.00 | | | | | | | | | | (589), (595), (597), (780), (1393), (1530),
% 109.38/16.00 | | | | | | | | | | (1533), (1534), (1553), (function-axioms) are
% 109.38/16.00 | | | | | | | | | | inconsistent by sub-proof #306.
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | End of split
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | Case 2:
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | | (1554) all_48_0 = e3
% 109.38/16.00 | | | | | | | | | (1555) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | | COMBINE_EQS: (782), (1554) imply:
% 109.38/16.00 | | | | | | | | | (1556) all_8_0 = e3
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | | REDUCE: (847), (1556) imply:
% 109.38/16.00 | | | | | | | | | (1557) op(e1, all_8_2) = e3
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | | BETA: splitting (1555) gives:
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | | Case 1:
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | (1558) ~ (all_48_1 = e1)
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | REDUCE: (846), (1558) imply:
% 109.38/16.00 | | | | | | | | | | (1559) $false
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | CLOSE: (1559) is inconsistent.
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | Case 2:
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | (1560) ~ (all_48_2 = e0)
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | REDUCE: (547), (1560) imply:
% 109.38/16.00 | | | | | | | | | | (1561) ~ (all_8_2 = e0)
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | BETA: splitting (274) gives:
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | Case 1:
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | | (1562) ~ (all_56_14 = e2)
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | | REDUCE: (555), (1562) imply:
% 109.38/16.00 | | | | | | | | | | | (1563) ~ (all_6_2 = e2)
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | | REF_CLOSE: (6), (37), (38), (41), (52), (154), (156), (161),
% 109.38/16.00 | | | | | | | | | | | (165), (167), (169), (170), (172), (177), (179),
% 109.38/16.00 | | | | | | | | | | | (180), (183), (184), (185), (187), (188), (189),
% 109.38/16.00 | | | | | | | | | | | (190), (192), (193), (202), (203), (209), (211),
% 109.38/16.00 | | | | | | | | | | | (214), (233), (234), (235), (236), (237), (238),
% 109.38/16.00 | | | | | | | | | | | (240), (242), (243), (244), (245), (246), (247),
% 109.38/16.00 | | | | | | | | | | | (248), (270), (271), (272), (274), (275), (276),
% 109.38/16.00 | | | | | | | | | | | (277), (278), (279), (281), (282), (284), (285),
% 109.38/16.00 | | | | | | | | | | | (287), (288), (290), (291), (292), (293), (294),
% 109.38/16.00 | | | | | | | | | | | (295), (296), (298), (302), (305), (323), (324),
% 109.38/16.00 | | | | | | | | | | | (326), (327), (329), (331), (332), (334), (335),
% 109.38/16.00 | | | | | | | | | | | (338), (339), (340), (341), (342), (344), (346),
% 109.38/16.00 | | | | | | | | | | | (347), (349), (351), (352), (356), (362), (365),
% 109.38/16.00 | | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 109.38/16.00 | | | | | | | | | | | (407), (412), (413), (424), (426), (430), (434),
% 109.38/16.00 | | | | | | | | | | | (436), (440), (446), (450), (458), (460), (462),
% 109.38/16.00 | | | | | | | | | | | (464), (466), (470), (474), (475), (477), (479),
% 109.38/16.00 | | | | | | | | | | | (551), (552), (553), (554), (555), (556), (557),
% 109.38/16.00 | | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 109.38/16.00 | | | | | | | | | | | (565), (566), (567), (568), (569), (571), (573),
% 109.38/16.00 | | | | | | | | | | | (575), (577), (579), (581), (582), (583), (584),
% 109.38/16.00 | | | | | | | | | | | (585), (587), (589), (591), (593), (594), (595),
% 109.38/16.00 | | | | | | | | | | | (596), (597), (599), (601), (602), (603), (604),
% 109.38/16.00 | | | | | | | | | | | (605), (848), (1389), (1391), (1557), (1561),
% 109.38/16.00 | | | | | | | | | | | (1563), (function-axioms) are inconsistent by
% 109.38/16.00 | | | | | | | | | | | sub-proof #48.
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | Case 2:
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | | (1564) all_56_14 = e2
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 109.38/16.00 | | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 109.38/16.00 | | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 109.38/16.00 | | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 109.38/16.00 | | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 109.38/16.00 | | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 109.38/16.00 | | | | | | | | | | | (589), (595), (597), (780), (1393), (1530),
% 109.38/16.00 | | | | | | | | | | | (1533), (1534), (1564), (function-axioms) are
% 109.38/16.00 | | | | | | | | | | | inconsistent by sub-proof #306.
% 109.38/16.00 | | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | | End of split
% 109.38/16.00 | | | | | | | | | |
% 109.38/16.00 | | | | | | | | | End of split
% 109.38/16.00 | | | | | | | | |
% 109.38/16.00 | | | | | | | | End of split
% 109.38/16.00 | | | | | | | |
% 109.38/16.00 | | | | | | | End of split
% 109.38/16.00 | | | | | | |
% 109.38/16.00 | | | | | | Case 2:
% 109.38/16.00 | | | | | | |
% 109.38/16.00 | | | | | | | (1565) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 109.38/16.00 | | | | | | |
% 109.76/16.01 | | | | | | | REF_CLOSE: (4), (8), (37), (42), (52), (150), (157), (162), (165),
% 109.76/16.01 | | | | | | | (167), (169), (170), (172), (179), (185), (188), (189),
% 109.76/16.01 | | | | | | | (190), (192), (193), (202), (204), (208), (209), (211),
% 109.76/16.01 | | | | | | | (212), (214), (233), (236), (237), (238), (240), (243),
% 109.76/16.01 | | | | | | | (244), (245), (246), (248), (270), (271), (272), (273),
% 109.76/16.01 | | | | | | | (274), (275), (276), (277), (278), (279), (281), (284),
% 109.76/16.01 | | | | | | | (286), (287), (288), (289), (290), (291), (292), (293),
% 109.76/16.01 | | | | | | | (294), (295), (296), (298), (299), (300), (301), (302),
% 109.76/16.01 | | | | | | | (303), (304), (305), (323), (324), (326), (327), (331),
% 109.76/16.01 | | | | | | | (332), (335), (338), (339), (340), (341), (342), (344),
% 109.76/16.01 | | | | | | | (347), (352), (356), (362), (365), (370), (371), (385),
% 109.76/16.01 | | | | | | | (386), (391), (394), (406), (407), (412), (413), (424),
% 109.76/16.01 | | | | | | | (426), (430), (434), (436), (440), (446), (450), (460),
% 109.76/16.01 | | | | | | | (462), (464), (470), (474), (475), (522), (548), (551),
% 109.76/16.01 | | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 109.76/16.01 | | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 109.76/16.01 | | | | | | | (568), (569), (571), (573), (577), (579), (581), (582),
% 109.76/16.01 | | | | | | | (583), (584), (585), (589), (591), (593), (594), (596),
% 109.76/16.01 | | | | | | | (597), (599), (601), (602), (603), (604), (605), (683),
% 109.76/16.01 | | | | | | | (705), (785), (848), (1388), (1389), (1565),
% 109.76/16.01 | | | | | | | (function-axioms) are inconsistent by sub-proof #47.
% 109.76/16.01 | | | | | | |
% 109.76/16.01 | | | | | | End of split
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | Case 2:
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | (1566) all_26_0 = e1
% 109.76/16.01 | | | | | | (1567) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | COMBINE_EQS: (778), (1566) imply:
% 109.76/16.01 | | | | | | (1568) all_4_0 = e1
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | COMBINE_EQS: (727), (1568) imply:
% 109.76/16.01 | | | | | | (1569) all_44_0 = e1
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | REDUCE: (784), (1568) imply:
% 109.76/16.01 | | | | | | (1570) ~ (e3 = e1)
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | REDUCE: (38), (1568) imply:
% 109.76/16.01 | | | | | | (1571) op(all_4_1, all_4_2) = e1
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | BETA: splitting (98) gives:
% 109.76/16.01 | | | | | |
% 109.76/16.01 | | | | | | Case 1:
% 109.76/16.01 | | | | | | |
% 109.76/16.01 | | | | | | | (1572) ~ (all_28_0 = e2)
% 109.76/16.01 | | | | | | |
% 109.76/16.01 | | | | | | | REDUCE: (758), (1572) imply:
% 109.76/16.01 | | | | | | | (1573) ~ (all_6_0 = e2)
% 109.76/16.01 | | | | | | |
% 109.76/16.01 | | | | | | | BETA: splitting (116) gives:
% 109.76/16.01 | | | | | | |
% 109.76/16.01 | | | | | | | Case 1:
% 109.76/16.01 | | | | | | | |
% 109.76/16.01 | | | | | | | | (1574) ~ (all_36_1 = e3)
% 109.76/16.01 | | | | | | | |
% 109.76/16.01 | | | | | | | | REDUCE: (670), (1574) imply:
% 109.76/16.01 | | | | | | | | (1575) ~ (all_6_1 = e3)
% 109.76/16.01 | | | | | | | |
% 109.76/16.01 | | | | | | | | BETA: splitting (270) gives:
% 109.76/16.01 | | | | | | | |
% 109.76/16.01 | | | | | | | | Case 1:
% 109.76/16.01 | | | | | | | | |
% 109.76/16.01 | | | | | | | | | (1576) ~ (all_56_15 = e1)
% 109.76/16.01 | | | | | | | | |
% 109.76/16.01 | | | | | | | | | REDUCE: (554), (1576) imply:
% 109.76/16.01 | | | | | | | | | (1577) ~ (all_4_2 = e1)
% 109.76/16.01 | | | | | | | | |
% 109.76/16.01 | | | | | | | | | BETA: splitting (272) gives:
% 109.76/16.01 | | | | | | | | |
% 109.76/16.01 | | | | | | | | | Case 1:
% 109.76/16.01 | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | (1578) ~ (all_56_12 = e1)
% 109.76/16.01 | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | REDUCE: (426), (1578) imply:
% 109.76/16.01 | | | | | | | | | | (1579) ~ (all_10_2 = e1)
% 109.76/16.01 | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | BETA: splitting (273) gives:
% 109.76/16.01 | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | Case 1:
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | (1580) ~ (all_56_15 = e2)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REDUCE: (554), (1580) imply:
% 109.76/16.01 | | | | | | | | | | | (1581) ~ (all_4_2 = e2)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REF_CLOSE: (37), (188), (203), (207), (233), (236), (276),
% 109.76/16.01 | | | | | | | | | | | (356), (450), (475), (540), (554), (569), (584),
% 109.76/16.01 | | | | | | | | | | | (675), (1567), (1571), (1577), (1581),
% 109.76/16.01 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.76/16.01 | | | | | | | | | | | #236.
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | Case 2:
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | (1582) all_56_15 = e2
% 109.76/16.01 | | | | | | | | | | | (1583) ~ (all_56_10 = e0)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | COMBINE_EQS: (554), (1582) imply:
% 109.76/16.01 | | | | | | | | | | | (1584) all_4_2 = e2
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | SIMP: (1584) implies:
% 109.76/16.01 | | | | | | | | | | | (1585) all_4_2 = e2
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REDUCE: (365), (1583) imply:
% 109.76/16.01 | | | | | | | | | | | (1586) ~ (all_52_7 = e0)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REDUCE: (602), (1585) imply:
% 109.76/16.01 | | | | | | | | | | | (1587) ~ (all_52_11 = e2)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REDUCE: (603), (1585) imply:
% 109.76/16.01 | | | | | | | | | | | (1588) ~ (all_52_12 = e2)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.01 | | | | | | | | | | | REDUCE: (604), (1585) imply:
% 109.76/16.01 | | | | | | | | | | | (1589) ~ (all_52_13 = e2)
% 109.76/16.01 | | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | | REF_CLOSE: (4), (8), (37), (42), (52), (156), (162), (165),
% 109.76/16.02 | | | | | | | | | | | (167), (169), (170), (172), (177), (178), (179),
% 109.76/16.02 | | | | | | | | | | | (180), (185), (187), (188), (190), (192), (193),
% 109.76/16.02 | | | | | | | | | | | (202), (204), (208), (209), (211), (214), (233),
% 109.76/16.02 | | | | | | | | | | | (235), (236), (237), (238), (240), (243), (244),
% 109.76/16.02 | | | | | | | | | | | (245), (246), (247), (248), (270), (271), (276),
% 109.76/16.02 | | | | | | | | | | | (277), (278), (279), (282), (287), (288), (289),
% 109.76/16.02 | | | | | | | | | | | (292), (294), (296), (298), (299), (300), (301),
% 109.76/16.02 | | | | | | | | | | | (303), (305), (323), (324), (326), (327), (331),
% 109.76/16.02 | | | | | | | | | | | (332), (338), (339), (340), (341), (342), (344),
% 109.76/16.02 | | | | | | | | | | | (346), (347), (352), (356), (362), (370), (371),
% 109.76/16.02 | | | | | | | | | | | (385), (386), (391), (394), (406), (407), (412),
% 109.76/16.02 | | | | | | | | | | | (413), (424), (426), (430), (434), (436), (440),
% 109.76/16.02 | | | | | | | | | | | (446), (450), (458), (460), (462), (464), (470),
% 109.76/16.02 | | | | | | | | | | | (474), (475), (477), (551), (552), (553), (554),
% 109.76/16.02 | | | | | | | | | | | (555), (556), (557), (558), (559), (560), (561),
% 109.76/16.02 | | | | | | | | | | | (562), (563), (564), (565), (566), (567), (568),
% 109.76/16.02 | | | | | | | | | | | (569), (571), (573), (577), (579), (581), (582),
% 109.76/16.02 | | | | | | | | | | | (583), (584), (585), (589), (591), (593), (594),
% 109.76/16.02 | | | | | | | | | | | (596), (597), (601), (602), (603), (604), (605),
% 109.76/16.02 | | | | | | | | | | | (785), (848), (1389), (1575), (1579), (1582),
% 109.76/16.02 | | | | | | | | | | | (1586), (1587), (1588), (1589), (function-axioms)
% 109.76/16.02 | | | | | | | | | | | are inconsistent by sub-proof #55.
% 109.76/16.02 | | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | End of split
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | Case 2:
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | (1590) all_56_12 = e1
% 109.76/16.02 | | | | | | | | | | (1591) ~ (all_56_11 = e0)
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | COMBINE_EQS: (426), (1590) imply:
% 109.76/16.02 | | | | | | | | | | (1592) all_10_2 = e1
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | SIMP: (1592) implies:
% 109.76/16.02 | | | | | | | | | | (1593) all_10_2 = e1
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 109.76/16.02 | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 109.76/16.02 | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 109.76/16.02 | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 109.76/16.02 | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 109.76/16.02 | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 109.76/16.02 | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 109.76/16.02 | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 109.76/16.02 | | | | | | | | | | (589), (591), (593), (602), (603), (604), (848),
% 109.76/16.02 | | | | | | | | | | (1577), (1590), (1591), (1593), (function-axioms)
% 109.76/16.02 | | | | | | | | | | are inconsistent by sub-proof #74.
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | End of split
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | Case 2:
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | (1594) all_56_15 = e1
% 109.76/16.02 | | | | | | | | | (1595) ~ (all_56_11 = e0)
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | REF_CLOSE: (42), (189), (190), (204), (209), (211), (237),
% 109.76/16.02 | | | | | | | | | (238), (243), (244), (248), (274), (278), (284),
% 109.76/16.02 | | | | | | | | | (286), (288), (289), (290), (291), (295), (298),
% 109.76/16.02 | | | | | | | | | (300), (304), (323), (331), (335), (338), (340),
% 109.76/16.02 | | | | | | | | | (352), (362), (365), (370), (385), (386), (391),
% 109.76/16.02 | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 109.76/16.02 | | | | | | | | | (430), (434), (436), (440), (446), (450), (464),
% 109.76/16.02 | | | | | | | | | (474), (551), (552), (553), (554), (555), (556),
% 109.76/16.02 | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 109.76/16.02 | | | | | | | | | (564), (565), (566), (567), (568), (569), (571),
% 109.76/16.02 | | | | | | | | | (579), (582), (591), (593), (601), (602), (605),
% 109.76/16.02 | | | | | | | | | (785), (848), (1575), (1594), (1595),
% 109.76/16.02 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.76/16.02 | | | | | | | | | #54.
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | End of split
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | Case 2:
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | (1596) all_36_1 = e3
% 109.76/16.02 | | | | | | | | (1597) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | COMBINE_EQS: (670), (1596) imply:
% 109.76/16.02 | | | | | | | | (1598) all_6_1 = e3
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | SIMP: (1598) implies:
% 109.76/16.02 | | | | | | | | (1599) all_6_1 = e3
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | REDUCE: (43), (1599) imply:
% 109.76/16.02 | | | | | | | | (1600) op(e3, all_6_2) = all_6_0
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | REDUCE: (42), (1599) imply:
% 109.76/16.02 | | | | | | | | (1601) op(e1, all_6_2) = e3
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | BETA: splitting (136) gives:
% 109.76/16.02 | | | | | | | |
% 109.76/16.02 | | | | | | | | Case 1:
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | (1602) ~ (all_44_0 = e1)
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | REDUCE: (1569), (1602) imply:
% 109.76/16.02 | | | | | | | | | (1603) $false
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | CLOSE: (1603) is inconsistent.
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | Case 2:
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | (1604) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | BETA: splitting (270) gives:
% 109.76/16.02 | | | | | | | | |
% 109.76/16.02 | | | | | | | | | Case 1:
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | (1605) ~ (all_56_15 = e1)
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | REDUCE: (554), (1605) imply:
% 109.76/16.02 | | | | | | | | | | (1606) ~ (all_4_2 = e1)
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | REF_CLOSE: (37), (172), (188), (202), (203), (206), (207),
% 109.76/16.02 | | | | | | | | | | (233), (235), (236), (273), (276), (356), (365),
% 109.76/16.02 | | | | | | | | | | (450), (475), (477), (540), (545), (554), (569),
% 109.76/16.02 | | | | | | | | | | (584), (595), (649), (675), (1567), (1571),
% 109.76/16.02 | | | | | | | | | | (1604), (1606), (function-axioms) are inconsistent
% 109.76/16.02 | | | | | | | | | | by sub-proof #232.
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | Case 2:
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | (1607) all_56_15 = e1
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | COMBINE_EQS: (554), (1607) imply:
% 109.76/16.02 | | | | | | | | | | (1608) all_4_2 = e1
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | SIMP: (1608) implies:
% 109.76/16.02 | | | | | | | | | | (1609) all_4_2 = e1
% 109.76/16.02 | | | | | | | | | |
% 109.76/16.02 | | | | | | | | | | REDUCE: (602), (1609) imply:
% 109.76/16.03 | | | | | | | | | | (1610) ~ (all_52_11 = e1)
% 109.76/16.03 | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | REDUCE: (605), (1609) imply:
% 109.76/16.03 | | | | | | | | | | (1611) ~ (all_52_14 = e1)
% 109.76/16.03 | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | BETA: splitting (291) gives:
% 109.76/16.03 | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | Case 1:
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | (1612) ~ (all_56_4 = e2)
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | REDUCE: (436), (1612) imply:
% 109.76/16.03 | | | | | | | | | | | (1613) ~ (all_52_9 = e2)
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | BETA: splitting (274) gives:
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | Case 1:
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | | (1614) ~ (all_56_14 = e2)
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | | REF_CLOSE: (9), (37), (41), (42), (162), (183), (184), (188),
% 109.76/16.03 | | | | | | | | | | | | (189), (190), (192), (193), (203), (207), (208),
% 109.76/16.03 | | | | | | | | | | | | (209), (211), (233), (234), (236), (238), (241),
% 109.76/16.03 | | | | | | | | | | | | (242), (243), (244), (248), (272), (273), (276),
% 109.76/16.03 | | | | | | | | | | | | (277), (279), (281), (282), (284), (286), (287),
% 109.76/16.03 | | | | | | | | | | | | (288), (289), (290), (292), (294), (295), (297),
% 109.76/16.03 | | | | | | | | | | | | (298), (299), (300), (323), (324), (329), (331),
% 109.76/16.03 | | | | | | | | | | | | (335), (338), (340), (341), (349), (352), (356),
% 109.76/16.03 | | | | | | | | | | | | (362), (365), (370), (371), (385), (386), (391),
% 109.76/16.03 | | | | | | | | | | | | (394), (406), (407), (412), (424), (426), (430),
% 109.76/16.03 | | | | | | | | | | | | (434), (436), (440), (446), (450), (464), (466),
% 109.76/16.03 | | | | | | | | | | | | (468), (475), (479), (540), (551), (552), (553),
% 109.76/16.03 | | | | | | | | | | | | (554), (555), (556), (557), (558), (559), (560),
% 109.76/16.03 | | | | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 109.76/16.03 | | | | | | | | | | | | (568), (569), (571), (573), (575), (579), (581),
% 109.76/16.03 | | | | | | | | | | | | (582), (584), (585), (587), (589), (591), (593),
% 109.76/16.03 | | | | | | | | | | | | (594), (597), (599), (601), (602), (604), (605),
% 109.76/16.03 | | | | | | | | | | | | (675), (848), (1567), (1571), (1610), (1611),
% 109.76/16.03 | | | | | | | | | | | | (1613), (1614), (function-axioms) are inconsistent
% 109.76/16.03 | | | | | | | | | | | | by sub-proof #88.
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | Case 2:
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | | (1615) all_56_14 = e2
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 109.76/16.03 | | | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 109.76/16.03 | | | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 109.76/16.03 | | | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 109.76/16.03 | | | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 109.76/16.03 | | | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 109.76/16.03 | | | | | | | | | | | | (589), (595), (597), (780), (1573), (1597),
% 109.76/16.03 | | | | | | | | | | | | (1600), (1601), (1615), (function-axioms) are
% 109.76/16.03 | | | | | | | | | | | | inconsistent by sub-proof #306.
% 109.76/16.03 | | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | End of split
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | Case 2:
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | (1616) ~ (all_56_15 = e1)
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | REDUCE: (1607), (1616) imply:
% 109.76/16.03 | | | | | | | | | | | (1617) $false
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | | CLOSE: (1617) is inconsistent.
% 109.76/16.03 | | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | | End of split
% 109.76/16.03 | | | | | | | | | |
% 109.76/16.03 | | | | | | | | | End of split
% 109.76/16.03 | | | | | | | | |
% 109.76/16.03 | | | | | | | | End of split
% 109.76/16.03 | | | | | | | |
% 109.76/16.03 | | | | | | | End of split
% 109.76/16.03 | | | | | | |
% 109.76/16.03 | | | | | | Case 2:
% 109.76/16.03 | | | | | | |
% 109.76/16.03 | | | | | | | (1618) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 109.76/16.03 | | | | | | |
% 109.76/16.04 | | | | | | | REF_CLOSE: (4), (8), (37), (42), (52), (150), (157), (162), (165),
% 109.76/16.04 | | | | | | | (167), (169), (170), (172), (179), (185), (188), (189),
% 109.76/16.04 | | | | | | | (190), (192), (193), (202), (204), (208), (209), (211),
% 109.76/16.04 | | | | | | | (212), (214), (233), (236), (237), (238), (240), (243),
% 109.76/16.04 | | | | | | | (244), (245), (246), (248), (270), (271), (272), (273),
% 109.76/16.04 | | | | | | | (274), (275), (276), (277), (278), (279), (281), (284),
% 109.76/16.04 | | | | | | | (286), (287), (288), (289), (290), (291), (292), (293),
% 109.76/16.04 | | | | | | | (294), (295), (296), (298), (299), (300), (301), (302),
% 109.76/16.04 | | | | | | | (303), (304), (305), (323), (324), (326), (327), (331),
% 109.76/16.04 | | | | | | | (332), (335), (338), (339), (340), (341), (342), (344),
% 109.76/16.04 | | | | | | | (347), (352), (356), (362), (365), (370), (371), (385),
% 109.76/16.04 | | | | | | | (386), (391), (394), (406), (407), (412), (413), (424),
% 109.76/16.04 | | | | | | | (426), (430), (434), (436), (440), (446), (450), (460),
% 109.76/16.04 | | | | | | | (462), (464), (470), (474), (475), (522), (548), (551),
% 109.76/16.04 | | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 109.76/16.04 | | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 109.76/16.04 | | | | | | | (568), (569), (571), (573), (577), (579), (581), (582),
% 109.76/16.04 | | | | | | | (583), (584), (585), (589), (591), (593), (594), (596),
% 109.76/16.04 | | | | | | | (597), (599), (601), (602), (603), (604), (605), (683),
% 109.76/16.04 | | | | | | | (705), (785), (848), (1388), (1389), (1618),
% 109.76/16.04 | | | | | | | (function-axioms) are inconsistent by sub-proof #47.
% 109.76/16.04 | | | | | | |
% 109.76/16.04 | | | | | | End of split
% 109.76/16.04 | | | | | |
% 109.76/16.04 | | | | | End of split
% 109.76/16.04 | | | | |
% 109.76/16.04 | | | | End of split
% 109.76/16.04 | | | |
% 109.76/16.04 | | | End of split
% 109.76/16.04 | | |
% 109.76/16.04 | | Case 2:
% 109.76/16.04 | | |
% 109.76/16.04 | | | (1619) all_6_1 = e2
% 109.76/16.04 | | | (1620) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 109.76/16.04 | | |
% 109.76/16.04 | | | COMBINE_EQS: (692), (1619) imply:
% 109.76/16.04 | | | (1621) all_18_1 = e2
% 109.76/16.04 | | |
% 109.76/16.04 | | | REDUCE: (43), (1619) imply:
% 109.76/16.04 | | | (1622) op(e2, all_6_2) = all_6_0
% 109.76/16.04 | | |
% 109.76/16.04 | | | REDUCE: (42), (1619) imply:
% 109.76/16.04 | | | (1623) op(e1, all_6_2) = e2
% 109.76/16.04 | | |
% 109.76/16.04 | | | BETA: splitting (49) gives:
% 109.76/16.04 | | |
% 109.76/16.04 | | | Case 1:
% 109.76/16.04 | | | |
% 109.76/16.04 | | | | (1624) ~ (all_8_1 = e1)
% 109.76/16.04 | | | |
% 109.76/16.04 | | | | BETA: splitting (54) gives:
% 109.76/16.04 | | | |
% 109.76/16.04 | | | | Case 1:
% 109.76/16.04 | | | | |
% 109.76/16.04 | | | | | (1625) ~ (all_10_0 = e2)
% 109.76/16.04 | | | | |
% 109.76/16.04 | | | | | BETA: splitting (68) gives:
% 109.76/16.04 | | | | |
% 109.76/16.04 | | | | | Case 1:
% 109.76/16.04 | | | | | |
% 109.76/16.04 | | | | | | (1626) ~ (all_16_0 = e1)
% 109.76/16.04 | | | | | |
% 109.76/16.04 | | | | | | REDUCE: (775), (1626) imply:
% 109.76/16.04 | | | | | | (1627) ~ (all_10_0 = e1)
% 109.76/16.04 | | | | | |
% 109.91/16.04 | | | | | | REF_CLOSE: (6), (37), (41), (47), (52), (53), (73), (107), (121),
% 109.91/16.04 | | | | | | (156), (157), (162), (164), (165), (169), (172), (179),
% 109.91/16.04 | | | | | | (183), (187), (188), (189), (192), (201), (202), (204),
% 109.91/16.04 | | | | | | (206), (207), (208), (211), (212), (213), (214), (233),
% 109.91/16.04 | | | | | | (234), (235), (236), (238), (239), (240), (241), (243),
% 109.91/16.04 | | | | | | (244), (245), (246), (247), (248), (270), (271), (272),
% 109.91/16.04 | | | | | | (273), (274), (275), (276), (277), (281), (282), (283),
% 109.91/16.04 | | | | | | (284), (285), (286), (288), (290), (291), (292), (293),
% 109.91/16.04 | | | | | | (294), (295), (296), (297), (298), (299), (300), (302),
% 109.91/16.04 | | | | | | (303), (304), (305), (323), (327), (328), (331), (335),
% 109.91/16.04 | | | | | | (336), (338), (340), (341), (343), (344), (346), (352),
% 109.91/16.04 | | | | | | (356), (362), (365), (370), (371), (385), (386), (391),
% 109.91/16.04 | | | | | | (394), (406), (407), (412), (413), (424), (426), (430),
% 109.91/16.04 | | | | | | (434), (436), (440), (446), (450), (458), (460), (462),
% 109.91/16.04 | | | | | | (464), (468), (470), (472), (475), (477), (479), (524),
% 109.91/16.04 | | | | | | (533), (551), (552), (553), (554), (555), (556), (557),
% 109.91/16.04 | | | | | | (558), (559), (560), (561), (562), (563), (564), (565),
% 109.91/16.04 | | | | | | (566), (567), (568), (569), (571), (573), (575), (577),
% 109.91/16.04 | | | | | | (579), (581), (582), (583), (584), (585), (587), (589),
% 109.91/16.04 | | | | | | (591), (593), (594), (595), (596), (597), (599), (602),
% 109.91/16.04 | | | | | | (603), (604), (605), (700), (702), (771), (779), (1620),
% 109.91/16.04 | | | | | | (1621), (1622), (1623), (1624), (1625), (1627),
% 109.91/16.04 | | | | | | (function-axioms) are inconsistent by sub-proof #28.
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | Case 2:
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | (1628) all_16_0 = e1
% 109.91/16.04 | | | | | | (1629) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | COMBINE_EQS: (775), (1628) imply:
% 109.91/16.04 | | | | | | (1630) all_10_0 = e1
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | SIMP: (1630) implies:
% 109.91/16.04 | | | | | | (1631) all_10_0 = e1
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | COMBINE_EQS: (759), (1631) imply:
% 109.91/16.04 | | | | | | (1632) all_24_0 = e1
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | REDUCE: (53), (1631) imply:
% 109.91/16.04 | | | | | | (1633) op(all_10_1, all_10_2) = e1
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | BETA: splitting (73) gives:
% 109.91/16.04 | | | | | |
% 109.91/16.04 | | | | | | Case 1:
% 109.91/16.04 | | | | | | |
% 109.91/16.04 | | | | | | | (1634) ~ (all_18_0 = e3)
% 109.91/16.04 | | | | | | |
% 109.91/16.05 | | | | | | | REF_CLOSE: (8), (37), (38), (41), (47), (52), (88), (156), (157),
% 109.91/16.05 | | | | | | | (164), (169), (178), (179), (180), (183), (201), (203),
% 109.91/16.05 | | | | | | | (204), (206), (208), (211), (212), (214), (233), (234),
% 109.91/16.05 | | | | | | | (235), (236), (238), (241), (243), (244), (245), (247),
% 109.91/16.05 | | | | | | | (248), (270), (272), (273), (274), (275), (276), (277),
% 109.91/16.05 | | | | | | | (279), (281), (282), (286), (288), (291), (293), (295),
% 109.91/16.05 | | | | | | | (297), (298), (299), (300), (305), (323), (331), (336),
% 109.91/16.05 | | | | | | | (338), (340), (351), (352), (356), (362), (365), (370),
% 109.91/16.05 | | | | | | | (371), (385), (386), (391), (394), (406), (407), (412),
% 109.91/16.05 | | | | | | | (413), (424), (426), (430), (434), (436), (440), (446),
% 109.91/16.05 | | | | | | | (450), (458), (462), (464), (468), (475), (477), (479),
% 109.91/16.05 | | | | | | | (530), (537), (551), (552), (553), (554), (555), (556),
% 109.91/16.05 | | | | | | | (557), (558), (559), (560), (561), (562), (563), (564),
% 109.91/16.05 | | | | | | | (565), (566), (567), (568), (569), (571), (573), (575),
% 109.91/16.05 | | | | | | | (577), (581), (582), (583), (584), (585), (587), (589),
% 109.91/16.05 | | | | | | | (593), (594), (595), (596), (599), (602), (603), (604),
% 109.91/16.05 | | | | | | | (605), (661), (695), (771), (784), (1620), (1622),
% 109.91/16.05 | | | | | | | (1623), (1629), (1632), (1633), (1634),
% 109.91/16.05 | | | | | | | (function-axioms) are inconsistent by sub-proof #26.
% 109.91/16.05 | | | | | | |
% 109.91/16.05 | | | | | | Case 2:
% 109.91/16.05 | | | | | | |
% 109.91/16.05 | | | | | | | (1635) all_18_0 = e3
% 109.91/16.05 | | | | | | | (1636) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 109.91/16.05 | | | | | | |
% 109.91/16.05 | | | | | | | REF_CLOSE: (41), (47), (188), (189), (192), (206), (207), (208),
% 109.91/16.05 | | | | | | | (211), (236), (238), (241), (243), (248), (274), (277),
% 109.91/16.05 | | | | | | | (290), (292), (295), (340), (346), (391), (394), (406),
% 109.91/16.05 | | | | | | | (424), (426), (430), (436), (446), (450), (468), (475),
% 109.91/16.05 | | | | | | | (533), (551), (552), (553), (555), (556), (564), (567),
% 109.91/16.05 | | | | | | | (568), (571), (573), (575), (582), (593), (594), (771),
% 109.91/16.05 | | | | | | | (1621), (1622), (1623), (1624), (1635), (1636),
% 109.91/16.05 | | | | | | | (function-axioms) are inconsistent by sub-proof #29.
% 109.91/16.05 | | | | | | |
% 109.91/16.05 | | | | | | End of split
% 109.91/16.05 | | | | | |
% 109.91/16.05 | | | | | End of split
% 109.91/16.05 | | | | |
% 109.91/16.05 | | | | Case 2:
% 109.91/16.05 | | | | |
% 109.91/16.05 | | | | | (1637) all_10_0 = e2
% 109.91/16.05 | | | | | (1638) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 109.91/16.05 | | | | |
% 109.91/16.06 | | | | | REF_CLOSE: (37), (41), (47), (52), (53), (73), (150), (154), (156),
% 109.91/16.06 | | | | | (157), (161), (164), (167), (169), (170), (172), (177),
% 109.91/16.06 | | | | | (178), (179), (180), (183), (185), (188), (189), (190),
% 109.91/16.06 | | | | | (192), (193), (201), (202), (204), (206), (207), (208),
% 109.91/16.06 | | | | | (209), (211), (212), (213), (214), (233), (234), (235),
% 109.91/16.06 | | | | | (236), (237), (238), (239), (240), (241), (243), (245),
% 109.91/16.06 | | | | | (246), (247), (248), (270), (271), (272), (274), (275),
% 109.91/16.06 | | | | | (276), (277), (279), (281), (284), (286), (287), (288),
% 109.91/16.06 | | | | | (290), (291), (292), (293), (295), (297), (298), (299),
% 109.91/16.06 | | | | | (300), (302), (304), (305), (323), (327), (328), (331),
% 109.91/16.06 | | | | | (336), (339), (340), (342), (343), (346), (352), (356),
% 109.91/16.06 | | | | | (362), (365), (370), (371), (385), (386), (391), (394),
% 109.91/16.06 | | | | | (406), (407), (412), (413), (424), (426), (430), (434),
% 109.91/16.06 | | | | | (436), (440), (446), (450), (458), (460), (462), (468),
% 109.91/16.06 | | | | | (470), (472), (474), (475), (477), (479), (533), (548),
% 109.91/16.06 | | | | | (551), (552), (553), (554), (555), (556), (557), (558),
% 109.91/16.06 | | | | | (559), (560), (561), (562), (563), (564), (565), (566),
% 109.91/16.06 | | | | | (567), (568), (569), (571), (573), (575), (577), (579),
% 109.91/16.06 | | | | | (581), (582), (583), (584), (585), (587), (589), (591),
% 109.91/16.06 | | | | | (593), (594), (595), (596), (599), (601), (602), (603),
% 109.91/16.06 | | | | | (604), (605), (705), (771), (783), (1621), (1622), (1623),
% 109.91/16.06 | | | | | (1624), (1637), (1638), (function-axioms) are inconsistent
% 109.91/16.06 | | | | | by sub-proof #21.
% 109.91/16.06 | | | | |
% 109.91/16.06 | | | | End of split
% 109.91/16.06 | | | |
% 109.91/16.06 | | | Case 2:
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | (1639) all_8_1 = e1
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | COMBINE_EQS: (704), (1639) imply:
% 109.91/16.06 | | | | (1640) all_48_1 = e1
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | REDUCE: (48), (1639) imply:
% 109.91/16.06 | | | | (1641) op(e1, all_8_2) = all_8_0
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | REDUCE: (47), (1639) imply:
% 109.91/16.06 | | | | (1642) op(e2, all_8_2) = e1
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | BETA: splitting (54) gives:
% 109.91/16.06 | | | |
% 109.91/16.06 | | | | Case 1:
% 109.91/16.06 | | | | |
% 109.91/16.06 | | | | | (1643) ~ (all_10_0 = e2)
% 109.91/16.06 | | | | |
% 109.91/16.06 | | | | | BETA: splitting (68) gives:
% 109.91/16.06 | | | | |
% 109.91/16.06 | | | | | Case 1:
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | (1644) ~ (all_16_0 = e1)
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | REDUCE: (775), (1644) imply:
% 109.91/16.06 | | | | | | (1645) ~ (all_10_0 = e1)
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | REF_CLOSE: (4), (8), (9), (37), (38), (41), (42), (52), (53), (93),
% 109.91/16.06 | | | | | | (107), (121), (154), (157), (162), (164), (165), (167),
% 109.91/16.06 | | | | | | (169), (172), (177), (178), (179), (180), (183), (184),
% 109.91/16.06 | | | | | | (185), (187), (188), (189), (190), (192), (193), (201),
% 109.91/16.06 | | | | | | (202), (203), (206), (207), (208), (209), (211), (212),
% 109.91/16.06 | | | | | | (213), (214), (233), (234), (235), (236), (238), (239),
% 109.91/16.06 | | | | | | (240), (241), (242), (243), (244), (245), (246), (247),
% 109.91/16.06 | | | | | | (248), (270), (271), (272), (273), (274), (275), (276),
% 109.91/16.06 | | | | | | (277), (278), (279), (280), (281), (282), (283), (284),
% 109.91/16.06 | | | | | | (285), (286), (287), (288), (289), (290), (291), (292),
% 109.91/16.06 | | | | | | (293), (294), (295), (296), (297), (298), (299), (300),
% 109.91/16.06 | | | | | | (301), (302), (304), (305), (323), (324), (329), (330),
% 109.91/16.06 | | | | | | (331), (332), (333), (334), (335), (336), (338), (339),
% 109.91/16.06 | | | | | | (340), (341), (343), (344), (348), (349), (350), (351),
% 109.91/16.06 | | | | | | (352), (356), (362), (365), (370), (371), (385), (386),
% 109.91/16.06 | | | | | | (391), (394), (406), (407), (412), (413), (424), (426),
% 109.91/16.06 | | | | | | (430), (434), (436), (440), (446), (450), (458), (460),
% 109.91/16.06 | | | | | | (462), (464), (466), (468), (470), (472), (475), (477),
% 109.91/16.06 | | | | | | (479), (524), (540), (551), (552), (553), (554), (555),
% 109.91/16.06 | | | | | | (556), (557), (558), (559), (560), (561), (562), (563),
% 109.91/16.06 | | | | | | (564), (565), (566), (567), (568), (569), (571), (573),
% 109.91/16.06 | | | | | | (575), (577), (579), (581), (582), (583), (584), (585),
% 109.91/16.06 | | | | | | (587), (589), (591), (593), (594), (595), (596), (597),
% 109.91/16.06 | | | | | | (599), (601), (602), (603), (604), (605), (675), (700),
% 109.91/16.06 | | | | | | (702), (778), (779), (784), (1642), (1643), (1645),
% 109.91/16.06 | | | | | | (function-axioms) are inconsistent by sub-proof #86.
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | Case 2:
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | (1646) all_16_0 = e1
% 109.91/16.06 | | | | | | (1647) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | COMBINE_EQS: (775), (1646) imply:
% 109.91/16.06 | | | | | | (1648) all_10_0 = e1
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | COMBINE_EQS: (759), (1648) imply:
% 109.91/16.06 | | | | | | (1649) all_24_0 = e1
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | REDUCE: (53), (1648) imply:
% 109.91/16.06 | | | | | | (1650) op(all_10_1, all_10_2) = e1
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | BETA: splitting (73) gives:
% 109.91/16.06 | | | | | |
% 109.91/16.06 | | | | | | Case 1:
% 109.91/16.06 | | | | | | |
% 109.91/16.06 | | | | | | | (1651) ~ (all_18_0 = e3)
% 109.91/16.06 | | | | | | |
% 109.91/16.07 | | | | | | | REF_CLOSE: (8), (37), (38), (41), (47), (52), (88), (156), (157),
% 109.91/16.07 | | | | | | | (164), (169), (178), (179), (180), (183), (201), (203),
% 109.91/16.07 | | | | | | | (204), (206), (208), (211), (212), (214), (233), (234),
% 109.91/16.07 | | | | | | | (235), (236), (238), (241), (243), (244), (245), (247),
% 109.91/16.07 | | | | | | | (248), (270), (272), (273), (274), (275), (276), (277),
% 109.91/16.07 | | | | | | | (279), (281), (282), (286), (288), (291), (293), (295),
% 109.91/16.07 | | | | | | | (297), (298), (299), (300), (305), (323), (331), (336),
% 109.91/16.07 | | | | | | | (338), (340), (351), (352), (356), (362), (365), (370),
% 109.91/16.07 | | | | | | | (371), (385), (386), (391), (394), (406), (407), (412),
% 109.91/16.07 | | | | | | | (413), (424), (426), (430), (434), (436), (440), (446),
% 109.91/16.07 | | | | | | | (450), (458), (462), (464), (468), (475), (477), (479),
% 109.91/16.07 | | | | | | | (530), (537), (551), (552), (553), (554), (555), (556),
% 109.91/16.07 | | | | | | | (557), (558), (559), (560), (561), (562), (563), (564),
% 109.91/16.07 | | | | | | | (565), (566), (567), (568), (569), (571), (573), (575),
% 109.91/16.07 | | | | | | | (577), (581), (582), (583), (584), (585), (587), (589),
% 109.91/16.07 | | | | | | | (593), (594), (595), (596), (599), (602), (603), (604),
% 109.91/16.07 | | | | | | | (605), (661), (695), (771), (784), (1620), (1622),
% 109.91/16.07 | | | | | | | (1623), (1647), (1649), (1650), (1651),
% 109.91/16.07 | | | | | | | (function-axioms) are inconsistent by sub-proof #26.
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | Case 2:
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | (1652) all_18_0 = e3
% 109.91/16.07 | | | | | | | (1653) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | COMBINE_EQS: (771), (1652) imply:
% 109.91/16.07 | | | | | | | (1654) all_6_0 = e3
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | SIMP: (1654) implies:
% 109.91/16.07 | | | | | | | (1655) all_6_0 = e3
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | REDUCE: (1622), (1655) imply:
% 109.91/16.07 | | | | | | | (1656) op(e2, all_6_2) = e3
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | BETA: splitting (1653) gives:
% 109.91/16.07 | | | | | | |
% 109.91/16.07 | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | (1657) ~ (all_18_1 = e2)
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | REDUCE: (1621), (1657) imply:
% 109.91/16.07 | | | | | | | | (1658) $false
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | CLOSE: (1658) is inconsistent.
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | (1659) ~ (all_18_2 = e0)
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | REDUCE: (533), (1659) imply:
% 109.91/16.07 | | | | | | | | (1660) ~ (all_6_2 = e0)
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | BETA: splitting (274) gives:
% 109.91/16.07 | | | | | | | |
% 109.91/16.07 | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | |
% 109.91/16.07 | | | | | | | | | (1661) ~ (all_56_14 = e2)
% 109.91/16.07 | | | | | | | | |
% 109.91/16.07 | | | | | | | | | REDUCE: (555), (1661) imply:
% 109.91/16.07 | | | | | | | | | (1662) ~ (all_6_2 = e2)
% 109.91/16.07 | | | | | | | | |
% 109.91/16.07 | | | | | | | | | BETA: splitting (238) gives:
% 109.91/16.07 | | | | | | | | |
% 109.91/16.07 | | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | (1663) all_54_10 = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | COMBINE_EQS: (551), (1663) imply:
% 109.91/16.07 | | | | | | | | | | (1664) all_6_2 = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | SIMP: (1664) implies:
% 109.91/16.07 | | | | | | | | | | (1665) all_6_2 = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | COMBINE_EQS: (555), (1665) imply:
% 109.91/16.07 | | | | | | | | | | (1666) all_56_14 = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | REDUCE: (1656), (1665) imply:
% 109.91/16.07 | | | | | | | | | | (1667) op(e2, e3) = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | REDUCE: (1623), (1665) imply:
% 109.91/16.07 | | | | | | | | | | (1668) op(e1, e3) = e2
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | REDUCE: (41), (1665) imply:
% 109.91/16.07 | | | | | | | | | | (1669) op(e1, e1) = e3
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | BETA: splitting (277) gives:
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | (1670) ~ (all_56_14 = e3)
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | REDUCE: (1666), (1670) imply:
% 109.91/16.07 | | | | | | | | | | | (1671) $false
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | CLOSE: (1671) is inconsistent.
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | (1672) ~ (all_56_9 = e0)
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | REDUCE: (450), (1672) imply:
% 109.91/16.07 | | | | | | | | | | | (1673) ~ (all_52_3 = e0)
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | BETA: splitting (295) gives:
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | (1674) ~ (all_56_3 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REDUCE: (430), (1674) imply:
% 109.91/16.07 | | | | | | | | | | | | (1675) ~ (all_52_1 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 109.91/16.07 | | | | | | | | | | | | e3, e1, simplifying with (207), (1668) gives:
% 109.91/16.07 | | | | | | | | | | | | (1676) all_52_2 = e2
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 109.91/16.07 | | | | | | | | | | | | e3, e2, simplifying with (211), (1667) gives:
% 109.91/16.07 | | | | | | | | | | | | (1677) all_52_1 = e3
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REDUCE: (192), (1677) imply:
% 109.91/16.07 | | | | | | | | | | | | (1678) ~ (all_52_3 = e3)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | SIMP: (1678) implies:
% 109.91/16.07 | | | | | | | | | | | | (1679) ~ (all_52_3 = e3)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REDUCE: (571), (1677) imply:
% 109.91/16.07 | | | | | | | | | | | | (1680) ~ (all_10_2 = e3)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REDUCE: (188), (1676) imply:
% 109.91/16.07 | | | | | | | | | | | | (1681) ~ (all_52_3 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | SIMP: (1681) implies:
% 109.91/16.07 | | | | | | | | | | | | (1682) ~ (all_52_3 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REDUCE: (573), (1676) imply:
% 109.91/16.07 | | | | | | | | | | | | (1683) ~ (all_10_2 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | SIMP: (1683) implies:
% 109.91/16.07 | | | | | | | | | | | | (1684) ~ (all_10_2 = e2)
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | BETA: splitting (346) gives:
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | (1685) all_58_0 = e0
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | COMBINE_EQS: (424), (1685) imply:
% 109.91/16.07 | | | | | | | | | | | | | (1686) all_10_2 = e0
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | COMBINE_EQS: (426), (1686) imply:
% 109.91/16.07 | | | | | | | | | | | | | (1687) all_56_12 = e0
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | BETA: splitting (290) gives:
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | Case 1:
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | (1688) ~ (all_56_5 = e2)
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | REDUCE: (446), (1688) imply:
% 109.91/16.07 | | | | | | | | | | | | | | (1689) ~ (all_52_13 = e2)
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | REF_CLOSE: (52), (204), (212), (245), (248), (281), (293),
% 109.91/16.07 | | | | | | | | | | | | | | (299), (340), (371), (391), (394), (406), (407),
% 109.91/16.07 | | | | | | | | | | | | | | (426), (436), (462), (537), (553), (564), (566),
% 109.91/16.07 | | | | | | | | | | | | | | (567), (581), (695), (1647), (1650), (1675),
% 109.91/16.07 | | | | | | | | | | | | | | (1684), (1689), (function-axioms) are inconsistent
% 109.91/16.07 | | | | | | | | | | | | | | by sub-proof #189.
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | (1690) ~ (all_56_12 = e0)
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | REDUCE: (1687), (1690) imply:
% 109.91/16.07 | | | | | | | | | | | | | | (1691) $false
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | | CLOSE: (1691) is inconsistent.
% 109.91/16.07 | | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | End of split
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | (1692) ~ (all_58_0 = e0)
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | | REF_CLOSE: (236), (248), (424), (475), (553), (566), (575),
% 109.91/16.07 | | | | | | | | | | | | | (1673), (1679), (1682), (1684), (1692) are
% 109.91/16.07 | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 109.91/16.07 | | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | End of split
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | (1693) all_56_3 = e2
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | | REF_CLOSE: (41), (295), (555), (1669), (1693),
% 109.91/16.07 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.91/16.07 | | | | | | | | | | | | #121.
% 109.91/16.07 | | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | | End of split
% 109.91/16.07 | | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | | End of split
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.07 | | | | | | | | | Case 2:
% 109.91/16.07 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | (1694) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | REF_CLOSE: (551), (568), (1660), (1662), (1694) are
% 109.91/16.08 | | | | | | | | | | inconsistent by sub-proof #435.
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | End of split
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | (1695) all_56_14 = e2
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | COMBINE_EQS: (555), (1695) imply:
% 109.91/16.08 | | | | | | | | | (1696) all_6_2 = e2
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | REF_CLOSE: (206), (594), (1623), (1696), (function-axioms) are
% 109.91/16.08 | | | | | | | | | inconsistent by sub-proof #39.
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | End of split
% 109.91/16.08 | | | | | | | |
% 109.91/16.08 | | | | | | | End of split
% 109.91/16.08 | | | | | | |
% 109.91/16.08 | | | | | | End of split
% 109.91/16.08 | | | | | |
% 109.91/16.08 | | | | | End of split
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | Case 2:
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | | (1697) all_10_0 = e2
% 109.91/16.08 | | | | | (1698) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | | COMBINE_EQS: (783), (1697) imply:
% 109.91/16.08 | | | | | (1699) all_50_0 = e2
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | | REDUCE: (53), (1697) imply:
% 109.91/16.08 | | | | | (1700) op(all_10_1, all_10_2) = e2
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | | BETA: splitting (73) gives:
% 109.91/16.08 | | | | |
% 109.91/16.08 | | | | | Case 1:
% 109.91/16.08 | | | | | |
% 109.91/16.08 | | | | | | (1701) ~ (all_18_0 = e3)
% 109.91/16.08 | | | | | |
% 109.91/16.08 | | | | | | REDUCE: (771), (1701) imply:
% 109.91/16.08 | | | | | | (1702) ~ (all_6_0 = e3)
% 109.91/16.08 | | | | | |
% 109.91/16.08 | | | | | | BETA: splitting (93) gives:
% 109.91/16.08 | | | | | |
% 109.91/16.08 | | | | | | Case 1:
% 109.91/16.08 | | | | | | |
% 109.91/16.08 | | | | | | | (1703) ~ (all_26_0 = e1)
% 109.91/16.08 | | | | | | |
% 109.91/16.08 | | | | | | | REDUCE: (778), (1703) imply:
% 109.91/16.08 | | | | | | | (1704) ~ (all_4_0 = e1)
% 109.91/16.08 | | | | | | |
% 109.91/16.08 | | | | | | | BETA: splitting (145) gives:
% 109.91/16.08 | | | | | | |
% 109.91/16.08 | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | |
% 109.91/16.08 | | | | | | | | (1705) ~ (all_48_0 = e3)
% 109.91/16.08 | | | | | | | |
% 109.91/16.08 | | | | | | | | REDUCE: (782), (1705) imply:
% 109.91/16.08 | | | | | | | | (1706) ~ (all_8_0 = e3)
% 109.91/16.08 | | | | | | | |
% 109.91/16.08 | | | | | | | | BETA: splitting (150) gives:
% 109.91/16.08 | | | | | | | |
% 109.91/16.08 | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | (1707) ~ (all_50_0 = e2)
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | REDUCE: (1699), (1707) imply:
% 109.91/16.08 | | | | | | | | | (1708) $false
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | CLOSE: (1708) is inconsistent.
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | (1709) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | BETA: splitting (270) gives:
% 109.91/16.08 | | | | | | | | |
% 109.91/16.08 | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | (1710) ~ (all_56_15 = e1)
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | REDUCE: (554), (1710) imply:
% 109.91/16.08 | | | | | | | | | | (1711) ~ (all_4_2 = e1)
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | BETA: splitting (272) gives:
% 109.91/16.08 | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | (1712) ~ (all_56_12 = e1)
% 109.91/16.08 | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | REDUCE: (426), (1712) imply:
% 109.91/16.08 | | | | | | | | | | | (1713) ~ (all_10_2 = e1)
% 109.91/16.08 | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | BETA: splitting (271) gives:
% 109.91/16.08 | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | (1714) ~ (all_56_13 = e1)
% 109.91/16.08 | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | REDUCE: (556), (1714) imply:
% 109.91/16.08 | | | | | | | | | | | | (1715) ~ (all_8_2 = e1)
% 109.91/16.08 | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | BETA: splitting (273) gives:
% 109.91/16.08 | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | (1716) ~ (all_56_15 = e2)
% 109.91/16.08 | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | REDUCE: (554), (1716) imply:
% 109.91/16.08 | | | | | | | | | | | | | (1717) ~ (all_4_2 = e2)
% 109.91/16.08 | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | BETA: splitting (233) gives:
% 109.91/16.08 | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | (1718) all_54_15 = e3
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | COMBINE_EQS: (356), (1718) imply:
% 109.91/16.08 | | | | | | | | | | | | | | (1719) all_4_2 = e3
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | SIMP: (1719) implies:
% 109.91/16.08 | | | | | | | | | | | | | | (1720) all_4_2 = e3
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | COMBINE_EQS: (554), (1720) imply:
% 109.91/16.08 | | | | | | | | | | | | | | (1721) all_56_15 = e3
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | REDUCE: (584), (1720) imply:
% 109.91/16.08 | | | | | | | | | | | | | | (1722) ~ (all_52_3 = e3)
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | REDUCE: (38), (1720) imply:
% 109.91/16.08 | | | | | | | | | | | | | | (1723) op(all_4_1, e3) = all_4_0
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | REDUCE: (37), (1720) imply:
% 109.91/16.08 | | | | | | | | | | | | | | (1724) op(e0, e3) = all_4_1
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 109.91/16.08 | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | (1725) ~ (all_56_6 = e1)
% 109.91/16.08 | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | REDUCE: (386), (1725) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | (1726) ~ (all_52_2 = e1)
% 109.91/16.08 | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 109.91/16.08 | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | (1727) ~ (all_56_15 = e3)
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | REDUCE: (1721), (1727) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | (1728) $false
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | CLOSE: (1728) is inconsistent.
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | (1729) ~ (all_56_9 = e0)
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | REDUCE: (450), (1729) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | (1730) ~ (all_52_3 = e0)
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1731) ~ (all_56_3 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | REDUCE: (430), (1731) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1732) ~ (all_52_1 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 109.91/16.08 | | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (1724)
% 109.91/16.08 | | | | | | | | | | | | | | | | | gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1733) all_52_3 = all_4_1
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1734) all_54_12 = all_4_1
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1735) all_58_12 = all_4_1
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | REDUCE: (192), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1736) ~ (all_52_1 = all_4_1)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | REDUCE: (575), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1737) ~ (all_10_2 = all_4_1)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | SIMP: (1737) implies:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1738) ~ (all_10_2 = all_4_1)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | REDUCE: (1722), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1739) ~ (all_4_1 = e3)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | REDUCE: (1730), (1733) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | (1740) ~ (all_4_1 = e0)
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | (1741) ~ (all_56_14 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | REDUCE: (555), (1741) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | (1742) ~ (all_6_2 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | (1743) ~ (all_56_5 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | REDUCE: (446), (1743) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | (1744) ~ (all_52_13 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | (1745) all_58_2 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (1732), (1745) are inconsistent by
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | (1746) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1746) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | (1747) all_58_3 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (1747) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | (1748) all_8_2 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1748) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | (1749) $false
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1749) is inconsistent.
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | (1750) ~ (all_58_3 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | (1751) all_58_5 = e2 | all_58_10 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (1752) ~ (all_56_12 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1752) imply:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (1753) ~ (all_10_2 = e2)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (157), (208), (212), (245), (248), (281),
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (291), (293), (299), (327), (371), (391), (394),
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (407), (426), (436), (462), (548), (553), (554),
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (557), (560), (561), (566), (581), (705), (1700),
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (1709), (1744), (1751), (1753), (function-axioms)
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #19.
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | | (1754) all_56_12 = e2
% 109.91/16.08 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (208), (211), (236), (241), (243), (244),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (248), (281), (284), (289), (331), (338), (346),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (371), (385), (391), (394), (406), (424), (426),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (440), (446), (464), (468), (552), (553), (556),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (560), (562), (563), (564), (566), (567), (568),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (571), (582), (591), (593), (1642), (1713),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1715), (1726), (1734), (1736), (1738), (1739),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1740), (1754), (function-axioms) are inconsistent
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #18.
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | (1755) all_56_5 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | (1756) ~ (all_56_12 = e0)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (1755) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | (1757) all_52_13 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | REDUCE: (426), (1756) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | (1758) ~ (all_10_2 = e0)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | REDUCE: (593), (1757) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | (1759) ~ (all_8_2 = e2)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | (1760) ~ (all_56_5 = e2)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (1755), (1760) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | (1761) $false
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | CLOSE: (1761) is inconsistent.
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | (1762) ~ (all_56_14 = e0)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (1762) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | (1763) ~ (all_6_2 = e0)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | (1764) all_54_0 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (1764) are inconsistent by sub-proof
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | #451.
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | (1765) ~ (all_54_0 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | (1766) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1766) gives:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1767) all_54_0 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (1767) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1768) all_10_2 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1768) implies:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1769) all_10_2 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (426), (1769) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1770) all_56_12 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (208), (211), (236), (241), (243), (244),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (248), (281), (284), (289), (331), (338), (346),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (371), (385), (391), (394), (406), (424), (426),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (440), (446), (464), (468), (552), (553), (556),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (560), (562), (563), (564), (566), (567), (568),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (571), (582), (591), (593), (1642), (1713),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1715), (1726), (1734), (1736), (1738), (1739),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1740), (1770), (function-axioms) are inconsistent
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #18.
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1771) all_54_0 = e1 | all_54_0 = e0
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (211), (236), (238), (351), (406), (424), (551),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (553), (563), (568), (583), (784), (1723), (1734),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1735), (1738), (1739), (1740), (1742), (1758),
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | (1763), (1771), (function-axioms) are inconsistent
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #314.
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1772) all_56_14 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (555), (1772) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1773) all_6_2 = e2
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (206), (594), (1623), (1773), (function-axioms)
% 109.91/16.09 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #39.
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1774) ~ (all_56_15 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | REDUCE: (1721), (1774) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1775) $false
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | CLOSE: (1775) is inconsistent.
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | (1776) ~ (all_56_15 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | REDUCE: (1721), (1776) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | (1777) $false
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | CLOSE: (1777) is inconsistent.
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | (1778) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (1711), (1717), (1778) are
% 109.91/16.09 | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | End of split
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | (1779) all_56_15 = e2
% 109.91/16.09 | | | | | | | | | | | | | (1780) ~ (all_56_10 = e0)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | COMBINE_EQS: (554), (1779) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1781) all_4_2 = e2
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | SIMP: (1781) implies:
% 109.91/16.09 | | | | | | | | | | | | | (1782) all_4_2 = e2
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | COMBINE_EQS: (557), (1782) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1783) all_58_15 = e2
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | REDUCE: (365), (1780) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1784) ~ (all_52_7 = e0)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | REDUCE: (595), (1782) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1785) ~ (all_52_7 = e2)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | REDUCE: (603), (1782) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1786) ~ (all_52_12 = e2)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | REDUCE: (604), (1782) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1787) ~ (all_52_13 = e2)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | REDUCE: (605), (1782) imply:
% 109.91/16.09 | | | | | | | | | | | | | (1788) ~ (all_52_14 = e2)
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | BETA: splitting (282) gives:
% 109.91/16.09 | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | (1789) ~ (all_56_7 = e1)
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | REDUCE: (440), (1789) imply:
% 109.91/16.09 | | | | | | | | | | | | | | (1790) ~ (all_52_6 = e1)
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 109.91/16.09 | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | (1791) ~ (all_56_0 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | REDUCE: (413), (1791) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | (1792) ~ (all_52_4 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 109.91/16.09 | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | (1793) ~ (all_56_2 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | REDUCE: (407), (1793) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | (1794) ~ (all_52_12 = e3)
% 109.91/16.09 | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 109.91/16.09 | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1795) all_58_0 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (1795) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1796) all_10_2 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | REDUCE: (566), (1796) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1797) $false
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | CLOSE: (1797) is inconsistent.
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | (1798) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | BETA: splitting (1798) gives:
% 109.91/16.09 | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1799) all_58_1 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (1799) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1800) all_52_4 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | REDUCE: (1792), (1800) imply:
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1801) $false
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | CLOSE: (1801) is inconsistent.
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.09 | | | | | | | | | | | | | | | | | | (1802) all_58_4 = e3 | all_58_9 = e3
% 109.91/16.09 | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | BETA: splitting (1802) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1803) all_58_4 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (412), (1803) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1804) all_52_8 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (165), (1804) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1805) ~ (all_52_11 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | SIMP: (1805) implies:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1806) ~ (all_52_11 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (164), (1804) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1807) ~ (all_52_12 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (596), (1804) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1808) ~ (all_6_2 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | SIMP: (1808) implies:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1809) ~ (all_6_2 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1810) ~ (all_56_3 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | REDUCE: (430), (1810) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1811) ~ (all_52_1 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | (1812) all_58_2 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (1811), (1812) are inconsistent by
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | (1813) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1813) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | (1814) all_58_3 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (1814) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | (1815) all_8_2 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (1815) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | (1816) $false
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1816) is inconsistent.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | (1817) all_58_5 = e2 | all_58_10 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1817) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1818) all_58_5 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (394), (1818) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1819) all_52_9 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1819) implies:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1820) all_52_9 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (1820) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1821) ~ (all_8_2 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1820) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1822) ~ (all_6_2 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1822) implies:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1823) ~ (all_6_2 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_54_10 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (551), (1809), (1824) are inconsistent by
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #352.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (1825) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (192), (193), (204), (237), (238), (244),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (271), (277), (279), (288), (292), (323), (326),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (329), (331), (340), (342), (343), (344), (362),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (370), (371), (385), (391), (394), (406), (436),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (446), (450), (464), (474), (551), (555), (556),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (564), (567), (568), (569), (587), (594), (599),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (601), (1641), (1706), (1783), (1784), (1785),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (1788), (1790), (1794), (1806), (1811), (1823),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | (1825), (function-axioms) are inconsistent by
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #17.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | (1826) all_58_10 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (391), (1787), (1826) are inconsistent by
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #95.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1827) all_56_3 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (1827) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1828) all_52_1 = e2
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1828) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1829) ~ (all_10_2 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | SIMP: (1829) implies:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1830) ~ (all_10_2 = e2)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (157), (208), (212), (245), (248), (281),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (299), (302), (327), (371), (391), (407), (412),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (426), (434), (462), (548), (553), (557), (560),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (561), (579), (581), (705), (1700), (1709),
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | (1711), (1794), (1802), (1830), (function-axioms)
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #16.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1831) all_58_9 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (1831) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1832) all_52_12 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | REDUCE: (1794), (1832) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | (1833) $false
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | | CLOSE: (1833) is inconsistent.
% 109.91/16.10 | | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | End of split
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | (1834) all_56_2 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | | (1835) ~ (all_56_12 = e0)
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (1834) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | (1836) all_52_12 = e3
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | REDUCE: (426), (1835) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | (1837) ~ (all_10_2 = e0)
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | REDUCE: (581), (1836) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | (1838) ~ (all_10_2 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 109.91/16.10 | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | Case 1:
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | (1839) ~ (all_56_2 = e3)
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | REDUCE: (1834), (1839) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | (1840) $false
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | CLOSE: (1840) is inconsistent.
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | Case 2:
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | (1841) ~ (all_56_13 = e0)
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.10 | | | | | | | | | | | | | | | | | REDUCE: (556), (1841) imply:
% 109.91/16.10 | | | | | | | | | | | | | | | | | (1842) ~ (all_8_2 = e0)
% 109.91/16.10 | | | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (52), (156), (165), (167), (169), (170),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (172), (177), (179), (180), (185), (187), (188),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (190), (192), (193), (202), (209), (211), (214),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (233), (235), (236), (238), (240), (243), (244),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (245), (246), (247), (248), (270), (271), (277),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (278), (279), (287), (288), (292), (298), (305),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (323), (324), (326), (327), (331), (332), (339),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (340), (342), (344), (346), (347), (352), (356),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (362), (370), (371), (385), (386), (391), (394),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (406), (407), (412), (413), (424), (426), (436),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (446), (450), (458), (460), (462), (464), (470),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (475), (477), (551), (552), (553), (554), (555),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (556), (557), (558), (559), (560), (561), (562),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (571), (573), (577), (582), (583), (584), (585),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (589), (591), (594), (596), (597), (601), (602),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (603), (604), (605), (1642), (1700), (1713),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (1784), (1786), (1787), (1790), (1792), (1837),
% 109.91/16.11 | | | | | | | | | | | | | | | | | (1842), (function-axioms) are inconsistent by
% 109.91/16.11 | | | | | | | | | | | | | | | | | sub-proof #56.
% 109.91/16.11 | | | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | (1843) ~ (all_56_15 = e2)
% 109.91/16.11 | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | REDUCE: (1779), (1843) imply:
% 109.91/16.11 | | | | | | | | | | | | | | | (1844) $false
% 109.91/16.11 | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | | CLOSE: (1844) is inconsistent.
% 109.91/16.11 | | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | (1845) ~ (all_56_15 = e2)
% 109.91/16.11 | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | REDUCE: (1779), (1845) imply:
% 109.91/16.11 | | | | | | | | | | | | | | (1846) $false
% 109.91/16.11 | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | | CLOSE: (1846) is inconsistent.
% 109.91/16.11 | | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | (1847) all_56_13 = e1
% 109.91/16.11 | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | COMBINE_EQS: (556), (1847) imply:
% 109.91/16.11 | | | | | | | | | | | | (1848) all_8_2 = e1
% 109.91/16.11 | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | | REF_CLOSE: (209), (591), (1642), (1848), (function-axioms)
% 109.91/16.11 | | | | | | | | | | | | are inconsistent by sub-proof #109.
% 109.91/16.11 | | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | (1849) all_56_12 = e1
% 109.91/16.11 | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | | REF_CLOSE: (52), (167), (209), (213), (246), (302), (426),
% 109.91/16.11 | | | | | | | | | | | (434), (460), (579), (1698), (1700), (1849),
% 109.91/16.11 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.91/16.11 | | | | | | | | | | | #15.
% 109.91/16.11 | | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | (1850) all_56_15 = e1
% 109.91/16.11 | | | | | | | | | | (1851) ~ (all_56_11 = e0)
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | REF_CLOSE: (37), (52), (156), (157), (167), (169), (172),
% 109.91/16.11 | | | | | | | | | | (179), (201), (204), (206), (208), (209), (213),
% 109.91/16.11 | | | | | | | | | | (234), (235), (238), (241), (243), (245), (246),
% 109.91/16.11 | | | | | | | | | | (248), (275), (277), (286), (288), (291), (297),
% 109.91/16.11 | | | | | | | | | | (299), (300), (304), (323), (331), (340), (352),
% 109.91/16.11 | | | | | | | | | | (362), (365), (370), (385), (386), (391), (394),
% 109.91/16.11 | | | | | | | | | | (406), (407), (412), (413), (424), (426), (434),
% 109.91/16.11 | | | | | | | | | | (436), (446), (450), (460), (462), (468), (477),
% 109.91/16.11 | | | | | | | | | | (479), (551), (552), (553), (554), (555), (557),
% 109.91/16.11 | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 109.91/16.11 | | | | | | | | | | (565), (566), (567), (568), (569), (571), (579),
% 109.91/16.11 | | | | | | | | | | (583), (585), (587), (589), (594), (599), (602),
% 109.91/16.11 | | | | | | | | | | (603), (604), (605), (1622), (1623), (1698),
% 109.91/16.11 | | | | | | | | | | (1700), (1702), (1850), (1851), (function-axioms)
% 109.91/16.11 | | | | | | | | | | are inconsistent by sub-proof #14.
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | End of split
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | End of split
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | | (1852) all_48_0 = e3
% 109.91/16.11 | | | | | | | | (1853) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | | COMBINE_EQS: (782), (1852) imply:
% 109.91/16.11 | | | | | | | | (1854) all_8_0 = e3
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | | REDUCE: (1641), (1854) imply:
% 109.91/16.11 | | | | | | | | (1855) op(e1, all_8_2) = e3
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | | BETA: splitting (1853) gives:
% 109.91/16.11 | | | | | | | |
% 109.91/16.11 | | | | | | | | Case 1:
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | (1856) ~ (all_48_1 = e1)
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | REDUCE: (1640), (1856) imply:
% 109.91/16.11 | | | | | | | | | (1857) $false
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | CLOSE: (1857) is inconsistent.
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | Case 2:
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | (1858) ~ (all_48_2 = e0)
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | REDUCE: (547), (1858) imply:
% 109.91/16.11 | | | | | | | | | (1859) ~ (all_8_2 = e0)
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | BETA: splitting (274) gives:
% 109.91/16.11 | | | | | | | | |
% 109.91/16.11 | | | | | | | | | Case 1:
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | (1860) ~ (all_56_14 = e2)
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.11 | | | | | | | | | | REDUCE: (555), (1860) imply:
% 109.91/16.11 | | | | | | | | | | (1861) ~ (all_6_2 = e2)
% 109.91/16.11 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | REF_CLOSE: (6), (37), (38), (41), (52), (154), (156), (161),
% 109.91/16.12 | | | | | | | | | | (165), (167), (169), (170), (172), (177), (179),
% 109.91/16.12 | | | | | | | | | | (180), (183), (184), (185), (187), (188), (189),
% 109.91/16.12 | | | | | | | | | | (190), (192), (193), (202), (203), (209), (211),
% 109.91/16.12 | | | | | | | | | | (214), (233), (234), (235), (236), (237), (238),
% 109.91/16.12 | | | | | | | | | | (240), (242), (243), (244), (245), (246), (247),
% 109.91/16.12 | | | | | | | | | | (248), (270), (271), (272), (274), (275), (276),
% 109.91/16.12 | | | | | | | | | | (277), (278), (279), (281), (282), (284), (285),
% 109.91/16.12 | | | | | | | | | | (287), (288), (290), (291), (292), (293), (294),
% 109.91/16.12 | | | | | | | | | | (295), (296), (298), (302), (305), (323), (324),
% 109.91/16.12 | | | | | | | | | | (326), (327), (329), (331), (332), (334), (335),
% 109.91/16.12 | | | | | | | | | | (338), (339), (340), (341), (342), (344), (346),
% 109.91/16.12 | | | | | | | | | | (347), (349), (351), (352), (356), (362), (365),
% 109.91/16.12 | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 109.91/16.12 | | | | | | | | | | (407), (412), (413), (424), (426), (430), (434),
% 109.91/16.12 | | | | | | | | | | (436), (440), (446), (450), (458), (460), (462),
% 109.91/16.12 | | | | | | | | | | (464), (466), (470), (474), (475), (477), (479),
% 109.91/16.12 | | | | | | | | | | (551), (552), (553), (554), (555), (556), (557),
% 109.91/16.12 | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 109.91/16.12 | | | | | | | | | | (565), (566), (567), (568), (569), (571), (573),
% 109.91/16.12 | | | | | | | | | | (575), (577), (579), (581), (582), (583), (584),
% 109.91/16.12 | | | | | | | | | | (585), (587), (589), (591), (593), (594), (595),
% 109.91/16.12 | | | | | | | | | | (596), (597), (599), (601), (602), (603), (604),
% 109.91/16.12 | | | | | | | | | | (605), (1642), (1700), (1704), (1855), (1859),
% 109.91/16.12 | | | | | | | | | | (1861), (function-axioms) are inconsistent by
% 109.91/16.12 | | | | | | | | | | sub-proof #48.
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | Case 2:
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | (1862) all_56_14 = e2
% 109.91/16.12 | | | | | | | | | | (1863) ~ (all_56_10 = e0)
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | REF_CLOSE: (4), (8), (162), (167), (208), (209), (211),
% 109.91/16.12 | | | | | | | | | | (233), (243), (271), (276), (278), (289), (294),
% 109.91/16.12 | | | | | | | | | | (296), (298), (300), (301), (304), (323), (338),
% 109.91/16.12 | | | | | | | | | | (340), (341), (352), (356), (362), (365), (370),
% 109.91/16.12 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 109.91/16.12 | | | | | | | | | | (430), (434), (446), (450), (552), (554), (555),
% 109.91/16.12 | | | | | | | | | | (556), (557), (558), (559), (561), (564), (565),
% 109.91/16.12 | | | | | | | | | | (566), (567), (569), (582), (591), (593), (597),
% 109.91/16.12 | | | | | | | | | | (599), (604), (1642), (1862), (1863),
% 109.91/16.12 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.91/16.12 | | | | | | | | | | #104.
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | End of split
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | End of split
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | End of split
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | Case 2:
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | (1864) all_26_0 = e1
% 109.91/16.12 | | | | | | | (1865) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | COMBINE_EQS: (778), (1864) imply:
% 109.91/16.12 | | | | | | | (1866) all_4_0 = e1
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | COMBINE_EQS: (727), (1866) imply:
% 109.91/16.12 | | | | | | | (1867) all_44_0 = e1
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | REDUCE: (38), (1866) imply:
% 109.91/16.12 | | | | | | | (1868) op(all_4_1, all_4_2) = e1
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | BETA: splitting (136) gives:
% 109.91/16.12 | | | | | | |
% 109.91/16.12 | | | | | | | Case 1:
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | (1869) ~ (all_44_0 = e1)
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | REDUCE: (1867), (1869) imply:
% 109.91/16.12 | | | | | | | | (1870) $false
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | CLOSE: (1870) is inconsistent.
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | Case 2:
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | (1871) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | BETA: splitting (270) gives:
% 109.91/16.12 | | | | | | | |
% 109.91/16.12 | | | | | | | | Case 1:
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | (1872) ~ (all_56_15 = e1)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (554), (1872) imply:
% 109.91/16.12 | | | | | | | | | (1873) ~ (all_4_2 = e1)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REF_CLOSE: (37), (172), (188), (202), (203), (206), (207),
% 109.91/16.12 | | | | | | | | | (233), (235), (236), (273), (276), (356), (365),
% 109.91/16.12 | | | | | | | | | (450), (475), (477), (540), (545), (554), (569),
% 109.91/16.12 | | | | | | | | | (584), (595), (649), (675), (1865), (1868), (1871),
% 109.91/16.12 | | | | | | | | | (1873), (function-axioms) are inconsistent by
% 109.91/16.12 | | | | | | | | | sub-proof #232.
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | Case 2:
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | (1874) all_56_15 = e1
% 109.91/16.12 | | | | | | | | | (1875) ~ (all_56_11 = e0)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | COMBINE_EQS: (554), (1874) imply:
% 109.91/16.12 | | | | | | | | | (1876) all_4_2 = e1
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | SIMP: (1876) implies:
% 109.91/16.12 | | | | | | | | | (1877) all_4_2 = e1
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (362), (1875) imply:
% 109.91/16.12 | | | | | | | | | (1878) ~ (all_52_11 = e0)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (602), (1877) imply:
% 109.91/16.12 | | | | | | | | | (1879) ~ (all_52_11 = e1)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (603), (1877) imply:
% 109.91/16.12 | | | | | | | | | (1880) ~ (all_52_12 = e1)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (604), (1877) imply:
% 109.91/16.12 | | | | | | | | | (1881) ~ (all_52_13 = e1)
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | REDUCE: (37), (1877) imply:
% 109.91/16.12 | | | | | | | | | (1882) op(e0, e1) = all_4_1
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | BETA: splitting (300) gives:
% 109.91/16.12 | | | | | | | | |
% 109.91/16.12 | | | | | | | | | Case 1:
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | (1883) ~ (all_56_1 = e3)
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | REDUCE: (434), (1883) imply:
% 109.91/16.12 | | | | | | | | | | (1884) ~ (all_52_8 = e3)
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | BETA: splitting (291) gives:
% 109.91/16.12 | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | Case 1:
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | (1885) ~ (all_56_4 = e2)
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | REDUCE: (436), (1885) imply:
% 109.91/16.12 | | | | | | | | | | | (1886) ~ (all_52_9 = e2)
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 109.91/16.12 | | | | | | | | | | | all_4_1, e1, e0, simplifying with (201), (1882)
% 109.91/16.12 | | | | | | | | | | | gives:
% 109.91/16.12 | | | | | | | | | | | (1887) all_52_11 = all_4_1
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | COMBINE_EQS: (479), (1887) imply:
% 109.91/16.12 | | | | | | | | | | | (1888) all_54_14 = all_4_1
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | REDUCE: (169), (1887) imply:
% 109.91/16.12 | | | | | | | | | | | (1889) ~ (all_52_7 = all_4_1)
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | REDUCE: (599), (1887) imply:
% 109.91/16.12 | | | | | | | | | | | (1890) ~ (all_6_2 = all_4_1)
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | SIMP: (1890) implies:
% 109.91/16.12 | | | | | | | | | | | (1891) ~ (all_6_2 = all_4_1)
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | BETA: splitting (275) gives:
% 109.91/16.12 | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | Case 1:
% 109.91/16.12 | | | | | | | | | | | |
% 109.91/16.12 | | | | | | | | | | | | (1892) ~ (all_56_12 = e2)
% 109.91/16.12 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | REDUCE: (426), (1892) imply:
% 109.91/16.13 | | | | | | | | | | | | (1893) ~ (all_10_2 = e2)
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | BETA: splitting (304) gives:
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | (1894) ~ (all_56_0 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (413), (1894) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1895) ~ (all_52_4 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REF_CLOSE: (52), (167), (209), (213), (246), (248), (299),
% 109.91/16.13 | | | | | | | | | | | | | (352), (407), (412), (424), (426), (460), (553),
% 109.91/16.13 | | | | | | | | | | | | | (561), (565), (566), (579), (1698), (1700),
% 109.91/16.13 | | | | | | | | | | | | | (1884), (1893), (1895), (function-axioms) are
% 109.91/16.13 | | | | | | | | | | | | | inconsistent by sub-proof #142.
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | (1896) all_56_0 = e3
% 109.91/16.13 | | | | | | | | | | | | | (1897) ~ (all_56_14 = e2)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | COMBINE_EQS: (413), (1896) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1898) all_52_4 = e3
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (555), (1897) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1899) ~ (all_6_2 = e2)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (179), (1898) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1900) ~ (all_52_7 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | SIMP: (1900) implies:
% 109.91/16.13 | | | | | | | | | | | | | (1901) ~ (all_52_7 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (585), (1898) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1902) ~ (all_8_2 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | SIMP: (1902) implies:
% 109.91/16.13 | | | | | | | | | | | | | (1903) ~ (all_8_2 = e3)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | BETA: splitting (286) gives:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | (1904) ~ (all_56_6 = e1)
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | REDUCE: (386), (1904) imply:
% 109.91/16.13 | | | | | | | | | | | | | | (1905) ~ (all_52_2 = e1)
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | (1906) all_58_6 = e1
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | REF_CLOSE: (563), (1905), (1906) are inconsistent by
% 109.91/16.13 | | | | | | | | | | | | | | | sub-proof #452.
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | (1907) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | BETA: splitting (1907) gives:
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | | (1908) all_58_7 = e1
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | | REF_CLOSE: (156), (157), (172), (204), (208), (234), (235),
% 109.91/16.13 | | | | | | | | | | | | | | | | (238), (241), (243), (245), (288), (297), (385),
% 109.91/16.13 | | | | | | | | | | | | | | | | (407), (446), (462), (468), (477), (479), (551),
% 109.91/16.13 | | | | | | | | | | | | | | | | (552), (555), (567), (587), (589), (594), (1622),
% 109.91/16.13 | | | | | | | | | | | | | | | | (1623), (1702), (1878), (1879), (1880), (1881),
% 109.91/16.13 | | | | | | | | | | | | | | | | (1888), (1889), (1891), (1899), (1901), (1903),
% 109.91/16.13 | | | | | | | | | | | | | | | | (1908), (function-axioms) are inconsistent by
% 109.91/16.13 | | | | | | | | | | | | | | | | sub-proof #25.
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | | (1909) all_58_8 = e1 | all_58_11 = e1
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | | REF_CLOSE: (37), (172), (188), (202), (203), (206), (207),
% 109.91/16.13 | | | | | | | | | | | | | | | | (233), (235), (236), (273), (276), (356), (365),
% 109.91/16.13 | | | | | | | | | | | | | | | | (450), (475), (477), (540), (545), (554), (560),
% 109.91/16.13 | | | | | | | | | | | | | | | | (562), (568), (569), (584), (595), (605), (649),
% 109.91/16.13 | | | | | | | | | | | | | | | | (675), (1865), (1868), (1871), (1909),
% 109.91/16.13 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.91/16.13 | | | | | | | | | | | | | | | | #227.
% 109.91/16.13 | | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | (1910) all_56_6 = e1
% 109.91/16.13 | | | | | | | | | | | | | | (1911) ~ (all_56_14 = e3)
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | REF_CLOSE: (156), (157), (204), (208), (238), (241), (245),
% 109.91/16.13 | | | | | | | | | | | | | | (288), (297), (386), (407), (446), (462), (468),
% 109.91/16.13 | | | | | | | | | | | | | | (551), (555), (583), (1622), (1623), (1702),
% 109.91/16.13 | | | | | | | | | | | | | | (1880), (1881), (1899), (1910), (1911),
% 109.91/16.13 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 109.91/16.13 | | | | | | | | | | | | | | #24.
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | (1912) all_56_12 = e2
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | COMBINE_EQS: (426), (1912) imply:
% 109.91/16.13 | | | | | | | | | | | | (1913) all_10_2 = e2
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | SIMP: (1913) implies:
% 109.91/16.13 | | | | | | | | | | | | (1914) all_10_2 = e2
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | REDUCE: (571), (1914) imply:
% 109.91/16.13 | | | | | | | | | | | | (1915) ~ (all_52_1 = e2)
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | BETA: splitting (284) gives:
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | (1916) ~ (all_56_7 = e1)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (440), (1916) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1917) ~ (all_52_6 = e1)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | BETA: splitting (277) gives:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | (1918) ~ (all_56_14 = e3)
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | REF_CLOSE: (206), (238), (288), (340), (391), (394), (406),
% 109.91/16.13 | | | | | | | | | | | | | | (446), (551), (555), (564), (567), (568), (594),
% 109.91/16.13 | | | | | | | | | | | | | | (1623), (1886), (1915), (1918), (function-axioms)
% 109.91/16.13 | | | | | | | | | | | | | | are inconsistent by sub-proof #23.
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | (1919) all_56_14 = e3
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | Case 1:
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | (1920) ~ (all_56_6 = e1)
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | REDUCE: (386), (1920) imply:
% 109.91/16.13 | | | | | | | | | | | | | | | (1921) ~ (all_52_2 = e1)
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | REF_CLOSE: (37), (172), (188), (202), (203), (206), (207),
% 109.91/16.13 | | | | | | | | | | | | | | | (233), (235), (236), (273), (276), (331), (356),
% 109.91/16.13 | | | | | | | | | | | | | | | (365), (385), (450), (475), (477), (540), (545),
% 109.91/16.13 | | | | | | | | | | | | | | | (554), (560), (562), (563), (568), (569), (584),
% 109.91/16.13 | | | | | | | | | | | | | | | (595), (605), (649), (675), (1865), (1868),
% 109.91/16.13 | | | | | | | | | | | | | | | (1871), (1917), (1921), (function-axioms) are
% 109.91/16.13 | | | | | | | | | | | | | | | inconsistent by sub-proof #226.
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | (1922) ~ (all_56_14 = e3)
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | REDUCE: (1919), (1922) imply:
% 109.91/16.13 | | | | | | | | | | | | | | | (1923) $false
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | | CLOSE: (1923) is inconsistent.
% 109.91/16.13 | | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | (1924) ~ (all_56_12 = e2)
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | REDUCE: (1912), (1924) imply:
% 109.91/16.13 | | | | | | | | | | | | | (1925) $false
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | | CLOSE: (1925) is inconsistent.
% 109.91/16.13 | | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | (1926) ~ (all_56_15 = e1)
% 109.91/16.13 | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | REDUCE: (1874), (1926) imply:
% 109.91/16.13 | | | | | | | | | | | (1927) $false
% 109.91/16.13 | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | | CLOSE: (1927) is inconsistent.
% 109.91/16.13 | | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | Case 2:
% 109.91/16.13 | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | (1928) ~ (all_56_15 = e1)
% 109.91/16.13 | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | REDUCE: (1874), (1928) imply:
% 109.91/16.13 | | | | | | | | | | (1929) $false
% 109.91/16.13 | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | | CLOSE: (1929) is inconsistent.
% 109.91/16.13 | | | | | | | | | |
% 109.91/16.13 | | | | | | | | | End of split
% 109.91/16.13 | | | | | | | | |
% 109.91/16.13 | | | | | | | | End of split
% 109.91/16.13 | | | | | | | |
% 109.91/16.13 | | | | | | | End of split
% 109.91/16.13 | | | | | | |
% 109.91/16.13 | | | | | | End of split
% 109.91/16.13 | | | | | |
% 109.91/16.13 | | | | | Case 2:
% 109.91/16.13 | | | | | |
% 109.91/16.13 | | | | | | (1930) all_18_0 = e3
% 109.91/16.13 | | | | | | (1931) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 109.91/16.14 | | | | | |
% 109.91/16.14 | | | | | | COMBINE_EQS: (771), (1930) imply:
% 109.91/16.14 | | | | | | (1932) all_6_0 = e3
% 109.91/16.14 | | | | | |
% 109.91/16.14 | | | | | | REDUCE: (1622), (1932) imply:
% 109.91/16.14 | | | | | | (1933) op(e2, all_6_2) = e3
% 109.91/16.14 | | | | | |
% 110.29/16.14 | | | | | | REF_CLOSE: (41), (52), (150), (157), (167), (206), (207), (208),
% 110.29/16.14 | | | | | | (209), (211), (212), (213), (238), (245), (246), (248),
% 110.29/16.14 | | | | | | (274), (281), (290), (291), (293), (295), (299), (327),
% 110.29/16.14 | | | | | | (340), (346), (371), (391), (394), (406), (407), (424),
% 110.29/16.14 | | | | | | (426), (430), (436), (446), (460), (462), (533), (548),
% 110.29/16.14 | | | | | | (551), (553), (554), (555), (557), (560), (561), (564),
% 110.29/16.14 | | | | | | (567), (568), (571), (573), (579), (581), (594), (596),
% 110.29/16.14 | | | | | | (705), (1621), (1623), (1698), (1699), (1700), (1931),
% 110.29/16.14 | | | | | | (1933), (function-axioms) are inconsistent by sub-proof
% 110.29/16.14 | | | | | | #12.
% 110.29/16.14 | | | | | |
% 110.29/16.14 | | | | | End of split
% 110.29/16.14 | | | | |
% 110.29/16.14 | | | | End of split
% 110.29/16.14 | | | |
% 110.29/16.14 | | | End of split
% 110.29/16.14 | | |
% 110.29/16.14 | | End of split
% 110.29/16.14 | |
% 110.29/16.14 | Case 2:
% 110.29/16.14 | |
% 110.29/16.14 | | (1934) all_4_0 = e3
% 110.29/16.14 | | (1935) ~ (all_4_1 = e1) | ~ (all_4_2 = e2)
% 110.29/16.14 | |
% 110.29/16.14 | | COMBINE_EQS: (764), (1934) imply:
% 110.29/16.14 | | (1936) all_20_0 = e3
% 110.29/16.14 | |
% 110.29/16.14 | | REDUCE: (38), (1934) imply:
% 110.29/16.14 | | (1937) op(all_4_1, all_4_2) = e3
% 110.29/16.14 | |
% 110.29/16.14 | | BETA: splitting (44) gives:
% 110.29/16.14 | |
% 110.29/16.14 | | Case 1:
% 110.29/16.14 | | |
% 110.29/16.14 | | | (1938) ~ (all_6_1 = e2)
% 110.29/16.14 | | |
% 110.29/16.14 | | | BETA: splitting (49) gives:
% 110.29/16.14 | | |
% 110.29/16.14 | | | Case 1:
% 110.29/16.14 | | | |
% 110.29/16.14 | | | | (1939) ~ (all_8_1 = e1)
% 110.29/16.14 | | | |
% 110.29/16.14 | | | | BETA: splitting (54) gives:
% 110.29/16.14 | | | |
% 110.29/16.14 | | | | Case 1:
% 110.29/16.14 | | | | |
% 110.29/16.14 | | | | | (1940) ~ (all_10_0 = e2)
% 110.29/16.14 | | | | |
% 110.29/16.14 | | | | | BETA: splitting (63) gives:
% 110.29/16.14 | | | | |
% 110.29/16.14 | | | | | Case 1:
% 110.29/16.14 | | | | | |
% 110.29/16.14 | | | | | | (1941) ~ (all_14_0 = e1)
% 110.29/16.14 | | | | | |
% 110.29/16.14 | | | | | | REDUCE: (776), (1941) imply:
% 110.29/16.14 | | | | | | (1942) ~ (all_8_0 = e1)
% 110.29/16.14 | | | | | |
% 110.29/16.14 | | | | | | BETA: splitting (68) gives:
% 110.29/16.14 | | | | | |
% 110.29/16.14 | | | | | | Case 1:
% 110.29/16.14 | | | | | | |
% 110.29/16.14 | | | | | | | (1943) ~ (all_16_0 = e1)
% 110.29/16.14 | | | | | | |
% 110.29/16.14 | | | | | | | REDUCE: (775), (1943) imply:
% 110.29/16.14 | | | | | | | (1944) ~ (all_10_0 = e1)
% 110.29/16.14 | | | | | | |
% 110.29/16.14 | | | | | | | BETA: splitting (78) gives:
% 110.29/16.14 | | | | | | |
% 110.29/16.14 | | | | | | | Case 1:
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | (1945) ~ (all_20_0 = e3)
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | REDUCE: (1936), (1945) imply:
% 110.29/16.14 | | | | | | | | (1946) $false
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | CLOSE: (1946) is inconsistent.
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | Case 2:
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | (1947) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | BETA: splitting (83) gives:
% 110.29/16.14 | | | | | | | |
% 110.29/16.14 | | | | | | | | Case 1:
% 110.29/16.14 | | | | | | | | |
% 110.29/16.14 | | | | | | | | | (1948) ~ (all_22_1 = e3)
% 110.29/16.14 | | | | | | | | |
% 110.29/16.14 | | | | | | | | | REDUCE: (690), (1948) imply:
% 110.29/16.14 | | | | | | | | | (1949) ~ (all_8_1 = e3)
% 110.29/16.14 | | | | | | | | |
% 110.29/16.14 | | | | | | | | | BETA: splitting (98) gives:
% 110.29/16.14 | | | | | | | | |
% 110.29/16.14 | | | | | | | | | Case 1:
% 110.29/16.14 | | | | | | | | | |
% 110.29/16.14 | | | | | | | | | | (1950) ~ (all_28_0 = e2)
% 110.29/16.14 | | | | | | | | | |
% 110.29/16.14 | | | | | | | | | | REF_CLOSE: (6), (8), (37), (42), (43), (52), (53), (107),
% 110.29/16.14 | | | | | | | | | | (116), (121), (126), (154), (157), (162), (164),
% 110.29/16.14 | | | | | | | | | | (165), (169), (170), (172), (179), (183), (185),
% 110.29/16.14 | | | | | | | | | | (187), (188), (201), (202), (203), (204), (206),
% 110.29/16.14 | | | | | | | | | | (207), (208), (209), (212), (213), (214), (233),
% 110.29/16.14 | | | | | | | | | | (234), (235), (236), (237), (238), (239), (240),
% 110.29/16.14 | | | | | | | | | | (241), (242), (243), (245), (246), (247), (248),
% 110.29/16.14 | | | | | | | | | | (270), (271), (272), (273), (274), (275), (276),
% 110.29/16.14 | | | | | | | | | | (277), (278), (279), (281), (282), (283), (284),
% 110.29/16.14 | | | | | | | | | | (285), (286), (287), (288), (289), (290), (291),
% 110.29/16.14 | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298),
% 110.29/16.14 | | | | | | | | | | (299), (300), (302), (303), (304), (305), (323),
% 110.29/16.14 | | | | | | | | | | (327), (328), (330), (331), (332), (335), (336),
% 110.29/16.14 | | | | | | | | | | (340), (342), (343), (344), (345), (352), (356),
% 110.29/16.14 | | | | | | | | | | (362), (365), (370), (371), (375), (385), (386),
% 110.29/16.14 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 110.29/16.14 | | | | | | | | | | (426), (430), (434), (436), (440), (446), (450),
% 110.29/16.14 | | | | | | | | | | (458), (460), (462), (466), (468), (470), (472),
% 110.29/16.14 | | | | | | | | | | (474), (475), (477), (479), (500), (502), (524),
% 110.29/16.15 | | | | | | | | | | (543), (551), (552), (553), (554), (555), (556),
% 110.29/16.15 | | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 110.29/16.15 | | | | | | | | | | (564), (565), (566), (567), (568), (569), (571),
% 110.29/16.15 | | | | | | | | | | (573), (575), (577), (579), (581), (582), (583),
% 110.29/16.15 | | | | | | | | | | (584), (585), (587), (589), (591), (594), (595),
% 110.29/16.15 | | | | | | | | | | (596), (597), (599), (601), (602), (603), (604),
% 110.29/16.15 | | | | | | | | | | (605), (670), (694), (700), (702), (703), (731),
% 110.29/16.15 | | | | | | | | | | (741), (758), (779), (780), (1937), (1938),
% 110.29/16.15 | | | | | | | | | | (1940), (1944), (1947), (1950), (function-axioms)
% 110.29/16.15 | | | | | | | | | | are inconsistent by sub-proof #8.
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | Case 2:
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | | (1951) all_28_0 = e2
% 110.29/16.15 | | | | | | | | | | (1952) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | | COMBINE_EQS: (758), (1951) imply:
% 110.29/16.15 | | | | | | | | | | (1953) all_6_0 = e2
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (37), (42), (43), (47), (52),
% 110.29/16.15 | | | | | | | | | | (53), (107), (121), (154), (161), (162), (164),
% 110.29/16.15 | | | | | | | | | | (165), (167), (169), (170), (172), (177), (178),
% 110.29/16.15 | | | | | | | | | | (179), (180), (185), (187), (188), (193), (201),
% 110.29/16.15 | | | | | | | | | | (202), (204), (206), (207), (208), (209), (212),
% 110.29/16.15 | | | | | | | | | | (213), (214), (233), (234), (235), (237), (238),
% 110.29/16.15 | | | | | | | | | | (239), (240), (242), (243), (245), (246), (247),
% 110.29/16.15 | | | | | | | | | | (248), (270), (271), (272), (273), (274), (275),
% 110.29/16.15 | | | | | | | | | | (276), (277), (278), (279), (280), (281), (283),
% 110.29/16.15 | | | | | | | | | | (284), (285), (286), (287), (288), (289), (290),
% 110.29/16.15 | | | | | | | | | | (291), (292), (293), (294), (295), (296), (298),
% 110.29/16.15 | | | | | | | | | | (299), (300), (301), (302), (303), (304), (305),
% 110.29/16.15 | | | | | | | | | | (323), (325), (327), (329), (331), (332), (335),
% 110.29/16.15 | | | | | | | | | | (336), (340), (342), (343), (344), (345), (352),
% 110.29/16.15 | | | | | | | | | | (356), (362), (365), (370), (371), (385), (386),
% 110.29/16.15 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 110.29/16.15 | | | | | | | | | | (426), (430), (434), (436), (440), (446), (450),
% 110.29/16.15 | | | | | | | | | | (458), (460), (462), (466), (470), (472), (474),
% 110.29/16.15 | | | | | | | | | | (477), (479), (502), (522), (524), (551), (552),
% 110.29/16.15 | | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 110.29/16.15 | | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 110.29/16.15 | | | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 110.29/16.15 | | | | | | | | | | (579), (581), (582), (583), (585), (587), (589),
% 110.29/16.15 | | | | | | | | | | (591), (593), (594), (595), (596), (597), (599),
% 110.29/16.15 | | | | | | | | | | (601), (602), (603), (604), (605), (683), (700),
% 110.29/16.15 | | | | | | | | | | (702), (741), (779), (1938), (1940), (1944),
% 110.29/16.15 | | | | | | | | | | (1949), (1952), (1953), (function-axioms) are
% 110.29/16.15 | | | | | | | | | | inconsistent by sub-proof #240.
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | End of split
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | Case 2:
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | (1954) all_22_1 = e3
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | COMBINE_EQS: (690), (1954) imply:
% 110.29/16.15 | | | | | | | | | (1955) all_8_1 = e3
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | SIMP: (1955) implies:
% 110.29/16.15 | | | | | | | | | (1956) all_8_1 = e3
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | REDUCE: (48), (1956) imply:
% 110.29/16.15 | | | | | | | | | (1957) op(e3, all_8_2) = all_8_0
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | REDUCE: (47), (1956) imply:
% 110.29/16.15 | | | | | | | | | (1958) op(e2, all_8_2) = e3
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | BETA: splitting (98) gives:
% 110.29/16.15 | | | | | | | | |
% 110.29/16.15 | | | | | | | | | Case 1:
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.15 | | | | | | | | | | (1959) ~ (all_28_0 = e2)
% 110.29/16.15 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | | REF_CLOSE: (6), (8), (37), (42), (43), (52), (53), (107),
% 110.29/16.16 | | | | | | | | | | (116), (121), (126), (154), (157), (162), (164),
% 110.29/16.16 | | | | | | | | | | (165), (169), (170), (172), (179), (183), (185),
% 110.29/16.16 | | | | | | | | | | (187), (188), (201), (202), (203), (204), (206),
% 110.29/16.16 | | | | | | | | | | (207), (208), (209), (212), (213), (214), (233),
% 110.29/16.16 | | | | | | | | | | (234), (235), (236), (237), (238), (239), (240),
% 110.29/16.16 | | | | | | | | | | (241), (242), (243), (245), (246), (247), (248),
% 110.29/16.16 | | | | | | | | | | (270), (271), (272), (273), (274), (275), (276),
% 110.29/16.16 | | | | | | | | | | (277), (278), (279), (281), (282), (283), (284),
% 110.29/16.16 | | | | | | | | | | (285), (286), (287), (288), (289), (290), (291),
% 110.29/16.16 | | | | | | | | | | (292), (293), (294), (295), (296), (297), (298),
% 110.29/16.16 | | | | | | | | | | (299), (300), (302), (303), (304), (305), (323),
% 110.29/16.16 | | | | | | | | | | (327), (328), (330), (331), (332), (335), (336),
% 110.29/16.16 | | | | | | | | | | (340), (342), (343), (344), (345), (352), (356),
% 110.29/16.16 | | | | | | | | | | (362), (365), (370), (371), (375), (385), (386),
% 110.29/16.16 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 110.29/16.16 | | | | | | | | | | (426), (430), (434), (436), (440), (446), (450),
% 110.29/16.16 | | | | | | | | | | (458), (460), (462), (466), (468), (470), (472),
% 110.29/16.16 | | | | | | | | | | (474), (475), (477), (479), (500), (502), (524),
% 110.29/16.16 | | | | | | | | | | (543), (551), (552), (553), (554), (555), (556),
% 110.29/16.16 | | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 110.29/16.16 | | | | | | | | | | (564), (565), (566), (567), (568), (569), (571),
% 110.29/16.16 | | | | | | | | | | (573), (575), (577), (579), (581), (582), (583),
% 110.29/16.16 | | | | | | | | | | (584), (585), (587), (589), (591), (594), (595),
% 110.29/16.16 | | | | | | | | | | (596), (597), (599), (601), (602), (603), (604),
% 110.29/16.16 | | | | | | | | | | (605), (670), (694), (700), (702), (703), (731),
% 110.29/16.16 | | | | | | | | | | (741), (758), (779), (780), (1937), (1938),
% 110.29/16.16 | | | | | | | | | | (1940), (1944), (1947), (1959), (function-axioms)
% 110.29/16.16 | | | | | | | | | | are inconsistent by sub-proof #8.
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | Case 2:
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | | (1960) all_28_0 = e2
% 110.29/16.16 | | | | | | | | | | (1961) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | | COMBINE_EQS: (758), (1960) imply:
% 110.29/16.16 | | | | | | | | | | (1962) all_6_0 = e2
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | | REDUCE: (43), (1962) imply:
% 110.29/16.16 | | | | | | | | | | (1963) op(all_6_1, all_6_2) = e2
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | | REF_CLOSE: (5), (8), (9), (37), (42), (52), (53), (107),
% 110.29/16.16 | | | | | | | | | | (121), (154), (161), (162), (164), (165), (167),
% 110.29/16.16 | | | | | | | | | | (169), (170), (172), (178), (179), (180), (184),
% 110.29/16.16 | | | | | | | | | | (185), (187), (188), (193), (201), (202), (204),
% 110.29/16.16 | | | | | | | | | | (206), (207), (208), (209), (211), (212), (213),
% 110.29/16.16 | | | | | | | | | | (214), (233), (234), (235), (237), (238), (239),
% 110.29/16.16 | | | | | | | | | | (240), (242), (243), (245), (246), (247), (248),
% 110.29/16.16 | | | | | | | | | | (270), (271), (272), (273), (274), (275), (276),
% 110.29/16.16 | | | | | | | | | | (277), (278), (279), (280), (281), (283), (284),
% 110.29/16.16 | | | | | | | | | | (285), (286), (287), (288), (289), (290), (291),
% 110.29/16.16 | | | | | | | | | | (292), (293), (294), (295), (296), (298), (299),
% 110.29/16.16 | | | | | | | | | | (300), (301), (302), (303), (304), (305), (323),
% 110.29/16.16 | | | | | | | | | | (325), (327), (331), (332), (335), (336), (337),
% 110.29/16.16 | | | | | | | | | | (340), (342), (343), (344), (345), (346), (349),
% 110.29/16.16 | | | | | | | | | | (352), (356), (362), (365), (370), (371), (385),
% 110.29/16.16 | | | | | | | | | | (386), (391), (394), (406), (407), (412), (413),
% 110.29/16.16 | | | | | | | | | | (424), (426), (430), (434), (436), (440), (446),
% 110.29/16.16 | | | | | | | | | | (450), (458), (460), (462), (466), (470), (472),
% 110.29/16.16 | | | | | | | | | | (474), (477), (479), (502), (522), (524), (551),
% 110.29/16.16 | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 110.29/16.16 | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 110.29/16.16 | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 110.29/16.16 | | | | | | | | | | (577), (579), (581), (582), (583), (584), (585),
% 110.29/16.16 | | | | | | | | | | (587), (589), (591), (593), (594), (595), (596),
% 110.29/16.16 | | | | | | | | | | (597), (599), (601), (602), (603), (604), (605),
% 110.29/16.16 | | | | | | | | | | (683), (700), (702), (741), (779), (1938), (1940),
% 110.29/16.16 | | | | | | | | | | (1942), (1944), (1957), (1958), (1961), (1963),
% 110.29/16.16 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.29/16.16 | | | | | | | | | | #216.
% 110.29/16.16 | | | | | | | | | |
% 110.29/16.16 | | | | | | | | | End of split
% 110.29/16.16 | | | | | | | | |
% 110.29/16.16 | | | | | | | | End of split
% 110.29/16.16 | | | | | | | |
% 110.29/16.16 | | | | | | | End of split
% 110.29/16.16 | | | | | | |
% 110.29/16.16 | | | | | | Case 2:
% 110.29/16.16 | | | | | | |
% 110.29/16.16 | | | | | | | (1964) all_16_0 = e1
% 110.29/16.16 | | | | | | | (1965) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 110.29/16.16 | | | | | | |
% 110.29/16.16 | | | | | | | COMBINE_EQS: (775), (1964) imply:
% 110.29/16.16 | | | | | | | (1966) all_10_0 = e1
% 110.29/16.16 | | | | | | |
% 110.29/16.17 | | | | | | | REF_CLOSE: (8), (37), (42), (43), (52), (53), (88), (98), (116),
% 110.29/16.17 | | | | | | | (126), (154), (156), (157), (161), (162), (165), (170),
% 110.29/16.17 | | | | | | | (172), (177), (178), (179), (180), (183), (185), (187),
% 110.29/16.17 | | | | | | | (188), (189), (190), (202), (204), (206), (207), (209),
% 110.29/16.17 | | | | | | | (212), (213), (214), (233), (234), (235), (236), (237),
% 110.29/16.17 | | | | | | | (238), (239), (240), (241), (242), (243), (245), (246),
% 110.29/16.17 | | | | | | | (247), (248), (270), (271), (272), (273), (274), (275),
% 110.29/16.17 | | | | | | | (276), (277), (278), (279), (281), (282), (283), (284),
% 110.29/16.17 | | | | | | | (286), (287), (288), (289), (290), (291), (293), (294),
% 110.29/16.17 | | | | | | | (295), (296), (297), (298), (299), (300), (302), (304),
% 110.29/16.17 | | | | | | | (305), (323), (328), (329), (330), (331), (332), (335),
% 110.29/16.17 | | | | | | | (336), (340), (342), (343), (344), (345), (352), (356),
% 110.29/16.17 | | | | | | | (362), (365), (370), (371), (375), (385), (386), (391),
% 110.29/16.17 | | | | | | | (394), (406), (407), (412), (413), (424), (426), (430),
% 110.29/16.17 | | | | | | | (434), (436), (440), (446), (450), (458), (460), (462),
% 110.29/16.17 | | | | | | | (466), (468), (470), (472), (474), (475), (477), (479),
% 110.29/16.17 | | | | | | | (522), (530), (537), (543), (551), (552), (553), (554),
% 110.29/16.17 | | | | | | | (555), (556), (557), (558), (559), (560), (561), (562),
% 110.29/16.17 | | | | | | | (563), (564), (565), (566), (567), (568), (569), (571),
% 110.29/16.17 | | | | | | | (573), (575), (577), (579), (581), (582), (583), (584),
% 110.29/16.17 | | | | | | | (585), (587), (589), (591), (593), (594), (595), (596),
% 110.29/16.17 | | | | | | | (597), (601), (602), (603), (604), (605), (661), (670),
% 110.29/16.17 | | | | | | | (683), (695), (703), (731), (758), (759), (780),
% 110.29/16.17 | | | | | | | (1938), (1940), (1965), (1966), (function-axioms) are
% 110.29/16.17 | | | | | | | inconsistent by sub-proof #5.
% 110.29/16.17 | | | | | | |
% 110.29/16.17 | | | | | | End of split
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | Case 2:
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | | (1967) all_14_0 = e1
% 110.29/16.17 | | | | | | (1968) ~ (all_14_1 = e3) | ~ (all_14_2 = e0)
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | | COMBINE_EQS: (776), (1967) imply:
% 110.29/16.17 | | | | | | (1969) all_8_0 = e1
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | | COMBINE_EQS: (781), (1969) imply:
% 110.29/16.17 | | | | | | (1970) all_42_0 = e1
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | | BETA: splitting (68) gives:
% 110.29/16.17 | | | | | |
% 110.29/16.17 | | | | | | Case 1:
% 110.29/16.17 | | | | | | |
% 110.29/16.17 | | | | | | | (1971) ~ (all_16_0 = e1)
% 110.29/16.17 | | | | | | |
% 110.29/16.17 | | | | | | | REDUCE: (775), (1971) imply:
% 110.29/16.17 | | | | | | | (1972) ~ (all_10_0 = e1)
% 110.29/16.17 | | | | | | |
% 110.29/16.17 | | | | | | | BETA: splitting (98) gives:
% 110.29/16.17 | | | | | | |
% 110.29/16.17 | | | | | | | Case 1:
% 110.29/16.17 | | | | | | | |
% 110.29/16.17 | | | | | | | | (1973) ~ (all_28_0 = e2)
% 110.29/16.17 | | | | | | | |
% 110.29/16.17 | | | | | | | | REDUCE: (758), (1973) imply:
% 110.29/16.17 | | | | | | | | (1974) ~ (all_6_0 = e2)
% 110.29/16.17 | | | | | | | |
% 110.29/16.17 | | | | | | | | BETA: splitting (107) gives:
% 110.29/16.17 | | | | | | | |
% 110.29/16.17 | | | | | | | | Case 1:
% 110.29/16.17 | | | | | | | | |
% 110.29/16.17 | | | | | | | | | (1975) ~ (all_32_1 = e1)
% 110.29/16.17 | | | | | | | | |
% 110.29/16.17 | | | | | | | | | REDUCE: (700), (1975) imply:
% 110.29/16.17 | | | | | | | | | (1976) ~ (all_10_1 = e1)
% 110.29/16.17 | | | | | | | | |
% 110.29/16.17 | | | | | | | | | BETA: splitting (116) gives:
% 110.29/16.17 | | | | | | | | |
% 110.29/16.17 | | | | | | | | | Case 1:
% 110.29/16.17 | | | | | | | | | |
% 110.29/16.17 | | | | | | | | | | (1977) ~ (all_36_1 = e3)
% 110.29/16.17 | | | | | | | | | |
% 110.29/16.17 | | | | | | | | | | REDUCE: (670), (1977) imply:
% 110.29/16.17 | | | | | | | | | | (1978) ~ (all_6_1 = e3)
% 110.29/16.17 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | REF_CLOSE: (8), (42), (43), (52), (53), (121), (126), (154),
% 110.29/16.18 | | | | | | | | | | (170), (172), (179), (183), (185), (187), (202),
% 110.29/16.18 | | | | | | | | | | (204), (206), (207), (208), (209), (212), (213),
% 110.29/16.18 | | | | | | | | | | (214), (233), (235), (236), (237), (238), (239),
% 110.29/16.18 | | | | | | | | | | (240), (242), (245), (247), (248), (270), (271),
% 110.29/16.18 | | | | | | | | | | (272), (273), (274), (276), (277), (278), (279),
% 110.29/16.18 | | | | | | | | | | (281), (283), (284), (285), (286), (287), (288),
% 110.29/16.18 | | | | | | | | | | (291), (292), (293), (295), (299), (303), (304),
% 110.29/16.18 | | | | | | | | | | (305), (323), (327), (331), (336), (340), (343),
% 110.29/16.18 | | | | | | | | | | (344), (345), (352), (356), (362), (370), (371),
% 110.29/16.18 | | | | | | | | | | (375), (385), (386), (391), (394), (406), (407),
% 110.29/16.18 | | | | | | | | | | (412), (413), (424), (426), (430), (436), (440),
% 110.29/16.18 | | | | | | | | | | (446), (450), (458), (462), (466), (470), (472),
% 110.29/16.18 | | | | | | | | | | (474), (475), (477), (502), (551), (553), (554),
% 110.29/16.18 | | | | | | | | | | (555), (556), (557), (558), (559), (560), (561),
% 110.29/16.18 | | | | | | | | | | (562), (563), (564), (565), (566), (567), (568),
% 110.29/16.18 | | | | | | | | | | (569), (571), (573), (575), (577), (579), (581),
% 110.29/16.18 | | | | | | | | | | (583), (584), (594), (596), (597), (601), (602),
% 110.29/16.18 | | | | | | | | | | (603), (605), (702), (703), (731), (741), (1938),
% 110.29/16.18 | | | | | | | | | | (1940), (1972), (1974), (1976), (1978),
% 110.29/16.18 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.29/16.18 | | | | | | | | | | #363.
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | Case 2:
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | (1979) all_36_1 = e3
% 110.29/16.18 | | | | | | | | | | (1980) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | COMBINE_EQS: (670), (1979) imply:
% 110.29/16.18 | | | | | | | | | | (1981) all_6_1 = e3
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | REDUCE: (43), (1981) imply:
% 110.29/16.18 | | | | | | | | | | (1982) op(e3, all_6_2) = all_6_0
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | REDUCE: (42), (1981) imply:
% 110.29/16.18 | | | | | | | | | | (1983) op(e1, all_6_2) = e3
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | BETA: splitting (121) gives:
% 110.29/16.18 | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | (1984) ~ (all_38_1 = e2)
% 110.29/16.18 | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | REDUCE: (702), (1984) imply:
% 110.29/16.18 | | | | | | | | | | | (1985) ~ (all_10_1 = e2)
% 110.29/16.18 | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | BETA: splitting (131) gives:
% 110.29/16.18 | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | (1986) ~ (all_42_0 = e1)
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | REDUCE: (1970), (1986) imply:
% 110.29/16.18 | | | | | | | | | | | | (1987) $false
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | CLOSE: (1987) is inconsistent.
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | Case 2:
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | (1988) ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | BETA: splitting (274) gives:
% 110.29/16.18 | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | (1989) ~ (all_56_14 = e2)
% 110.29/16.18 | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | REDUCE: (555), (1989) imply:
% 110.29/16.18 | | | | | | | | | | | | | (1990) ~ (all_6_2 = e2)
% 110.29/16.18 | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | BETA: splitting (275) gives:
% 110.29/16.18 | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | (1991) ~ (all_56_12 = e2)
% 110.29/16.18 | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | REDUCE: (426), (1991) imply:
% 110.29/16.18 | | | | | | | | | | | | | | (1992) ~ (all_10_2 = e2)
% 110.29/16.18 | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 110.29/16.18 | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | (1993) ~ (all_56_15 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (554), (1993) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (1994) ~ (all_4_2 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REF_CLOSE: (8), (52), (53), (154), (157), (179), (202),
% 110.29/16.18 | | | | | | | | | | | | | | | (204), (207), (212), (214), (233), (238), (241),
% 110.29/16.18 | | | | | | | | | | | | | | | (245), (247), (248), (271), (272), (273), (277),
% 110.29/16.18 | | | | | | | | | | | | | | | (279), (281), (282), (284), (286), (288), (291),
% 110.29/16.18 | | | | | | | | | | | | | | | (292), (295), (297), (299), (305), (323), (331),
% 110.29/16.18 | | | | | | | | | | | | | | | (332), (340), (343), (344), (356), (362), (365),
% 110.29/16.18 | | | | | | | | | | | | | | | (370), (371), (385), (386), (391), (394), (406),
% 110.29/16.18 | | | | | | | | | | | | | | | (407), (413), (426), (430), (436), (440), (446),
% 110.29/16.18 | | | | | | | | | | | | | | | (450), (458), (462), (468), (551), (553), (554),
% 110.29/16.18 | | | | | | | | | | | | | | | (555), (556), (557), (558), (559), (560), (562),
% 110.29/16.18 | | | | | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 110.29/16.18 | | | | | | | | | | | | | | | (571), (573), (577), (581), (583), (594), (603),
% 110.29/16.18 | | | | | | | | | | | | | | | (604), (605), (1940), (1972), (1974), (1976),
% 110.29/16.18 | | | | | | | | | | | | | | | (1982), (1983), (1985), (1990), (1992), (1994),
% 110.29/16.18 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.29/16.18 | | | | | | | | | | | | | | | #340.
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | Case 2:
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | (1995) all_56_15 = e3
% 110.29/16.18 | | | | | | | | | | | | | | | (1996) ~ (all_56_9 = e0)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (1995) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (1997) all_4_2 = e3
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | SIMP: (1997) implies:
% 110.29/16.18 | | | | | | | | | | | | | | | (1998) all_4_2 = e3
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (450), (1996) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (1999) ~ (all_52_3 = e0)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (584), (1998) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (2000) ~ (all_52_3 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (603), (1998) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (2001) ~ (all_52_12 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (604), (1998) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (2002) ~ (all_52_13 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | REDUCE: (37), (1998) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | (2003) op(e0, e3) = all_4_1
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 110.29/16.18 | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | (2004) ~ (all_56_3 = e2)
% 110.29/16.18 | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | REDUCE: (430), (2004) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | (2005) ~ (all_52_1 = e2)
% 110.29/16.18 | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 110.29/16.18 | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2006) ~ (all_56_6 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | REDUCE: (386), (2006) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2007) ~ (all_52_2 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 110.29/16.18 | | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (2003)
% 110.29/16.18 | | | | | | | | | | | | | | | | | gives:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2008) all_52_3 = all_4_1
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2008) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2009) all_54_12 = all_4_1
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | REDUCE: (188), (2008) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2010) ~ (all_52_2 = all_4_1)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | REDUCE: (575), (2008) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2011) ~ (all_10_2 = all_4_1)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | SIMP: (2011) implies:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2012) ~ (all_10_2 = all_4_1)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | REDUCE: (2000), (2008) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2013) ~ (all_4_1 = e3)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | REDUCE: (1999), (2008) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | (2014) ~ (all_4_1 = e0)
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 110.29/16.18 | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | (2015) ~ (all_56_8 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | REDUCE: (371), (2015) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | (2016) ~ (all_52_14 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 110.29/16.18 | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | (2017) all_58_6 = e1
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (563), (2007), (2017) are inconsistent by
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | sub-proof #452.
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | (2018) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (2018) gives:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | (2019) all_58_7 = e1
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2019) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | (2020) all_52_6 = e1
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (2020) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | (2021) ~ (all_52_14 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (2020) imply:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | (2022) ~ (all_8_2 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | SIMP: (2022) implies:
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | (2023) ~ (all_8_2 = e1)
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (2020) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | (2024) ~ (all_6_2 = e1)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2025) ~ (all_56_1 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (2025) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2026) ~ (all_52_8 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | (2027) all_58_0 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (2027) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | (2028) all_10_2 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (2028) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | (2029) $false
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2029) is inconsistent.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | (2030) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2030) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2031) all_58_1 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (2031) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2032) all_52_4 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2032) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2033) ~ (all_10_2 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (2032) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2034) ~ (all_8_2 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2034) implies:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2035) ~ (all_8_2 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | (2036) all_54_5 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (552), (2035), (2036) are inconsistent by
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2037) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | (2038) all_54_5 = e2
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (552), (567), (2038) are inconsistent by sub-proof
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | #338.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | (2039) ~ (all_54_5 = e2)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | (2040) all_54_5 = e1 | all_54_5 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2040) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2041) all_54_5 = e1
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (552), (2023), (2041) are inconsistent by
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2042) all_54_5 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (552), (2042) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2043) all_8_2 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2043) implies:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2044) all_8_2 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (2044) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2045) ~ (all_52_13 = e0)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (2044) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (2046) op(e2, e0) = all_8_1
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047) all_54_7 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (2002), (2047) are inconsistent by
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #350.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2048) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2048) gives:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2049) all_54_7 = e2
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (2049) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2050) all_52_13 = e2
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2050) implies:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051) all_52_13 = e2
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (2051) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2052) all_56_5 = e2
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (211), (238), (243), (244), (248), (286),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (290), (331), (346), (385), (386),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406), (424), (426), (464), (544), (551), (552),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553), (555), (556), (560), (562), (563), (566),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567), (568), (571), (582), (587), (657), (1988),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1990), (1992), (2005), (2016), (2052),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #4.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_54_7 = e1 | all_54_7 = e0
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (208), (468), (1939), (2045), (2046), (2053),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #33.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | (2054) all_58_4 = e3 | all_58_9 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (412), (561), (2001), (2026), (2054) are
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2055) all_56_1 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2056) ~ (all_56_12 = e1)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (434), (2055) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2057) all_52_8 = e3
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (2056) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2058) ~ (all_10_2 = e1)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (2057) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2059) ~ (all_52_12 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (2057) imply:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2060) ~ (all_10_2 = e3)
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (212), (245), (248), (284), (331), (385),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (426), (440), (462), (553), (560), (562), (563),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (566), (568), (581), (1976), (1985), (2001),
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | (2007), (2016), (2058), (function-axioms) are
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444.
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | | End of split
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.29/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | | (2061) all_58_8 = e1 | all_58_11 = e1
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (560), (562), (568), (2016), (2061) are
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #445.
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | (2062) all_56_8 = e1
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (2062) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | (2063) all_52_14 = e1
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | REDUCE: (156), (2063) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | (2064) ~ (all_52_12 = e1)
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | REDUCE: (154), (2063) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | (2065) ~ (all_52_13 = e1)
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | REDUCE: (601), (2063) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | (2066) ~ (all_6_2 = e1)
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (2067) ~ (all_56_8 = e1)
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | REDUCE: (2062), (2067) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (2068) $false
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | CLOSE: (2068) is inconsistent.
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (2069) ~ (all_56_12 = e0)
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | REDUCE: (426), (2069) imply:
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (2070) ~ (all_10_2 = e0)
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (157), (204), (207), (212), (236), (238),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (240), (241), (245), (248), (288), (297), (330),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (407), (446), (462), (468), (470), (551), (553),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (555), (563), (566), (568), (573), (583), (1974),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (1982), (1983), (1990), (1992), (2009), (2010),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (2012), (2013), (2014), (2064), (2065), (2070),
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.19 | | | | | | | | | | | | | | | | | | | #3.
% 110.51/16.19 | | | | | | | | | | | | | | | | | | |
% 110.51/16.19 | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.19 | | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | | (2071) ~ (all_56_15 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | | REDUCE: (1995), (2071) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | | (2072) $false
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | | CLOSE: (2072) is inconsistent.
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | (2073) ~ (all_56_15 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (1995), (2073) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2074) $false
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | CLOSE: (2074) is inconsistent.
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | (2075) all_56_12 = e2
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | COMBINE_EQS: (426), (2075) imply:
% 110.51/16.20 | | | | | | | | | | | | | | (2076) all_10_2 = e2
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | SIMP: (2076) implies:
% 110.51/16.20 | | | | | | | | | | | | | | (2077) all_10_2 = e2
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | REF_CLOSE: (52), (53), (179), (202), (214), (238), (247),
% 110.51/16.20 | | | | | | | | | | | | | | (271), (277), (284), (288), (292), (305), (323),
% 110.51/16.20 | | | | | | | | | | | | | | (340), (343), (344), (362), (370), (385), (391),
% 110.51/16.20 | | | | | | | | | | | | | | (394), (406), (413), (436), (440), (446), (450),
% 110.51/16.20 | | | | | | | | | | | | | | (458), (551), (555), (556), (557), (558), (559),
% 110.51/16.20 | | | | | | | | | | | | | | (564), (565), (567), (568), (569), (571), (577),
% 110.51/16.20 | | | | | | | | | | | | | | (594), (1940), (1972), (1976), (2075), (2077),
% 110.51/16.20 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.20 | | | | | | | | | | | | | | #425.
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | (2078) all_56_14 = e2
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 110.51/16.20 | | | | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 110.51/16.20 | | | | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 110.51/16.20 | | | | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 110.51/16.20 | | | | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 110.51/16.20 | | | | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 110.51/16.20 | | | | | | | | | | | | | (589), (595), (597), (780), (1974), (1980),
% 110.51/16.20 | | | | | | | | | | | | | (1982), (1983), (2078), (function-axioms) are
% 110.51/16.20 | | | | | | | | | | | | | inconsistent by sub-proof #306.
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | End of split
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | (2079) all_38_1 = e2
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | COMBINE_EQS: (702), (2079) imply:
% 110.51/16.20 | | | | | | | | | | | (2080) all_10_1 = e2
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | SIMP: (2080) implies:
% 110.51/16.20 | | | | | | | | | | | (2081) all_10_1 = e2
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | REDUCE: (53), (2081) imply:
% 110.51/16.20 | | | | | | | | | | | (2082) op(e2, all_10_2) = all_10_0
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | REDUCE: (52), (2081) imply:
% 110.51/16.20 | | | | | | | | | | | (2083) op(e3, all_10_2) = e2
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | BETA: splitting (131) gives:
% 110.51/16.20 | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | (2084) ~ (all_42_0 = e1)
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | REDUCE: (1970), (2084) imply:
% 110.51/16.20 | | | | | | | | | | | | (2085) $false
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | CLOSE: (2085) is inconsistent.
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | (2086) ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | BETA: splitting (274) gives:
% 110.51/16.20 | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | (2087) ~ (all_56_14 = e2)
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | REDUCE: (555), (2087) imply:
% 110.51/16.20 | | | | | | | | | | | | | (2088) ~ (all_6_2 = e2)
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | BETA: splitting (275) gives:
% 110.51/16.20 | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | (2089) ~ (all_56_12 = e2)
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | REDUCE: (426), (2089) imply:
% 110.51/16.20 | | | | | | | | | | | | | | (2090) ~ (all_10_2 = e2)
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 110.51/16.20 | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | (2091) ~ (all_56_15 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | REDUCE: (554), (2091) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2092) ~ (all_4_2 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | REF_CLOSE: (8), (154), (157), (185), (204), (207), (212),
% 110.51/16.20 | | | | | | | | | | | | | | | (233), (238), (241), (245), (248), (272), (273),
% 110.51/16.20 | | | | | | | | | | | | | | | (277), (279), (281), (282), (286), (288), (291),
% 110.51/16.20 | | | | | | | | | | | | | | | (295), (297), (323), (331), (332), (340), (356),
% 110.51/16.20 | | | | | | | | | | | | | | | (362), (365), (370), (371), (385), (386), (391),
% 110.51/16.20 | | | | | | | | | | | | | | | (394), (406), (407), (426), (430), (436), (440),
% 110.51/16.20 | | | | | | | | | | | | | | | (446), (450), (462), (468), (551), (553), (554),
% 110.51/16.20 | | | | | | | | | | | | | | | (555), (557), (558), (559), (560), (562), (563),
% 110.51/16.20 | | | | | | | | | | | | | | | (564), (566), (567), (568), (569), (573), (575),
% 110.51/16.20 | | | | | | | | | | | | | | | (583), (594), (599), (603), (604), (605), (1974),
% 110.51/16.20 | | | | | | | | | | | | | | | (1982), (1983), (2088), (2090), (2092),
% 110.51/16.20 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.20 | | | | | | | | | | | | | | | #302.
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | Case 2:
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | (2093) all_56_15 = e3
% 110.51/16.20 | | | | | | | | | | | | | | | (2094) ~ (all_56_9 = e0)
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2093) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2095) all_4_2 = e3
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | SIMP: (2095) implies:
% 110.51/16.20 | | | | | | | | | | | | | | | (2096) all_4_2 = e3
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | COMBINE_EQS: (557), (2096) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2097) all_58_15 = e3
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | REDUCE: (450), (2094) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2098) ~ (all_52_3 = e0)
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | REDUCE: (584), (2096) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2099) ~ (all_52_3 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | REDUCE: (37), (2096) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | (2100) op(e0, e3) = all_4_1
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 110.51/16.20 | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | (2101) ~ (all_56_3 = e2)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (430), (2101) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2102) ~ (all_52_1 = e2)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 110.51/16.20 | | | | | | | | | | | | | | | | all_4_1, e3, e0, simplifying with (203), (2100)
% 110.51/16.20 | | | | | | | | | | | | | | | | gives:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2103) all_52_3 = all_4_1
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | COMBINE_EQS: (475), (2103) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2104) all_54_12 = all_4_1
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (188), (2103) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2105) ~ (all_52_2 = all_4_1)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (575), (2103) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2106) ~ (all_10_2 = all_4_1)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | SIMP: (2106) implies:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2107) ~ (all_10_2 = all_4_1)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (2099), (2103) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2108) ~ (all_4_1 = e3)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | REDUCE: (2098), (2103) imply:
% 110.51/16.20 | | | | | | | | | | | | | | | | (2109) ~ (all_4_1 = e0)
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 110.51/16.20 | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.20 | | | | | | | | | | | | | | | | | (2110) ~ (all_56_8 = e1)
% 110.51/16.20 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | REDUCE: (371), (2110) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2111) ~ (all_52_14 = e1)
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | (2112) ~ (all_56_12 = e1)
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | REDUCE: (426), (2112) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | (2113) ~ (all_10_2 = e1)
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2114) all_54_0 = e3
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (2114) are inconsistent by sub-proof
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | #451.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2115) ~ (all_54_0 = e3)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2116) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (2116) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | (2117) all_54_0 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (2090), (2117) are inconsistent by
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | sub-proof #450.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | (2118) ~ (all_54_0 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | (2119) all_54_0 = e1 | all_54_0 = e0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2120) all_54_0 = e1
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (553), (2113), (2120) are inconsistent by
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | sub-proof #449.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2121) all_54_0 = e0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (2121) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2122) all_10_2 = e0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | SIMP: (2122) implies:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2123) all_10_2 = e0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2083), (2123) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2124) op(e3, e0) = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2082), (2123) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2125) op(e2, e0) = all_10_0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2126) all_58_2 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (2102), (2126) are inconsistent by
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2127) ~ (all_58_2 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2128) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2128) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | (2129) all_58_3 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (2129) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | (2130) all_8_2 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2130) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | (2131) $false
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2131) is inconsistent.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | (2132) ~ (all_58_3 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | (2133) all_58_5 = e2 | all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2133) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e0, e2, simplifying with (208), (2125)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_52_13 = all_10_0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (212), (2124) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_52_12 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2134) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2136) all_58_10 = all_10_0
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (2135) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_58_9 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (281), (327), (371), (426), (553),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (560), (1972), (2090), (2097), (2113), (2116),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2136), (2137) are inconsistent by sub-proof #368.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2138) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2139) all_52_13 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (2139) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_56_5 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (211), (238), (243), (244), (248), (286),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (288), (289), (290), (331), (346), (385), (386),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (406), (424), (426), (464), (544), (551), (552),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (553), (555), (556), (560), (562), (563), (566),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (567), (568), (571), (582), (587), (657), (2086),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (2088), (2090), (2102), (2111), (2140),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | | #4.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | (2141) all_56_12 = e1
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (426), (2141) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | (2142) all_10_2 = e1
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2143) ~ (all_56_4 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | REDUCE: (436), (2143) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2144) ~ (all_52_9 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | (2145) all_58_2 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (406), (2102), (2145) are inconsistent by
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | sub-proof #335.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | (2146) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2146) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2147) all_58_3 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (564), (2147) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2148) all_8_2 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (2148) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2149) $false
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2149) is inconsistent.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | (2150) all_58_5 = e2 | all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2150) gives:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2151) all_58_5 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (394), (2144), (2151) are inconsistent by
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #119.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2152) all_58_10 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2152) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2153) all_52_13 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (446), (2153) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2154) all_56_5 = e2
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (2153) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2155) ~ (all_8_2 = e2)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (211), (238), (243), (244), (248), (286),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (288), (289), (290), (331), (346), (385), (386),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (406), (424), (426), (464), (544), (551), (552),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (553), (555), (556), (560), (562), (563), (566),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (567), (568), (571), (582), (587), (657), (2086),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (2088), (2090), (2102), (2111), (2154),
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | | #4.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2156) ~ (all_56_12 = e1)
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | REDUCE: (2141), (2156) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | (2157) $false
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | | CLOSE: (2157) is inconsistent.
% 110.51/16.21 | | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | End of split
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | Case 2:
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2158) all_56_8 = e1
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2159) ~ (all_56_12 = e0)
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (2158) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2160) all_52_14 = e1
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | REDUCE: (426), (2159) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2161) ~ (all_10_2 = e0)
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.21 | | | | | | | | | | | | | | | | | REDUCE: (156), (2160) imply:
% 110.51/16.21 | | | | | | | | | | | | | | | | | (2162) ~ (all_52_12 = e1)
% 110.51/16.21 | | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | | REDUCE: (154), (2160) imply:
% 110.51/16.22 | | | | | | | | | | | | | | | | | (2163) ~ (all_52_13 = e1)
% 110.51/16.22 | | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | | REDUCE: (601), (2160) imply:
% 110.51/16.22 | | | | | | | | | | | | | | | | | (2164) ~ (all_6_2 = e1)
% 110.51/16.22 | | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (157), (204), (207), (212), (236), (238),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (240), (241), (245), (248), (288), (297), (330),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (407), (446), (462), (468), (470), (551), (553),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (555), (563), (566), (568), (573), (583), (1974),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (1982), (1983), (2088), (2090), (2104), (2105),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (2107), (2108), (2109), (2161), (2162), (2163),
% 110.51/16.22 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.22 | | | | | | | | | | | | | | | | | #3.
% 110.51/16.22 | | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | Case 2:
% 110.51/16.22 | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | (2165) ~ (all_56_15 = e3)
% 110.51/16.22 | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | REDUCE: (2093), (2165) imply:
% 110.51/16.22 | | | | | | | | | | | | | | | | (2166) $false
% 110.51/16.22 | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | | CLOSE: (2166) is inconsistent.
% 110.51/16.22 | | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | Case 2:
% 110.51/16.22 | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | (2167) all_56_12 = e2
% 110.51/16.22 | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | | REF_CLOSE: (214), (426), (577), (2083), (2167),
% 110.51/16.22 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.51/16.22 | | | | | | | | | | | | | | #300.
% 110.51/16.22 | | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | Case 2:
% 110.51/16.22 | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | (2168) all_56_14 = e2
% 110.51/16.22 | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 110.51/16.22 | | | | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 110.51/16.22 | | | | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 110.51/16.22 | | | | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 110.51/16.22 | | | | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 110.51/16.22 | | | | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 110.51/16.22 | | | | | | | | | | | | | (589), (595), (597), (780), (1974), (1980),
% 110.51/16.22 | | | | | | | | | | | | | (1982), (1983), (2168), (function-axioms) are
% 110.51/16.22 | | | | | | | | | | | | | inconsistent by sub-proof #306.
% 110.51/16.22 | | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | | |
% 110.51/16.22 | | | | | | | | | End of split
% 110.51/16.22 | | | | | | | | |
% 110.51/16.22 | | | | | | | | Case 2:
% 110.51/16.22 | | | | | | | | |
% 110.51/16.22 | | | | | | | | | (2169) all_32_1 = e1
% 110.51/16.22 | | | | | | | | | (2170) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 110.51/16.22 | | | | | | | | |
% 110.51/16.22 | | | | | | | | | REF_CLOSE: (6), (8), (42), (43), (52), (53), (116), (126),
% 110.51/16.22 | | | | | | | | | (169), (170), (172), (179), (185), (187), (202),
% 110.51/16.22 | | | | | | | | | (204), (206), (212), (213), (214), (233), (235),
% 110.51/16.22 | | | | | | | | | (237), (238), (239), (240), (243), (247), (248),
% 110.51/16.22 | | | | | | | | | (272), (273), (274), (275), (278), (279), (281),
% 110.51/16.22 | | | | | | | | | (282), (283), (284), (285), (286), (287), (289),
% 110.51/16.22 | | | | | | | | | (290), (291), (294), (298), (299), (300), (303),
% 110.51/16.22 | | | | | | | | | (304), (323), (328), (331), (336), (340), (342),
% 110.51/16.22 | | | | | | | | | (343), (344), (345), (352), (356), (362), (365),
% 110.51/16.22 | | | | | | | | | (370), (371), (375), (385), (386), (391), (394),
% 110.51/16.22 | | | | | | | | | (406), (407), (412), (413), (424), (426), (430),
% 110.51/16.22 | | | | | | | | | (434), (436), (440), (446), (450), (458), (470),
% 110.51/16.22 | | | | | | | | | (472), (474), (477), (524), (543), (551), (552),
% 110.51/16.22 | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 110.51/16.22 | | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 110.51/16.22 | | | | | | | | | (567), (568), (569), (573), (575), (577), (579),
% 110.51/16.22 | | | | | | | | | (583), (585), (587), (589), (594), (595), (596),
% 110.51/16.22 | | | | | | | | | (597), (599), (601), (670), (700), (703), (731),
% 110.51/16.22 | | | | | | | | | (779), (780), (1938), (1940), (1974), (2169),
% 110.51/16.22 | | | | | | | | | (2170), (function-axioms) are inconsistent by
% 110.51/16.22 | | | | | | | | | sub-proof #288.
% 110.51/16.22 | | | | | | | | |
% 110.51/16.22 | | | | | | | | End of split
% 110.51/16.22 | | | | | | | |
% 110.51/16.22 | | | | | | | Case 2:
% 110.51/16.22 | | | | | | | |
% 110.51/16.22 | | | | | | | | (2171) all_28_0 = e2
% 110.51/16.22 | | | | | | | | (2172) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 110.51/16.22 | | | | | | | |
% 110.51/16.23 | | | | | | | | REF_CLOSE: (5), (7), (9), (37), (42), (43), (47), (52), (53),
% 110.51/16.23 | | | | | | | | (107), (121), (131), (154), (161), (162), (164),
% 110.51/16.23 | | | | | | | | (165), (167), (169), (170), (172), (179), (180),
% 110.51/16.23 | | | | | | | | (185), (187), (188), (193), (201), (202), (204),
% 110.51/16.23 | | | | | | | | (206), (207), (208), (209), (211), (212), (213),
% 110.51/16.23 | | | | | | | | (214), (233), (234), (235), (237), (238), (239),
% 110.51/16.23 | | | | | | | | (240), (242), (243), (245), (246), (247), (248),
% 110.51/16.23 | | | | | | | | (270), (271), (272), (273), (274), (275), (277),
% 110.51/16.23 | | | | | | | | (278), (279), (280), (281), (283), (284), (285),
% 110.51/16.23 | | | | | | | | (286), (287), (288), (289), (290), (291), (292),
% 110.51/16.23 | | | | | | | | (293), (294), (295), (296), (298), (299), (300),
% 110.51/16.23 | | | | | | | | (301), (302), (303), (304), (305), (323), (325),
% 110.51/16.23 | | | | | | | | (327), (331), (332), (335), (336), (338), (340),
% 110.51/16.23 | | | | | | | | (341), (343), (344), (345), (352), (356), (362),
% 110.51/16.23 | | | | | | | | (365), (370), (371), (385), (386), (391), (394),
% 110.51/16.23 | | | | | | | | (406), (407), (412), (413), (424), (426), (430),
% 110.51/16.23 | | | | | | | | (434), (436), (440), (446), (450), (458), (460),
% 110.51/16.23 | | | | | | | | (462), (466), (470), (472), (474), (477), (479),
% 110.51/16.23 | | | | | | | | (502), (522), (524), (538), (544), (551), (552),
% 110.51/16.23 | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 110.51/16.23 | | | | | | | | (560), (561), (562), (563), (564), (565), (566),
% 110.51/16.23 | | | | | | | | (567), (568), (569), (571), (573), (575), (577),
% 110.51/16.23 | | | | | | | | (579), (581), (582), (583), (585), (587), (589),
% 110.51/16.23 | | | | | | | | (591), (593), (594), (595), (596), (597), (599),
% 110.51/16.23 | | | | | | | | (601), (602), (603), (604), (605), (657), (683),
% 110.51/16.23 | | | | | | | | (697), (700), (702), (741), (758), (779), (1938),
% 110.51/16.23 | | | | | | | | (1940), (1968), (1970), (1972), (2171), (2172),
% 110.51/16.23 | | | | | | | | (function-axioms) are inconsistent by sub-proof #171.
% 110.51/16.23 | | | | | | | |
% 110.51/16.23 | | | | | | | End of split
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | Case 2:
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | | (2173) all_16_0 = e1
% 110.51/16.23 | | | | | | | (2174) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | | COMBINE_EQS: (775), (2173) imply:
% 110.51/16.23 | | | | | | | (2175) all_10_0 = e1
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | | SIMP: (2175) implies:
% 110.51/16.23 | | | | | | | (2176) all_10_0 = e1
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | | REF_CLOSE: (8), (37), (42), (43), (52), (53), (88), (98), (116),
% 110.51/16.23 | | | | | | | (126), (154), (156), (157), (161), (162), (165), (170),
% 110.51/16.23 | | | | | | | (172), (177), (178), (179), (180), (183), (185), (187),
% 110.51/16.23 | | | | | | | (188), (189), (190), (202), (204), (206), (207), (209),
% 110.51/16.23 | | | | | | | (212), (213), (214), (233), (234), (235), (236), (237),
% 110.51/16.23 | | | | | | | (238), (239), (240), (241), (242), (243), (245), (246),
% 110.51/16.23 | | | | | | | (247), (248), (270), (271), (272), (273), (274), (275),
% 110.51/16.23 | | | | | | | (276), (277), (278), (279), (281), (282), (283), (284),
% 110.51/16.23 | | | | | | | (286), (287), (288), (289), (290), (291), (293), (294),
% 110.51/16.23 | | | | | | | (295), (296), (297), (298), (299), (300), (302), (304),
% 110.51/16.23 | | | | | | | (305), (323), (328), (329), (330), (331), (332), (335),
% 110.51/16.23 | | | | | | | (336), (340), (342), (343), (344), (345), (352), (356),
% 110.51/16.23 | | | | | | | (362), (365), (370), (371), (375), (385), (386), (391),
% 110.51/16.23 | | | | | | | (394), (406), (407), (412), (413), (424), (426), (430),
% 110.51/16.23 | | | | | | | (434), (436), (440), (446), (450), (458), (460), (462),
% 110.51/16.23 | | | | | | | (466), (468), (470), (472), (474), (475), (477), (479),
% 110.51/16.23 | | | | | | | (522), (530), (537), (543), (551), (552), (553), (554),
% 110.51/16.23 | | | | | | | (555), (556), (557), (558), (559), (560), (561), (562),
% 110.51/16.23 | | | | | | | (563), (564), (565), (566), (567), (568), (569), (571),
% 110.51/16.23 | | | | | | | (573), (575), (577), (579), (581), (582), (583), (584),
% 110.51/16.23 | | | | | | | (585), (587), (589), (591), (593), (594), (595), (596),
% 110.51/16.23 | | | | | | | (597), (601), (602), (603), (604), (605), (661), (670),
% 110.51/16.23 | | | | | | | (683), (695), (703), (731), (758), (759), (780),
% 110.51/16.23 | | | | | | | (1938), (1940), (2174), (2176), (function-axioms) are
% 110.51/16.23 | | | | | | | inconsistent by sub-proof #5.
% 110.51/16.23 | | | | | | |
% 110.51/16.23 | | | | | | End of split
% 110.51/16.23 | | | | | |
% 110.51/16.23 | | | | | End of split
% 110.51/16.23 | | | | |
% 110.51/16.23 | | | | Case 2:
% 110.51/16.23 | | | | |
% 110.51/16.23 | | | | | (2177) all_10_0 = e2
% 110.51/16.23 | | | | | (2178) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 110.51/16.23 | | | | |
% 110.51/16.24 | | | | | REF_CLOSE: (6), (8), (37), (38), (42), (43), (47), (52), (53), (93),
% 110.51/16.24 | | | | | (98), (116), (126), (136), (150), (154), (156), (157),
% 110.51/16.24 | | | | | (161), (164), (165), (167), (170), (172), (177), (178),
% 110.51/16.24 | | | | | (179), (180), (183), (184), (185), (187), (188), (192),
% 110.51/16.24 | | | | | (193), (201), (202), (203), (204), (206), (207), (208),
% 110.51/16.24 | | | | | (209), (211), (212), (213), (214), (233), (234), (235),
% 110.51/16.24 | | | | | (236), (237), (238), (239), (240), (241), (243), (244),
% 110.51/16.24 | | | | | (245), (246), (247), (248), (270), (271), (272), (273),
% 110.51/16.24 | | | | | (274), (275), (276), (277), (278), (279), (280), (281),
% 110.51/16.24 | | | | | (283), (284), (285), (286), (287), (288), (289), (290),
% 110.51/16.24 | | | | | (291), (292), (293), (294), (295), (297), (298), (299),
% 110.51/16.24 | | | | | (300), (301), (302), (304), (305), (323), (325), (326),
% 110.51/16.24 | | | | | (327), (328), (330), (331), (332), (333), (335), (336),
% 110.51/16.24 | | | | | (339), (340), (342), (343), (344), (345), (347), (351),
% 110.51/16.24 | | | | | (352), (356), (362), (365), (370), (371), (375), (385),
% 110.51/16.24 | | | | | (386), (391), (394), (406), (407), (412), (413), (424),
% 110.51/16.24 | | | | | (426), (430), (434), (436), (440), (446), (450), (458),
% 110.51/16.24 | | | | | (460), (462), (464), (468), (470), (472), (474), (475),
% 110.51/16.24 | | | | | (477), (479), (522), (540), (543), (545), (548), (551),
% 110.51/16.24 | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 110.51/16.24 | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 110.51/16.24 | | | | | (568), (569), (571), (573), (575), (577), (579), (581),
% 110.51/16.24 | | | | | (582), (583), (584), (585), (587), (589), (591), (593),
% 110.51/16.24 | | | | | (594), (595), (596), (597), (599), (601), (602), (603),
% 110.51/16.24 | | | | | (604), (605), (649), (670), (675), (683), (703), (705),
% 110.51/16.24 | | | | | (727), (731), (758), (778), (780), (783), (1938), (1939),
% 110.51/16.24 | | | | | (2177), (2178), (function-axioms) are inconsistent by
% 110.51/16.24 | | | | | sub-proof #137.
% 110.51/16.24 | | | | |
% 110.51/16.24 | | | | End of split
% 110.51/16.24 | | | |
% 110.51/16.24 | | | Case 2:
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | (2179) all_8_1 = e1
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | COMBINE_EQS: (704), (2179) imply:
% 110.51/16.24 | | | | (2180) all_48_1 = e1
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | REDUCE: (48), (2179) imply:
% 110.51/16.24 | | | | (2181) op(e1, all_8_2) = all_8_0
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | REDUCE: (47), (2179) imply:
% 110.51/16.24 | | | | (2182) op(e2, all_8_2) = e1
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | BETA: splitting (54) gives:
% 110.51/16.24 | | | |
% 110.51/16.24 | | | | Case 1:
% 110.51/16.24 | | | | |
% 110.51/16.24 | | | | | (2183) ~ (all_10_0 = e2)
% 110.51/16.24 | | | | |
% 110.51/16.24 | | | | | BETA: splitting (68) gives:
% 110.51/16.24 | | | | |
% 110.51/16.24 | | | | | Case 1:
% 110.51/16.24 | | | | | |
% 110.51/16.24 | | | | | | (2184) ~ (all_16_0 = e1)
% 110.51/16.24 | | | | | |
% 110.51/16.24 | | | | | | REDUCE: (775), (2184) imply:
% 110.51/16.24 | | | | | | (2185) ~ (all_10_0 = e1)
% 110.51/16.24 | | | | | |
% 110.51/16.24 | | | | | | BETA: splitting (78) gives:
% 110.51/16.24 | | | | | |
% 110.51/16.24 | | | | | | Case 1:
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | (2186) ~ (all_20_0 = e3)
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | REDUCE: (1936), (2186) imply:
% 110.51/16.24 | | | | | | | (2187) $false
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | CLOSE: (2187) is inconsistent.
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | Case 2:
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | (2188) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | BETA: splitting (98) gives:
% 110.51/16.24 | | | | | | |
% 110.51/16.24 | | | | | | | Case 1:
% 110.51/16.24 | | | | | | | |
% 110.51/16.24 | | | | | | | | (2189) ~ (all_28_0 = e2)
% 110.51/16.24 | | | | | | | |
% 110.51/16.25 | | | | | | | | REF_CLOSE: (6), (8), (37), (42), (43), (52), (53), (107), (116),
% 110.51/16.25 | | | | | | | | (121), (126), (154), (157), (162), (164), (165),
% 110.51/16.25 | | | | | | | | (169), (170), (172), (179), (183), (185), (187),
% 110.51/16.25 | | | | | | | | (188), (201), (202), (203), (204), (206), (207),
% 110.51/16.25 | | | | | | | | (208), (209), (212), (213), (214), (233), (234),
% 110.51/16.25 | | | | | | | | (235), (236), (237), (238), (239), (240), (241),
% 110.51/16.25 | | | | | | | | (242), (243), (245), (246), (247), (248), (270),
% 110.51/16.25 | | | | | | | | (271), (272), (273), (274), (275), (276), (277),
% 110.51/16.25 | | | | | | | | (278), (279), (281), (282), (283), (284), (285),
% 110.51/16.25 | | | | | | | | (286), (287), (288), (289), (290), (291), (292),
% 110.51/16.25 | | | | | | | | (293), (294), (295), (296), (297), (298), (299),
% 110.51/16.25 | | | | | | | | (300), (302), (303), (304), (305), (323), (327),
% 110.51/16.25 | | | | | | | | (328), (330), (331), (332), (335), (336), (340),
% 110.51/16.25 | | | | | | | | (342), (343), (344), (345), (352), (356), (362),
% 110.51/16.25 | | | | | | | | (365), (370), (371), (375), (385), (386), (391),
% 110.51/16.25 | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 110.51/16.25 | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 110.51/16.25 | | | | | | | | (460), (462), (466), (468), (470), (472), (474),
% 110.51/16.25 | | | | | | | | (475), (477), (479), (500), (502), (524), (543),
% 110.51/16.25 | | | | | | | | (551), (552), (553), (554), (555), (556), (557),
% 110.51/16.25 | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 110.51/16.25 | | | | | | | | (565), (566), (567), (568), (569), (571), (573),
% 110.51/16.25 | | | | | | | | (575), (577), (579), (581), (582), (583), (584),
% 110.51/16.25 | | | | | | | | (585), (587), (589), (591), (594), (595), (596),
% 110.51/16.25 | | | | | | | | (597), (599), (601), (602), (603), (604), (605),
% 110.51/16.25 | | | | | | | | (670), (694), (700), (702), (703), (731), (741),
% 110.51/16.25 | | | | | | | | (758), (779), (780), (1937), (1938), (2183), (2185),
% 110.51/16.25 | | | | | | | | (2188), (2189), (function-axioms) are inconsistent by
% 110.51/16.25 | | | | | | | | sub-proof #8.
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | Case 2:
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | | (2190) all_28_0 = e2
% 110.51/16.25 | | | | | | | | (2191) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | | COMBINE_EQS: (758), (2190) imply:
% 110.51/16.25 | | | | | | | | (2192) all_6_0 = e2
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | | REDUCE: (43), (2192) imply:
% 110.51/16.25 | | | | | | | | (2193) op(all_6_1, all_6_2) = e2
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | | BETA: splitting (107) gives:
% 110.51/16.25 | | | | | | | |
% 110.51/16.25 | | | | | | | | Case 1:
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | (2194) ~ (all_32_1 = e1)
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | REF_CLOSE: (5), (9), (37), (42), (52), (53), (121), (154),
% 110.51/16.25 | | | | | | | | | (161), (162), (164), (165), (167), (170), (172),
% 110.51/16.25 | | | | | | | | | (179), (180), (185), (187), (188), (193), (201),
% 110.51/16.25 | | | | | | | | | (202), (204), (206), (207), (208), (209), (212),
% 110.51/16.25 | | | | | | | | | (213), (214), (233), (234), (235), (237), (238),
% 110.51/16.25 | | | | | | | | | (240), (242), (243), (245), (246), (247), (248),
% 110.51/16.25 | | | | | | | | | (270), (271), (272), (273), (274), (275), (277),
% 110.51/16.25 | | | | | | | | | (278), (279), (280), (281), (283), (284), (285),
% 110.51/16.25 | | | | | | | | | (286), (287), (288), (289), (291), (292), (293),
% 110.51/16.25 | | | | | | | | | (294), (295), (296), (298), (299), (302), (303),
% 110.51/16.25 | | | | | | | | | (304), (305), (323), (325), (327), (331), (332),
% 110.51/16.25 | | | | | | | | | (335), (340), (343), (344), (345), (352), (356),
% 110.51/16.25 | | | | | | | | | (362), (365), (370), (371), (385), (386), (391),
% 110.51/16.25 | | | | | | | | | (394), (406), (407), (412), (413), (424), (426),
% 110.51/16.25 | | | | | | | | | (430), (434), (436), (440), (446), (450), (458),
% 110.51/16.25 | | | | | | | | | (460), (462), (466), (470), (474), (477), (479),
% 110.51/16.25 | | | | | | | | | (502), (522), (551), (552), (553), (554), (555),
% 110.51/16.25 | | | | | | | | | (556), (557), (558), (559), (560), (561), (562),
% 110.51/16.25 | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 110.51/16.25 | | | | | | | | | (571), (573), (575), (577), (579), (581), (582),
% 110.51/16.25 | | | | | | | | | (583), (585), (587), (591), (593), (594), (595),
% 110.51/16.25 | | | | | | | | | (596), (597), (599), (601), (602), (603), (604),
% 110.51/16.25 | | | | | | | | | (605), (683), (700), (702), (741), (1938), (2183),
% 110.51/16.25 | | | | | | | | | (2185), (2191), (2193), (2194), (function-axioms)
% 110.51/16.25 | | | | | | | | | are inconsistent by sub-proof #254.
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | Case 2:
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | (2195) all_32_1 = e1
% 110.51/16.25 | | | | | | | | | (2196) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | COMBINE_EQS: (700), (2195) imply:
% 110.51/16.25 | | | | | | | | | (2197) all_10_1 = e1
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | REDUCE: (53), (2197) imply:
% 110.51/16.25 | | | | | | | | | (2198) op(e1, all_10_2) = all_10_0
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | REDUCE: (52), (2197) imply:
% 110.51/16.25 | | | | | | | | | (2199) op(e3, all_10_2) = e1
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | BETA: splitting (274) gives:
% 110.51/16.25 | | | | | | | | |
% 110.51/16.25 | | | | | | | | | Case 1:
% 110.51/16.25 | | | | | | | | | |
% 110.51/16.25 | | | | | | | | | | (2200) ~ (all_56_14 = e2)
% 110.51/16.25 | | | | | | | | | |
% 110.51/16.25 | | | | | | | | | | REDUCE: (555), (2200) imply:
% 110.51/16.25 | | | | | | | | | | (2201) ~ (all_6_2 = e2)
% 110.51/16.25 | | | | | | | | | |
% 110.77/16.25 | | | | | | | | | | REF_CLOSE: (42), (169), (172), (187), (204), (206), (207),
% 110.77/16.25 | | | | | | | | | | (213), (214), (233), (237), (238), (239), (240),
% 110.77/16.25 | | | | | | | | | | (243), (248), (275), (278), (279), (284), (285),
% 110.77/16.25 | | | | | | | | | | (286), (290), (291), (292), (293), (295), (299),
% 110.77/16.25 | | | | | | | | | | (323), (336), (340), (344), (352), (356), (370),
% 110.77/16.25 | | | | | | | | | | (371), (385), (386), (391), (394), (406), (407),
% 110.77/16.25 | | | | | | | | | | (412), (424), (426), (430), (436), (440), (446),
% 110.77/16.25 | | | | | | | | | | (470), (472), (474), (522), (524), (551), (552),
% 110.77/16.25 | | | | | | | | | | (553), (554), (555), (556), (557), (558), (559),
% 110.77/16.25 | | | | | | | | | | (561), (562), (564), (565), (566), (567), (568),
% 110.77/16.25 | | | | | | | | | | (569), (573), (575), (577), (579), (583), (585),
% 110.77/16.25 | | | | | | | | | | (589), (591), (594), (595), (596), (597), (599),
% 110.77/16.25 | | | | | | | | | | (601), (683), (779), (1938), (2183), (2191),
% 110.77/16.25 | | | | | | | | | | (2196), (2198), (2199), (2201), (function-axioms)
% 110.77/16.25 | | | | | | | | | | are inconsistent by sub-proof #249.
% 110.77/16.25 | | | | | | | | | |
% 110.77/16.26 | | | | | | | | | Case 2:
% 110.77/16.26 | | | | | | | | | |
% 110.77/16.26 | | | | | | | | | | (2202) all_56_14 = e2
% 110.77/16.26 | | | | | | | | | | (2203) ~ (all_56_10 = e0)
% 110.77/16.26 | | | | | | | | | |
% 110.77/16.26 | | | | | | | | | | REF_CLOSE: (4), (8), (162), (167), (208), (209), (211),
% 110.77/16.26 | | | | | | | | | | (233), (243), (271), (276), (278), (289), (294),
% 110.77/16.26 | | | | | | | | | | (296), (298), (300), (301), (304), (323), (338),
% 110.77/16.26 | | | | | | | | | | (340), (341), (352), (356), (362), (365), (370),
% 110.77/16.26 | | | | | | | | | | (391), (394), (406), (407), (412), (413), (424),
% 110.77/16.26 | | | | | | | | | | (430), (434), (446), (450), (552), (554), (555),
% 110.77/16.26 | | | | | | | | | | (556), (557), (558), (559), (561), (564), (565),
% 110.77/16.26 | | | | | | | | | | (566), (567), (569), (582), (591), (593), (597),
% 110.77/16.26 | | | | | | | | | | (599), (604), (2182), (2202), (2203),
% 110.77/16.26 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.77/16.26 | | | | | | | | | | #104.
% 110.77/16.26 | | | | | | | | | |
% 110.77/16.26 | | | | | | | | | End of split
% 110.77/16.26 | | | | | | | | |
% 110.77/16.26 | | | | | | | | End of split
% 110.77/16.26 | | | | | | | |
% 110.77/16.26 | | | | | | | End of split
% 110.77/16.26 | | | | | | |
% 110.77/16.26 | | | | | | End of split
% 110.77/16.26 | | | | | |
% 110.77/16.26 | | | | | Case 2:
% 110.77/16.26 | | | | | |
% 110.77/16.26 | | | | | | (2204) all_16_0 = e1
% 110.77/16.26 | | | | | | (2205) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 110.77/16.26 | | | | | |
% 110.77/16.26 | | | | | | COMBINE_EQS: (775), (2204) imply:
% 110.77/16.26 | | | | | | (2206) all_10_0 = e1
% 110.77/16.26 | | | | | |
% 110.77/16.26 | | | | | | SIMP: (2206) implies:
% 110.77/16.26 | | | | | | (2207) all_10_0 = e1
% 110.77/16.26 | | | | | |
% 110.79/16.26 | | | | | | REF_CLOSE: (8), (37), (42), (43), (52), (53), (88), (98), (116),
% 110.79/16.26 | | | | | | (126), (154), (156), (157), (161), (162), (165), (170),
% 110.79/16.26 | | | | | | (172), (177), (178), (179), (180), (183), (185), (187),
% 110.79/16.26 | | | | | | (188), (189), (190), (202), (204), (206), (207), (209),
% 110.79/16.26 | | | | | | (212), (213), (214), (233), (234), (235), (236), (237),
% 110.79/16.26 | | | | | | (238), (239), (240), (241), (242), (243), (245), (246),
% 110.79/16.26 | | | | | | (247), (248), (270), (271), (272), (273), (274), (275),
% 110.79/16.26 | | | | | | (276), (277), (278), (279), (281), (282), (283), (284),
% 110.79/16.26 | | | | | | (286), (287), (288), (289), (290), (291), (293), (294),
% 110.79/16.26 | | | | | | (295), (296), (297), (298), (299), (300), (302), (304),
% 110.79/16.26 | | | | | | (305), (323), (328), (329), (330), (331), (332), (335),
% 110.79/16.26 | | | | | | (336), (340), (342), (343), (344), (345), (352), (356),
% 110.79/16.26 | | | | | | (362), (365), (370), (371), (375), (385), (386), (391),
% 110.79/16.26 | | | | | | (394), (406), (407), (412), (413), (424), (426), (430),
% 110.79/16.26 | | | | | | (434), (436), (440), (446), (450), (458), (460), (462),
% 110.79/16.26 | | | | | | (466), (468), (470), (472), (474), (475), (477), (479),
% 110.79/16.26 | | | | | | (522), (530), (537), (543), (551), (552), (553), (554),
% 110.79/16.26 | | | | | | (555), (556), (557), (558), (559), (560), (561), (562),
% 110.79/16.26 | | | | | | (563), (564), (565), (566), (567), (568), (569), (571),
% 110.79/16.26 | | | | | | (573), (575), (577), (579), (581), (582), (583), (584),
% 110.79/16.26 | | | | | | (585), (587), (589), (591), (593), (594), (595), (596),
% 110.79/16.26 | | | | | | (597), (601), (602), (603), (604), (605), (661), (670),
% 110.79/16.26 | | | | | | (683), (695), (703), (731), (758), (759), (780), (1938),
% 110.79/16.26 | | | | | | (2183), (2205), (2207), (function-axioms) are
% 110.79/16.26 | | | | | | inconsistent by sub-proof #5.
% 110.79/16.26 | | | | | |
% 110.79/16.26 | | | | | End of split
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | Case 2:
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | | (2208) all_10_0 = e2
% 110.79/16.26 | | | | | (2209) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | | COMBINE_EQS: (783), (2208) imply:
% 110.79/16.26 | | | | | (2210) all_50_0 = e2
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | | REDUCE: (53), (2208) imply:
% 110.79/16.26 | | | | | (2211) op(all_10_1, all_10_2) = e2
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | | BETA: splitting (98) gives:
% 110.79/16.26 | | | | |
% 110.79/16.26 | | | | | Case 1:
% 110.79/16.26 | | | | | |
% 110.79/16.26 | | | | | | (2212) ~ (all_28_0 = e2)
% 110.79/16.26 | | | | | |
% 110.79/16.26 | | | | | | REDUCE: (758), (2212) imply:
% 110.79/16.26 | | | | | | (2213) ~ (all_6_0 = e2)
% 110.79/16.26 | | | | | |
% 110.79/16.26 | | | | | | BETA: splitting (116) gives:
% 110.79/16.26 | | | | | |
% 110.79/16.26 | | | | | | Case 1:
% 110.79/16.26 | | | | | | |
% 110.79/16.26 | | | | | | | (2214) ~ (all_36_1 = e3)
% 110.79/16.26 | | | | | | |
% 110.79/16.26 | | | | | | | REDUCE: (670), (2214) imply:
% 110.79/16.26 | | | | | | | (2215) ~ (all_6_1 = e3)
% 110.79/16.26 | | | | | | |
% 110.79/16.27 | | | | | | | REF_CLOSE: (8), (37), (42), (43), (52), (126), (150), (154),
% 110.79/16.27 | | | | | | | (156), (157), (167), (170), (172), (177), (179), (180),
% 110.79/16.27 | | | | | | | (185), (187), (202), (204), (206), (208), (209), (212),
% 110.79/16.27 | | | | | | | (213), (214), (235), (237), (238), (239), (240), (243),
% 110.79/16.27 | | | | | | | (245), (246), (247), (248), (271), (272), (274), (275),
% 110.79/16.27 | | | | | | | (277), (278), (279), (280), (281), (283), (284), (286),
% 110.79/16.27 | | | | | | | (287), (288), (290), (291), (292), (293), (295), (299),
% 110.79/16.27 | | | | | | | (304), (305), (323), (327), (328), (331), (340), (342),
% 110.79/16.27 | | | | | | | (343), (344), (345), (352), (362), (365), (370), (371),
% 110.79/16.27 | | | | | | | (375), (385), (386), (391), (394), (406), (407), (413),
% 110.79/16.27 | | | | | | | (424), (426), (430), (436), (440), (446), (450), (458),
% 110.79/16.27 | | | | | | | (460), (462), (470), (472), (474), (477), (548), (551),
% 110.79/16.27 | | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 110.79/16.27 | | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 110.79/16.27 | | | | | | | (568), (569), (571), (573), (577), (579), (581), (583),
% 110.79/16.27 | | | | | | | (587), (589), (594), (595), (596), (601), (604), (703),
% 110.79/16.27 | | | | | | | (705), (731), (1938), (2209), (2210), (2211), (2213),
% 110.79/16.27 | | | | | | | (2215), (function-axioms) are inconsistent by sub-proof
% 110.79/16.27 | | | | | | | #156.
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | Case 2:
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | (2216) all_36_1 = e3
% 110.79/16.27 | | | | | | | (2217) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | COMBINE_EQS: (670), (2216) imply:
% 110.79/16.27 | | | | | | | (2218) all_6_1 = e3
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | REDUCE: (43), (2218) imply:
% 110.79/16.27 | | | | | | | (2219) op(e3, all_6_2) = all_6_0
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | REDUCE: (42), (2218) imply:
% 110.79/16.27 | | | | | | | (2220) op(e1, all_6_2) = e3
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | BETA: splitting (145) gives:
% 110.79/16.27 | | | | | | |
% 110.79/16.27 | | | | | | | Case 1:
% 110.79/16.27 | | | | | | | |
% 110.79/16.27 | | | | | | | | (2221) ~ (all_48_0 = e3)
% 110.79/16.27 | | | | | | | |
% 110.79/16.27 | | | | | | | | REDUCE: (782), (2221) imply:
% 110.79/16.27 | | | | | | | | (2222) ~ (all_8_0 = e3)
% 110.79/16.27 | | | | | | | |
% 110.79/16.27 | | | | | | | | BETA: splitting (150) gives:
% 110.79/16.27 | | | | | | | |
% 110.79/16.27 | | | | | | | | Case 1:
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | (2223) ~ (all_50_0 = e2)
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | REDUCE: (2210), (2223) imply:
% 110.79/16.27 | | | | | | | | | (2224) $false
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | CLOSE: (2224) is inconsistent.
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | Case 2:
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | (2225) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | BETA: splitting (274) gives:
% 110.79/16.27 | | | | | | | | |
% 110.79/16.27 | | | | | | | | | Case 1:
% 110.79/16.27 | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | (2226) ~ (all_56_14 = e2)
% 110.79/16.27 | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | REDUCE: (555), (2226) imply:
% 110.79/16.27 | | | | | | | | | | (2227) ~ (all_6_2 = e2)
% 110.79/16.27 | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | BETA: splitting (275) gives:
% 110.79/16.27 | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | Case 1:
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | (2228) ~ (all_56_12 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (426), (2228) imply:
% 110.79/16.27 | | | | | | | | | | | (2229) ~ (all_10_2 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REF_CLOSE: (9), (41), (52), (157), (167), (184), (188),
% 110.79/16.27 | | | | | | | | | | | (190), (192), (208), (209), (211), (212), (213),
% 110.79/16.27 | | | | | | | | | | | (233), (236), (238), (241), (242), (243), (244),
% 110.79/16.27 | | | | | | | | | | | (245), (246), (248), (272), (273), (276), (277),
% 110.79/16.27 | | | | | | | | | | | (279), (281), (282), (286), (287), (288), (289),
% 110.79/16.27 | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (297),
% 110.79/16.27 | | | | | | | | | | | (298), (299), (300), (302), (323), (324), (327),
% 110.79/16.27 | | | | | | | | | | | (329), (331), (335), (338), (340), (341), (352),
% 110.79/16.27 | | | | | | | | | | | (356), (362), (365), (370), (371), (385), (386),
% 110.79/16.27 | | | | | | | | | | | (391), (394), (406), (407), (412), (424), (426),
% 110.79/16.27 | | | | | | | | | | | (430), (434), (436), (440), (446), (450), (460),
% 110.79/16.27 | | | | | | | | | | | (462), (464), (466), (468), (475), (548), (551),
% 110.79/16.27 | | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 110.79/16.27 | | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 110.79/16.27 | | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 110.79/16.27 | | | | | | | | | | | (579), (581), (582), (584), (585), (587), (589),
% 110.79/16.27 | | | | | | | | | | | (591), (593), (594), (599), (601), (602), (604),
% 110.79/16.27 | | | | | | | | | | | (605), (705), (2182), (2209), (2211), (2225),
% 110.79/16.27 | | | | | | | | | | | (2227), (2229), (function-axioms) are inconsistent
% 110.79/16.27 | | | | | | | | | | | by sub-proof #2.
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | Case 2:
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | (2230) all_56_12 = e2
% 110.79/16.27 | | | | | | | | | | | (2231) ~ (all_56_10 = e0)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | COMBINE_EQS: (426), (2230) imply:
% 110.79/16.27 | | | | | | | | | | | (2232) all_10_2 = e2
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | SIMP: (2232) implies:
% 110.79/16.27 | | | | | | | | | | | (2233) all_10_2 = e2
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | COMBINE_EQS: (424), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2234) all_58_0 = e2
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (365), (2231) imply:
% 110.79/16.27 | | | | | | | | | | | (2235) ~ (all_52_7 = e0)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (571), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2236) ~ (all_52_1 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (573), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2237) ~ (all_52_2 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (577), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2238) ~ (all_52_4 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (579), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2239) ~ (all_52_8 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (566), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2240) ~ (e3 = e2)
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (2211), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2241) op(all_10_1, e2) = e2
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.27 | | | | | | | | | | | REDUCE: (52), (2233) imply:
% 110.79/16.27 | | | | | | | | | | | (2242) op(e3, e2) = all_10_1
% 110.79/16.27 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (165), (169), (170), (172), (179),
% 110.79/16.28 | | | | | | | | | | | (184), (185), (187), (188), (190), (192), (193),
% 110.79/16.28 | | | | | | | | | | | (202), (209), (214), (233), (236), (238), (240),
% 110.79/16.28 | | | | | | | | | | | (243), (244), (246), (270), (271), (277), (278),
% 110.79/16.28 | | | | | | | | | | | (280), (284), (285), (286), (287), (288), (291),
% 110.79/16.28 | | | | | | | | | | | (292), (298), (305), (323), (324), (326), (327),
% 110.79/16.28 | | | | | | | | | | | (331), (332), (339), (340), (342), (343), (344),
% 110.79/16.28 | | | | | | | | | | | (347), (352), (356), (362), (370), (371), (385),
% 110.79/16.28 | | | | | | | | | | | (386), (391), (394), (406), (407), (412), (413),
% 110.79/16.28 | | | | | | | | | | | (436), (440), (446), (450), (460), (464), (470),
% 110.79/16.28 | | | | | | | | | | | (475), (551), (552), (554), (555), (556), (557),
% 110.79/16.28 | | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 110.79/16.28 | | | | | | | | | | | (565), (567), (568), (569), (582), (583), (584),
% 110.79/16.28 | | | | | | | | | | | (585), (587), (591), (594), (595), (596), (599),
% 110.79/16.28 | | | | | | | | | | | (602), (603), (604), (605), (2181), (2182),
% 110.79/16.28 | | | | | | | | | | | (2220), (2222), (2227), (2230), (2234), (2235),
% 110.79/16.28 | | | | | | | | | | | (2236), (2237), (2238), (2239), (2241), (2242),
% 110.79/16.28 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.79/16.28 | | | | | | | | | | | #49.
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | End of split
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | (2243) all_56_14 = e2
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | REF_CLOSE: (172), (179), (206), (214), (233), (235), (243),
% 110.79/16.28 | | | | | | | | | | (247), (289), (294), (298), (300), (304), (340),
% 110.79/16.28 | | | | | | | | | | (342), (352), (356), (391), (394), (406), (407),
% 110.79/16.28 | | | | | | | | | | (412), (413), (424), (430), (434), (446), (458),
% 110.79/16.28 | | | | | | | | | | (477), (543), (552), (554), (555), (556), (561),
% 110.79/16.28 | | | | | | | | | | (564), (565), (566), (567), (569), (585), (587),
% 110.79/16.28 | | | | | | | | | | (589), (595), (597), (780), (2213), (2217),
% 110.79/16.28 | | | | | | | | | | (2219), (2220), (2243), (function-axioms) are
% 110.79/16.28 | | | | | | | | | | inconsistent by sub-proof #306.
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | End of split
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | End of split
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | (2244) all_48_0 = e3
% 110.79/16.28 | | | | | | | | (2245) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | COMBINE_EQS: (782), (2244) imply:
% 110.79/16.28 | | | | | | | | (2246) all_8_0 = e3
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | SIMP: (2246) implies:
% 110.79/16.28 | | | | | | | | (2247) all_8_0 = e3
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | REDUCE: (2181), (2247) imply:
% 110.79/16.28 | | | | | | | | (2248) op(e1, all_8_2) = e3
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | BETA: splitting (2245) gives:
% 110.79/16.28 | | | | | | | |
% 110.79/16.28 | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | (2249) ~ (all_48_1 = e1)
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | REDUCE: (2180), (2249) imply:
% 110.79/16.28 | | | | | | | | | (2250) $false
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | CLOSE: (2250) is inconsistent.
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | (2251) ~ (all_48_2 = e0)
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | REDUCE: (547), (2251) imply:
% 110.79/16.28 | | | | | | | | | (2252) ~ (all_8_2 = e0)
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | BETA: splitting (150) gives:
% 110.79/16.28 | | | | | | | | |
% 110.79/16.28 | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | (2253) ~ (all_50_0 = e2)
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | REDUCE: (2210), (2253) imply:
% 110.79/16.28 | | | | | | | | | | (2254) $false
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | CLOSE: (2254) is inconsistent.
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | (2255) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | BETA: splitting (243) gives:
% 110.79/16.28 | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | (2256) all_54_5 = e3
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | COMBINE_EQS: (552), (2256) imply:
% 110.79/16.28 | | | | | | | | | | | (2257) all_8_2 = e3
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | SIMP: (2257) implies:
% 110.79/16.28 | | | | | | | | | | | (2258) all_8_2 = e3
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | COMBINE_EQS: (556), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2259) all_56_13 = e3
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REDUCE: (585), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2260) ~ (all_52_4 = e3)
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REDUCE: (591), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2261) ~ (all_52_9 = e3)
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REDUCE: (593), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2262) ~ (all_52_13 = e3)
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REDUCE: (2182), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2263) op(e2, e3) = e1
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | REDUCE: (2248), (2258) imply:
% 110.79/16.28 | | | | | | | | | | | (2264) op(e1, e3) = e3
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | BETA: splitting (278) gives:
% 110.79/16.28 | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | (2265) ~ (all_56_13 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (2259), (2265) imply:
% 110.79/16.28 | | | | | | | | | | | | (2266) $false
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | CLOSE: (2266) is inconsistent.
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | (2267) ~ (all_56_9 = e0)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (450), (2267) imply:
% 110.79/16.28 | | | | | | | | | | | | (2268) ~ (all_52_3 = e0)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 110.79/16.28 | | | | | | | | | | | | e3, e1, simplifying with (207), (2264) gives:
% 110.79/16.28 | | | | | | | | | | | | (2269) all_52_2 = e3
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 110.79/16.28 | | | | | | | | | | | | e3, e2, simplifying with (211), (2263) gives:
% 110.79/16.28 | | | | | | | | | | | | (2270) all_52_1 = e1
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (192), (2270) imply:
% 110.79/16.28 | | | | | | | | | | | | (2271) ~ (all_52_3 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2271) implies:
% 110.79/16.28 | | | | | | | | | | | | (2272) ~ (all_52_3 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (190), (2270) imply:
% 110.79/16.28 | | | | | | | | | | | | (2273) ~ (all_52_9 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2273) implies:
% 110.79/16.28 | | | | | | | | | | | | (2274) ~ (all_52_9 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (189), (2270) imply:
% 110.79/16.28 | | | | | | | | | | | | (2275) ~ (all_52_13 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2275) implies:
% 110.79/16.28 | | | | | | | | | | | | (2276) ~ (all_52_13 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (571), (2270) imply:
% 110.79/16.28 | | | | | | | | | | | | (2277) ~ (all_10_2 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2277) implies:
% 110.79/16.28 | | | | | | | | | | | | (2278) ~ (all_10_2 = e1)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (188), (2269) imply:
% 110.79/16.28 | | | | | | | | | | | | (2279) ~ (all_52_3 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2279) implies:
% 110.79/16.28 | | | | | | | | | | | | (2280) ~ (all_52_3 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (573), (2269) imply:
% 110.79/16.28 | | | | | | | | | | | | (2281) ~ (all_10_2 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | REDUCE: (583), (2269) imply:
% 110.79/16.28 | | | | | | | | | | | | (2282) ~ (all_6_2 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | SIMP: (2282) implies:
% 110.79/16.28 | | | | | | | | | | | | (2283) ~ (all_6_2 = e3)
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | BETA: splitting (346) gives:
% 110.79/16.28 | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | (2284) all_58_0 = e0
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | COMBINE_EQS: (424), (2284) imply:
% 110.79/16.28 | | | | | | | | | | | | | (2285) all_10_2 = e0
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | COMBINE_EQS: (426), (2285) imply:
% 110.79/16.28 | | | | | | | | | | | | | (2286) all_56_12 = e0
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | REDUCE: (577), (2285) imply:
% 110.79/16.28 | | | | | | | | | | | | | (2287) ~ (all_52_4 = e0)
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | BETA: splitting (290) gives:
% 110.79/16.28 | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | (2288) ~ (all_56_5 = e2)
% 110.79/16.28 | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | REDUCE: (446), (2288) imply:
% 110.79/16.28 | | | | | | | | | | | | | | (2289) ~ (all_52_13 = e2)
% 110.79/16.28 | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 110.79/16.28 | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | (2290) all_54_7 = e3
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | REF_CLOSE: (468), (2262), (2290) are inconsistent by
% 110.79/16.28 | | | | | | | | | | | | | | | sub-proof #350.
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | (2291) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | BETA: splitting (2291) gives:
% 110.79/16.28 | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | Case 1:
% 110.79/16.28 | | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | | (2292) all_54_7 = e2
% 110.79/16.28 | | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | | REF_CLOSE: (468), (2289), (2292) are inconsistent by
% 110.79/16.28 | | | | | | | | | | | | | | | | sub-proof #34.
% 110.79/16.28 | | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | Case 2:
% 110.79/16.28 | | | | | | | | | | | | | | | |
% 110.79/16.28 | | | | | | | | | | | | | | | | (2293) all_54_7 = e1 | all_54_7 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | BETA: splitting (2293) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | (2294) all_54_7 = e1
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (468), (2276), (2294) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | sub-proof #349.
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | (2295) all_54_7 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | COMBINE_EQS: (468), (2295) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | (2296) all_52_13 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | SIMP: (2296) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | (2297) all_52_13 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | REDUCE: (161), (2297) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | (2298) ~ (all_52_9 = e0)
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2299) all_58_9 = e1
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (2299) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2300) all_52_12 = e1
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | REDUCE: (177), (2300) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2301) ~ (all_52_4 = e1)
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | REDUCE: (603), (2300) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2302) ~ (all_4_2 = e1)
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | SIMP: (2302) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2303) ~ (all_4_2 = e1)
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | (2304) all_54_1 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (458), (2260), (2304) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | sub-proof #222.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | (2305) ~ (all_54_1 = e3)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | (2306) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (2306) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2307) all_54_1 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (2307) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2308) all_52_4 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | SIMP: (2308) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2309) all_52_4 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (2309) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2310) all_58_1 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2309) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2311) ~ (all_10_2 = e2)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | SIMP: (2311) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2312) ~ (all_10_2 = e2)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (2260), (2309) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2313) ~ (e3 = e2)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2314) ~ (all_56_2 = e3)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (2314) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2315) ~ (all_52_12 = e3)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | (2316) all_58_0 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (2316) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | (2317) all_10_2 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (2317) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | (2318) $false
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2318) is inconsistent.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | (2319) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2319) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (2320) all_58_1 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2310), (2320) are inconsistent by sub-proof
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | #390.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (2321) all_58_4 = e3 | all_58_9 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (157), (208), (212), (245), (248), (281),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (299), (302), (327), (371), (391), (407), (412),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (426), (434), (462), (548), (553), (557), (560),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (561), (579), (581), (705), (2211), (2255),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | (2303), (2312), (2315), (2321), (function-axioms)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #16.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2322) all_56_2 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (2322) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2323) all_52_12 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (2323) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2324) ~ (all_52_8 = e3)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (167), (209), (213), (246), (248), (299),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (426), (460), (553), (566), (579), (2209), (2211),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2312), (2322), (2324), (function-axioms) are
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #143.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2325) all_54_1 = e1 | all_54_1 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (458), (2287), (2301), (2325) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | sub-proof #213.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2326) ~ (all_58_9 = e1)
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | REDUCE: (561), (2326) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | (2327) ~ (all_52_12 = e1)
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | (2328) all_54_6 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (2261), (2328) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | sub-proof #268.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | (2329) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (2329) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2330) all_54_6 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (2330) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2331) all_52_9 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | SIMP: (2331) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2332) all_52_9 = e2
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (2332) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2333) ~ (all_6_2 = e2)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | SIMP: (2333) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2334) ~ (all_6_2 = e2)
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2335) all_54_10 = e3
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (551), (2283), (2335) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | sub-proof #352.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2336) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (157), (204), (212), (241), (245), (288),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (297), (407), (446), (462), (468), (551), (555),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (568), (2213), (2219), (2220), (2276), (2327),
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2334), (2336), (function-axioms) are inconsistent
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | by sub-proof #348.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | (2337) all_54_6 = e1 | all_54_6 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2337) gives:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2338) all_54_6 = e1
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (466), (2274), (2338) are inconsistent by
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2339) all_54_6 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (2339) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2340) all_52_9 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | SIMP: (2340) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2341) all_52_9 = e0
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2298), (2341) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | (2342) $false
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2342) is inconsistent.
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | (2343) ~ (all_56_12 = e0)
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | REDUCE: (2286), (2343) imply:
% 110.79/16.29 | | | | | | | | | | | | | | (2344) $false
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | CLOSE: (2344) is inconsistent.
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | End of split
% 110.79/16.29 | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | (2345) ~ (all_58_0 = e0)
% 110.79/16.29 | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | REDUCE: (424), (2345) imply:
% 110.79/16.29 | | | | | | | | | | | | | (2346) ~ (all_10_2 = e0)
% 110.79/16.29 | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | BETA: splitting (248) gives:
% 110.79/16.29 | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | (2347) all_54_0 = e3
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | REF_CLOSE: (553), (566), (2347) are inconsistent by sub-proof
% 110.79/16.29 | | | | | | | | | | | | | | #451.
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | Case 2:
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | (2348) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | BETA: splitting (2348) gives:
% 110.79/16.29 | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | Case 1:
% 110.79/16.29 | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | (2349) all_54_0 = e2
% 110.79/16.29 | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | COMBINE_EQS: (553), (2349) imply:
% 110.79/16.29 | | | | | | | | | | | | | | | (2350) all_10_2 = e2
% 110.79/16.29 | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | SIMP: (2350) implies:
% 110.79/16.29 | | | | | | | | | | | | | | | (2351) all_10_2 = e2
% 110.79/16.29 | | | | | | | | | | | | | | |
% 110.79/16.29 | | | | | | | | | | | | | | | REDUCE: (575), (2351) imply:
% 110.79/16.30 | | | | | | | | | | | | | | | (2352) ~ (all_52_3 = e2)
% 110.79/16.30 | | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | | | REF_CLOSE: (236), (475), (2268), (2272), (2280), (2352) are
% 110.79/16.30 | | | | | | | | | | | | | | | inconsistent by sub-proof #405.
% 110.79/16.30 | | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | | Case 2:
% 110.79/16.30 | | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | | | (2353) all_54_0 = e1 | all_54_0 = e0
% 110.79/16.30 | | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | | | REF_CLOSE: (553), (2278), (2346), (2353) are inconsistent by
% 110.79/16.30 | | | | | | | | | | | | | | | sub-proof #423.
% 110.79/16.30 | | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | Case 2:
% 110.79/16.30 | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | (2354) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 110.79/16.30 | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | | REF_CLOSE: (209), (552), (567), (591), (2182), (2252),
% 110.79/16.30 | | | | | | | | | | | (2354), (function-axioms) are inconsistent by
% 110.79/16.30 | | | | | | | | | | | sub-proof #108.
% 110.79/16.30 | | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | | |
% 110.79/16.30 | | | | | | | | | End of split
% 110.79/16.30 | | | | | | | | |
% 110.79/16.30 | | | | | | | | End of split
% 110.79/16.30 | | | | | | | |
% 110.79/16.30 | | | | | | | End of split
% 110.79/16.30 | | | | | | |
% 110.79/16.30 | | | | | | End of split
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | Case 2:
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | | (2355) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | | REF_CLOSE: (4), (8), (37), (42), (52), (150), (157), (162), (165),
% 110.79/16.30 | | | | | | (167), (169), (170), (172), (179), (185), (188), (189),
% 110.79/16.30 | | | | | | (190), (192), (193), (202), (204), (208), (209), (211),
% 110.79/16.30 | | | | | | (212), (214), (233), (236), (237), (238), (240), (243),
% 110.79/16.30 | | | | | | (244), (245), (246), (248), (270), (271), (272), (273),
% 110.79/16.30 | | | | | | (274), (275), (276), (277), (278), (279), (281), (284),
% 110.79/16.30 | | | | | | (286), (287), (288), (289), (290), (291), (292), (293),
% 110.79/16.30 | | | | | | (294), (295), (296), (298), (299), (300), (301), (302),
% 110.79/16.30 | | | | | | (303), (304), (305), (323), (324), (326), (327), (331),
% 110.79/16.30 | | | | | | (332), (335), (338), (339), (340), (341), (342), (344),
% 110.79/16.30 | | | | | | (347), (352), (356), (362), (365), (370), (371), (385),
% 110.79/16.30 | | | | | | (386), (391), (394), (406), (407), (412), (413), (424),
% 110.79/16.30 | | | | | | (426), (430), (434), (436), (440), (446), (450), (460),
% 110.79/16.30 | | | | | | (462), (464), (470), (474), (475), (522), (548), (551),
% 110.79/16.30 | | | | | | (552), (553), (554), (555), (556), (557), (558), (559),
% 110.79/16.30 | | | | | | (560), (561), (562), (563), (564), (565), (566), (567),
% 110.79/16.30 | | | | | | (568), (569), (571), (573), (577), (579), (581), (582),
% 110.79/16.30 | | | | | | (583), (584), (585), (589), (591), (593), (594), (596),
% 110.79/16.30 | | | | | | (597), (599), (601), (602), (603), (604), (605), (683),
% 110.79/16.30 | | | | | | (705), (1938), (2182), (2210), (2211), (2355),
% 110.79/16.30 | | | | | | (function-axioms) are inconsistent by sub-proof #47.
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | End of split
% 110.79/16.30 | | | | |
% 110.79/16.30 | | | | End of split
% 110.79/16.30 | | | |
% 110.79/16.30 | | | End of split
% 110.79/16.30 | | |
% 110.79/16.30 | | Case 2:
% 110.79/16.30 | | |
% 110.79/16.30 | | | (2356) all_6_1 = e2
% 110.79/16.30 | | | (2357) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 110.79/16.30 | | |
% 110.79/16.30 | | | COMBINE_EQS: (692), (2356) imply:
% 110.79/16.30 | | | (2358) all_18_1 = e2
% 110.79/16.30 | | |
% 110.79/16.30 | | | REDUCE: (43), (2356) imply:
% 110.79/16.30 | | | (2359) op(e2, all_6_2) = all_6_0
% 110.79/16.30 | | |
% 110.79/16.30 | | | REDUCE: (42), (2356) imply:
% 110.79/16.30 | | | (2360) op(e1, all_6_2) = e2
% 110.79/16.30 | | |
% 110.79/16.30 | | | BETA: splitting (49) gives:
% 110.79/16.30 | | |
% 110.79/16.30 | | | Case 1:
% 110.79/16.30 | | | |
% 110.79/16.30 | | | | (2361) ~ (all_8_1 = e1)
% 110.79/16.30 | | | |
% 110.79/16.30 | | | | BETA: splitting (54) gives:
% 110.79/16.30 | | | |
% 110.79/16.30 | | | | Case 1:
% 110.79/16.30 | | | | |
% 110.79/16.30 | | | | | (2362) ~ (all_10_0 = e2)
% 110.79/16.30 | | | | |
% 110.79/16.30 | | | | | BETA: splitting (68) gives:
% 110.79/16.30 | | | | |
% 110.79/16.30 | | | | | Case 1:
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | | (2363) ~ (all_16_0 = e1)
% 110.79/16.30 | | | | | |
% 110.79/16.30 | | | | | | REDUCE: (775), (2363) imply:
% 110.79/16.30 | | | | | | (2364) ~ (all_10_0 = e1)
% 110.79/16.30 | | | | | |
% 110.96/16.31 | | | | | | REF_CLOSE: (6), (37), (41), (47), (52), (53), (73), (107), (121),
% 110.96/16.31 | | | | | | (156), (157), (162), (164), (165), (169), (172), (179),
% 110.96/16.31 | | | | | | (183), (187), (188), (189), (192), (201), (202), (204),
% 110.96/16.31 | | | | | | (206), (207), (208), (211), (212), (213), (214), (233),
% 110.96/16.31 | | | | | | (234), (235), (236), (238), (239), (240), (241), (243),
% 110.96/16.31 | | | | | | (244), (245), (246), (247), (248), (270), (271), (272),
% 110.96/16.31 | | | | | | (273), (274), (275), (276), (277), (281), (282), (283),
% 110.96/16.31 | | | | | | (284), (285), (286), (288), (290), (291), (292), (293),
% 110.96/16.31 | | | | | | (294), (295), (296), (297), (298), (299), (300), (302),
% 110.96/16.31 | | | | | | (303), (304), (305), (323), (327), (328), (331), (335),
% 110.96/16.31 | | | | | | (336), (338), (340), (341), (343), (344), (346), (352),
% 110.96/16.31 | | | | | | (356), (362), (365), (370), (371), (385), (386), (391),
% 110.96/16.31 | | | | | | (394), (406), (407), (412), (413), (424), (426), (430),
% 110.96/16.31 | | | | | | (434), (436), (440), (446), (450), (458), (460), (462),
% 110.96/16.31 | | | | | | (464), (468), (470), (472), (475), (477), (479), (524),
% 110.96/16.31 | | | | | | (533), (551), (552), (553), (554), (555), (556), (557),
% 110.96/16.31 | | | | | | (558), (559), (560), (561), (562), (563), (564), (565),
% 110.96/16.31 | | | | | | (566), (567), (568), (569), (571), (573), (575), (577),
% 110.96/16.31 | | | | | | (579), (581), (582), (583), (584), (585), (587), (589),
% 110.96/16.31 | | | | | | (591), (593), (594), (595), (596), (597), (599), (602),
% 110.96/16.31 | | | | | | (603), (604), (605), (700), (702), (771), (779), (2357),
% 110.96/16.31 | | | | | | (2358), (2359), (2360), (2361), (2362), (2364),
% 110.96/16.31 | | | | | | (function-axioms) are inconsistent by sub-proof #28.
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | Case 2:
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | (2365) all_16_0 = e1
% 110.96/16.31 | | | | | | (2366) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | COMBINE_EQS: (775), (2365) imply:
% 110.96/16.31 | | | | | | (2367) all_10_0 = e1
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | REF_CLOSE: (37), (52), (53), (78), (88), (162), (165), (180), (183),
% 110.96/16.31 | | | | | | (201), (204), (206), (209), (212), (213), (214), (233),
% 110.96/16.31 | | | | | | (234), (236), (238), (245), (247), (248), (270), (272),
% 110.96/16.31 | | | | | | (273), (274), (275), (276), (277), (279), (281), (282),
% 110.96/16.31 | | | | | | (286), (293), (299), (302), (304), (305), (323), (331),
% 110.96/16.31 | | | | | | (336), (352), (356), (362), (365), (370), (371), (385),
% 110.96/16.31 | | | | | | (386), (394), (407), (412), (413), (424), (426), (434),
% 110.96/16.31 | | | | | | (436), (440), (450), (458), (462), (475), (479), (500),
% 110.96/16.31 | | | | | | (530), (537), (551), (553), (554), (555), (557), (558),
% 110.96/16.31 | | | | | | (559), (560), (561), (562), (563), (565), (566), (568),
% 110.96/16.31 | | | | | | (569), (573), (575), (577), (581), (584), (594), (602),
% 110.96/16.31 | | | | | | (603), (605), (661), (694), (695), (759), (1936), (1937),
% 110.96/16.31 | | | | | | (2360), (2366), (2367), (function-axioms) are
% 110.96/16.31 | | | | | | inconsistent by sub-proof #1.
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | End of split
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | Case 2:
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | | (2368) all_10_0 = e2
% 110.96/16.31 | | | | | (2369) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | | REF_CLOSE: (37), (41), (47), (52), (53), (73), (150), (154), (156),
% 110.96/16.31 | | | | | (157), (161), (164), (167), (169), (170), (172), (177),
% 110.96/16.31 | | | | | (178), (179), (180), (183), (185), (188), (189), (190),
% 110.96/16.31 | | | | | (192), (193), (201), (202), (204), (206), (207), (208),
% 110.96/16.31 | | | | | (209), (211), (212), (213), (214), (233), (234), (235),
% 110.96/16.31 | | | | | (236), (237), (238), (239), (240), (241), (243), (245),
% 110.96/16.31 | | | | | (246), (247), (248), (270), (271), (272), (274), (275),
% 110.96/16.31 | | | | | (276), (277), (279), (281), (284), (286), (287), (288),
% 110.96/16.31 | | | | | (290), (291), (292), (293), (295), (297), (298), (299),
% 110.96/16.31 | | | | | (300), (302), (304), (305), (323), (327), (328), (331),
% 110.96/16.31 | | | | | (336), (339), (340), (342), (343), (346), (352), (356),
% 110.96/16.31 | | | | | (362), (365), (370), (371), (385), (386), (391), (394),
% 110.96/16.31 | | | | | (406), (407), (412), (413), (424), (426), (430), (434),
% 110.96/16.31 | | | | | (436), (440), (446), (450), (458), (460), (462), (468),
% 110.96/16.31 | | | | | (470), (472), (474), (475), (477), (479), (533), (548),
% 110.96/16.31 | | | | | (551), (552), (553), (554), (555), (556), (557), (558),
% 110.96/16.31 | | | | | (559), (560), (561), (562), (563), (564), (565), (566),
% 110.96/16.31 | | | | | (567), (568), (569), (571), (573), (575), (577), (579),
% 110.96/16.31 | | | | | (581), (582), (583), (584), (585), (587), (589), (591),
% 110.96/16.31 | | | | | (593), (594), (595), (596), (599), (601), (602), (603),
% 110.96/16.31 | | | | | (604), (605), (705), (771), (783), (2358), (2359), (2360),
% 110.96/16.31 | | | | | (2361), (2368), (2369), (function-axioms) are inconsistent
% 110.96/16.31 | | | | | by sub-proof #21.
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | End of split
% 110.96/16.31 | | | |
% 110.96/16.31 | | | Case 2:
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | (2370) all_8_1 = e1
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | COMBINE_EQS: (704), (2370) imply:
% 110.96/16.31 | | | | (2371) all_48_1 = e1
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | REDUCE: (48), (2370) imply:
% 110.96/16.31 | | | | (2372) op(e1, all_8_2) = all_8_0
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | REDUCE: (47), (2370) imply:
% 110.96/16.31 | | | | (2373) op(e2, all_8_2) = e1
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | BETA: splitting (54) gives:
% 110.96/16.31 | | | |
% 110.96/16.31 | | | | Case 1:
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | | (2374) ~ (all_10_0 = e2)
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | | BETA: splitting (68) gives:
% 110.96/16.31 | | | | |
% 110.96/16.31 | | | | | Case 1:
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | (2375) ~ (all_16_0 = e1)
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | REDUCE: (775), (2375) imply:
% 110.96/16.31 | | | | | | (2376) ~ (all_10_0 = e1)
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | BETA: splitting (73) gives:
% 110.96/16.31 | | | | | |
% 110.96/16.31 | | | | | | Case 1:
% 110.96/16.31 | | | | | | |
% 110.96/16.31 | | | | | | | (2377) ~ (all_18_0 = e3)
% 110.96/16.31 | | | | | | |
% 110.96/16.31 | | | | | | | REDUCE: (771), (2377) imply:
% 110.96/16.31 | | | | | | | (2378) ~ (all_6_0 = e3)
% 110.96/16.31 | | | | | | |
% 110.96/16.31 | | | | | | | BETA: splitting (78) gives:
% 110.96/16.31 | | | | | | |
% 110.96/16.31 | | | | | | | Case 1:
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | (2379) ~ (all_20_0 = e3)
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | REDUCE: (1936), (2379) imply:
% 110.96/16.31 | | | | | | | | (2380) $false
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | CLOSE: (2380) is inconsistent.
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | Case 2:
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | (2381) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | BETA: splitting (107) gives:
% 110.96/16.31 | | | | | | | |
% 110.96/16.31 | | | | | | | | Case 1:
% 110.96/16.31 | | | | | | | | |
% 110.96/16.31 | | | | | | | | | (2382) ~ (all_32_1 = e1)
% 110.96/16.31 | | | | | | | | |
% 110.96/16.31 | | | | | | | | | REDUCE: (700), (2382) imply:
% 110.96/16.31 | | | | | | | | | (2383) ~ (all_10_1 = e1)
% 110.96/16.31 | | | | | | | | |
% 110.96/16.31 | | | | | | | | | BETA: splitting (121) gives:
% 110.96/16.31 | | | | | | | | |
% 110.96/16.31 | | | | | | | | | Case 1:
% 110.96/16.31 | | | | | | | | | |
% 110.96/16.31 | | | | | | | | | | (2384) ~ (all_38_1 = e2)
% 110.96/16.31 | | | | | | | | | |
% 110.96/16.31 | | | | | | | | | | REDUCE: (702), (2384) imply:
% 110.96/16.31 | | | | | | | | | | (2385) ~ (all_10_1 = e2)
% 110.96/16.31 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | REF_CLOSE: (37), (41), (47), (52), (53), (156), (157), (162),
% 110.96/16.32 | | | | | | | | | | (164), (165), (169), (179), (183), (201), (202),
% 110.96/16.32 | | | | | | | | | | (204), (206), (208), (211), (212), (213), (214),
% 110.96/16.32 | | | | | | | | | | (233), (234), (235), (236), (238), (241), (243),
% 110.96/16.32 | | | | | | | | | | (244), (245), (246), (247), (248), (270), (271),
% 110.96/16.32 | | | | | | | | | | (272), (274), (275), (277), (283), (284), (286),
% 110.96/16.32 | | | | | | | | | | (288), (292), (293), (295), (296), (297), (298),
% 110.96/16.32 | | | | | | | | | | (299), (300), (302), (304), (305), (323), (331),
% 110.96/16.32 | | | | | | | | | | (335), (338), (340), (343), (344), (352), (356),
% 110.96/16.32 | | | | | | | | | | (362), (365), (370), (385), (386), (391), (394),
% 110.96/16.32 | | | | | | | | | | (406), (407), (412), (413), (424), (426), (430),
% 110.96/16.32 | | | | | | | | | | (434), (436), (440), (446), (450), (458), (460),
% 110.96/16.32 | | | | | | | | | | (462), (464), (468), (475), (477), (479), (551),
% 110.96/16.32 | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 110.96/16.32 | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 110.96/16.32 | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 110.96/16.32 | | | | | | | | | | (577), (579), (581), (582), (584), (585), (587),
% 110.96/16.32 | | | | | | | | | | (589), (591), (594), (595), (596), (599), (602),
% 110.96/16.32 | | | | | | | | | | (603), (604), (605), (2357), (2359), (2360),
% 110.96/16.32 | | | | | | | | | | (2374), (2376), (2378), (2383), (2385),
% 110.96/16.32 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 110.96/16.32 | | | | | | | | | | #38.
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | (2386) all_38_1 = e2
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | COMBINE_EQS: (702), (2386) imply:
% 110.96/16.32 | | | | | | | | | | (2387) all_10_1 = e2
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | REDUCE: (53), (2387) imply:
% 110.96/16.32 | | | | | | | | | | (2388) op(e2, all_10_2) = all_10_0
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | REDUCE: (52), (2387) imply:
% 110.96/16.32 | | | | | | | | | | (2389) op(e3, all_10_2) = e2
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | BETA: splitting (270) gives:
% 110.96/16.32 | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | (2390) ~ (all_56_15 = e1)
% 110.96/16.32 | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | REDUCE: (554), (2390) imply:
% 110.96/16.32 | | | | | | | | | | | (2391) ~ (all_4_2 = e1)
% 110.96/16.32 | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | BETA: splitting (272) gives:
% 110.96/16.32 | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | (2392) ~ (all_56_12 = e1)
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | REDUCE: (426), (2392) imply:
% 110.96/16.32 | | | | | | | | | | | | (2393) ~ (all_10_2 = e1)
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | BETA: splitting (271) gives:
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | (2394) ~ (all_56_13 = e1)
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | REDUCE: (556), (2394) imply:
% 110.96/16.32 | | | | | | | | | | | | | (2395) ~ (all_8_2 = e1)
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | BETA: splitting (273) gives:
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | (2396) ~ (all_56_15 = e2)
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | REDUCE: (554), (2396) imply:
% 110.96/16.32 | | | | | | | | | | | | | | (2397) ~ (all_4_2 = e2)
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | (2398) all_54_15 = e3
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (2398) imply:
% 110.96/16.32 | | | | | | | | | | | | | | | (2399) all_4_2 = e3
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | COMBINE_EQS: (554), (2399) imply:
% 110.96/16.32 | | | | | | | | | | | | | | | (2400) all_56_15 = e3
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | Case 1:
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | | (2401) ~ (all_56_6 = e1)
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (53), (179), (202), (208), (212),
% 110.96/16.32 | | | | | | | | | | | | | | | | (214), (233), (238), (247), (248), (271), (277),
% 110.96/16.32 | | | | | | | | | | | | | | | | (281), (284), (288), (292), (305), (323), (327),
% 110.96/16.32 | | | | | | | | | | | | | | | | (331), (340), (343), (344), (356), (362), (370),
% 110.96/16.32 | | | | | | | | | | | | | | | | (371), (385), (386), (391), (394), (406), (413),
% 110.96/16.32 | | | | | | | | | | | | | | | | (426), (436), (440), (446), (450), (458), (551),
% 110.96/16.32 | | | | | | | | | | | | | | | | (553), (555), (556), (557), (558), (559), (560),
% 110.96/16.32 | | | | | | | | | | | | | | | | (561), (562), (563), (564), (565), (566), (567),
% 110.96/16.32 | | | | | | | | | | | | | | | | (568), (569), (571), (577), (594), (601), (603),
% 110.96/16.32 | | | | | | | | | | | | | | | | (2374), (2376), (2383), (2388), (2389), (2391),
% 110.96/16.32 | | | | | | | | | | | | | | | | (2393), (2401), (function-axioms) are inconsistent
% 110.96/16.32 | | | | | | | | | | | | | | | | by sub-proof #366.
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | | (2402) ~ (all_56_15 = e3)
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | | REDUCE: (2400), (2402) imply:
% 110.96/16.32 | | | | | | | | | | | | | | | | (2403) $false
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | | CLOSE: (2403) is inconsistent.
% 110.96/16.32 | | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | End of split
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | (2404) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (2391), (2397), (2404) are
% 110.96/16.32 | | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 110.96/16.32 | | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | End of split
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | (2405) all_56_15 = e2
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | | REF_CLOSE: (52), (53), (157), (179), (202), (208), (214),
% 110.96/16.32 | | | | | | | | | | | | | | (238), (243), (245), (247), (248), (271), (277),
% 110.96/16.32 | | | | | | | | | | | | | | (281), (282), (284), (287), (288), (292), (298),
% 110.96/16.32 | | | | | | | | | | | | | | (299), (305), (323), (331), (340), (343), (344),
% 110.96/16.32 | | | | | | | | | | | | | | (362), (370), (371), (385), (386), (391), (394),
% 110.96/16.32 | | | | | | | | | | | | | | (406), (407), (413), (426), (436), (440), (446),
% 110.96/16.32 | | | | | | | | | | | | | | (450), (458), (462), (551), (552), (553), (554),
% 110.96/16.32 | | | | | | | | | | | | | | (555), (556), (557), (558), (559), (560), (562),
% 110.96/16.32 | | | | | | | | | | | | | | (563), (564), (565), (566), (567), (568), (569),
% 110.96/16.32 | | | | | | | | | | | | | | (571), (573), (577), (581), (583), (594), (601),
% 110.96/16.32 | | | | | | | | | | | | | | (603), (2373), (2374), (2376), (2383), (2393),
% 110.96/16.32 | | | | | | | | | | | | | | (2395), (2405), (function-axioms) are inconsistent
% 110.96/16.32 | | | | | | | | | | | | | | by sub-proof #94.
% 110.96/16.32 | | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | End of split
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | (2406) all_56_13 = e1
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | COMBINE_EQS: (556), (2406) imply:
% 110.96/16.32 | | | | | | | | | | | | | (2407) all_8_2 = e1
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | | REF_CLOSE: (209), (591), (2373), (2407), (function-axioms)
% 110.96/16.32 | | | | | | | | | | | | | are inconsistent by sub-proof #109.
% 110.96/16.32 | | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | End of split
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | Case 2:
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | (2408) all_56_12 = e1
% 110.96/16.32 | | | | | | | | | | | | (2409) ~ (all_56_11 = e0)
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | COMBINE_EQS: (426), (2408) imply:
% 110.96/16.32 | | | | | | | | | | | | (2410) all_10_2 = e1
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.32 | | | | | | | | | | | | SIMP: (2410) implies:
% 110.96/16.32 | | | | | | | | | | | | (2411) all_10_2 = e1
% 110.96/16.32 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | REF_CLOSE: (4), (162), (167), (208), (209), (211), (233),
% 110.96/16.33 | | | | | | | | | | | | (243), (271), (273), (276), (278), (289), (293),
% 110.96/16.33 | | | | | | | | | | | | (294), (296), (298), (300), (301), (302), (303),
% 110.96/16.33 | | | | | | | | | | | | (323), (338), (340), (341), (352), (356), (362),
% 110.96/16.33 | | | | | | | | | | | | (365), (370), (391), (394), (406), (407), (412),
% 110.96/16.33 | | | | | | | | | | | | (413), (424), (430), (434), (436), (446), (450),
% 110.96/16.33 | | | | | | | | | | | | (552), (554), (556), (557), (558), (559), (561),
% 110.96/16.33 | | | | | | | | | | | | (564), (565), (566), (567), (569), (582), (585),
% 110.96/16.33 | | | | | | | | | | | | (589), (591), (593), (602), (603), (604), (2373),
% 110.96/16.33 | | | | | | | | | | | | (2391), (2408), (2409), (2411), (function-axioms)
% 110.96/16.33 | | | | | | | | | | | | are inconsistent by sub-proof #74.
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | (2412) all_56_15 = e1
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | REF_CLOSE: (37), (165), (201), (213), (234), (270), (362),
% 110.96/16.33 | | | | | | | | | | | (479), (500), (554), (602), (694), (1937), (2381),
% 110.96/16.33 | | | | | | | | | | | (2412), (function-axioms) are inconsistent by
% 110.96/16.33 | | | | | | | | | | | sub-proof #10.
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | (2413) all_32_1 = e1
% 110.96/16.33 | | | | | | | | | (2414) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | COMBINE_EQS: (700), (2413) imply:
% 110.96/16.33 | | | | | | | | | (2415) all_10_1 = e1
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | SIMP: (2415) implies:
% 110.96/16.33 | | | | | | | | | (2416) all_10_1 = e1
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | REF_CLOSE: (6), (52), (53), (169), (172), (187), (204), (206),
% 110.96/16.33 | | | | | | | | | (212), (213), (214), (233), (238), (239), (240),
% 110.96/16.33 | | | | | | | | | (248), (272), (273), (274), (275), (281), (282),
% 110.96/16.33 | | | | | | | | | (284), (285), (286), (290), (291), (323), (328),
% 110.96/16.33 | | | | | | | | | (331), (336), (344), (356), (365), (370), (371),
% 110.96/16.33 | | | | | | | | | (385), (386), (391), (394), (412), (426), (436),
% 110.96/16.33 | | | | | | | | | (440), (446), (470), (472), (524), (551), (553),
% 110.96/16.33 | | | | | | | | | (554), (555), (557), (558), (559), (560), (561),
% 110.96/16.33 | | | | | | | | | (562), (563), (564), (565), (566), (567), (568),
% 110.96/16.33 | | | | | | | | | (569), (573), (575), (577), (579), (583), (594),
% 110.96/16.33 | | | | | | | | | (595), (597), (599), (779), (2360), (2374), (2414),
% 110.96/16.33 | | | | | | | | | (2416), (function-axioms) are inconsistent by
% 110.96/16.33 | | | | | | | | | sub-proof #30.
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | End of split
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | End of split
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | Case 2:
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | | (2417) all_18_0 = e3
% 110.96/16.33 | | | | | | | (2418) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | | COMBINE_EQS: (771), (2417) imply:
% 110.96/16.33 | | | | | | | (2419) all_6_0 = e3
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | | REDUCE: (2359), (2419) imply:
% 110.96/16.33 | | | | | | | (2420) op(e2, all_6_2) = e3
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | | BETA: splitting (2418) gives:
% 110.96/16.33 | | | | | | |
% 110.96/16.33 | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | (2421) ~ (all_18_1 = e2)
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | REDUCE: (2358), (2421) imply:
% 110.96/16.33 | | | | | | | | (2422) $false
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | CLOSE: (2422) is inconsistent.
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | (2423) ~ (all_18_2 = e0)
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | REDUCE: (533), (2423) imply:
% 110.96/16.33 | | | | | | | | (2424) ~ (all_6_2 = e0)
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | BETA: splitting (107) gives:
% 110.96/16.33 | | | | | | | |
% 110.96/16.33 | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | (2425) ~ (all_32_1 = e1)
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | REDUCE: (700), (2425) imply:
% 110.96/16.33 | | | | | | | | | (2426) ~ (all_10_1 = e1)
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | BETA: splitting (121) gives:
% 110.96/16.33 | | | | | | | | |
% 110.96/16.33 | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | (2427) ~ (all_38_1 = e2)
% 110.96/16.33 | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | REDUCE: (702), (2427) imply:
% 110.96/16.33 | | | | | | | | | | (2428) ~ (all_10_1 = e2)
% 110.96/16.33 | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | BETA: splitting (274) gives:
% 110.96/16.33 | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | (2429) ~ (all_56_14 = e2)
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | REDUCE: (555), (2429) imply:
% 110.96/16.33 | | | | | | | | | | | (2430) ~ (all_6_2 = e2)
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | BETA: splitting (238) gives:
% 110.96/16.33 | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | (2431) all_54_10 = e3
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | COMBINE_EQS: (551), (2431) imply:
% 110.96/16.33 | | | | | | | | | | | | (2432) all_6_2 = e3
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | SIMP: (2432) implies:
% 110.96/16.33 | | | | | | | | | | | | (2433) all_6_2 = e3
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | COMBINE_EQS: (555), (2433) imply:
% 110.96/16.33 | | | | | | | | | | | | (2434) all_56_14 = e3
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | REDUCE: (2420), (2433) imply:
% 110.96/16.33 | | | | | | | | | | | | (2435) op(e2, e3) = e3
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | REDUCE: (2360), (2433) imply:
% 110.96/16.33 | | | | | | | | | | | | (2436) op(e1, e3) = e2
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | BETA: splitting (277) gives:
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | (2437) ~ (all_56_14 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (2434), (2437) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2438) $false
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | CLOSE: (2438) is inconsistent.
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | (2439) ~ (all_56_9 = e0)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (450), (2439) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2440) ~ (all_52_3 = e0)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 110.96/16.33 | | | | | | | | | | | | | e3, e1, simplifying with (207), (2436) gives:
% 110.96/16.33 | | | | | | | | | | | | | (2441) all_52_2 = e2
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 110.96/16.33 | | | | | | | | | | | | | e3, e2, simplifying with (211), (2435) gives:
% 110.96/16.33 | | | | | | | | | | | | | (2442) all_52_1 = e3
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (192), (2442) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2443) ~ (all_52_3 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | SIMP: (2443) implies:
% 110.96/16.33 | | | | | | | | | | | | | (2444) ~ (all_52_3 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (571), (2442) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2445) ~ (all_10_2 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (582), (2442) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2446) ~ (all_8_2 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | SIMP: (2446) implies:
% 110.96/16.33 | | | | | | | | | | | | | (2447) ~ (all_8_2 = e3)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (188), (2441) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2448) ~ (all_52_3 = e2)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | SIMP: (2448) implies:
% 110.96/16.33 | | | | | | | | | | | | | (2449) ~ (all_52_3 = e2)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | REDUCE: (573), (2441) imply:
% 110.96/16.33 | | | | | | | | | | | | | (2450) ~ (all_10_2 = e2)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | SIMP: (2450) implies:
% 110.96/16.33 | | | | | | | | | | | | | (2451) ~ (all_10_2 = e2)
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | BETA: splitting (346) gives:
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | (2452) all_58_0 = e0
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | COMBINE_EQS: (424), (2452) imply:
% 110.96/16.33 | | | | | | | | | | | | | | (2453) all_10_2 = e0
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | REDUCE: (581), (2453) imply:
% 110.96/16.33 | | | | | | | | | | | | | | (2454) ~ (all_52_12 = e0)
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | REDUCE: (52), (2453) imply:
% 110.96/16.33 | | | | | | | | | | | | | | (2455) op(e3, e0) = all_10_1
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | Case 1:
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | | (2456) ~ (all_56_2 = e3)
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | | REDUCE: (407), (2456) imply:
% 110.96/16.33 | | | | | | | | | | | | | | | (2457) ~ (all_52_12 = e3)
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | | REF_CLOSE: (212), (245), (462), (2426), (2428), (2454),
% 110.96/16.33 | | | | | | | | | | | | | | | (2455), (2457), (function-axioms) are inconsistent
% 110.96/16.33 | | | | | | | | | | | | | | | by sub-proof #447.
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | | (2458) all_56_2 = e3
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | | REF_CLOSE: (209), (243), (298), (552), (556), (567), (591),
% 110.96/16.33 | | | | | | | | | | | | | | | (2373), (2447), (2458), (function-axioms) are
% 110.96/16.33 | | | | | | | | | | | | | | | inconsistent by sub-proof #107.
% 110.96/16.33 | | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | Case 2:
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | (2459) ~ (all_58_0 = e0)
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | | REF_CLOSE: (236), (248), (424), (475), (553), (566), (575),
% 110.96/16.33 | | | | | | | | | | | | | | (2440), (2444), (2449), (2451), (2459) are
% 110.96/16.33 | | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 110.96/16.33 | | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | | | | | |
% 110.96/16.33 | | | | | | | | | | | | End of split
% 110.96/16.33 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | Case 2:
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | (2460) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | REF_CLOSE: (551), (568), (2424), (2430), (2460) are
% 110.96/16.34 | | | | | | | | | | | | inconsistent by sub-proof #435.
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | End of split
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | Case 2:
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | (2461) all_56_14 = e2
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | COMBINE_EQS: (555), (2461) imply:
% 110.96/16.34 | | | | | | | | | | | (2462) all_6_2 = e2
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | REF_CLOSE: (206), (594), (2360), (2462), (function-axioms)
% 110.96/16.34 | | | | | | | | | | | are inconsistent by sub-proof #39.
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | End of split
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | Case 2:
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | (2463) all_38_1 = e2
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | COMBINE_EQS: (702), (2463) imply:
% 110.96/16.34 | | | | | | | | | | (2464) all_10_1 = e2
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | REDUCE: (53), (2464) imply:
% 110.96/16.34 | | | | | | | | | | (2465) op(e2, all_10_2) = all_10_0
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | REDUCE: (52), (2464) imply:
% 110.96/16.34 | | | | | | | | | | (2466) op(e3, all_10_2) = e2
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | BETA: splitting (274) gives:
% 110.96/16.34 | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | Case 1:
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | (2467) ~ (all_56_14 = e2)
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | REDUCE: (555), (2467) imply:
% 110.96/16.34 | | | | | | | | | | | (2468) ~ (all_6_2 = e2)
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | BETA: splitting (238) gives:
% 110.96/16.34 | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | Case 1:
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | (2469) all_54_10 = e3
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | COMBINE_EQS: (551), (2469) imply:
% 110.96/16.34 | | | | | | | | | | | | (2470) all_6_2 = e3
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | SIMP: (2470) implies:
% 110.96/16.34 | | | | | | | | | | | | (2471) all_6_2 = e3
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | COMBINE_EQS: (555), (2471) imply:
% 110.96/16.34 | | | | | | | | | | | | (2472) all_56_14 = e3
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | REDUCE: (2420), (2471) imply:
% 110.96/16.34 | | | | | | | | | | | | (2473) op(e2, e3) = e3
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | REDUCE: (2360), (2471) imply:
% 110.96/16.34 | | | | | | | | | | | | (2474) op(e1, e3) = e2
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | BETA: splitting (277) gives:
% 110.96/16.34 | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | Case 1:
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | (2475) ~ (all_56_14 = e3)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (2472), (2475) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2476) $false
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | CLOSE: (2476) is inconsistent.
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | Case 2:
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | (2477) ~ (all_56_9 = e0)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (450), (2477) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2478) ~ (all_52_3 = e0)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 110.96/16.34 | | | | | | | | | | | | | e3, e1, simplifying with (207), (2474) gives:
% 110.96/16.34 | | | | | | | | | | | | | (2479) all_52_2 = e2
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 110.96/16.34 | | | | | | | | | | | | | e3, e2, simplifying with (211), (2473) gives:
% 110.96/16.34 | | | | | | | | | | | | | (2480) all_52_1 = e3
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | COMBINE_EQS: (386), (2479) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2481) all_56_6 = e2
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | COMBINE_EQS: (563), (2479) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2482) all_58_6 = e2
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | COMBINE_EQS: (406), (2480) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2483) all_58_2 = e3
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (192), (2480) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2484) ~ (all_52_3 = e3)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | SIMP: (2484) implies:
% 110.96/16.34 | | | | | | | | | | | | | (2485) ~ (all_52_3 = e3)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (571), (2480) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2486) ~ (all_10_2 = e3)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (188), (2479) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2487) ~ (all_52_3 = e2)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | SIMP: (2487) implies:
% 110.96/16.34 | | | | | | | | | | | | | (2488) ~ (all_52_3 = e2)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | REDUCE: (573), (2479) imply:
% 110.96/16.34 | | | | | | | | | | | | | (2489) ~ (all_10_2 = e2)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | SIMP: (2489) implies:
% 110.96/16.34 | | | | | | | | | | | | | (2490) ~ (all_10_2 = e2)
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | BETA: splitting (346) gives:
% 110.96/16.34 | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | Case 1:
% 110.96/16.34 | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | (2491) all_58_0 = e0
% 110.96/16.34 | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | COMBINE_EQS: (424), (2491) imply:
% 110.96/16.34 | | | | | | | | | | | | | | (2492) all_10_2 = e0
% 110.96/16.34 | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | COMBINE_EQS: (426), (2492) imply:
% 110.96/16.34 | | | | | | | | | | | | | | (2493) all_56_12 = e0
% 110.96/16.34 | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 110.96/16.34 | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | Case 1:
% 110.96/16.34 | | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | | (2494) all_58_0 = e1
% 110.96/16.34 | | | | | | | | | | | | | | |
% 110.96/16.34 | | | | | | | | | | | | | | | COMBINE_EQS: (2491), (2494) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | (2495) e1 = e0
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | SIMP: (2495) implies:
% 111.11/16.34 | | | | | | | | | | | | | | | (2496) e1 = e0
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | REDUCE: (4), (2496) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | (2497) $false
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | CLOSE: (2497) is inconsistent.
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | (2498) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | Case 1:
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | (2499) ~ (all_56_5 = e2)
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | REDUCE: (446), (2499) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | (2500) ~ (all_52_13 = e2)
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | BETA: splitting (2498) gives:
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | (2501) all_58_2 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2483), (2501) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | (2502) e3 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | REDUCE: (8), (2502) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | (2503) $false
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | CLOSE: (2503) is inconsistent.
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | (2504) all_58_6 = e1 | all_58_12 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | BETA: splitting (2504) gives:
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2505) all_58_6 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2482), (2505) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2506) e2 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2481), (2506) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2507) all_56_6 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (238), (286), (551), (555), (568), (2424), (2468),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2507) are inconsistent by sub-proof #305.
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2508) all_58_12 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2508) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2509) all_52_3 = e1
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | REDUCE: (584), (2509) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2510) ~ (all_4_2 = e1)
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | SIMP: (2510) implies:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2511) ~ (all_4_2 = e1)
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | REDUCE: (2488), (2509) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2512) ~ (e2 = e1)
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (208), (212), (233), (238), (248), (272),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (273), (277), (281), (282), (286), (292), (293),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (294), (297), (299), (303), (323), (327), (331),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (336), (340), (352), (356), (362), (365), (370),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (371), (385), (386), (391), (394), (406), (407),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (412), (413), (424), (426), (430), (436), (440),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (450), (551), (553), (554), (555), (557), (558),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (566), (567), (568), (569), (571), (579), (581),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (602), (603), (605), (2376), (2465), (2466),
% 111.11/16.34 | | | | | | | | | | | | | | | | | | (2468), (2490), (2500), (2511), (function-axioms)
% 111.11/16.34 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #35.
% 111.11/16.34 | | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | (2513) ~ (all_56_12 = e0)
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | REDUCE: (2493), (2513) imply:
% 111.11/16.34 | | | | | | | | | | | | | | | | (2514) $false
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | | CLOSE: (2514) is inconsistent.
% 111.11/16.34 | | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | (2515) ~ (all_58_0 = e0)
% 111.11/16.34 | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | | REF_CLOSE: (236), (248), (424), (475), (553), (566), (575),
% 111.11/16.34 | | | | | | | | | | | | | | (2478), (2485), (2488), (2490), (2515) are
% 111.11/16.34 | | | | | | | | | | | | | | inconsistent by sub-proof #20.
% 111.11/16.34 | | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | (2516) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.34 | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | | REF_CLOSE: (551), (568), (2424), (2468), (2516) are
% 111.11/16.34 | | | | | | | | | | | | inconsistent by sub-proof #435.
% 111.11/16.34 | | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | End of split
% 111.11/16.34 | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | Case 2:
% 111.11/16.34 | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | (2517) all_56_14 = e2
% 111.11/16.34 | | | | | | | | | | |
% 111.11/16.34 | | | | | | | | | | | COMBINE_EQS: (555), (2517) imply:
% 111.11/16.35 | | | | | | | | | | | (2518) all_6_2 = e2
% 111.11/16.35 | | | | | | | | | | |
% 111.11/16.35 | | | | | | | | | | | REF_CLOSE: (206), (594), (2360), (2518), (function-axioms)
% 111.11/16.35 | | | | | | | | | | | are inconsistent by sub-proof #39.
% 111.11/16.35 | | | | | | | | | | |
% 111.11/16.35 | | | | | | | | | | End of split
% 111.11/16.35 | | | | | | | | | |
% 111.11/16.35 | | | | | | | | | End of split
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | Case 2:
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | (2519) all_32_1 = e1
% 111.11/16.35 | | | | | | | | | (2520) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | COMBINE_EQS: (700), (2519) imply:
% 111.11/16.35 | | | | | | | | | (2521) all_10_1 = e1
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | SIMP: (2521) implies:
% 111.11/16.35 | | | | | | | | | (2522) all_10_1 = e1
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | REF_CLOSE: (6), (52), (53), (169), (172), (187), (204), (206),
% 111.11/16.35 | | | | | | | | | (212), (213), (214), (233), (238), (239), (240),
% 111.11/16.35 | | | | | | | | | (248), (272), (273), (274), (275), (281), (282),
% 111.11/16.35 | | | | | | | | | (284), (285), (286), (290), (291), (323), (328),
% 111.11/16.35 | | | | | | | | | (331), (336), (344), (356), (365), (370), (371),
% 111.11/16.35 | | | | | | | | | (385), (386), (391), (394), (412), (426), (436),
% 111.11/16.35 | | | | | | | | | (440), (446), (470), (472), (524), (551), (553),
% 111.11/16.35 | | | | | | | | | (554), (555), (557), (558), (559), (560), (561),
% 111.11/16.35 | | | | | | | | | (562), (563), (564), (565), (566), (567), (568),
% 111.11/16.35 | | | | | | | | | (569), (573), (575), (577), (579), (583), (594),
% 111.11/16.35 | | | | | | | | | (595), (597), (599), (779), (2360), (2374), (2520),
% 111.11/16.35 | | | | | | | | | (2522), (function-axioms) are inconsistent by
% 111.11/16.35 | | | | | | | | | sub-proof #30.
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | End of split
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | End of split
% 111.11/16.35 | | | | | | |
% 111.11/16.35 | | | | | | End of split
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | Case 2:
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | (2523) all_16_0 = e1
% 111.11/16.35 | | | | | | (2524) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | COMBINE_EQS: (775), (2523) imply:
% 111.11/16.35 | | | | | | (2525) all_10_0 = e1
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | SIMP: (2525) implies:
% 111.11/16.35 | | | | | | (2526) all_10_0 = e1
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | REF_CLOSE: (37), (52), (53), (78), (88), (162), (165), (180), (183),
% 111.11/16.35 | | | | | | (201), (204), (206), (209), (212), (213), (214), (233),
% 111.11/16.35 | | | | | | (234), (236), (238), (245), (247), (248), (270), (272),
% 111.11/16.35 | | | | | | (273), (274), (275), (276), (277), (279), (281), (282),
% 111.11/16.35 | | | | | | (286), (293), (299), (302), (304), (305), (323), (331),
% 111.11/16.35 | | | | | | (336), (352), (356), (362), (365), (370), (371), (385),
% 111.11/16.35 | | | | | | (386), (394), (407), (412), (413), (424), (426), (434),
% 111.11/16.35 | | | | | | (436), (440), (450), (458), (462), (475), (479), (500),
% 111.11/16.35 | | | | | | (530), (537), (551), (553), (554), (555), (557), (558),
% 111.11/16.35 | | | | | | (559), (560), (561), (562), (563), (565), (566), (568),
% 111.11/16.35 | | | | | | (569), (573), (575), (577), (581), (584), (594), (602),
% 111.11/16.35 | | | | | | (603), (605), (661), (694), (695), (759), (1936), (1937),
% 111.11/16.35 | | | | | | (2360), (2524), (2526), (function-axioms) are
% 111.11/16.35 | | | | | | inconsistent by sub-proof #1.
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | End of split
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | Case 2:
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | | (2527) all_10_0 = e2
% 111.11/16.35 | | | | | (2528) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | | COMBINE_EQS: (783), (2527) imply:
% 111.11/16.35 | | | | | (2529) all_50_0 = e2
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | | REDUCE: (53), (2527) imply:
% 111.11/16.35 | | | | | (2530) op(all_10_1, all_10_2) = e2
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | | BETA: splitting (73) gives:
% 111.11/16.35 | | | | |
% 111.11/16.35 | | | | | Case 1:
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | (2531) ~ (all_18_0 = e3)
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | REDUCE: (771), (2531) imply:
% 111.11/16.35 | | | | | | (2532) ~ (all_6_0 = e3)
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | BETA: splitting (145) gives:
% 111.11/16.35 | | | | | |
% 111.11/16.35 | | | | | | Case 1:
% 111.11/16.35 | | | | | | |
% 111.11/16.35 | | | | | | | (2533) ~ (all_48_0 = e3)
% 111.11/16.35 | | | | | | |
% 111.11/16.35 | | | | | | | REDUCE: (782), (2533) imply:
% 111.11/16.35 | | | | | | | (2534) ~ (all_8_0 = e3)
% 111.11/16.35 | | | | | | |
% 111.11/16.35 | | | | | | | BETA: splitting (150) gives:
% 111.11/16.35 | | | | | | |
% 111.11/16.35 | | | | | | | Case 1:
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | (2535) ~ (all_50_0 = e2)
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | REDUCE: (2529), (2535) imply:
% 111.11/16.35 | | | | | | | | (2536) $false
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | CLOSE: (2536) is inconsistent.
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | Case 2:
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | (2537) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | BETA: splitting (274) gives:
% 111.11/16.35 | | | | | | | |
% 111.11/16.35 | | | | | | | | Case 1:
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | (2538) ~ (all_56_14 = e2)
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | REDUCE: (555), (2538) imply:
% 111.11/16.35 | | | | | | | | | (2539) ~ (all_6_2 = e2)
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | BETA: splitting (275) gives:
% 111.11/16.35 | | | | | | | | |
% 111.11/16.35 | | | | | | | | | Case 1:
% 111.11/16.35 | | | | | | | | | |
% 111.11/16.35 | | | | | | | | | | (2540) ~ (all_56_12 = e2)
% 111.11/16.35 | | | | | | | | | |
% 111.11/16.35 | | | | | | | | | | REDUCE: (426), (2540) imply:
% 111.11/16.35 | | | | | | | | | | (2541) ~ (all_10_2 = e2)
% 111.11/16.35 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | REF_CLOSE: (9), (41), (52), (157), (167), (184), (188),
% 111.11/16.36 | | | | | | | | | | (190), (192), (208), (209), (211), (212), (213),
% 111.11/16.36 | | | | | | | | | | (233), (236), (238), (241), (242), (243), (244),
% 111.11/16.36 | | | | | | | | | | (245), (246), (248), (272), (273), (276), (277),
% 111.11/16.36 | | | | | | | | | | (279), (281), (282), (286), (287), (288), (289),
% 111.11/16.36 | | | | | | | | | | (290), (291), (292), (293), (294), (295), (297),
% 111.11/16.36 | | | | | | | | | | (298), (299), (300), (302), (323), (324), (327),
% 111.11/16.36 | | | | | | | | | | (329), (331), (335), (338), (340), (341), (352),
% 111.11/16.36 | | | | | | | | | | (356), (362), (365), (370), (371), (385), (386),
% 111.11/16.36 | | | | | | | | | | (391), (394), (406), (407), (412), (424), (426),
% 111.11/16.36 | | | | | | | | | | (430), (434), (436), (440), (446), (450), (460),
% 111.11/16.36 | | | | | | | | | | (462), (464), (466), (468), (475), (548), (551),
% 111.11/16.36 | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 111.11/16.36 | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 111.11/16.36 | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 111.11/16.36 | | | | | | | | | | (579), (581), (582), (584), (585), (587), (589),
% 111.11/16.36 | | | | | | | | | | (591), (593), (594), (599), (601), (602), (604),
% 111.11/16.36 | | | | | | | | | | (605), (705), (2373), (2528), (2530), (2537),
% 111.11/16.36 | | | | | | | | | | (2539), (2541), (function-axioms) are inconsistent
% 111.11/16.36 | | | | | | | | | | by sub-proof #2.
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | (2542) all_56_12 = e2
% 111.11/16.36 | | | | | | | | | | (2543) ~ (all_56_10 = e0)
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | COMBINE_EQS: (426), (2542) imply:
% 111.11/16.36 | | | | | | | | | | (2544) all_10_2 = e2
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | SIMP: (2544) implies:
% 111.11/16.36 | | | | | | | | | | (2545) all_10_2 = e2
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | COMBINE_EQS: (424), (2545) imply:
% 111.11/16.36 | | | | | | | | | | (2546) all_58_0 = e2
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | REDUCE: (365), (2543) imply:
% 111.11/16.36 | | | | | | | | | | (2547) ~ (all_52_7 = e0)
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | REDUCE: (571), (2545) imply:
% 111.11/16.36 | | | | | | | | | | (2548) ~ (all_52_1 = e2)
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | REDUCE: (566), (2545) imply:
% 111.11/16.36 | | | | | | | | | | (2549) ~ (e3 = e2)
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | REDUCE: (52), (2545) imply:
% 111.11/16.36 | | | | | | | | | | (2550) op(e3, e2) = all_10_1
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | BETA: splitting (284) gives:
% 111.11/16.36 | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | (2551) ~ (all_56_7 = e1)
% 111.11/16.36 | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | REDUCE: (440), (2551) imply:
% 111.11/16.36 | | | | | | | | | | | (2552) ~ (all_52_6 = e1)
% 111.11/16.36 | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | BETA: splitting (305) gives:
% 111.11/16.36 | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | (2553) ~ (all_56_0 = e3)
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | REDUCE: (413), (2553) imply:
% 111.11/16.36 | | | | | | | | | | | | (2554) ~ (all_52_4 = e3)
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 111.11/16.36 | | | | | | | | | | | | all_10_1, e2, e3, simplifying with (214), (2550)
% 111.11/16.36 | | | | | | | | | | | | gives:
% 111.11/16.36 | | | | | | | | | | | | (2555) all_52_4 = all_10_1
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | COMBINE_EQS: (565), (2555) imply:
% 111.11/16.36 | | | | | | | | | | | | (2556) all_58_1 = all_10_1
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | REDUCE: (2554), (2555) imply:
% 111.11/16.36 | | | | | | | | | | | | (2557) ~ (all_10_1 = e3)
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | BETA: splitting (270) gives:
% 111.11/16.36 | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | (2558) ~ (all_56_15 = e1)
% 111.11/16.36 | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | REDUCE: (554), (2558) imply:
% 111.11/16.36 | | | | | | | | | | | | | (2559) ~ (all_4_2 = e1)
% 111.11/16.36 | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | BETA: splitting (276) gives:
% 111.11/16.36 | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | (2560) ~ (all_56_15 = e3)
% 111.11/16.36 | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | REDUCE: (554), (2560) imply:
% 111.11/16.36 | | | | | | | | | | | | | | (2561) ~ (all_4_2 = e3)
% 111.11/16.36 | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 111.11/16.36 | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | (2562) all_54_15 = e3
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (2562) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | (2563) all_4_2 = e3
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | REDUCE: (2561), (2563) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | (2564) $false
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | CLOSE: (2564) is inconsistent.
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | (2565) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | BETA: splitting (2565) gives:
% 111.11/16.36 | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | (2566) all_54_15 = e2
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (2566) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | (2567) all_4_2 = e2
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (557), (2567) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | (2568) all_58_15 = e2
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | REDUCE: (595), (2567) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | (2569) ~ (all_52_7 = e2)
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | REDUCE: (605), (2567) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | (2570) ~ (all_52_14 = e2)
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | REDUCE: (37), (2567) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | (2571) op(e0, e2) = all_4_1
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | BETA: splitting (1935) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2572) ~ (all_4_1 = e1)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 111.11/16.36 | | | | | | | | | | | | | | | | | all_4_1, e2, e0, simplifying with (202), (2571)
% 111.11/16.36 | | | | | | | | | | | | | | | | | gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2573) all_52_7 = all_4_1
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (477), (2573) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2574) all_54_13 = all_4_1
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | REDUCE: (169), (2573) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2575) ~ (all_52_11 = all_4_1)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | SIMP: (2575) implies:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2576) ~ (all_52_11 = all_4_1)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | REDUCE: (589), (2573) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2577) ~ (all_8_2 = all_4_1)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | SIMP: (2577) implies:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2578) ~ (all_8_2 = all_4_1)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | REDUCE: (2569), (2573) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2579) ~ (all_4_1 = e2)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | REDUCE: (2547), (2573) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | (2580) ~ (all_4_1 = e0)
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | (2581) all_54_13 = e3
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2574), (2581) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | (2582) all_4_1 = e3
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | REDUCE: (2576), (2582) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | (2583) ~ (all_52_11 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | REDUCE: (2578), (2582) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | (2584) ~ (all_8_2 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2585) all_58_6 = e1
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (563), (2585) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2586) all_52_2 = e1
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | SIMP: (2586) implies:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2587) all_52_2 = e1
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (2587) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2588) all_56_6 = e1
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | REDUCE: (583), (2587) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2589) ~ (all_6_2 = e1)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | (2590) ~ (all_56_6 = e1)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (2588), (2590) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | (2591) $false
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | CLOSE: (2591) is inconsistent.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | (2592) ~ (all_56_14 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2592) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | (2593) ~ (all_6_2 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | (2594) all_54_10 = e3
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (551), (2593), (2594) are inconsistent by
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | sub-proof #352.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | (2595) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (2596) ~ (all_56_2 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (2596) imply:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (2597) ~ (all_52_12 = e3)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (192), (193), (204), (237), (238), (244),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (271), (277), (279), (288), (292), (323), (326),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (329), (331), (340), (342), (343), (344), (362),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (370), (371), (385), (391), (394), (406), (436),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (446), (450), (464), (474), (551), (555), (556),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (557), (558), (559), (560), (561), (562), (563),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (564), (567), (568), (569), (587), (594), (599),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (601), (2372), (2534), (2539), (2547), (2548),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (2552), (2568), (2569), (2570), (2583), (2595),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (2597), (function-axioms) are inconsistent by
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | sub-proof #17.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | (2598) all_56_2 = e3
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (551), (555), (568), (2539), (2595), (2598)
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #351.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2599) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (209), (243), (280), (371), (385), (552), (556),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (560), (562), (567), (568), (591), (2373), (2552),
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2584), (2599), (function-axioms) are inconsistent
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | by sub-proof #53.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | (2600) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | BETA: splitting (2600) gives:
% 111.11/16.36 | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | (2601) all_54_13 = e2
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2574), (2579), (2601) are inconsistent by
% 111.11/16.36 | | | | | | | | | | | | | | | | | | | sub-proof #234.
% 111.11/16.36 | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | (2602) all_54_13 = e1 | all_54_13 = e0
% 111.11/16.37 | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (2602) gives:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | (2603) all_54_13 = e1
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2574), (2603) imply:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | (2604) all_4_1 = e1
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | SIMP: (2604) implies:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | (2605) all_4_1 = e1
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | REDUCE: (2572), (2605) imply:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | (2606) $false
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | CLOSE: (2606) is inconsistent.
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | (2607) all_54_13 = e0
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2574), (2580), (2607) are inconsistent by
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | | sub-proof #233.
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | (2608) ~ (all_4_2 = e2)
% 111.11/16.37 | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (2559), (2565), (2608) are
% 111.11/16.37 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #417.
% 111.11/16.37 | | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | (2609) all_54_15 = e1 | all_54_15 = e0
% 111.11/16.37 | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | | REF_CLOSE: (356), (569), (2559), (2609) are inconsistent by
% 111.11/16.37 | | | | | | | | | | | | | | | | sub-proof #418.
% 111.11/16.37 | | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | (2610) all_56_15 = e3
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | COMBINE_EQS: (554), (2610) imply:
% 111.11/16.37 | | | | | | | | | | | | | | (2611) all_4_2 = e3
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | SIMP: (2611) implies:
% 111.11/16.37 | | | | | | | | | | | | | | (2612) all_4_2 = e3
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | REDUCE: (603), (2612) imply:
% 111.11/16.37 | | | | | | | | | | | | | | (2613) ~ (all_52_12 = e3)
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | | REF_CLOSE: (9), (238), (279), (285), (331), (352), (371),
% 111.11/16.37 | | | | | | | | | | | | | | (385), (386), (412), (551), (555), (560), (561),
% 111.11/16.37 | | | | | | | | | | | | | | (562), (563), (568), (596), (601), (2539), (2546),
% 111.11/16.37 | | | | | | | | | | | | | | (2552), (2556), (2557), (2610), (2613) are
% 111.11/16.37 | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 111.11/16.37 | | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | (2614) all_56_15 = e1
% 111.11/16.37 | | | | | | | | | | | | | (2615) ~ (all_56_11 = e0)
% 111.11/16.37 | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | | REF_CLOSE: (37), (52), (156), (157), (167), (169), (172),
% 111.11/16.37 | | | | | | | | | | | | | (179), (201), (204), (206), (208), (209), (213),
% 111.11/16.37 | | | | | | | | | | | | | (234), (235), (238), (241), (243), (245), (246),
% 111.11/16.37 | | | | | | | | | | | | | (248), (275), (277), (286), (288), (291), (297),
% 111.11/16.37 | | | | | | | | | | | | | (299), (300), (304), (323), (331), (340), (352),
% 111.11/16.37 | | | | | | | | | | | | | (362), (365), (370), (385), (386), (391), (394),
% 111.11/16.37 | | | | | | | | | | | | | (406), (407), (412), (413), (424), (426), (434),
% 111.11/16.37 | | | | | | | | | | | | | (436), (446), (450), (460), (462), (468), (477),
% 111.11/16.37 | | | | | | | | | | | | | (479), (551), (552), (553), (554), (555), (557),
% 111.11/16.37 | | | | | | | | | | | | | (558), (559), (560), (561), (562), (563), (564),
% 111.11/16.37 | | | | | | | | | | | | | (565), (566), (567), (568), (569), (571), (579),
% 111.11/16.37 | | | | | | | | | | | | | (583), (585), (587), (589), (594), (599), (602),
% 111.11/16.37 | | | | | | | | | | | | | (603), (604), (605), (2359), (2360), (2528),
% 111.11/16.37 | | | | | | | | | | | | | (2530), (2532), (2614), (2615), (function-axioms)
% 111.11/16.37 | | | | | | | | | | | | | are inconsistent by sub-proof #14.
% 111.11/16.37 | | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | (2616) ~ (all_56_12 = e2)
% 111.11/16.37 | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | REDUCE: (2542), (2616) imply:
% 111.11/16.37 | | | | | | | | | | | | (2617) $false
% 111.11/16.37 | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | | CLOSE: (2617) is inconsistent.
% 111.11/16.37 | | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | (2618) ~ (all_56_12 = e2)
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | REDUCE: (2542), (2618) imply:
% 111.11/16.37 | | | | | | | | | | | (2619) $false
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | CLOSE: (2619) is inconsistent.
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | End of split
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | (2620) all_56_14 = e2
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | COMBINE_EQS: (555), (2620) imply:
% 111.11/16.37 | | | | | | | | | (2621) all_6_2 = e2
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | REF_CLOSE: (206), (594), (2360), (2621), (function-axioms) are
% 111.11/16.37 | | | | | | | | | inconsistent by sub-proof #39.
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | End of split
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | End of split
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | Case 2:
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | | (2622) all_48_0 = e3
% 111.11/16.37 | | | | | | | (2623) ~ (all_48_1 = e1) | ~ (all_48_2 = e0)
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | | COMBINE_EQS: (782), (2622) imply:
% 111.11/16.37 | | | | | | | (2624) all_8_0 = e3
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | | REDUCE: (2372), (2624) imply:
% 111.11/16.37 | | | | | | | (2625) op(e1, all_8_2) = e3
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | | BETA: splitting (2623) gives:
% 111.11/16.37 | | | | | | |
% 111.11/16.37 | | | | | | | Case 1:
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | (2626) ~ (all_48_1 = e1)
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | REDUCE: (2371), (2626) imply:
% 111.11/16.37 | | | | | | | | (2627) $false
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | CLOSE: (2627) is inconsistent.
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | (2628) ~ (all_48_2 = e0)
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | REDUCE: (547), (2628) imply:
% 111.11/16.37 | | | | | | | | (2629) ~ (all_8_2 = e0)
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | BETA: splitting (150) gives:
% 111.11/16.37 | | | | | | | |
% 111.11/16.37 | | | | | | | | Case 1:
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | (2630) ~ (all_50_0 = e2)
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | REDUCE: (2529), (2630) imply:
% 111.11/16.37 | | | | | | | | | (2631) $false
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | CLOSE: (2631) is inconsistent.
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | Case 2:
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | (2632) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | BETA: splitting (274) gives:
% 111.11/16.37 | | | | | | | | |
% 111.11/16.37 | | | | | | | | | Case 1:
% 111.11/16.37 | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | (2633) ~ (all_56_14 = e2)
% 111.11/16.37 | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | REDUCE: (555), (2633) imply:
% 111.11/16.37 | | | | | | | | | | (2634) ~ (all_6_2 = e2)
% 111.11/16.37 | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | BETA: splitting (275) gives:
% 111.11/16.37 | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | Case 1:
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | (2635) ~ (all_56_12 = e2)
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.37 | | | | | | | | | | | REDUCE: (426), (2635) imply:
% 111.11/16.37 | | | | | | | | | | | (2636) ~ (all_10_2 = e2)
% 111.11/16.37 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | REF_CLOSE: (9), (41), (52), (157), (167), (184), (188),
% 111.11/16.38 | | | | | | | | | | | (190), (192), (208), (209), (211), (212), (213),
% 111.11/16.38 | | | | | | | | | | | (233), (236), (238), (241), (242), (243), (244),
% 111.11/16.38 | | | | | | | | | | | (245), (246), (248), (272), (273), (276), (277),
% 111.11/16.38 | | | | | | | | | | | (279), (281), (282), (286), (287), (288), (289),
% 111.11/16.38 | | | | | | | | | | | (290), (291), (292), (293), (294), (295), (297),
% 111.11/16.38 | | | | | | | | | | | (298), (299), (300), (302), (323), (324), (327),
% 111.11/16.38 | | | | | | | | | | | (329), (331), (335), (338), (340), (341), (352),
% 111.11/16.38 | | | | | | | | | | | (356), (362), (365), (370), (371), (385), (386),
% 111.11/16.38 | | | | | | | | | | | (391), (394), (406), (407), (412), (424), (426),
% 111.11/16.38 | | | | | | | | | | | (430), (434), (436), (440), (446), (450), (460),
% 111.11/16.38 | | | | | | | | | | | (462), (464), (466), (468), (475), (548), (551),
% 111.11/16.38 | | | | | | | | | | | (552), (553), (554), (555), (556), (557), (558),
% 111.11/16.38 | | | | | | | | | | | (559), (560), (561), (562), (563), (564), (565),
% 111.11/16.38 | | | | | | | | | | | (566), (567), (568), (569), (571), (573), (575),
% 111.11/16.38 | | | | | | | | | | | (579), (581), (582), (584), (585), (587), (589),
% 111.11/16.38 | | | | | | | | | | | (591), (593), (594), (599), (601), (602), (604),
% 111.11/16.38 | | | | | | | | | | | (605), (705), (2373), (2528), (2530), (2632),
% 111.11/16.38 | | | | | | | | | | | (2634), (2636), (function-axioms) are inconsistent
% 111.11/16.38 | | | | | | | | | | | by sub-proof #2.
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | (2637) all_56_12 = e2
% 111.11/16.38 | | | | | | | | | | | (2638) ~ (all_56_10 = e0)
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | COMBINE_EQS: (426), (2637) imply:
% 111.11/16.38 | | | | | | | | | | | (2639) all_10_2 = e2
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | SIMP: (2639) implies:
% 111.11/16.38 | | | | | | | | | | | (2640) all_10_2 = e2
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | REDUCE: (365), (2638) imply:
% 111.11/16.38 | | | | | | | | | | | (2641) ~ (all_52_7 = e0)
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | REDUCE: (575), (2640) imply:
% 111.11/16.38 | | | | | | | | | | | (2642) ~ (all_52_3 = e2)
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | BETA: splitting (271) gives:
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | Case 1:
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | (2643) ~ (all_56_13 = e1)
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | REDUCE: (556), (2643) imply:
% 111.11/16.38 | | | | | | | | | | | | (2644) ~ (all_8_2 = e1)
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | BETA: splitting (243) gives:
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | Case 1:
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | (2645) all_54_5 = e3
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | COMBINE_EQS: (552), (2645) imply:
% 111.11/16.38 | | | | | | | | | | | | | (2646) all_8_2 = e3
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | SIMP: (2646) implies:
% 111.11/16.38 | | | | | | | | | | | | | (2647) all_8_2 = e3
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | REDUCE: (2373), (2647) imply:
% 111.11/16.38 | | | | | | | | | | | | | (2648) op(e2, e3) = e1
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | REDUCE: (2625), (2647) imply:
% 111.11/16.38 | | | | | | | | | | | | | (2649) op(e1, e3) = e3
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | BETA: splitting (323) gives:
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | Case 1:
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | (2650) all_58_15 = e0
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | COMBINE_EQS: (557), (2650) imply:
% 111.11/16.38 | | | | | | | | | | | | | | (2651) all_4_2 = e0
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | REDUCE: (569), (2651) imply:
% 111.11/16.38 | | | | | | | | | | | | | | (2652) $false
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | CLOSE: (2652) is inconsistent.
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | (2653) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 111.11/16.38 | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 111.11/16.38 | | | | | | | | | | | | | | e0)
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | ALPHA: (2653) implies:
% 111.11/16.38 | | | | | | | | | | | | | | (2654) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | BETA: splitting (2654) gives:
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | Case 1:
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | (2655) all_58_12 = e0
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2655) imply:
% 111.11/16.38 | | | | | | | | | | | | | | | (2656) all_52_3 = e0
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | SIMP: (2656) implies:
% 111.11/16.38 | | | | | | | | | | | | | | | (2657) all_52_3 = e0
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | COMBINE_EQS: (450), (2657) imply:
% 111.11/16.38 | | | | | | | | | | | | | | | (2658) all_56_9 = e0
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | REF_CLOSE: (209), (243), (278), (552), (556), (567), (591),
% 111.11/16.38 | | | | | | | | | | | | | | | (2373), (2629), (2658), (function-axioms) are
% 111.11/16.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #73.
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | (2659) all_58_13 = e0 | all_58_14 = e0
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | | REF_CLOSE: (183), (188), (192), (207), (211), (236), (475),
% 111.11/16.38 | | | | | | | | | | | | | | | (558), (559), (2641), (2642), (2648), (2649),
% 111.11/16.38 | | | | | | | | | | | | | | | (2659), (function-axioms) are inconsistent by
% 111.11/16.38 | | | | | | | | | | | | | | | sub-proof #148.
% 111.11/16.38 | | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | (2660) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | | REF_CLOSE: (552), (567), (2629), (2644), (2660) are
% 111.11/16.38 | | | | | | | | | | | | | inconsistent by sub-proof #310.
% 111.11/16.38 | | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | (2661) all_56_13 = e1
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | COMBINE_EQS: (556), (2661) imply:
% 111.11/16.38 | | | | | | | | | | | | (2662) all_8_2 = e1
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | | REF_CLOSE: (209), (591), (2373), (2662), (function-axioms)
% 111.11/16.38 | | | | | | | | | | | | are inconsistent by sub-proof #109.
% 111.11/16.38 | | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | Case 2:
% 111.11/16.38 | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | (2663) all_56_14 = e2
% 111.11/16.38 | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | COMBINE_EQS: (555), (2663) imply:
% 111.11/16.38 | | | | | | | | | | (2664) all_6_2 = e2
% 111.11/16.38 | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | | REF_CLOSE: (206), (594), (2360), (2664), (function-axioms)
% 111.11/16.38 | | | | | | | | | | are inconsistent by sub-proof #39.
% 111.11/16.38 | | | | | | | | | |
% 111.11/16.38 | | | | | | | | | End of split
% 111.11/16.38 | | | | | | | | |
% 111.11/16.38 | | | | | | | | End of split
% 111.11/16.38 | | | | | | | |
% 111.11/16.38 | | | | | | | End of split
% 111.11/16.38 | | | | | | |
% 111.11/16.38 | | | | | | End of split
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | Case 2:
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | | (2665) all_18_0 = e3
% 111.11/16.38 | | | | | | (2666) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | | COMBINE_EQS: (771), (2665) imply:
% 111.11/16.38 | | | | | | (2667) all_6_0 = e3
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | | REDUCE: (2359), (2667) imply:
% 111.11/16.38 | | | | | | (2668) op(e2, all_6_2) = e3
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | | REF_CLOSE: (41), (52), (150), (157), (167), (206), (207), (208),
% 111.11/16.38 | | | | | | (209), (211), (212), (213), (238), (245), (246), (248),
% 111.11/16.38 | | | | | | (274), (281), (290), (291), (293), (295), (299), (327),
% 111.11/16.38 | | | | | | (340), (346), (371), (391), (394), (406), (407), (424),
% 111.11/16.38 | | | | | | (426), (430), (436), (446), (460), (462), (533), (548),
% 111.11/16.38 | | | | | | (551), (553), (554), (555), (557), (560), (561), (564),
% 111.11/16.38 | | | | | | (567), (568), (571), (573), (579), (581), (594), (596),
% 111.11/16.38 | | | | | | (705), (2358), (2360), (2528), (2529), (2530), (2666),
% 111.11/16.38 | | | | | | (2668), (function-axioms) are inconsistent by sub-proof
% 111.11/16.38 | | | | | | #12.
% 111.11/16.38 | | | | | |
% 111.11/16.38 | | | | | End of split
% 111.11/16.38 | | | | |
% 111.11/16.38 | | | | End of split
% 111.11/16.38 | | | |
% 111.11/16.38 | | | End of split
% 111.11/16.38 | | |
% 111.11/16.38 | | End of split
% 111.11/16.38 | |
% 111.11/16.38 | End of split
% 111.11/16.38 |
% 111.11/16.38 End of proof
% 111.11/16.38
% 111.11/16.38 Sub-proof #1 shows that the following formulas are inconsistent:
% 111.11/16.38 ----------------------------------------------------------------
% 111.11/16.38 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.11/16.38 (2) ~ (all_52_2 = all_10_2)
% 111.11/16.38 (3) all_20_2 = all_4_2
% 111.11/16.38 (4) all_58_7 = all_52_6
% 111.11/16.38 (5) ~ (all_52_8 = all_52_11)
% 111.11/16.38 (6) all_20_1 = all_4_1
% 111.11/16.38 (7) ~ (all_4_2 = e0)
% 111.11/16.38 (8) op(e3, e2) = all_52_4
% 111.11/16.38 (9) all_56_14 = all_6_2
% 111.11/16.38 (10) all_54_0 = all_10_2
% 111.11/16.38 (11) all_54_3 = all_52_12
% 111.11/16.38 (12) all_56_11 = all_52_11
% 111.11/16.38 (13) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.11/16.39 (14) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.11/16.39 (15) ~ (all_52_12 = all_10_2)
% 111.11/16.39 (16) all_56_12 = all_10_2
% 111.11/16.39 (17) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 111.11/16.39 (18) all_58_0 = all_10_2
% 111.11/16.39 (19) all_56_10 = all_52_7
% 111.11/16.39 (20) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.11/16.39 (21) all_54_14 = all_52_11
% 111.11/16.39 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.39 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.11/16.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.11/16.39 (24) op(e1, all_6_2) = e2
% 111.11/16.39 (25) all_54_10 = all_6_2
% 111.11/16.39 (26) op(e3, e0) = all_52_12
% 111.11/16.39 (27) all_58_4 = all_52_8
% 111.11/16.39 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.11/16.39 (29) all_56_2 = all_52_12
% 111.11/16.39 (30) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.11/16.39 (31) all_58_11 = all_52_14
% 111.11/16.39 (32) op(e3, e1) = all_52_8
% 111.11/16.39 (33) all_16_1 = all_10_1
% 111.11/16.39 (34) op(all_10_1, all_10_2) = all_10_0
% 111.11/16.39 (35) ~ (all_20_0 = e3) | ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 111.11/16.39 (36) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.11/16.39 (37) all_24_0 = all_10_0
% 111.11/16.39 (38) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.11/16.39 (39) op(e1, e0) = all_52_14
% 111.11/16.39 (40) all_58_5 = all_52_9
% 111.11/16.39 (41) all_56_9 = all_52_3
% 111.11/16.39 (42) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 111.11/16.39 (43) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 111.11/16.39 (44) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.11/16.39 (45) op(all_4_1, all_4_2) = e3
% 111.11/16.39 (46) all_58_15 = all_4_2
% 111.11/16.39 (47) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.11/16.39 (48) ~ (all_10_2 = e3)
% 111.11/16.39 (49) all_58_13 = all_52_7
% 111.11/16.39 (50) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 111.11/16.39 (51) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.11/16.39 (52) ~ (all_52_14 = all_4_2)
% 111.11/16.39 (53) all_58_6 = all_52_2
% 111.11/16.39 (54) all_56_15 = all_4_2
% 111.11/16.39 (55) ~ (all_52_11 = all_4_2)
% 111.11/16.39 (56) op(e3, all_10_2) = all_10_1
% 111.11/16.39 (57) all_58_1 = all_52_4
% 111.11/16.39 (58) ~ (all_52_9 = all_52_11)
% 111.11/16.39 (59) all_58_14 = all_52_11
% 111.11/16.39 (60) all_54_1 = all_52_4
% 111.11/16.39 (61) op(e0, e1) = all_52_11
% 111.11/16.39 (62) op(e1, e2) = all_52_6
% 111.11/16.39 (63) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.11/16.39 (64) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.11/16.39 (65) all_56_7 = all_52_6
% 111.11/16.39 (66) ~ (all_52_4 = all_52_6)
% 111.11/16.39 (67) all_56_1 = all_52_8
% 111.11/16.39 (68) op(e0, all_4_2) = all_4_1
% 111.11/16.39 (69) all_58_8 = all_6_2
% 111.11/16.39 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.39 (71) all_20_0 = e3
% 111.11/16.39 (72) all_10_0 = e1
% 111.11/16.39 (73) all_16_2 = all_10_2
% 111.11/16.39 (74) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.11/16.39 (75) all_56_4 = all_52_9
% 111.11/16.39 (76) all_58_9 = all_52_12
% 111.11/16.39 (77) op(e2, e1) = all_52_9
% 111.11/16.39 (78) ~ (all_52_3 = all_4_2)
% 111.11/16.39 (79) ~ (all_52_6 = all_6_2)
% 111.11/16.39 (80) all_56_6 = all_52_2
% 111.11/16.39 (81) all_58_12 = all_52_3
% 111.11/16.39 (82) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.11/16.39 (83) ~ (all_52_12 = all_4_2)
% 111.11/16.39 (84) ~ (all_52_3 = all_10_2)
% 111.11/16.39 (85) all_24_1 = all_10_1
% 111.11/16.39 (86) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 111.11/16.39 (87) all_24_2 = all_10_2
% 111.11/16.39 (88) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.11/16.39 (89) all_56_8 = all_52_14
% 111.11/16.39 (90) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.11/16.39 (91) ~ (all_52_4 = all_10_2)
% 111.11/16.39 (92) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.11/16.39 (93) all_56_0 = all_52_4
% 111.11/16.39 (94) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.11/16.39 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.11/16.39 (95) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.11/16.39 (96) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.11/16.39 (97) all_54_15 = all_4_2
% 111.11/16.39 (98) ~ (all_6_2 = e1)
% 111.11/16.39 (99) ~ (all_52_3 = all_52_11)
% 111.11/16.39 (100) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.11/16.39 (101) all_54_12 = all_52_3
% 111.11/16.39
% 111.11/16.39 Begin of proof
% 111.11/16.39 |
% 111.11/16.39 | COMBINE_EQS: (37), (72) imply:
% 111.11/16.39 | (102) all_24_0 = e1
% 111.11/16.39 |
% 111.11/16.39 | REDUCE: (34), (72) imply:
% 111.11/16.39 | (103) op(all_10_1, all_10_2) = e1
% 111.11/16.39 |
% 111.11/16.39 | BETA: splitting (35) gives:
% 111.11/16.39 |
% 111.11/16.39 | Case 1:
% 111.11/16.39 | |
% 111.11/16.39 | | (104) ~ (all_20_0 = e3)
% 111.11/16.39 | |
% 111.11/16.39 | | REDUCE: (71), (104) imply:
% 111.11/16.39 | | (105) $false
% 111.11/16.39 | |
% 111.11/16.39 | | CLOSE: (105) is inconsistent.
% 111.11/16.39 | |
% 111.11/16.39 | Case 2:
% 111.11/16.39 | |
% 111.11/16.39 | | (106) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 111.11/16.39 | |
% 111.11/16.39 | | BETA: splitting (90) gives:
% 111.11/16.39 | |
% 111.11/16.39 | | Case 1:
% 111.11/16.39 | | |
% 111.11/16.39 | | | (107) ~ (all_24_0 = e1)
% 111.11/16.39 | | |
% 111.11/16.39 | | | REDUCE: (102), (107) imply:
% 111.11/16.39 | | | (108) $false
% 111.11/16.39 | | |
% 111.11/16.39 | | | CLOSE: (108) is inconsistent.
% 111.11/16.39 | | |
% 111.11/16.39 | | Case 2:
% 111.11/16.39 | | |
% 111.11/16.40 | | | (109) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.11/16.40 | | |
% 111.11/16.40 | | | BETA: splitting (42) gives:
% 111.11/16.40 | | |
% 111.11/16.40 | | | Case 1:
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | (110) ~ (all_56_15 = e1)
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REDUCE: (54), (110) imply:
% 111.11/16.40 | | | | (111) ~ (all_4_2 = e1)
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | BETA: splitting (50) gives:
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | Case 1:
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | (112) ~ (all_56_14 = e2)
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | REDUCE: (9), (112) imply:
% 111.11/16.40 | | | | | (113) ~ (all_6_2 = e2)
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 111.11/16.40 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 111.11/16.40 | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (36), (38),
% 111.11/16.40 | | | | | (39), (40), (41), (43), (44), (46), (47), (48), (49), (51),
% 111.11/16.40 | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (62),
% 111.11/16.40 | | | | | (63), (64), (65), (66), (67), (69), (70), (73), (74), (75),
% 111.11/16.40 | | | | | (76), (77), (78), (80), (81), (82), (83), (84), (85), (86),
% 111.11/16.40 | | | | | (87), (88), (89), (91), (92), (93), (94), (95), (96), (97),
% 111.11/16.40 | | | | | (98), (99), (100), (101), (103), (109), (111), (113) are
% 111.11/16.40 | | | | | inconsistent by sub-proof #7.
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | Case 2:
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | (114) all_56_14 = e2
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | COMBINE_EQS: (9), (114) imply:
% 111.11/16.40 | | | | | (115) all_6_2 = e2
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | | REF_CLOSE: (23), (24), (62), (79), (115) are inconsistent by sub-proof
% 111.11/16.40 | | | | | #39.
% 111.11/16.40 | | | | |
% 111.11/16.40 | | | | End of split
% 111.11/16.40 | | | |
% 111.11/16.40 | | | Case 2:
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | (116) all_56_15 = e1
% 111.11/16.40 | | | | (117) ~ (all_56_11 = e0)
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | COMBINE_EQS: (54), (116) imply:
% 111.11/16.40 | | | | (118) all_4_2 = e1
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | SIMP: (118) implies:
% 111.11/16.40 | | | | (119) all_4_2 = e1
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | COMBINE_EQS: (3), (119) imply:
% 111.11/16.40 | | | | (120) all_20_2 = e1
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REDUCE: (12), (117) imply:
% 111.11/16.40 | | | | (121) ~ (all_52_11 = e0)
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REDUCE: (55), (119) imply:
% 111.11/16.40 | | | | (122) ~ (all_52_11 = e1)
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REDUCE: (45), (119) imply:
% 111.11/16.40 | | | | (123) op(all_4_1, e1) = e3
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REDUCE: (68), (119) imply:
% 111.11/16.40 | | | | (124) op(e0, e1) = all_4_1
% 111.11/16.40 | | | |
% 111.11/16.40 | | | | REF_CLOSE: (5), (6), (21), (23), (32), (61), (100), (106), (120), (121),
% 111.11/16.40 | | | | (122), (123), (124) are inconsistent by sub-proof #11.
% 111.11/16.40 | | | |
% 111.11/16.40 | | | End of split
% 111.11/16.40 | | |
% 111.11/16.40 | | End of split
% 111.11/16.40 | |
% 111.11/16.40 | End of split
% 111.11/16.40 |
% 111.11/16.40 End of proof
% 111.11/16.40
% 111.11/16.40 Sub-proof #2 shows that the following formulas are inconsistent:
% 111.11/16.40 ----------------------------------------------------------------
% 111.11/16.40 (1) ~ (all_52_8 = all_10_2)
% 111.11/16.40 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.11/16.40 (3) ~ (all_52_2 = all_10_2)
% 111.11/16.40 (4) all_54_2 = all_52_8
% 111.11/16.40 (5) all_58_7 = all_52_6
% 111.11/16.40 (6) ~ (all_52_9 = all_8_2)
% 111.11/16.40 (7) ~ (all_4_2 = e0)
% 111.11/16.40 (8) all_56_14 = all_6_2
% 111.11/16.40 (9) all_56_3 = all_52_1
% 111.11/16.40 (10) all_54_0 = all_10_2
% 111.11/16.40 (11) all_54_3 = all_52_12
% 111.11/16.40 (12) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.11/16.40 (13) all_56_11 = all_52_11
% 111.11/16.40 (14) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.11/16.40 (15) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.11/16.40 (16) ~ (all_52_12 = all_10_2)
% 111.11/16.40 (17) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 111.11/16.40 (18) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.11/16.40 (19) all_56_12 = all_10_2
% 111.11/16.40 (20) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 111.11/16.40 (21) all_58_0 = all_10_2
% 111.11/16.40 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.11/16.40 (23) ~ (all_52_14 = all_6_2)
% 111.11/16.40 (24) all_56_10 = all_52_7
% 111.11/16.40 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.40 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.11/16.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.11/16.40 (27) ~ (all_52_1 = all_52_9)
% 111.11/16.40 (28) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 111.11/16.40 (29) ~ (all_10_2 = e2)
% 111.11/16.40 (30) all_54_10 = all_6_2
% 111.11/16.40 (31) op(e3, e0) = all_52_12
% 111.11/16.40 (32) all_58_4 = all_52_8
% 111.11/16.40 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.11/16.40 (34) all_50_1 = all_10_1
% 111.11/16.40 (35) all_56_2 = all_52_12
% 111.11/16.40 (36) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.11/16.40 (37) all_58_3 = all_8_2
% 111.11/16.40 (38) all_54_6 = all_52_9
% 111.11/16.40 (39) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.11/16.40 (40) all_58_11 = all_52_14
% 111.11/16.40 (41) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 111.11/16.40 (42) op(e3, e1) = all_52_8
% 111.11/16.40 (43) ~ (all_52_2 = all_52_3)
% 111.11/16.40 (44) all_54_7 = all_52_13
% 111.11/16.40 (45) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.11/16.40 (46) ~ (all_52_11 = all_6_2)
% 111.11/16.40 (47) op(e2, e3) = all_52_1
% 111.11/16.40 (48) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 111.11/16.40 (49) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.11/16.40 (50) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 111.11/16.40 (51) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 111.11/16.40 (52) all_50_2 = all_10_2
% 111.11/16.40 (53) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.11/16.40 (54) ~ (all_52_7 = all_8_2)
% 111.11/16.40 (55) ~ (all_52_4 = all_8_2)
% 111.11/16.40 (56) all_58_5 = all_52_9
% 111.11/16.40 (57) all_56_9 = all_52_3
% 111.11/16.40 (58) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.11/16.40 (59) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 111.11/16.40 (60) all_58_15 = all_4_2
% 111.11/16.40 (61) all_58_2 = all_52_1
% 111.11/16.40 (62) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.11/16.40 (63) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.11/16.40 (64) ~ (all_10_2 = e3)
% 111.11/16.40 (65) ~ (all_52_12 = all_52_13)
% 111.11/16.40 (66) all_58_13 = all_52_7
% 111.11/16.40 (67) ~ (all_52_14 = all_4_2)
% 111.11/16.40 (68) all_58_6 = all_52_2
% 111.11/16.40 (69) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.11/16.40 (70) ~ (all_52_1 = all_10_2)
% 111.11/16.41 (71) all_54_5 = all_8_2
% 111.11/16.41 (72) all_56_15 = all_4_2
% 111.11/16.41 (73) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.11/16.41 (74) all_58_10 = all_52_13
% 111.11/16.41 (75) ~ (all_52_13 = all_8_2)
% 111.11/16.41 (76) ~ (all_52_11 = all_4_2)
% 111.11/16.41 (77) op(e3, all_10_2) = all_10_1
% 111.11/16.41 (78) ~ (all_52_6 = all_8_2)
% 111.11/16.41 (79) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.11/16.41 (80) all_58_1 = all_52_4
% 111.11/16.41 (81) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 111.11/16.41 (82) all_58_14 = all_52_11
% 111.11/16.41 (83) all_56_13 = all_8_2
% 111.11/16.41 (84) ~ (all_52_1 = all_8_2)
% 111.11/16.41 (85) ~ (all_8_2 = e2)
% 111.11/16.41 (86) ~ (all_6_2 = e2)
% 111.11/16.41 (87) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.11/16.41 (88) all_56_7 = all_52_6
% 111.11/16.41 (89) ~ (all_52_1 = all_52_3)
% 111.11/16.41 (90) all_56_1 = all_52_8
% 111.11/16.41 (91) all_58_8 = all_6_2
% 111.11/16.41 (92) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.41 (93) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.11/16.41 (94) all_56_4 = all_52_9
% 111.11/16.41 (95) all_58_9 = all_52_12
% 111.11/16.41 (96) all_56_5 = all_52_13
% 111.11/16.41 (97) op(e2, e1) = all_52_9
% 111.11/16.41 (98) ~ (all_52_3 = all_4_2)
% 111.11/16.41 (99) ~ (all_52_6 = all_6_2)
% 111.11/16.41 (100) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.11/16.41 (101) all_56_6 = all_52_2
% 111.11/16.41 (102) ~ (all_52_13 = all_4_2)
% 111.11/16.41 (103) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 111.11/16.41 (104) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 111.11/16.41 (105) all_58_12 = all_52_3
% 111.11/16.41 (106) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.11/16.41 (107) ~ (all_52_8 = all_52_9)
% 111.11/16.41 (108) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.11/16.41 (109) op(e2, e0) = all_52_13
% 111.11/16.41 (110) ~ (all_52_3 = all_10_2)
% 111.11/16.41 (111) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 111.11/16.41 (112) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 111.11/16.41 (113) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.11/16.41 (114) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.11/16.41 (115) op(e1, e1) = all_6_2
% 111.11/16.41 (116) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.11/16.41 (117) all_56_8 = all_52_14
% 111.11/16.41 (118) op(all_10_1, all_10_2) = e2
% 111.11/16.41 (119) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.11/16.41 (120) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.11/16.41 (121) ~ (e3 = e2)
% 111.11/16.41 (122) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.11/16.41 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.11/16.41 (123) all_54_4 = all_52_1
% 111.11/16.41 (124) all_54_15 = all_4_2
% 111.11/16.41 (125) op(e2, all_8_2) = e1
% 111.11/16.41 (126) ~ (all_6_2 = e1)
% 111.11/16.41 (127) all_54_12 = all_52_3
% 111.11/16.41 (128) ~ (all_52_3 = all_52_7)
% 111.11/16.41
% 111.11/16.41 Begin of proof
% 111.11/16.41 |
% 111.11/16.41 | BETA: splitting (93) gives:
% 111.11/16.41 |
% 111.11/16.41 | Case 1:
% 111.11/16.41 | |
% 111.11/16.41 | | (129) ~ (all_56_15 = e3)
% 111.11/16.41 | |
% 111.11/16.41 | | REDUCE: (72), (129) imply:
% 111.11/16.41 | | (130) ~ (all_4_2 = e3)
% 111.11/16.41 | |
% 111.11/16.41 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (13), (14), (16),
% 111.11/16.41 | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 111.11/16.41 | | (29), (30), (32), (33), (35), (36), (37), (38), (39), (40), (41),
% 111.11/16.41 | | (43), (44), (45), (46), (47), (48), (50), (51), (53), (54), (55),
% 111.11/16.41 | | (56), (57), (58), (59), (60), (61), (64), (66), (67), (68), (69),
% 111.11/16.41 | | (70), (71), (72), (73), (74), (75), (76), (78), (79), (80), (81),
% 111.11/16.41 | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 111.11/16.41 | | (94), (95), (96), (97), (98), (99), (101), (102), (103), (104),
% 111.11/16.41 | | (105), (108), (109), (110), (111), (112), (115), (116), (117),
% 111.11/16.41 | | (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 111.11/16.41 | | (128), (130) are inconsistent by sub-proof #120.
% 111.11/16.41 | |
% 111.11/16.41 | Case 2:
% 111.11/16.41 | |
% 111.11/16.41 | | (131) all_56_15 = e3
% 111.11/16.41 | |
% 111.11/16.41 | | BETA: splitting (28) gives:
% 111.11/16.41 | |
% 111.11/16.41 | | Case 1:
% 111.11/16.41 | | |
% 111.11/16.41 | | | (132) ~ (all_56_3 = e2)
% 111.11/16.41 | | |
% 111.11/16.41 | | | REDUCE: (9), (132) imply:
% 111.11/16.41 | | | (133) ~ (all_52_1 = e2)
% 111.11/16.41 | | |
% 111.11/16.41 | | | BETA: splitting (119) gives:
% 111.11/16.41 | | |
% 111.11/16.41 | | | Case 1:
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | (134) ~ (all_56_12 = e1)
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | REDUCE: (19), (134) imply:
% 111.11/16.41 | | | | (135) ~ (all_10_2 = e1)
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | BETA: splitting (92) gives:
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | Case 1:
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | | (136) all_54_0 = e3
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | | REF_CLOSE: (10), (64), (136) are inconsistent by sub-proof #451.
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | Case 2:
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | | (137) ~ (all_54_0 = e3)
% 111.11/16.41 | | | | | (138) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | | BETA: splitting (138) gives:
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | | Case 1:
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | | (139) all_54_0 = e2
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | | REF_CLOSE: (10), (29), (139) are inconsistent by sub-proof #450.
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | Case 2:
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | | (140) ~ (all_54_0 = e2)
% 111.11/16.41 | | | | | | (141) all_54_0 = e1 | all_54_0 = e0
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | | BETA: splitting (141) gives:
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | | Case 1:
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | (142) all_54_0 = e1
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | REF_CLOSE: (10), (135), (142) are inconsistent by sub-proof #449.
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | Case 2:
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | (143) all_54_0 = e0
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | COMBINE_EQS: (10), (143) imply:
% 111.11/16.41 | | | | | | | (144) all_10_2 = e0
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | SIMP: (144) implies:
% 111.11/16.41 | | | | | | | (145) all_10_2 = e0
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | | REF_CLOSE: (2), (10), (11), (15), (16), (19), (26), (29), (31),
% 111.11/16.41 | | | | | | | (34), (35), (37), (40), (52), (56), (58), (60), (61),
% 111.11/16.41 | | | | | | | (62), (63), (64), (65), (72), (74), (77), (85), (92),
% 111.11/16.41 | | | | | | | (94), (95), (96), (106), (109), (113), (114), (117),
% 111.11/16.41 | | | | | | | (118), (120), (133), (145) are inconsistent by
% 111.11/16.41 | | | | | | | sub-proof #13.
% 111.11/16.41 | | | | | | |
% 111.11/16.41 | | | | | | End of split
% 111.11/16.41 | | | | | |
% 111.11/16.41 | | | | | End of split
% 111.11/16.41 | | | | |
% 111.11/16.41 | | | | End of split
% 111.11/16.41 | | | |
% 111.11/16.41 | | | Case 2:
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | (146) all_56_12 = e1
% 111.11/16.41 | | | |
% 111.11/16.41 | | | | REF_CLOSE: (1), (4), (12), (19), (26), (42), (49), (77), (90), (97),
% 111.11/16.41 | | | | (100), (107), (118), (146) are inconsistent by sub-proof #15.
% 111.11/16.41 | | | |
% 111.11/16.41 | | | End of split
% 111.11/16.41 | | |
% 111.11/16.41 | | Case 2:
% 111.11/16.41 | | |
% 111.11/16.41 | | | (147) ~ (all_56_15 = e3)
% 111.11/16.41 | | |
% 111.11/16.41 | | | REDUCE: (131), (147) imply:
% 111.11/16.41 | | | (148) $false
% 111.11/16.41 | | |
% 111.11/16.41 | | | CLOSE: (148) is inconsistent.
% 111.11/16.41 | | |
% 111.11/16.41 | | End of split
% 111.11/16.41 | |
% 111.11/16.41 | End of split
% 111.11/16.41 |
% 111.11/16.42 End of proof
% 111.11/16.42
% 111.11/16.42 Sub-proof #3 shows that the following formulas are inconsistent:
% 111.11/16.42 ----------------------------------------------------------------
% 111.11/16.42 (1) ~ (all_52_2 = all_10_2)
% 111.11/16.42 (2) ~ (all_52_13 = all_52_14)
% 111.11/16.42 (3) all_56_14 = all_6_2
% 111.11/16.42 (4) all_54_0 = all_10_2
% 111.11/16.42 (5) all_54_3 = all_52_12
% 111.11/16.42 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.11/16.42 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.42 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.11/16.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.11/16.42 (9) all_54_8 = all_52_2
% 111.11/16.42 (10) ~ (all_52_2 = all_6_2)
% 111.11/16.42 (11) ~ (all_10_2 = all_4_1)
% 111.11/16.42 (12) ~ (all_10_2 = e2)
% 111.11/16.42 (13) all_54_10 = all_6_2
% 111.11/16.42 (14) op(e3, e0) = all_52_12
% 111.11/16.42 (15) all_56_2 = all_52_12
% 111.11/16.42 (16) ~ (all_52_12 = e1)
% 111.11/16.42 (17) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.11/16.42 (18) op(e3, all_6_2) = all_6_0
% 111.11/16.42 (19) all_54_7 = all_52_13
% 111.11/16.42 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.11/16.42 (21) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.11/16.42 (22) op(e1, e0) = all_52_14
% 111.11/16.42 (23) ~ (all_10_2 = e3)
% 111.11/16.42 (24) ~ (all_52_12 = all_52_13)
% 111.11/16.42 (25) ~ (all_4_1 = e0)
% 111.11/16.42 (26) all_58_6 = all_52_2
% 111.11/16.42 (27) ~ (all_52_13 = e1)
% 111.11/16.42 (28) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.11/16.42 (29) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 111.11/16.42 (30) ~ (all_6_0 = e2)
% 111.11/16.42 (31) op(e1, all_6_2) = e3
% 111.11/16.42 (32) ~ (all_6_2 = e2)
% 111.11/16.42 (33) ~ (all_10_2 = e0)
% 111.11/16.42 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.42 (35) all_56_5 = all_52_13
% 111.11/16.42 (36) ~ (all_52_2 = all_4_1)
% 111.11/16.42 (37) all_54_12 = all_4_1
% 111.11/16.42 (38) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.11/16.42 (39) op(e1, e3) = all_52_2
% 111.11/16.42 (40) ~ (all_4_1 = e3)
% 111.11/16.42 (41) ~ (all_6_2 = e1)
% 111.11/16.42
% 111.11/16.42 Begin of proof
% 111.11/16.42 |
% 111.11/16.42 | BETA: splitting (7) gives:
% 111.11/16.42 |
% 111.11/16.42 | Case 1:
% 111.11/16.42 | |
% 111.11/16.42 | | (42) all_54_10 = e3
% 111.11/16.42 | |
% 111.11/16.42 | | COMBINE_EQS: (13), (42) imply:
% 111.11/16.42 | | (43) all_6_2 = e3
% 111.11/16.42 | |
% 111.11/16.42 | | SIMP: (43) implies:
% 111.11/16.42 | | (44) all_6_2 = e3
% 111.11/16.42 | |
% 111.11/16.42 | | REDUCE: (10), (44) imply:
% 111.11/16.42 | | (45) ~ (all_52_2 = e3)
% 111.11/16.42 | |
% 111.11/16.42 | | REDUCE: (31), (44) imply:
% 111.11/16.42 | | (46) op(e1, e3) = e3
% 111.11/16.42 | |
% 111.11/16.42 | | REF_CLOSE: (1), (4), (8), (9), (11), (12), (21), (23), (25), (26), (29),
% 111.11/16.42 | | (33), (34), (36), (37), (38), (39), (40), (45), (46) are
% 111.11/16.42 | | inconsistent by sub-proof #9.
% 111.11/16.42 | |
% 111.11/16.42 | Case 2:
% 111.11/16.42 | |
% 111.11/16.42 | | (47) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.42 | |
% 111.11/16.42 | | REF_CLOSE: (2), (3), (5), (6), (8), (13), (14), (15), (16), (17), (18),
% 111.11/16.42 | | (19), (20), (22), (24), (27), (28), (30), (31), (32), (35), (41),
% 111.11/16.42 | | (47) are inconsistent by sub-proof #348.
% 111.11/16.42 | |
% 111.11/16.42 | End of split
% 111.11/16.42 |
% 111.11/16.42 End of proof
% 111.11/16.42
% 111.11/16.42 Sub-proof #4 shows that the following formulas are inconsistent:
% 111.11/16.42 ----------------------------------------------------------------
% 111.11/16.42 (1) all_58_7 = all_52_6
% 111.11/16.42 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 111.11/16.42 (3) ~ (all_52_1 = e2)
% 111.11/16.42 (4) all_56_14 = all_6_2
% 111.11/16.42 (5) all_54_0 = all_10_2
% 111.11/16.42 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.11/16.42 (7) all_56_12 = all_10_2
% 111.11/16.42 (8) all_58_0 = all_10_2
% 111.11/16.42 (9) all_42_2 = all_8_2
% 111.11/16.42 (10) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.11/16.42 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.11/16.42 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.11/16.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.11/16.42 (13) ~ (all_10_2 = e2)
% 111.11/16.42 (14) all_54_10 = all_6_2
% 111.11/16.42 (15) ~ (all_52_14 = e1)
% 111.11/16.42 (16) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.11/16.42 (17) all_58_11 = all_52_14
% 111.11/16.42 (18) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 111.11/16.42 (19) op(e2, e3) = all_52_1
% 111.11/16.42 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.11/16.42 (21) all_58_2 = all_52_1
% 111.11/16.42 (22) ~ (all_10_2 = e3)
% 111.11/16.42 (23) all_58_6 = all_52_2
% 111.11/16.42 (24) ~ (all_52_1 = all_10_2)
% 111.11/16.42 (25) all_54_5 = all_8_2
% 111.11/16.42 (26) op(e2, all_8_2) = all_8_1
% 111.11/16.42 (27) ~ (all_52_6 = all_8_2)
% 111.11/16.42 (28) all_56_5 = e2
% 111.11/16.42 (29) all_56_13 = all_8_2
% 111.11/16.42 (30) ~ (all_52_1 = all_8_2)
% 111.11/16.42 (31) ~ (all_8_2 = e2)
% 111.11/16.42 (32) ~ (all_6_2 = e2)
% 111.11/16.42 (33) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.11/16.42 (34) all_58_8 = all_6_2
% 111.11/16.42 (35) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.42 (36) all_56_6 = all_52_2
% 111.11/16.42 (37) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.11/16.42 (38) ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 111.11/16.42 (39) all_42_1 = all_8_1
% 111.11/16.42 (40) all_54_4 = all_52_1
% 111.11/16.43 (41) ~ (all_6_2 = e1)
% 111.11/16.43
% 111.11/16.43 Begin of proof
% 111.11/16.43 |
% 111.11/16.43 | BETA: splitting (20) gives:
% 111.11/16.43 |
% 111.11/16.43 | Case 1:
% 111.11/16.43 | |
% 111.11/16.43 | | (42) ~ (all_56_5 = e2)
% 111.11/16.43 | |
% 111.11/16.43 | | REDUCE: (28), (42) imply:
% 111.11/16.43 | | (43) $false
% 111.11/16.43 | |
% 111.11/16.43 | | CLOSE: (43) is inconsistent.
% 111.11/16.43 | |
% 111.11/16.43 | Case 2:
% 111.11/16.43 | |
% 111.11/16.43 | | (44) ~ (all_56_14 = e0)
% 111.11/16.43 | |
% 111.11/16.43 | | REDUCE: (4), (44) imply:
% 111.11/16.43 | | (45) ~ (all_6_2 = e0)
% 111.11/16.43 | |
% 111.11/16.43 | | BETA: splitting (18) gives:
% 111.11/16.43 | |
% 111.11/16.43 | | Case 1:
% 111.11/16.43 | | |
% 111.11/16.43 | | | (46) ~ (all_56_5 = e2)
% 111.11/16.43 | | |
% 111.11/16.43 | | | REDUCE: (28), (46) imply:
% 111.11/16.43 | | | (47) $false
% 111.11/16.43 | | |
% 111.11/16.43 | | | CLOSE: (47) is inconsistent.
% 111.11/16.43 | | |
% 111.11/16.43 | | Case 2:
% 111.11/16.43 | | |
% 111.11/16.43 | | | (48) ~ (all_56_13 = e0)
% 111.11/16.43 | | |
% 111.11/16.43 | | | REDUCE: (29), (48) imply:
% 111.11/16.43 | | | (49) ~ (all_8_2 = e0)
% 111.11/16.43 | | |
% 111.11/16.43 | | | BETA: splitting (33) gives:
% 111.11/16.43 | | |
% 111.11/16.43 | | | Case 1:
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | (50) all_58_6 = e1
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | COMBINE_EQS: (23), (50) imply:
% 111.11/16.43 | | | | (51) all_52_2 = e1
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | SIMP: (51) implies:
% 111.11/16.43 | | | | (52) all_52_2 = e1
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | COMBINE_EQS: (36), (52) imply:
% 111.11/16.43 | | | | (53) all_56_6 = e1
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | REF_CLOSE: (4), (11), (14), (16), (32), (41), (45), (53) are
% 111.11/16.43 | | | | inconsistent by sub-proof #305.
% 111.11/16.43 | | | |
% 111.11/16.43 | | | Case 2:
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | (54) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | BETA: splitting (37) gives:
% 111.11/16.43 | | | |
% 111.11/16.43 | | | | Case 1:
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | (55) ~ (all_56_5 = e2)
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | REDUCE: (28), (55) imply:
% 111.11/16.43 | | | | | (56) $false
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | CLOSE: (56) is inconsistent.
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | Case 2:
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | (57) ~ (all_56_12 = e0)
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | REDUCE: (7), (57) imply:
% 111.11/16.43 | | | | | (58) ~ (all_10_2 = e0)
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | BETA: splitting (35) gives:
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | | Case 1:
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | | (59) all_54_0 = e3
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | | REF_CLOSE: (5), (22), (59) are inconsistent by sub-proof #451.
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | Case 2:
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | | (60) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | | BETA: splitting (54) gives:
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | | Case 1:
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | (61) all_58_7 = e1
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | COMBINE_EQS: (1), (61) imply:
% 111.11/16.43 | | | | | | | (62) all_52_6 = e1
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | REDUCE: (27), (62) imply:
% 111.11/16.43 | | | | | | | (63) ~ (all_8_2 = e1)
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | SIMP: (63) implies:
% 111.11/16.43 | | | | | | | (64) ~ (all_8_2 = e1)
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | BETA: splitting (6) gives:
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | (65) all_54_5 = e3
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | COMBINE_EQS: (25), (65) imply:
% 111.11/16.43 | | | | | | | | (66) all_8_2 = e3
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | SIMP: (66) implies:
% 111.11/16.43 | | | | | | | | (67) all_8_2 = e3
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | REDUCE: (30), (67) imply:
% 111.11/16.43 | | | | | | | | (68) ~ (all_52_1 = e3)
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | BETA: splitting (2) gives:
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | (69) all_58_0 = e0
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | COMBINE_EQS: (8), (69) imply:
% 111.11/16.43 | | | | | | | | | (70) all_10_2 = e0
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | REDUCE: (58), (70) imply:
% 111.11/16.43 | | | | | | | | | (71) $false
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | CLOSE: (71) is inconsistent.
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | (72) ~ (all_58_0 = e0)
% 111.11/16.43 | | | | | | | | | (73) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | BETA: splitting (73) gives:
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | (74) all_58_2 = e0
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | COMBINE_EQS: (21), (74) imply:
% 111.11/16.43 | | | | | | | | | | (75) all_52_1 = e0
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | REDUCE: (19), (75) imply:
% 111.11/16.43 | | | | | | | | | | (76) op(e2, e3) = e0
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | BETA: splitting (6) gives:
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | COMBINE_EQS: (9), (67) imply:
% 111.11/16.43 | | | | | | | | | | | (77) all_42_2 = e3
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | REDUCE: (26), (67) imply:
% 111.11/16.43 | | | | | | | | | | | (78) op(e2, e3) = all_8_1
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | BETA: splitting (38) gives:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | (79) ~ (all_42_2 = e3)
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | REDUCE: (77), (79) imply:
% 111.11/16.43 | | | | | | | | | | | | (80) $false
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | CLOSE: (80) is inconsistent.
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | (81) ~ (all_42_1 = e0)
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | REDUCE: (39), (81) imply:
% 111.11/16.43 | | | | | | | | | | | | (82) ~ (all_8_1 = e0)
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | GROUND_INST: instantiating (12) with e0, all_8_1, e3, e2,
% 111.11/16.43 | | | | | | | | | | | | simplifying with (76), (78) gives:
% 111.11/16.43 | | | | | | | | | | | | (83) all_8_1 = e0
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | REDUCE: (82), (83) imply:
% 111.11/16.43 | | | | | | | | | | | | (84) $false
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | CLOSE: (84) is inconsistent.
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | End of split
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | (85) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | REF_CLOSE: (25), (31), (49), (64), (85) are inconsistent by
% 111.11/16.43 | | | | | | | | | | | sub-proof #310.
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | End of split
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | (86) ~ (all_58_2 = e0)
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | REDUCE: (21), (86) imply:
% 111.11/16.43 | | | | | | | | | | (87) ~ (all_52_1 = e0)
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | BETA: splitting (10) gives:
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | (88) all_54_4 = e3
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | REF_CLOSE: (40), (68), (88) are inconsistent by sub-proof
% 111.11/16.43 | | | | | | | | | | | #329.
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | (89) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | BETA: splitting (60) gives:
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | Case 1:
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | (90) all_54_0 = e2
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | COMBINE_EQS: (5), (90) imply:
% 111.11/16.43 | | | | | | | | | | | | (91) all_10_2 = e2
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | REDUCE: (13), (91) imply:
% 111.11/16.43 | | | | | | | | | | | | (92) $false
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | CLOSE: (92) is inconsistent.
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | (93) all_54_0 = e1 | all_54_0 = e0
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | | REF_CLOSE: (3), (5), (24), (40), (58), (87), (89), (93) are
% 111.11/16.43 | | | | | | | | | | | | inconsistent by sub-proof #126.
% 111.11/16.43 | | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | | End of split
% 111.11/16.43 | | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | | End of split
% 111.11/16.43 | | | | | | | | | |
% 111.11/16.43 | | | | | | | | | End of split
% 111.11/16.43 | | | | | | | | |
% 111.11/16.43 | | | | | | | | End of split
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | Case 2:
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | (94) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | | REF_CLOSE: (25), (31), (49), (64), (94) are inconsistent by
% 111.11/16.43 | | | | | | | | sub-proof #310.
% 111.11/16.43 | | | | | | | |
% 111.11/16.43 | | | | | | | End of split
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | Case 2:
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | (95) all_58_8 = e1 | all_58_11 = e1
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | | REF_CLOSE: (15), (17), (34), (41), (95) are inconsistent by
% 111.11/16.43 | | | | | | | sub-proof #445.
% 111.11/16.43 | | | | | | |
% 111.11/16.43 | | | | | | End of split
% 111.11/16.43 | | | | | |
% 111.11/16.43 | | | | | End of split
% 111.11/16.43 | | | | |
% 111.11/16.43 | | | | End of split
% 111.11/16.43 | | | |
% 111.11/16.43 | | | End of split
% 111.11/16.43 | | |
% 111.11/16.43 | | End of split
% 111.11/16.43 | |
% 111.11/16.43 | End of split
% 111.11/16.43 |
% 111.11/16.43 End of proof
% 111.11/16.43
% 111.11/16.43 Sub-proof #5 shows that the following formulas are inconsistent:
% 111.11/16.43 ----------------------------------------------------------------
% 111.11/16.43 (1) ~ (all_52_8 = all_10_2)
% 111.11/16.43 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.11/16.43 (3) ~ (all_52_2 = all_10_2)
% 111.11/16.43 (4) ~ (all_52_6 = all_52_14)
% 111.11/16.43 (5) all_54_2 = all_52_8
% 111.11/16.43 (6) all_58_7 = all_52_6
% 111.11/16.43 (7) all_36_2 = all_6_2
% 111.11/16.43 (8) ~ (all_52_8 = all_52_11)
% 111.11/16.43 (9) ~ (all_52_9 = all_8_2)
% 111.50/16.43 (10) all_28_1 = all_6_1
% 111.50/16.43 (11) ~ (all_52_13 = all_52_14)
% 111.50/16.43 (12) ~ (all_4_2 = e0)
% 111.50/16.43 (13) op(e3, e2) = all_52_4
% 111.50/16.43 (14) all_56_14 = all_6_2
% 111.50/16.43 (15) all_56_3 = all_52_1
% 111.50/16.43 (16) all_54_0 = all_10_2
% 111.50/16.43 (17) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.50/16.43 (18) all_54_3 = all_52_12
% 111.50/16.43 (19) ~ (all_52_2 = all_52_6)
% 111.50/16.43 (20) ~ (all_52_12 = all_52_14)
% 111.50/16.43 (21) op(e0, e2) = all_52_7
% 111.50/16.43 (22) ~ (all_52_7 = all_4_2)
% 111.50/16.43 (23) all_56_11 = all_52_11
% 111.50/16.43 (24) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 111.50/16.43 (25) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.50/16.43 (26) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.50/16.43 (27) ~ (all_52_4 = all_52_8)
% 111.50/16.43 (28) ~ (all_52_12 = all_10_2)
% 111.50/16.44 (29) ~ (e3 = e1)
% 111.50/16.44 (30) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.50/16.44 (31) all_56_12 = all_10_2
% 111.50/16.44 (32) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 111.50/16.44 (33) all_58_0 = all_10_2
% 111.50/16.44 (34) op(all_6_1, all_6_2) = all_6_0
% 111.50/16.44 (35) all_54_11 = all_52_14
% 111.50/16.44 (36) all_54_13 = all_52_7
% 111.50/16.44 (37) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 111.50/16.44 (38) all_36_1 = all_6_1
% 111.50/16.44 (39) ~ (all_52_14 = all_6_2)
% 111.50/16.44 (40) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 111.50/16.44 (41) all_56_10 = all_52_7
% 111.50/16.44 (42) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.50/16.44 (43) all_54_14 = all_52_11
% 111.50/16.44 (44) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.50/16.44 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.50/16.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.50/16.44 (46) all_54_8 = all_52_2
% 111.50/16.44 (47) ~ (all_52_2 = all_6_2)
% 111.50/16.44 (48) ~ (all_52_1 = all_52_9)
% 111.50/16.44 (49) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 111.50/16.44 (50) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 111.50/16.44 (51) all_54_10 = all_6_2
% 111.50/16.44 (52) all_36_0 = all_6_0
% 111.50/16.44 (53) op(e3, e0) = all_52_12
% 111.50/16.44 (54) ~ (all_52_8 = all_6_2)
% 111.50/16.44 (55) all_58_4 = all_52_8
% 111.50/16.44 (56) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.50/16.44 (57) ~ (all_52_4 = all_52_7)
% 111.50/16.44 (58) all_56_2 = all_52_12
% 111.50/16.44 (59) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.50/16.44 (60) all_58_3 = all_8_2
% 111.50/16.44 (61) all_54_6 = all_52_9
% 111.50/16.44 (62) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.50/16.44 (63) ~ (all_10_0 = e2)
% 111.50/16.44 (64) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 111.50/16.44 (65) all_58_11 = all_52_14
% 111.50/16.44 (66) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 111.50/16.44 (67) all_54_9 = all_52_6
% 111.50/16.44 (68) op(e3, e1) = all_52_8
% 111.50/16.44 (69) ~ (all_52_2 = all_52_3)
% 111.50/16.44 (70) all_54_7 = all_52_13
% 111.50/16.44 (71) all_16_1 = all_10_1
% 111.50/16.44 (72) op(all_10_1, all_10_2) = all_10_0
% 111.50/16.44 (73) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.50/16.44 (74) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 111.50/16.44 (75) all_24_0 = all_10_0
% 111.50/16.44 (76) all_28_2 = all_6_2
% 111.50/16.44 (77) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 111.50/16.44 (78) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.50/16.44 (79) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 111.50/16.44 (80) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.50/16.44 (81) ~ (all_52_7 = all_8_2)
% 111.50/16.44 (82) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.50/16.44 (83) ~ (all_52_4 = all_8_2)
% 111.50/16.44 (84) op(e1, e0) = all_52_14
% 111.50/16.44 (85) all_58_5 = all_52_9
% 111.50/16.44 (86) ~ (all_52_9 = all_52_13)
% 111.50/16.44 (87) all_40_0 = all_6_0
% 111.50/16.44 (88) all_56_9 = all_52_3
% 111.50/16.44 (89) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 111.50/16.44 (90) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 111.50/16.44 (91) op(e1, all_6_2) = all_6_1
% 111.50/16.44 (92) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.50/16.44 (93) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 111.50/16.44 (94) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 111.50/16.44 (95) all_58_15 = all_4_2
% 111.50/16.44 (96) all_58_2 = all_52_1
% 111.50/16.44 (97) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.50/16.44 (98) ~ (all_52_1 = all_52_13)
% 111.50/16.44 (99) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 111.50/16.44 (100) ~ (all_10_2 = e3)
% 111.50/16.44 (101) ~ (all_52_12 = all_52_13)
% 111.50/16.44 (102) all_58_13 = all_52_7
% 111.50/16.44 (103) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 111.50/16.44 (104) all_40_1 = all_6_1
% 111.50/16.44 (105) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 111.50/16.44 (106) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.50/16.44 (107) ~ (all_52_14 = all_4_2)
% 111.50/16.44 (108) all_58_6 = all_52_2
% 111.50/16.44 (109) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.50/16.44 (110) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 111.50/16.44 (111) ~ (all_52_1 = all_10_2)
% 111.50/16.44 (112) all_54_5 = all_8_2
% 111.50/16.44 (113) all_56_15 = all_4_2
% 111.50/16.44 (114) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.50/16.44 (115) all_58_10 = all_52_13
% 111.50/16.44 (116) ~ (all_52_13 = all_8_2)
% 111.50/16.44 (117) ~ (all_52_11 = all_4_2)
% 111.50/16.44 (118) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 111.50/16.44 (119) op(e3, all_10_2) = all_10_1
% 111.50/16.44 (120) ~ (all_52_6 = all_8_2)
% 111.50/16.44 (121) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.50/16.44 (122) all_28_0 = all_6_0
% 111.50/16.44 (123) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 111.50/16.44 (124) all_58_1 = all_52_4
% 111.50/16.44 (125) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 111.50/16.44 (126) ~ (all_52_9 = all_52_11)
% 111.50/16.44 (127) all_58_14 = all_52_11
% 111.50/16.44 (128) all_54_1 = all_52_4
% 111.50/16.44 (129) all_56_13 = all_8_2
% 111.50/16.44 (130) ~ (all_52_1 = all_8_2)
% 111.50/16.44 (131) ~ (all_8_2 = e2)
% 111.50/16.45 (132) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 111.50/16.45 (133) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 111.50/16.45 (134) op(e1, e2) = all_52_6
% 111.50/16.45 (135) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.50/16.45 (136) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.50/16.45 (137) all_56_7 = all_52_6
% 111.50/16.45 (138) ~ (all_52_9 = all_6_2)
% 111.50/16.45 (139) ~ (all_52_4 = all_52_6)
% 111.50/16.45 (140) ~ (all_52_4 = all_52_12)
% 111.50/16.45 (141) all_56_1 = all_52_8
% 111.50/16.45 (142) op(e0, all_4_2) = all_4_1
% 111.50/16.45 (143) all_58_8 = all_6_2
% 111.50/16.45 (144) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.50/16.45 (145) all_10_0 = e1
% 111.50/16.45 (146) all_16_2 = all_10_2
% 111.50/16.45 (147) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.50/16.45 (148) all_40_2 = all_6_2
% 111.50/16.45 (149) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.50/16.45 (150) all_56_4 = all_52_9
% 111.50/16.45 (151) all_58_9 = all_52_12
% 111.50/16.45 (152) all_56_5 = all_52_13
% 111.50/16.45 (153) op(e2, e1) = all_52_9
% 111.50/16.45 (154) ~ (all_52_3 = all_4_2)
% 111.50/16.45 (155) ~ (all_52_6 = all_6_2)
% 111.50/16.45 (156) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.50/16.45 (157) all_56_6 = all_52_2
% 111.50/16.45 (158) ~ (all_52_13 = all_4_2)
% 111.50/16.45 (159) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 111.50/16.45 (160) all_58_12 = all_52_3
% 111.50/16.45 (161) ~ (all_52_2 = all_52_14)
% 111.50/16.45 (162) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.50/16.45 (163) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.50/16.45 (164) ~ (all_52_12 = all_4_2)
% 111.50/16.45 (165) ~ (all_52_3 = all_10_2)
% 111.50/16.45 (166) all_24_1 = all_10_1
% 111.50/16.45 (167) op(e1, e3) = all_52_2
% 111.50/16.45 (168) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 111.50/16.45 (169) all_24_2 = all_10_2
% 111.50/16.45 (170) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.50/16.45 (171) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.50/16.45 (172) all_56_8 = all_52_14
% 111.50/16.45 (173) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.50/16.45 (174) ~ (all_52_4 = all_10_2)
% 111.50/16.45 (175) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.50/16.45 (176) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.50/16.45 (177) all_56_0 = all_52_4
% 111.50/16.45 (178) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 111.50/16.45 (179) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.50/16.45 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.50/16.45 (180) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.50/16.45 (181) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.50/16.45 (182) all_54_15 = all_4_2
% 111.50/16.45 (183) ~ (all_6_2 = e1)
% 111.50/16.45 (184) ~ (all_6_1 = e2)
% 111.50/16.45 (185) ~ (all_52_6 = all_52_7)
% 111.50/16.45 (186) ~ (all_52_3 = all_52_11)
% 111.50/16.45 (187) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.50/16.45 (188) all_54_12 = all_52_3
% 111.50/16.45 (189) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 111.50/16.45
% 111.50/16.45 Begin of proof
% 111.50/16.45 |
% 111.50/16.45 | COMBINE_EQS: (75), (145) imply:
% 111.50/16.45 | (190) all_24_0 = e1
% 111.50/16.45 |
% 111.50/16.45 | REDUCE: (63), (145) imply:
% 111.50/16.45 | (191) ~ (e2 = e1)
% 111.50/16.45 |
% 111.50/16.45 | SIMP: (191) implies:
% 111.50/16.45 | (192) ~ (e2 = e1)
% 111.50/16.45 |
% 111.50/16.45 | REDUCE: (72), (145) imply:
% 111.50/16.45 | (193) op(all_10_1, all_10_2) = e1
% 111.50/16.45 |
% 111.50/16.45 | BETA: splitting (173) gives:
% 111.50/16.45 |
% 111.50/16.45 | Case 1:
% 111.50/16.45 | |
% 111.50/16.45 | | (194) ~ (all_24_0 = e1)
% 111.50/16.45 | |
% 111.50/16.45 | | REDUCE: (190), (194) imply:
% 111.50/16.45 | | (195) $false
% 111.50/16.45 | |
% 111.50/16.45 | | CLOSE: (195) is inconsistent.
% 111.50/16.45 | |
% 111.50/16.45 | Case 2:
% 111.50/16.45 | |
% 111.50/16.45 | | (196) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.50/16.45 | |
% 111.50/16.45 | | BETA: splitting (110) gives:
% 111.50/16.45 | |
% 111.50/16.45 | | Case 1:
% 111.50/16.45 | | |
% 111.50/16.45 | | | (197) ~ (all_28_0 = e2)
% 111.50/16.45 | | |
% 111.50/16.45 | | | REDUCE: (122), (197) imply:
% 111.50/16.45 | | | (198) ~ (all_6_0 = e2)
% 111.50/16.45 | | |
% 111.50/16.45 | | | BETA: splitting (123) gives:
% 111.50/16.45 | | |
% 111.50/16.45 | | | Case 1:
% 111.50/16.45 | | | |
% 111.50/16.45 | | | | (199) ~ (all_36_1 = e3)
% 111.50/16.45 | | | |
% 111.50/16.45 | | | | REDUCE: (38), (199) imply:
% 111.50/16.45 | | | | (200) ~ (all_6_1 = e3)
% 111.50/16.45 | | | |
% 111.50/16.45 | | | | BETA: splitting (50) gives:
% 111.50/16.45 | | | |
% 111.50/16.45 | | | | Case 1:
% 111.50/16.45 | | | | |
% 111.50/16.45 | | | | | (201) ~ (all_40_0 = e3)
% 111.50/16.45 | | | | |
% 111.50/16.45 | | | | | REDUCE: (87), (201) imply:
% 111.50/16.45 | | | | | (202) ~ (all_6_0 = e3)
% 111.50/16.45 | | | | |
% 111.50/16.45 | | | | | BETA: splitting (89) gives:
% 111.50/16.45 | | | | |
% 111.50/16.45 | | | | | Case 1:
% 111.50/16.45 | | | | | |
% 111.50/16.45 | | | | | | (203) ~ (all_56_15 = e1)
% 111.50/16.45 | | | | | |
% 111.50/16.45 | | | | | | REDUCE: (113), (203) imply:
% 111.50/16.45 | | | | | | (204) ~ (all_4_2 = e1)
% 111.50/16.45 | | | | | |
% 111.50/16.45 | | | | | | BETA: splitting (105) gives:
% 111.50/16.45 | | | | | |
% 111.50/16.45 | | | | | | Case 1:
% 111.50/16.45 | | | | | | |
% 111.50/16.45 | | | | | | | (205) ~ (all_56_14 = e2)
% 111.50/16.45 | | | | | | |
% 111.50/16.45 | | | | | | | REDUCE: (14), (205) imply:
% 111.50/16.45 | | | | | | | (206) ~ (all_6_2 = e2)
% 111.50/16.45 | | | | | | |
% 111.50/16.45 | | | | | | | REF_CLOSE: (2), (3), (6), (12), (13), (14), (16), (18), (23),
% 111.50/16.45 | | | | | | | (25), (26), (28), (31), (32), (33), (41), (42), (43),
% 111.50/16.45 | | | | | | | (44), (45), (51), (53), (55), (56), (58), (59), (65),
% 111.50/16.45 | | | | | | | (68), (71), (73), (78), (84), (85), (88), (90), (92),
% 111.50/16.45 | | | | | | | (95), (97), (100), (102), (106), (107), (108), (113),
% 111.50/16.45 | | | | | | | (117), (119), (124), (126), (127), (128), (134), (135),
% 111.50/16.45 | | | | | | | (136), (137), (139), (141), (143), (144), (146), (147),
% 111.50/16.45 | | | | | | | (150), (151), (153), (154), (157), (160), (163), (164),
% 111.50/16.45 | | | | | | | (165), (166), (168), (169), (171), (172), (174), (175),
% 111.50/16.45 | | | | | | | (177), (179), (180), (181), (182), (183), (186), (187),
% 111.50/16.45 | | | | | | | (188), (193), (196), (204), (206) are inconsistent by
% 111.50/16.45 | | | | | | | sub-proof #7.
% 111.50/16.45 | | | | | | |
% 111.50/16.45 | | | | | | Case 2:
% 111.50/16.45 | | | | | | |
% 111.50/16.45 | | | | | | | (207) all_56_14 = e2
% 111.50/16.45 | | | | | | |
% 111.50/16.46 | | | | | | | REF_CLOSE: (3), (4), (6), (12), (14), (16), (17), (19), (21),
% 111.50/16.46 | | | | | | | (23), (29), (31), (34), (35), (36), (37), (39), (40),
% 111.50/16.46 | | | | | | | (45), (46), (47), (57), (60), (64), (67), (82), (88),
% 111.50/16.46 | | | | | | | (91), (92), (94), (95), (99), (102), (124), (127),
% 111.50/16.46 | | | | | | | (129), (131), (132), (134), (137), (144), (149), (155),
% 111.50/16.46 | | | | | | | (157), (160), (161), (172), (174), (175), (177), (178),
% 111.50/16.46 | | | | | | | (179), (180), (183), (185), (198), (200), (202), (207)
% 111.50/16.46 | | | | | | | are inconsistent by sub-proof #374.
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | End of split
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | Case 2:
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | (208) all_56_15 = e1
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | REF_CLOSE: (2), (3), (4), (6), (11), (13), (14), (15), (16), (18),
% 111.50/16.46 | | | | | | (25), (26), (28), (31), (33), (35), (39), (40), (44),
% 111.50/16.46 | | | | | | (45), (46), (47), (51), (53), (58), (59), (60), (65),
% 111.50/16.46 | | | | | | (71), (80), (82), (84), (85), (90), (91), (92), (93),
% 111.50/16.46 | | | | | | (96), (100), (107), (108), (111), (113), (115), (119),
% 111.50/16.46 | | | | | | (121), (128), (131), (134), (135), (136), (137), (139),
% 111.50/16.46 | | | | | | (143), (144), (146), (149), (150), (152), (155), (157),
% 111.50/16.46 | | | | | | (161), (162), (166), (167), (169), (170), (171), (172),
% 111.50/16.46 | | | | | | (174), (176), (177), (181), (183), (184), (193), (196),
% 111.50/16.46 | | | | | | (200), (208) are inconsistent by sub-proof #6.
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | End of split
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | Case 2:
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | (209) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | BETA: splitting (89) gives:
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | Case 1:
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | (210) ~ (all_56_15 = e1)
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | REDUCE: (113), (210) imply:
% 111.50/16.46 | | | | | | (211) ~ (all_4_2 = e1)
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | BETA: splitting (105) gives:
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | Case 1:
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | | (212) ~ (all_56_14 = e2)
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | | REDUCE: (14), (212) imply:
% 111.50/16.46 | | | | | | | (213) ~ (all_6_2 = e2)
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | | REF_CLOSE: (2), (3), (6), (12), (13), (14), (16), (18), (23),
% 111.50/16.46 | | | | | | | (25), (26), (28), (31), (32), (33), (41), (42), (43),
% 111.50/16.46 | | | | | | | (44), (45), (51), (53), (55), (56), (58), (59), (65),
% 111.50/16.46 | | | | | | | (68), (71), (73), (78), (84), (85), (88), (90), (92),
% 111.50/16.46 | | | | | | | (95), (97), (100), (102), (106), (107), (108), (113),
% 111.50/16.46 | | | | | | | (117), (119), (124), (126), (127), (128), (134), (135),
% 111.50/16.46 | | | | | | | (136), (137), (139), (141), (143), (144), (146), (147),
% 111.50/16.46 | | | | | | | (150), (151), (153), (154), (157), (160), (163), (164),
% 111.50/16.46 | | | | | | | (165), (166), (168), (169), (171), (172), (174), (175),
% 111.50/16.46 | | | | | | | (177), (179), (180), (181), (182), (183), (186), (187),
% 111.50/16.46 | | | | | | | (188), (193), (196), (211), (213) are inconsistent by
% 111.50/16.46 | | | | | | | sub-proof #7.
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | Case 2:
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | | (214) all_56_14 = e2
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | | REF_CLOSE: (14), (40), (45), (64), (67), (91), (104), (134),
% 111.50/16.46 | | | | | | | (137), (148), (155), (200), (209), (214) are
% 111.50/16.46 | | | | | | | inconsistent by sub-proof #372.
% 111.50/16.46 | | | | | | |
% 111.50/16.46 | | | | | | End of split
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | Case 2:
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | (215) all_56_15 = e1
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | | REF_CLOSE: (2), (3), (4), (6), (11), (13), (14), (15), (16), (18),
% 111.50/16.46 | | | | | | (25), (26), (28), (31), (33), (35), (39), (40), (44),
% 111.50/16.46 | | | | | | (45), (46), (47), (51), (53), (58), (59), (60), (65),
% 111.50/16.46 | | | | | | (71), (80), (82), (84), (85), (90), (91), (92), (93),
% 111.50/16.46 | | | | | | (96), (100), (107), (108), (111), (113), (115), (119),
% 111.50/16.46 | | | | | | (121), (128), (131), (134), (135), (136), (137), (139),
% 111.50/16.46 | | | | | | (143), (144), (146), (149), (150), (152), (155), (157),
% 111.50/16.46 | | | | | | (161), (162), (166), (167), (169), (170), (171), (172),
% 111.50/16.46 | | | | | | (174), (176), (177), (181), (183), (184), (193), (196),
% 111.50/16.46 | | | | | | (200), (215) are inconsistent by sub-proof #6.
% 111.50/16.46 | | | | | |
% 111.50/16.46 | | | | | End of split
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | End of split
% 111.50/16.46 | | | |
% 111.50/16.46 | | | Case 2:
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | (216) all_36_1 = e3
% 111.50/16.46 | | | | (217) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | COMBINE_EQS: (38), (216) imply:
% 111.50/16.46 | | | | (218) all_6_1 = e3
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | SIMP: (218) implies:
% 111.50/16.46 | | | | (219) all_6_1 = e3
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (184), (219) imply:
% 111.50/16.46 | | | | (220) ~ (e3 = e2)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (34), (219) imply:
% 111.50/16.46 | | | | (221) op(e3, all_6_2) = all_6_0
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (91), (219) imply:
% 111.50/16.46 | | | | (222) op(e1, all_6_2) = e3
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (11), (12), (13), (14), (15),
% 111.50/16.46 | | | | (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 111.50/16.46 | | | | (27), (28), (29), (30), (31), (32), (33), (35), (36), (39),
% 111.50/16.46 | | | | (40), (41), (42), (44), (45), (46), (47), (48), (49), (51),
% 111.50/16.46 | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 111.50/16.46 | | | | (62), (65), (66), (69), (70), (71), (73), (77), (79), (80),
% 111.50/16.46 | | | | (81), (82), (83), (84), (85), (86), (88), (89), (90), (91),
% 111.50/16.46 | | | | (92), (95), (96), (97), (98), (100), (101), (102), (103),
% 111.50/16.46 | | | | (105), (106), (107), (108), (109), (112), (113), (114),
% 111.50/16.46 | | | | (115), (116), (117), (118), (119), (120), (121), (124),
% 111.50/16.46 | | | | (125), (127), (128), (129), (130), (131), (133), (134),
% 111.50/16.46 | | | | (135), (136), (137), (138), (139), (140), (141), (143),
% 111.50/16.46 | | | | (144), (146), (147), (149), (150), (151), (152), (154),
% 111.50/16.46 | | | | (155), (157), (158), (159), (160), (161), (162), (163),
% 111.50/16.46 | | | | (164), (165), (166), (167), (168), (169), (170), (171),
% 111.50/16.46 | | | | (172), (174), (175), (176), (177), (179), (180), (181),
% 111.50/16.46 | | | | (182), (183), (184), (185), (186), (188), (189), (192),
% 111.50/16.46 | | | | (193), (196), (198), (217), (220), (221), (222) are
% 111.50/16.46 | | | | inconsistent by sub-proof #182.
% 111.50/16.46 | | | |
% 111.50/16.46 | | | End of split
% 111.50/16.46 | | |
% 111.50/16.46 | | Case 2:
% 111.50/16.46 | | |
% 111.50/16.46 | | | (223) all_28_0 = e2
% 111.50/16.46 | | | (224) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 111.50/16.46 | | |
% 111.50/16.46 | | | COMBINE_EQS: (122), (223) imply:
% 111.50/16.46 | | | (225) all_6_0 = e2
% 111.50/16.46 | | |
% 111.50/16.46 | | | SIMP: (225) implies:
% 111.50/16.46 | | | (226) all_6_0 = e2
% 111.50/16.46 | | |
% 111.50/16.46 | | | REDUCE: (34), (226) imply:
% 111.50/16.46 | | | (227) op(all_6_1, all_6_2) = e2
% 111.50/16.46 | | |
% 111.50/16.46 | | | BETA: splitting (89) gives:
% 111.50/16.46 | | |
% 111.50/16.46 | | | Case 1:
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | (228) ~ (all_56_15 = e1)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (113), (228) imply:
% 111.50/16.46 | | | | (229) ~ (all_4_2 = e1)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | BETA: splitting (105) gives:
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | Case 1:
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | (230) ~ (all_56_14 = e2)
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | REDUCE: (14), (230) imply:
% 111.50/16.46 | | | | | (231) ~ (all_6_2 = e2)
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | REF_CLOSE: (2), (3), (6), (12), (13), (14), (16), (18), (23), (25),
% 111.50/16.46 | | | | | (26), (28), (31), (32), (33), (41), (42), (43), (44), (45),
% 111.50/16.46 | | | | | (51), (53), (55), (56), (58), (59), (65), (68), (71), (73),
% 111.50/16.46 | | | | | (78), (84), (85), (88), (90), (92), (95), (97), (100),
% 111.50/16.46 | | | | | (102), (106), (107), (108), (113), (117), (119), (124),
% 111.50/16.46 | | | | | (126), (127), (128), (134), (135), (136), (137), (139),
% 111.50/16.46 | | | | | (141), (143), (144), (146), (147), (150), (151), (153),
% 111.50/16.46 | | | | | (154), (157), (160), (163), (164), (165), (166), (168),
% 111.50/16.46 | | | | | (169), (171), (172), (174), (175), (177), (179), (180),
% 111.50/16.46 | | | | | (181), (182), (183), (186), (187), (188), (193), (196),
% 111.50/16.46 | | | | | (229), (231) are inconsistent by sub-proof #7.
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | Case 2:
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | (232) all_56_14 = e2
% 111.50/16.46 | | | | | (233) ~ (all_56_10 = e0)
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (12), (13), (14), (16),
% 111.50/16.46 | | | | | (17), (18), (19), (21), (22), (23), (26), (28), (30), (31),
% 111.50/16.46 | | | | | (36), (40), (41), (45), (46), (47), (53), (54), (56), (58),
% 111.50/16.46 | | | | | (60), (64), (65), (66), (67), (69), (71), (74), (78), (82),
% 111.50/16.46 | | | | | (84), (85), (88), (90), (91), (92), (94), (95), (96),
% 111.50/16.46 | | | | | (100), (102), (107), (108), (111), (112), (113), (115),
% 111.50/16.46 | | | | | (118), (119), (127), (128), (129), (131), (134), (135),
% 111.50/16.46 | | | | | (136), (137), (138), (139), (141), (142), (143), (144),
% 111.50/16.46 | | | | | (146), (147), (152), (154), (155), (156), (157), (160),
% 111.50/16.46 | | | | | (165), (166), (169), (172), (174), (175), (176), (177),
% 111.50/16.46 | | | | | (179), (180), (182), (183), (185), (193), (196), (227),
% 111.50/16.46 | | | | | (232), (233) are inconsistent by sub-proof #177.
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | End of split
% 111.50/16.46 | | | |
% 111.50/16.46 | | | Case 2:
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | (234) all_56_15 = e1
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | COMBINE_EQS: (113), (234) imply:
% 111.50/16.46 | | | | (235) all_4_2 = e1
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | SIMP: (235) implies:
% 111.50/16.46 | | | | (236) all_4_2 = e1
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (158), (236) imply:
% 111.50/16.46 | | | | (237) ~ (all_52_13 = e1)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | REDUCE: (107), (236) imply:
% 111.50/16.46 | | | | (238) ~ (all_52_14 = e1)
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | BETA: splitting (105) gives:
% 111.50/16.46 | | | |
% 111.50/16.46 | | | | Case 1:
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | (239) ~ (all_56_14 = e2)
% 111.50/16.46 | | | | |
% 111.50/16.46 | | | | | REDUCE: (14), (239) imply:
% 111.50/16.46 | | | | | (240) ~ (all_6_2 = e2)
% 111.50/16.46 | | | | |
% 111.50/16.47 | | | | | REF_CLOSE: (4), (6), (10), (11), (14), (15), (33), (35), (39), (44),
% 111.50/16.47 | | | | | (45), (47), (51), (59), (60), (65), (76), (80), (84), (85),
% 111.50/16.47 | | | | | (86), (91), (96), (100), (108), (115), (121), (131), (135),
% 111.50/16.47 | | | | | (143), (149), (150), (152), (155), (157), (161), (162),
% 111.50/16.47 | | | | | (167), (171), (176), (183), (184), (189), (224), (234),
% 111.50/16.47 | | | | | (237), (238), (240) are inconsistent by sub-proof #270.
% 111.50/16.47 | | | | |
% 111.50/16.47 | | | | Case 2:
% 111.50/16.47 | | | | |
% 111.50/16.47 | | | | | (241) all_56_14 = e2
% 111.50/16.47 | | | | | (242) ~ (all_56_10 = e0)
% 111.50/16.47 | | | | |
% 111.50/16.47 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (12), (13), (14), (16),
% 111.50/16.47 | | | | | (17), (18), (19), (21), (22), (23), (26), (28), (30), (31),
% 111.50/16.47 | | | | | (36), (40), (41), (45), (46), (47), (53), (54), (56), (58),
% 111.50/16.47 | | | | | (60), (64), (65), (66), (67), (69), (71), (74), (78), (82),
% 111.50/16.47 | | | | | (84), (85), (88), (90), (91), (92), (94), (95), (96),
% 111.50/16.47 | | | | | (100), (102), (107), (108), (111), (112), (113), (115),
% 111.50/16.47 | | | | | (118), (119), (127), (128), (129), (131), (134), (135),
% 111.50/16.47 | | | | | (136), (137), (138), (139), (141), (142), (143), (144),
% 111.50/16.47 | | | | | (146), (147), (152), (154), (155), (156), (157), (160),
% 111.50/16.47 | | | | | (165), (166), (169), (172), (174), (175), (176), (177),
% 111.50/16.47 | | | | | (179), (180), (182), (183), (185), (193), (196), (227),
% 111.50/16.47 | | | | | (241), (242) are inconsistent by sub-proof #177.
% 111.50/16.47 | | | | |
% 111.50/16.47 | | | | End of split
% 111.50/16.47 | | | |
% 111.50/16.47 | | | End of split
% 111.50/16.47 | | |
% 111.50/16.47 | | End of split
% 111.50/16.47 | |
% 111.50/16.47 | End of split
% 111.50/16.47 |
% 111.50/16.47 End of proof
% 111.50/16.47
% 111.50/16.47 Sub-proof #6 shows that the following formulas are inconsistent:
% 111.50/16.47 ----------------------------------------------------------------
% 111.50/16.47 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.50/16.47 (2) ~ (all_52_2 = all_10_2)
% 111.50/16.47 (3) ~ (all_52_6 = all_52_14)
% 111.50/16.47 (4) all_58_7 = all_52_6
% 111.50/16.47 (5) ~ (all_52_13 = all_52_14)
% 111.50/16.47 (6) op(e3, e2) = all_52_4
% 111.50/16.47 (7) all_56_14 = all_6_2
% 111.50/16.47 (8) all_56_3 = all_52_1
% 111.50/16.47 (9) all_54_0 = all_10_2
% 111.50/16.47 (10) all_54_3 = all_52_12
% 111.50/16.47 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.50/16.47 (12) ~ (all_6_1 = e3)
% 111.50/16.47 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.50/16.47 (14) ~ (all_52_12 = all_10_2)
% 111.50/16.47 (15) all_56_12 = all_10_2
% 111.50/16.47 (16) all_58_0 = all_10_2
% 111.50/16.47 (17) all_54_11 = all_52_14
% 111.50/16.47 (18) op(all_10_1, all_10_2) = e1
% 111.50/16.47 (19) ~ (all_52_14 = all_6_2)
% 111.50/16.47 (20) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 111.50/16.47 (21) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.50/16.47 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.50/16.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.50/16.47 (23) all_54_8 = all_52_2
% 111.50/16.47 (24) ~ (all_52_2 = all_6_2)
% 111.50/16.47 (25) all_54_10 = all_6_2
% 111.50/16.47 (26) op(e3, e0) = all_52_12
% 111.50/16.47 (27) all_56_2 = all_52_12
% 111.50/16.47 (28) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.50/16.47 (29) all_58_3 = all_8_2
% 111.50/16.47 (30) all_58_11 = all_52_14
% 111.50/16.47 (31) all_16_1 = all_10_1
% 111.50/16.47 (32) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.50/16.47 (33) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.50/16.47 (34) all_56_15 = e1
% 111.50/16.47 (35) op(e1, e0) = all_52_14
% 111.50/16.47 (36) all_58_5 = all_52_9
% 111.50/16.47 (37) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.50/16.47 (38) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 111.50/16.47 (39) op(e1, all_6_2) = all_6_1
% 111.50/16.47 (40) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.50/16.47 (41) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 111.50/16.47 (42) all_58_2 = all_52_1
% 111.50/16.47 (43) ~ (all_10_2 = e3)
% 111.50/16.47 (44) ~ (all_52_14 = all_4_2)
% 111.50/16.47 (45) all_58_6 = all_52_2
% 111.50/16.47 (46) ~ (all_52_1 = all_10_2)
% 111.50/16.47 (47) all_56_15 = all_4_2
% 111.50/16.47 (48) all_58_10 = all_52_13
% 111.50/16.47 (49) op(e3, all_10_2) = all_10_1
% 111.50/16.47 (50) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.50/16.47 (51) all_54_1 = all_52_4
% 111.50/16.47 (52) ~ (all_8_2 = e2)
% 111.50/16.47 (53) op(e1, e2) = all_52_6
% 111.50/16.47 (54) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.50/16.47 (55) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.50/16.47 (56) all_56_7 = all_52_6
% 111.50/16.47 (57) ~ (all_52_4 = all_52_6)
% 111.50/16.47 (58) all_58_8 = all_6_2
% 111.50/16.47 (59) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.50/16.47 (60) all_16_2 = all_10_2
% 111.50/16.47 (61) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.50/16.47 (62) all_56_4 = all_52_9
% 111.50/16.47 (63) all_56_5 = all_52_13
% 111.50/16.47 (64) ~ (all_52_6 = all_6_2)
% 111.50/16.47 (65) all_56_6 = all_52_2
% 111.50/16.47 (66) ~ (all_52_2 = all_52_14)
% 111.50/16.47 (67) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.50/16.47 (68) all_24_1 = all_10_1
% 111.50/16.47 (69) op(e1, e3) = all_52_2
% 111.50/16.47 (70) all_24_2 = all_10_2
% 111.50/16.47 (71) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.50/16.47 (72) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.50/16.47 (73) all_56_8 = all_52_14
% 111.50/16.47 (74) ~ (all_52_4 = all_10_2)
% 111.50/16.47 (75) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.50/16.47 (76) all_56_0 = all_52_4
% 111.50/16.47 (77) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.50/16.47 (78) ~ (all_6_2 = e1)
% 111.50/16.47 (79) ~ (all_6_1 = e2)
% 111.50/16.47
% 111.50/16.47 Begin of proof
% 111.50/16.47 |
% 111.50/16.47 | COMBINE_EQS: (34), (47) imply:
% 111.50/16.47 | (80) all_4_2 = e1
% 111.50/16.47 |
% 111.50/16.47 | SIMP: (80) implies:
% 111.50/16.47 | (81) all_4_2 = e1
% 111.50/16.47 |
% 111.50/16.47 | REDUCE: (44), (81) imply:
% 111.50/16.47 | (82) ~ (all_52_14 = e1)
% 111.50/16.47 |
% 111.50/16.48 | BETA: splitting (67) gives:
% 111.50/16.48 |
% 111.50/16.48 | Case 1:
% 111.50/16.48 | |
% 111.50/16.48 | | (83) ~ (all_56_4 = e2)
% 111.50/16.48 | |
% 111.50/16.48 | | REDUCE: (62), (83) imply:
% 111.50/16.48 | | (84) ~ (all_52_9 = e2)
% 111.50/16.48 | |
% 111.50/16.48 | | BETA: splitting (41) gives:
% 111.50/16.48 | |
% 111.50/16.48 | | Case 1:
% 111.50/16.48 | | |
% 111.50/16.48 | | | (85) ~ (all_56_7 = e1)
% 111.50/16.48 | | |
% 111.50/16.48 | | | REDUCE: (56), (85) imply:
% 111.50/16.48 | | | (86) ~ (all_52_6 = e1)
% 111.50/16.48 | | |
% 111.50/16.48 | | | BETA: splitting (54) gives:
% 111.50/16.48 | | |
% 111.50/16.48 | | | Case 1:
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | (87) all_58_6 = e1
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | COMBINE_EQS: (45), (87) imply:
% 111.50/16.48 | | | | (88) all_52_2 = e1
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | SIMP: (88) implies:
% 111.50/16.48 | | | | (89) all_52_2 = e1
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | REDUCE: (2), (89) imply:
% 111.50/16.48 | | | | (90) ~ (all_10_2 = e1)
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | SIMP: (90) implies:
% 111.50/16.48 | | | | (91) ~ (all_10_2 = e1)
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | BETA: splitting (71) gives:
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | Case 1:
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | (92) ~ (all_56_5 = e2)
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | REF_CLOSE: (1), (9), (10), (13), (14), (15), (18), (22), (26), (27),
% 111.50/16.48 | | | | | (29), (31), (35), (36), (38), (40), (42), (43), (46), (48),
% 111.50/16.48 | | | | | (49), (52), (59), (60), (63), (73), (75), (84), (91), (92)
% 111.50/16.48 | | | | | are inconsistent by sub-proof #178.
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | Case 2:
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | (93) ~ (all_56_12 = e0)
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | REDUCE: (15), (93) imply:
% 111.50/16.48 | | | | | (94) ~ (all_10_2 = e0)
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | BETA: splitting (59) gives:
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | | Case 1:
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | | (95) all_54_0 = e3
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | | REF_CLOSE: (9), (43), (95) are inconsistent by sub-proof #451.
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | Case 2:
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | | (96) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | | BETA: splitting (96) gives:
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | | Case 1:
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | (97) all_54_0 = e2
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | COMBINE_EQS: (9), (97) imply:
% 111.50/16.48 | | | | | | | (98) all_10_2 = e2
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | SIMP: (98) implies:
% 111.50/16.48 | | | | | | | (99) all_10_2 = e2
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | COMBINE_EQS: (70), (99) imply:
% 111.50/16.48 | | | | | | | (100) all_24_2 = e2
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | COMBINE_EQS: (15), (99) imply:
% 111.50/16.48 | | | | | | | (101) all_56_12 = e2
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | REF_CLOSE: (6), (18), (22), (37), (49), (51), (53), (55), (57),
% 111.50/16.48 | | | | | | | (68), (74), (76), (77), (99), (100), (101) are
% 111.50/16.48 | | | | | | | inconsistent by sub-proof #196.
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | Case 2:
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | (102) all_54_0 = e1 | all_54_0 = e0
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | | REF_CLOSE: (9), (91), (94), (102) are inconsistent by sub-proof
% 111.50/16.48 | | | | | | | #423.
% 111.50/16.48 | | | | | | |
% 111.50/16.48 | | | | | | End of split
% 111.50/16.48 | | | | | |
% 111.50/16.48 | | | | | End of split
% 111.50/16.48 | | | | |
% 111.50/16.48 | | | | End of split
% 111.50/16.48 | | | |
% 111.50/16.48 | | | Case 2:
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | (103) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | REF_CLOSE: (4), (30), (58), (78), (82), (86), (103) are inconsistent by
% 111.50/16.48 | | | | sub-proof #354.
% 111.50/16.48 | | | |
% 111.50/16.48 | | | End of split
% 111.50/16.48 | | |
% 111.50/16.48 | | Case 2:
% 111.50/16.48 | | |
% 111.50/16.48 | | | (104) all_56_7 = e1
% 111.50/16.48 | | |
% 111.50/16.48 | | | COMBINE_EQS: (56), (104) imply:
% 111.50/16.48 | | | (105) all_52_6 = e1
% 111.50/16.48 | | |
% 111.50/16.48 | | | REDUCE: (3), (105) imply:
% 111.50/16.48 | | | (106) ~ (all_52_14 = e1)
% 111.50/16.48 | | |
% 111.50/16.48 | | | REDUCE: (64), (105) imply:
% 111.50/16.48 | | | (107) ~ (all_6_2 = e1)
% 111.50/16.48 | | |
% 111.50/16.48 | | | BETA: splitting (20) gives:
% 111.50/16.48 | | |
% 111.50/16.48 | | | Case 1:
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | (108) ~ (all_56_7 = e1)
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | REDUCE: (104), (108) imply:
% 111.50/16.48 | | | | (109) $false
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | CLOSE: (109) is inconsistent.
% 111.50/16.48 | | | |
% 111.50/16.48 | | | Case 2:
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | (110) ~ (all_56_14 = e2)
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | REDUCE: (7), (110) imply:
% 111.50/16.48 | | | | (111) ~ (all_6_2 = e2)
% 111.50/16.48 | | | |
% 111.50/16.48 | | | | REF_CLOSE: (5), (7), (8), (11), (12), (16), (17), (19), (21), (22),
% 111.50/16.48 | | | | (23), (24), (25), (28), (29), (32), (33), (34), (35), (36),
% 111.50/16.48 | | | | (39), (42), (43), (48), (50), (52), (61), (62), (63), (65),
% 111.50/16.48 | | | | (66), (67), (69), (72), (73), (75), (78), (79), (82), (111)
% 111.50/16.48 | | | | are inconsistent by sub-proof #393.
% 111.50/16.48 | | | |
% 111.50/16.48 | | | End of split
% 111.50/16.48 | | |
% 111.50/16.48 | | End of split
% 111.50/16.48 | |
% 111.50/16.48 | Case 2:
% 111.50/16.48 | |
% 111.50/16.48 | | (112) ~ (all_56_15 = e1)
% 111.50/16.48 | |
% 111.50/16.48 | | REDUCE: (34), (112) imply:
% 111.50/16.48 | | (113) $false
% 111.50/16.48 | |
% 111.50/16.48 | | CLOSE: (113) is inconsistent.
% 111.50/16.48 | |
% 111.50/16.48 | End of split
% 111.50/16.48 |
% 111.50/16.48 End of proof
% 111.50/16.48
% 111.50/16.48 Sub-proof #7 shows that the following formulas are inconsistent:
% 111.50/16.48 ----------------------------------------------------------------
% 111.50/16.48 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.50/16.48 (2) ~ (all_52_2 = all_10_2)
% 111.50/16.48 (3) all_58_7 = all_52_6
% 111.50/16.48 (4) ~ (all_4_2 = e0)
% 111.50/16.48 (5) op(e3, e2) = all_52_4
% 111.50/16.48 (6) all_56_14 = all_6_2
% 111.50/16.48 (7) all_54_0 = all_10_2
% 111.50/16.48 (8) all_54_3 = all_52_12
% 111.50/16.48 (9) ~ (all_4_2 = e1)
% 111.50/16.48 (10) all_56_11 = all_52_11
% 111.50/16.48 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.50/16.48 (12) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.50/16.48 (13) ~ (all_52_12 = all_10_2)
% 111.50/16.48 (14) all_56_12 = all_10_2
% 111.50/16.48 (15) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 111.50/16.48 (16) all_58_0 = all_10_2
% 111.50/16.48 (17) op(all_10_1, all_10_2) = e1
% 111.50/16.48 (18) all_56_10 = all_52_7
% 111.50/16.48 (19) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.50/16.48 (20) all_54_14 = all_52_11
% 111.50/16.48 (21) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.50/16.48 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.50/16.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.50/16.48 (23) all_54_10 = all_6_2
% 111.50/16.48 (24) op(e3, e0) = all_52_12
% 111.50/16.48 (25) all_58_4 = all_52_8
% 111.50/16.48 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.50/16.48 (27) all_56_2 = all_52_12
% 111.50/16.48 (28) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.50/16.48 (29) all_58_11 = all_52_14
% 111.50/16.48 (30) op(e3, e1) = all_52_8
% 111.50/16.48 (31) all_16_1 = all_10_1
% 111.50/16.48 (32) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.50/16.48 (33) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.50/16.48 (34) op(e1, e0) = all_52_14
% 111.50/16.48 (35) all_58_5 = all_52_9
% 111.50/16.48 (36) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 111.50/16.48 (37) all_56_9 = all_52_3
% 111.50/16.48 (38) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 111.50/16.48 (39) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.50/16.48 (40) all_58_15 = all_4_2
% 111.50/16.48 (41) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.50/16.48 (42) ~ (all_10_2 = e3)
% 111.50/16.48 (43) all_58_13 = all_52_7
% 111.50/16.48 (44) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.50/16.48 (45) ~ (all_52_14 = all_4_2)
% 111.50/16.48 (46) all_58_6 = all_52_2
% 111.50/16.48 (47) all_56_15 = all_4_2
% 111.50/16.48 (48) ~ (all_52_11 = all_4_2)
% 111.50/16.49 (49) op(e3, all_10_2) = all_10_1
% 111.50/16.49 (50) all_58_1 = all_52_4
% 111.50/16.49 (51) ~ (all_52_9 = all_52_11)
% 111.50/16.49 (52) all_58_14 = all_52_11
% 111.50/16.49 (53) all_54_1 = all_52_4
% 111.50/16.49 (54) ~ (all_6_2 = e2)
% 111.50/16.49 (55) op(e1, e2) = all_52_6
% 111.50/16.49 (56) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.50/16.49 (57) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.50/16.49 (58) all_56_7 = all_52_6
% 111.50/16.49 (59) ~ (all_52_4 = all_52_6)
% 111.50/16.49 (60) all_56_1 = all_52_8
% 111.50/16.49 (61) all_58_8 = all_6_2
% 111.50/16.49 (62) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.50/16.49 (63) all_16_2 = all_10_2
% 111.50/16.49 (64) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.50/16.49 (65) all_56_4 = all_52_9
% 111.50/16.49 (66) all_58_9 = all_52_12
% 111.50/16.49 (67) op(e2, e1) = all_52_9
% 111.50/16.49 (68) ~ (all_52_3 = all_4_2)
% 111.50/16.49 (69) all_56_6 = all_52_2
% 111.50/16.49 (70) all_58_12 = all_52_3
% 111.50/16.49 (71) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.50/16.49 (72) ~ (all_52_12 = all_4_2)
% 111.50/16.49 (73) ~ (all_52_3 = all_10_2)
% 111.50/16.49 (74) all_24_1 = all_10_1
% 111.50/16.49 (75) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 111.50/16.49 (76) all_24_2 = all_10_2
% 111.50/16.49 (77) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.50/16.49 (78) all_56_8 = all_52_14
% 111.50/16.49 (79) ~ (all_52_4 = all_10_2)
% 111.50/16.49 (80) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.50/16.49 (81) all_56_0 = all_52_4
% 111.50/16.49 (82) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.50/16.49 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.50/16.49 (83) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.50/16.49 (84) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.50/16.49 (85) all_54_15 = all_4_2
% 111.50/16.49 (86) ~ (all_6_2 = e1)
% 111.50/16.49 (87) ~ (all_52_3 = all_52_11)
% 111.50/16.49 (88) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.50/16.49 (89) all_54_12 = all_52_3
% 111.50/16.49
% 111.50/16.49 Begin of proof
% 111.50/16.49 |
% 111.50/16.49 | BETA: splitting (44) gives:
% 111.50/16.49 |
% 111.50/16.49 | Case 1:
% 111.50/16.49 | |
% 111.50/16.49 | | (90) ~ (all_56_12 = e2)
% 111.50/16.49 | |
% 111.50/16.49 | | REDUCE: (14), (90) imply:
% 111.50/16.49 | | (91) ~ (all_10_2 = e2)
% 111.50/16.49 | |
% 111.50/16.49 | | BETA: splitting (80) gives:
% 111.50/16.49 | |
% 111.50/16.49 | | Case 1:
% 111.50/16.49 | | |
% 111.50/16.49 | | | (92) ~ (all_56_12 = e1)
% 111.50/16.49 | | |
% 111.50/16.49 | | | REDUCE: (14), (92) imply:
% 111.50/16.49 | | | (93) ~ (all_10_2 = e1)
% 111.50/16.49 | | |
% 111.71/16.49 | | | REF_CLOSE: (1), (7), (8), (12), (13), (14), (17), (22), (24), (27), (31),
% 111.71/16.49 | | | (34), (38), (39), (42), (49), (62), (63), (78), (91), (93) are
% 111.71/16.49 | | | inconsistent by sub-proof #193.
% 111.71/16.49 | | |
% 111.71/16.49 | | Case 2:
% 111.71/16.49 | | |
% 111.71/16.49 | | | (94) all_56_12 = e1
% 111.71/16.49 | | | (95) ~ (all_56_11 = e0)
% 111.71/16.49 | | |
% 111.71/16.49 | | | COMBINE_EQS: (14), (94) imply:
% 111.71/16.49 | | | (96) all_10_2 = e1
% 111.71/16.49 | | |
% 111.71/16.49 | | | SIMP: (96) implies:
% 111.71/16.49 | | | (97) all_10_2 = e1
% 111.71/16.49 | | |
% 111.71/16.49 | | | COMBINE_EQS: (16), (97) imply:
% 111.71/16.49 | | | (98) all_58_0 = e1
% 111.71/16.49 | | |
% 111.71/16.49 | | | REDUCE: (10), (95) imply:
% 111.71/16.49 | | | (99) ~ (all_52_11 = e0)
% 111.71/16.49 | | |
% 111.71/16.49 | | | REDUCE: (73), (97) imply:
% 111.71/16.49 | | | (100) ~ (all_52_3 = e1)
% 111.71/16.49 | | |
% 111.71/16.49 | | | REDUCE: (42), (97) imply:
% 111.71/16.49 | | | (101) ~ (e3 = e1)
% 111.71/16.49 | | |
% 111.71/16.49 | | | SIMP: (101) implies:
% 111.71/16.49 | | | (102) ~ (e3 = e1)
% 111.71/16.49 | | |
% 111.71/16.49 | | | REDUCE: (17), (97) imply:
% 111.71/16.49 | | | (103) op(all_10_1, e1) = e1
% 111.71/16.49 | | |
% 111.71/16.49 | | | REDUCE: (49), (97) imply:
% 111.71/16.49 | | | (104) op(e3, e1) = all_10_1
% 111.71/16.49 | | |
% 111.71/16.49 | | | BETA: splitting (33) gives:
% 111.71/16.49 | | |
% 111.71/16.49 | | | Case 1:
% 111.71/16.49 | | | |
% 111.71/16.49 | | | | (105) ~ (all_56_1 = e3)
% 111.71/16.49 | | | |
% 111.71/16.49 | | | | REDUCE: (60), (105) imply:
% 111.71/16.49 | | | | (106) ~ (all_52_8 = e3)
% 111.71/16.49 | | | |
% 111.71/16.49 | | | | BETA: splitting (41) gives:
% 111.71/16.49 | | | |
% 111.71/16.49 | | | | Case 1:
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | (107) ~ (all_56_4 = e2)
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | REDUCE: (65), (107) imply:
% 111.71/16.49 | | | | | (108) ~ (all_52_9 = e2)
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | GROUND_INST: instantiating (22) with all_52_8, all_10_1, e1, e3,
% 111.71/16.49 | | | | | simplifying with (30), (104) gives:
% 111.71/16.49 | | | | | (109) all_52_8 = all_10_1
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | COMBINE_EQS: (25), (109) imply:
% 111.71/16.49 | | | | | (110) all_58_4 = all_10_1
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | BETA: splitting (64) gives:
% 111.71/16.49 | | | | |
% 111.71/16.49 | | | | | Case 1:
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | (111) ~ (all_56_15 = e3)
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | REDUCE: (47), (111) imply:
% 111.71/16.49 | | | | | | (112) ~ (all_4_2 = e3)
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | BETA: splitting (26) gives:
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | Case 1:
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | | (113) all_54_15 = e3
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | | REF_CLOSE: (85), (112), (113) are inconsistent by sub-proof #312.
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | Case 2:
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | | (114) ~ (all_54_15 = e3)
% 111.71/16.49 | | | | | | | (115) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | | BETA: splitting (115) gives:
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | | Case 1:
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | (116) all_54_15 = e2
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | COMBINE_EQS: (85), (116) imply:
% 111.71/16.49 | | | | | | | | (117) all_4_2 = e2
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | SIMP: (117) implies:
% 111.71/16.49 | | | | | | | | (118) all_4_2 = e2
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12),
% 111.71/16.49 | | | | | | | | (13), (14), (15), (17), (18), (21), (22), (23), (24),
% 111.71/16.49 | | | | | | | | (26), (27), (28), (29), (31), (32), (34), (37), (38),
% 111.71/16.49 | | | | | | | | (39), (40), (42), (43), (45), (46), (47), (49), (52),
% 111.71/16.49 | | | | | | | | (54), (56), (58), (61), (62), (63), (69), (70), (75),
% 111.71/16.49 | | | | | | | | (78), (80), (82), (85), (86), (91), (102), (112),
% 111.71/16.49 | | | | | | | | (118) are inconsistent by sub-proof #27.
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | Case 2:
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | (119) all_54_15 = e1 | all_54_15 = e0
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | | REF_CLOSE: (4), (9), (85), (119) are inconsistent by sub-proof
% 111.71/16.49 | | | | | | | | #418.
% 111.71/16.49 | | | | | | | |
% 111.71/16.49 | | | | | | | End of split
% 111.71/16.49 | | | | | | |
% 111.71/16.49 | | | | | | End of split
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | Case 2:
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | (120) all_56_15 = e3
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | COMBINE_EQS: (47), (120) imply:
% 111.71/16.49 | | | | | | (121) all_4_2 = e3
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | SIMP: (121) implies:
% 111.71/16.49 | | | | | | (122) all_4_2 = e3
% 111.71/16.49 | | | | | |
% 111.71/16.49 | | | | | | REDUCE: (68), (122) imply:
% 111.71/16.50 | | | | | | (123) ~ (all_52_3 = e3)
% 111.71/16.50 | | | | | |
% 111.71/16.50 | | | | | | REDUCE: (48), (122) imply:
% 111.71/16.50 | | | | | | (124) ~ (all_52_11 = e3)
% 111.71/16.50 | | | | | |
% 111.71/16.50 | | | | | | REDUCE: (72), (122) imply:
% 111.71/16.50 | | | | | | (125) ~ (all_52_12 = e3)
% 111.71/16.50 | | | | | |
% 111.71/16.50 | | | | | | BETA: splitting (77) gives:
% 111.71/16.50 | | | | | |
% 111.71/16.50 | | | | | | Case 1:
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | | (126) all_58_0 = e3
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | | REF_CLOSE: (98), (102), (126) are inconsistent by sub-proof #319.
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | Case 2:
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | | (127) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | | BETA: splitting (64) gives:
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | (128) ~ (all_56_15 = e3)
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | REDUCE: (120), (128) imply:
% 111.71/16.50 | | | | | | | | (129) $false
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | CLOSE: (129) is inconsistent.
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | (130) ~ (all_56_9 = e0)
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | REDUCE: (37), (130) imply:
% 111.71/16.50 | | | | | | | | (131) ~ (all_52_3 = e0)
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | BETA: splitting (127) gives:
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | (132) all_58_1 = e3
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | COMBINE_EQS: (50), (132) imply:
% 111.71/16.50 | | | | | | | | | (133) all_52_4 = e3
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | COMBINE_EQS: (81), (133) imply:
% 111.71/16.50 | | | | | | | | | (134) all_56_0 = e3
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | BETA: splitting (83) gives:
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | (135) ~ (all_56_0 = e3)
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | REDUCE: (134), (135) imply:
% 111.71/16.50 | | | | | | | | | | (136) $false
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | CLOSE: (136) is inconsistent.
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | (137) ~ (all_56_14 = e2)
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | BETA: splitting (71) gives:
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | (138) all_54_12 = e3
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | REF_CLOSE: (89), (123), (138) are inconsistent by sub-proof
% 111.71/16.50 | | | | | | | | | | | #410.
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | (139) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | BETA: splitting (139) gives:
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | (140) all_54_12 = e2
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | COMBINE_EQS: (89), (140) imply:
% 111.71/16.50 | | | | | | | | | | | | (141) all_52_3 = e2
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | SIMP: (141) implies:
% 111.71/16.50 | | | | | | | | | | | | (142) all_52_3 = e2
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | REDUCE: (87), (142) imply:
% 111.71/16.50 | | | | | | | | | | | | (143) ~ (all_52_11 = e2)
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | SIMP: (143) implies:
% 111.71/16.50 | | | | | | | | | | | | (144) ~ (all_52_11 = e2)
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | BETA: splitting (88) gives:
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | (145) all_54_14 = e3
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | REF_CLOSE: (20), (124), (145) are inconsistent by sub-proof
% 111.71/16.50 | | | | | | | | | | | | | #93.
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | (146) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | BETA: splitting (146) gives:
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | (147) all_54_14 = e2
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | REF_CLOSE: (20), (144), (147) are inconsistent by sub-proof
% 111.71/16.50 | | | | | | | | | | | | | | #92.
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | (148) all_54_14 = e1 | all_54_14 = e0
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | (149) all_54_14 = e1
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | COMBINE_EQS: (20), (149) imply:
% 111.71/16.50 | | | | | | | | | | | | | | | (150) all_52_11 = e1
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | SIMP: (150) implies:
% 111.71/16.50 | | | | | | | | | | | | | | | (151) all_52_11 = e1
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | REDUCE: (51), (151) imply:
% 111.71/16.50 | | | | | | | | | | | | | | | (152) ~ (all_52_9 = e1)
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | Case 1:
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | (153) all_58_4 = e2
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (153) imply:
% 111.71/16.50 | | | | | | | | | | | | | | | | (154) all_10_1 = e2
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | REDUCE: (103), (154) imply:
% 111.71/16.50 | | | | | | | | | | | | | | | | (155) op(e2, e1) = e1
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (67), (152), (155) are inconsistent by
% 111.71/16.50 | | | | | | | | | | | | | | | | sub-proof #110.
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | (156) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (26), (35), (37), (47), (48), (52),
% 111.71/16.50 | | | | | | | | | | | | | | | | (54), (61), (64), (68), (71), (85), (87), (89),
% 111.71/16.50 | | | | | | | | | | | | | | | | (100), (108), (156) are inconsistent by sub-proof
% 111.71/16.50 | | | | | | | | | | | | | | | | #404.
% 111.71/16.50 | | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | (157) all_54_14 = e0
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | | REF_CLOSE: (20), (99), (157) are inconsistent by sub-proof
% 111.71/16.50 | | | | | | | | | | | | | | | #140.
% 111.71/16.50 | | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | (158) all_54_12 = e1 | all_54_12 = e0
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | | REF_CLOSE: (89), (100), (131), (158) are inconsistent by
% 111.71/16.50 | | | | | | | | | | | | sub-proof #185.
% 111.71/16.50 | | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | | |
% 111.71/16.50 | | | | | | | | | End of split
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | Case 2:
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | (159) all_58_4 = e3 | all_58_9 = e3
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | | REF_CLOSE: (25), (66), (106), (125), (159) are inconsistent by
% 111.71/16.50 | | | | | | | | | sub-proof #184.
% 111.71/16.50 | | | | | | | | |
% 111.71/16.50 | | | | | | | | End of split
% 111.71/16.50 | | | | | | | |
% 111.71/16.50 | | | | | | | End of split
% 111.71/16.50 | | | | | | |
% 111.71/16.50 | | | | | | End of split
% 111.71/16.50 | | | | | |
% 111.71/16.50 | | | | | End of split
% 111.71/16.50 | | | | |
% 111.71/16.50 | | | | Case 2:
% 111.71/16.50 | | | | |
% 111.71/16.50 | | | | | (160) all_56_4 = e2
% 111.71/16.50 | | | | |
% 111.71/16.50 | | | | | REF_CLOSE: (1), (7), (8), (12), (13), (14), (17), (22), (24), (27),
% 111.71/16.50 | | | | | (31), (34), (38), (39), (41), (42), (49), (62), (63), (78),
% 111.71/16.50 | | | | | (91), (160) are inconsistent by sub-proof #190.
% 111.71/16.50 | | | | |
% 111.71/16.50 | | | | End of split
% 111.71/16.50 | | | |
% 111.71/16.50 | | | Case 2:
% 111.71/16.50 | | | |
% 111.71/16.50 | | | | (161) ~ (all_56_12 = e1)
% 111.71/16.50 | | | |
% 111.71/16.50 | | | | REDUCE: (94), (161) imply:
% 111.71/16.50 | | | | (162) $false
% 111.71/16.50 | | | |
% 111.71/16.50 | | | | CLOSE: (162) is inconsistent.
% 111.71/16.50 | | | |
% 111.71/16.50 | | | End of split
% 111.71/16.50 | | |
% 111.71/16.50 | | End of split
% 111.71/16.50 | |
% 111.71/16.50 | Case 2:
% 111.71/16.50 | |
% 111.71/16.50 | | (163) all_56_12 = e2
% 111.71/16.50 | |
% 111.71/16.50 | | REF_CLOSE: (5), (14), (17), (22), (36), (49), (53), (55), (57), (59), (74),
% 111.71/16.50 | | (76), (79), (81), (84), (163) are inconsistent by sub-proof #195.
% 111.71/16.50 | |
% 111.71/16.50 | End of split
% 111.71/16.50 |
% 111.71/16.50 End of proof
% 111.71/16.50
% 111.71/16.50 Sub-proof #8 shows that the following formulas are inconsistent:
% 111.71/16.50 ----------------------------------------------------------------
% 111.71/16.50 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.50 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.50 (3) ~ (all_52_2 = all_10_2)
% 111.71/16.50 (4) all_20_2 = all_4_2
% 111.71/16.50 (5) ~ (all_52_6 = all_52_14)
% 111.71/16.50 (6) all_54_2 = all_52_8
% 111.71/16.50 (7) all_58_7 = all_52_6
% 111.71/16.50 (8) all_36_2 = all_6_2
% 111.71/16.50 (9) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 111.71/16.50 (10) ~ (all_52_8 = all_52_11)
% 111.71/16.50 (11) ~ (all_52_9 = all_8_2)
% 111.71/16.50 (12) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 111.71/16.50 (13) all_20_1 = all_4_1
% 111.71/16.50 (14) ~ (all_52_13 = all_52_14)
% 111.71/16.50 (15) ~ (all_4_2 = e0)
% 111.71/16.50 (16) op(e3, e2) = all_52_4
% 111.71/16.50 (17) all_56_14 = all_6_2
% 111.71/16.50 (18) all_56_3 = all_52_1
% 111.71/16.50 (19) all_38_1 = all_10_1
% 111.71/16.50 (20) all_54_0 = all_10_2
% 111.71/16.50 (21) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.71/16.50 (22) all_54_3 = all_52_12
% 111.71/16.50 (23) ~ (all_52_2 = all_52_6)
% 111.71/16.50 (24) op(e0, e2) = all_52_7
% 111.71/16.50 (25) ~ (all_52_7 = all_4_2)
% 111.71/16.50 (26) all_56_11 = all_52_11
% 111.71/16.50 (27) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 111.71/16.50 (28) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.71/16.50 (29) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.50 (30) ~ (all_52_12 = all_10_2)
% 111.71/16.50 (31) ~ (e3 = e1)
% 111.71/16.50 (32) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 111.71/16.50 (33) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.50 (34) all_56_12 = all_10_2
% 111.71/16.50 (35) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 111.71/16.51 (36) all_58_0 = all_10_2
% 111.71/16.51 (37) op(all_6_1, all_6_2) = all_6_0
% 111.71/16.51 (38) all_54_11 = all_52_14
% 111.71/16.51 (39) all_54_13 = all_52_7
% 111.71/16.51 (40) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 111.71/16.51 (41) all_36_1 = all_6_1
% 111.71/16.51 (42) ~ (all_52_14 = all_6_2)
% 111.71/16.51 (43) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 111.71/16.51 (44) all_56_10 = all_52_7
% 111.71/16.51 (45) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.71/16.51 (46) all_54_14 = all_52_11
% 111.71/16.51 (47) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.51 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.51 (49) all_54_8 = all_52_2
% 111.71/16.51 (50) ~ (all_52_2 = all_6_2)
% 111.71/16.51 (51) all_32_2 = all_10_2
% 111.71/16.51 (52) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 111.71/16.51 (53) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 111.71/16.51 (54) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 111.71/16.51 (55) all_54_10 = all_6_2
% 111.71/16.51 (56) ~ (e2 = e1)
% 111.71/16.51 (57) all_36_0 = all_6_0
% 111.71/16.51 (58) op(e3, e0) = all_52_12
% 111.71/16.51 (59) all_38_0 = all_10_0
% 111.71/16.51 (60) ~ (all_52_8 = all_6_2)
% 111.71/16.51 (61) all_58_4 = all_52_8
% 111.71/16.51 (62) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.71/16.51 (63) ~ (all_52_4 = all_52_7)
% 111.71/16.51 (64) all_56_2 = all_52_12
% 111.71/16.51 (65) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.71/16.51 (66) all_58_3 = all_8_2
% 111.71/16.51 (67) all_54_6 = all_52_9
% 111.71/16.51 (68) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.51 (69) ~ (all_10_0 = e2)
% 111.71/16.51 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 111.71/16.51 (71) all_58_11 = all_52_14
% 111.71/16.51 (72) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 111.71/16.51 (73) all_54_9 = all_52_6
% 111.71/16.51 (74) op(e3, e1) = all_52_8
% 111.71/16.51 (75) ~ (all_52_2 = all_52_3)
% 111.71/16.51 (76) all_54_7 = all_52_13
% 111.71/16.51 (77) op(all_10_1, all_10_2) = all_10_0
% 111.71/16.51 (78) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.71/16.51 (79) ~ (all_52_11 = all_6_2)
% 111.71/16.51 (80) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 111.71/16.51 (81) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 111.71/16.51 (82) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.71/16.51 (83) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.51 (84) ~ (all_52_7 = all_8_2)
% 111.71/16.51 (85) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.71/16.51 (86) ~ (all_52_4 = all_8_2)
% 111.71/16.51 (87) op(e1, e0) = all_52_14
% 111.71/16.51 (88) all_58_5 = all_52_9
% 111.71/16.51 (89) all_40_0 = all_6_0
% 111.71/16.51 (90) all_56_9 = all_52_3
% 111.71/16.51 (91) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 111.71/16.51 (92) op(e1, all_6_2) = all_6_1
% 111.71/16.51 (93) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.51 (94) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 111.71/16.51 (95) all_32_0 = all_10_0
% 111.71/16.51 (96) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 111.71/16.51 (97) op(all_4_1, all_4_2) = e3
% 111.71/16.51 (98) all_58_15 = all_4_2
% 111.71/16.51 (99) all_58_2 = all_52_1
% 111.71/16.51 (100) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.71/16.51 (101) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.51 (102) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 111.71/16.51 (103) op(e0, e3) = all_52_3
% 111.71/16.51 (104) ~ (all_10_2 = e3)
% 111.71/16.51 (105) ~ (all_52_12 = all_52_13)
% 111.71/16.51 (106) all_58_13 = all_52_7
% 111.71/16.51 (107) all_32_1 = all_10_1
% 111.71/16.51 (108) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 111.71/16.51 (109) all_40_1 = all_6_1
% 111.71/16.51 (110) ~ (all_28_0 = e2)
% 111.71/16.51 (111) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 111.71/16.51 (112) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.71/16.51 (113) ~ (all_52_14 = all_4_2)
% 111.71/16.51 (114) all_58_6 = all_52_2
% 111.71/16.51 (115) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.71/16.51 (116) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 111.71/16.51 (117) ~ (all_52_1 = all_10_2)
% 111.71/16.51 (118) all_54_5 = all_8_2
% 111.71/16.51 (119) all_56_15 = all_4_2
% 111.71/16.51 (120) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.51 (121) all_58_10 = all_52_13
% 111.71/16.51 (122) ~ (all_52_11 = all_4_2)
% 111.71/16.51 (123) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 111.71/16.51 (124) op(e3, all_10_2) = all_10_1
% 111.71/16.51 (125) ~ (all_52_6 = all_8_2)
% 111.71/16.51 (126) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.71/16.51 (127) all_28_0 = all_6_0
% 111.71/16.51 (128) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 111.71/16.51 (129) all_38_2 = all_10_2
% 111.71/16.51 (130) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 111.71/16.51 (131) all_58_1 = all_52_4
% 111.71/16.51 (132) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 111.71/16.51 (133) ~ (all_52_9 = all_52_11)
% 111.71/16.51 (134) all_58_14 = all_52_11
% 111.71/16.51 (135) all_54_1 = all_52_4
% 111.71/16.51 (136) all_56_13 = all_8_2
% 111.71/16.51 (137) op(e0, e1) = all_52_11
% 111.71/16.51 (138) ~ (all_52_1 = all_8_2)
% 111.71/16.51 (139) ~ (all_8_2 = e2)
% 111.71/16.52 (140) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 111.71/16.52 (141) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 111.71/16.52 (142) ~ (all_52_7 = all_52_11)
% 111.71/16.52 (143) op(e1, e2) = all_52_6
% 111.71/16.52 (144) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.52 (145) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.71/16.52 (146) all_56_7 = all_52_6
% 111.71/16.52 (147) ~ (all_52_9 = all_6_2)
% 111.71/16.52 (148) all_56_1 = all_52_8
% 111.71/16.52 (149) op(e0, all_4_2) = all_4_1
% 111.71/16.52 (150) all_58_8 = all_6_2
% 111.71/16.52 (151) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.52 (152) ~ (all_10_0 = e1)
% 111.71/16.52 (153) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.71/16.52 (154) all_40_2 = all_6_2
% 111.71/16.52 (155) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.71/16.52 (156) all_56_4 = all_52_9
% 111.71/16.52 (157) all_58_9 = all_52_12
% 111.71/16.52 (158) all_56_5 = all_52_13
% 111.71/16.52 (159) op(e2, e1) = all_52_9
% 111.71/16.52 (160) ~ (all_52_3 = all_4_2)
% 111.71/16.52 (161) ~ (all_52_6 = all_6_2)
% 111.71/16.52 (162) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.52 (163) all_56_6 = all_52_2
% 111.71/16.52 (164) ~ (all_52_13 = all_4_2)
% 111.71/16.52 (165) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 111.71/16.52 (166) all_58_12 = all_52_3
% 111.71/16.52 (167) ~ (all_52_2 = all_52_14)
% 111.71/16.52 (168) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.52 (169) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.52 (170) op(e2, e0) = all_52_13
% 111.71/16.52 (171) ~ (all_52_12 = all_4_2)
% 111.71/16.52 (172) ~ (all_52_3 = all_10_2)
% 111.71/16.52 (173) op(e1, e3) = all_52_2
% 111.71/16.52 (174) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 111.71/16.52 (175) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.71/16.52 (176) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.52 (177) ~ (all_52_8 = all_52_12)
% 111.71/16.52 (178) all_56_8 = all_52_14
% 111.71/16.52 (179) ~ (all_52_4 = all_10_2)
% 111.71/16.52 (180) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.71/16.52 (181) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.52 (182) all_56_0 = all_52_4
% 111.71/16.52 (183) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 111.71/16.52 (184) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.52 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.71/16.52 (185) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.71/16.52 (186) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.71/16.52 (187) all_54_15 = all_4_2
% 111.71/16.52 (188) ~ (all_6_2 = e1)
% 111.71/16.52 (189) ~ (all_6_1 = e2)
% 111.71/16.52 (190) ~ (all_52_6 = all_52_7)
% 111.71/16.52 (191) ~ (all_52_3 = all_52_11)
% 111.71/16.52 (192) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.52 (193) all_54_12 = all_52_3
% 111.71/16.52 (194) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 111.71/16.52
% 111.71/16.52 Begin of proof
% 111.71/16.52 |
% 111.71/16.52 | REDUCE: (110), (127) imply:
% 111.71/16.52 | (195) ~ (all_6_0 = e2)
% 111.71/16.52 |
% 111.71/16.52 | BETA: splitting (9) gives:
% 111.71/16.52 |
% 111.71/16.52 | Case 1:
% 111.71/16.52 | |
% 111.71/16.52 | | (196) ~ (all_32_1 = e1)
% 111.71/16.52 | |
% 111.71/16.52 | | REDUCE: (107), (196) imply:
% 111.71/16.52 | | (197) ~ (all_10_1 = e1)
% 111.71/16.52 | |
% 111.71/16.52 | | BETA: splitting (130) gives:
% 111.71/16.52 | |
% 111.71/16.52 | | Case 1:
% 111.71/16.52 | | |
% 111.71/16.52 | | | (198) ~ (all_36_1 = e3)
% 111.71/16.52 | | |
% 111.71/16.52 | | | REDUCE: (41), (198) imply:
% 111.71/16.52 | | | (199) ~ (all_6_1 = e3)
% 111.71/16.52 | | |
% 111.71/16.52 | | | REF_CLOSE: (1), (2), (3), (5), (7), (12), (14), (15), (16), (17), (18),
% 111.71/16.52 | | | (19), (20), (21), (22), (23), (24), (26), (28), (29), (30),
% 111.71/16.52 | | | (31), (32), (34), (36), (37), (38), (39), (40), (42), (43),
% 111.71/16.52 | | | (45), (47), (48), (49), (50), (53), (54), (55), (58), (59),
% 111.71/16.52 | | | (60), (61), (62), (63), (64), (65), (66), (67), (69), (70),
% 111.71/16.52 | | | (71), (73), (74), (77), (78), (80), (83), (85), (87), (88),
% 111.71/16.52 | | | (89), (90), (91), (92), (93), (94), (96), (98), (99), (100),
% 111.71/16.52 | | | (101), (102), (104), (106), (109), (111), (113), (114), (117),
% 111.71/16.52 | | | (119), (121), (122), (124), (126), (128), (129), (131), (134),
% 111.71/16.52 | | | (135), (136), (139), (140), (143), (144), (145), (146), (147),
% 111.71/16.52 | | | (150), (151), (152), (153), (154), (155), (156), (157), (158),
% 111.71/16.52 | | | (159), (160), (161), (163), (165), (166), (167), (168), (169),
% 111.71/16.52 | | | (170), (171), (172), (173), (174), (176), (178), (179), (180),
% 111.71/16.52 | | | (181), (182), (183), (184), (185), (186), (187), (188), (189),
% 111.71/16.52 | | | (190), (191), (193), (195), (197), (199) are inconsistent by
% 111.71/16.52 | | | sub-proof #363.
% 111.71/16.52 | | |
% 111.71/16.52 | | Case 2:
% 111.71/16.52 | | |
% 111.71/16.52 | | | (200) all_36_1 = e3
% 111.71/16.52 | | | (201) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 111.71/16.52 | | |
% 111.71/16.52 | | | COMBINE_EQS: (41), (200) imply:
% 111.71/16.52 | | | (202) all_6_1 = e3
% 111.71/16.52 | | |
% 111.71/16.52 | | | SIMP: (202) implies:
% 111.71/16.52 | | | (203) all_6_1 = e3
% 111.71/16.52 | | |
% 111.71/16.52 | | | REDUCE: (37), (203) imply:
% 111.71/16.52 | | | (204) op(e3, all_6_2) = all_6_0
% 111.71/16.52 | | |
% 111.71/16.52 | | | REDUCE: (92), (203) imply:
% 111.71/16.52 | | | (205) op(e1, all_6_2) = e3
% 111.71/16.52 | | |
% 111.71/16.52 | | | BETA: splitting (54) gives:
% 111.71/16.52 | | |
% 111.71/16.52 | | | Case 1:
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | (206) ~ (all_38_1 = e2)
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | REDUCE: (19), (206) imply:
% 111.71/16.52 | | | | (207) ~ (all_10_1 = e2)
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | BETA: splitting (91) gives:
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | Case 1:
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | | (208) ~ (all_56_15 = e1)
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (11), (15), (16), (17), (18),
% 111.71/16.52 | | | | | (20), (22), (24), (26), (27), (29), (30), (32), (33), (34),
% 111.71/16.52 | | | | | (40), (46), (47), (48), (55), (58), (61), (62), (63), (64),
% 111.71/16.52 | | | | | (66), (69), (74), (77), (78), (80), (81), (82), (83), (88),
% 111.71/16.52 | | | | | (90), (94), (98), (99), (100), (104), (106), (112), (117),
% 111.71/16.52 | | | | | (118), (119), (121), (122), (124), (131), (132), (133),
% 111.71/16.52 | | | | | (134), (135), (136), (137), (138), (139), (145), (146),
% 111.71/16.52 | | | | | (148), (150), (151), (152), (156), (158), (161), (162),
% 111.71/16.52 | | | | | (164), (166), (171), (177), (179), (180), (181), (182),
% 111.71/16.52 | | | | | (183), (184), (186), (187), (188), (192), (197), (207),
% 111.71/16.52 | | | | | (208) are inconsistent by sub-proof #46.
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | Case 2:
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | | (209) all_56_15 = e1
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | | REF_CLOSE: (4), (10), (13), (26), (46), (48), (74), (91), (97), (116),
% 111.71/16.52 | | | | | (119), (122), (137), (149), (192), (209) are inconsistent
% 111.71/16.52 | | | | | by sub-proof #10.
% 111.71/16.52 | | | | |
% 111.71/16.52 | | | | End of split
% 111.71/16.52 | | | |
% 111.71/16.52 | | | Case 2:
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | (210) all_38_1 = e2
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | COMBINE_EQS: (19), (210) imply:
% 111.71/16.52 | | | | (211) all_10_1 = e2
% 111.71/16.52 | | | |
% 111.71/16.52 | | | | REDUCE: (77), (211) imply:
% 111.71/16.52 | | | | (212) op(e2, all_10_2) = all_10_0
% 111.71/16.53 | | | |
% 111.71/16.53 | | | | REDUCE: (124), (211) imply:
% 111.71/16.53 | | | | (213) op(e3, all_10_2) = e2
% 111.71/16.53 | | | |
% 111.71/16.53 | | | | BETA: splitting (111) gives:
% 111.71/16.53 | | | |
% 111.71/16.53 | | | | Case 1:
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | (214) ~ (all_56_14 = e2)
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | REDUCE: (17), (214) imply:
% 111.71/16.53 | | | | | (215) ~ (all_6_2 = e2)
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | BETA: splitting (91) gives:
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | Case 1:
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | (216) ~ (all_56_15 = e1)
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | REDUCE: (119), (216) imply:
% 111.71/16.53 | | | | | | (217) ~ (all_4_2 = e1)
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | BETA: splitting (112) gives:
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | Case 1:
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | (218) ~ (all_56_12 = e2)
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | REDUCE: (34), (218) imply:
% 111.71/16.53 | | | | | | | (219) ~ (all_10_2 = e2)
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | BETA: splitting (153) gives:
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | Case 1:
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | (220) ~ (all_56_15 = e3)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REF_CLOSE: (1), (2), (7), (15), (17), (20), (26), (30), (34),
% 111.71/16.53 | | | | | | | | (35), (36), (44), (45), (47), (48), (55), (58), (61),
% 111.71/16.53 | | | | | | | | (62), (64), (65), (68), (71), (78), (88), (90), (93),
% 111.71/16.53 | | | | | | | | (98), (100), (101), (104), (106), (113), (114),
% 111.71/16.53 | | | | | | | | (119), (121), (122), (128), (131), (134), (144),
% 111.71/16.53 | | | | | | | | (146), (150), (151), (152), (156), (157), (163),
% 111.71/16.53 | | | | | | | | (166), (170), (171), (174), (176), (178), (180),
% 111.71/16.53 | | | | | | | | (182), (184), (187), (188), (212), (213), (215),
% 111.71/16.53 | | | | | | | | (217), (219), (220) are inconsistent by sub-proof
% 111.71/16.53 | | | | | | | | #36.
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | Case 2:
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | (221) all_56_15 = e3
% 111.71/16.53 | | | | | | | | (222) ~ (all_56_9 = e0)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | COMBINE_EQS: (119), (221) imply:
% 111.71/16.53 | | | | | | | | (223) all_4_2 = e3
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | SIMP: (223) implies:
% 111.71/16.53 | | | | | | | | (224) all_4_2 = e3
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (90), (222) imply:
% 111.71/16.53 | | | | | | | | (225) ~ (all_52_3 = e0)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (160), (224) imply:
% 111.71/16.53 | | | | | | | | (226) ~ (all_52_3 = e3)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (149), (224) imply:
% 111.71/16.53 | | | | | | | | (227) op(e0, e3) = all_4_1
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | GROUND_INST: instantiating (48) with all_52_3, all_4_1, e3, e0,
% 111.71/16.53 | | | | | | | | simplifying with (103), (227) gives:
% 111.71/16.53 | | | | | | | | (228) all_52_3 = all_4_1
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | COMBINE_EQS: (193), (228) imply:
% 111.71/16.53 | | | | | | | | (229) all_54_12 = all_4_1
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (75), (228) imply:
% 111.71/16.53 | | | | | | | | (230) ~ (all_52_2 = all_4_1)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (172), (228) imply:
% 111.71/16.53 | | | | | | | | (231) ~ (all_10_2 = all_4_1)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | SIMP: (231) implies:
% 111.71/16.53 | | | | | | | | (232) ~ (all_10_2 = all_4_1)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (226), (228) imply:
% 111.71/16.53 | | | | | | | | (233) ~ (all_4_1 = e3)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | REDUCE: (225), (228) imply:
% 111.71/16.53 | | | | | | | | (234) ~ (all_4_1 = e0)
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | BETA: splitting (83) gives:
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | | Case 1:
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | (235) ~ (all_56_5 = e2)
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | REDUCE: (158), (235) imply:
% 111.71/16.53 | | | | | | | | | (236) ~ (all_52_13 = e2)
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | REF_CLOSE: (1), (2), (7), (15), (17), (18), (20), (26), (30),
% 111.71/16.53 | | | | | | | | | (32), (34), (35), (36), (44), (45), (47), (48),
% 111.71/16.53 | | | | | | | | | (52), (55), (56), (58), (61), (62), (64), (65),
% 111.71/16.53 | | | | | | | | | (66), (68), (71), (78), (88), (90), (93), (98),
% 111.71/16.53 | | | | | | | | | (99), (100), (101), (104), (106), (113), (114),
% 111.71/16.53 | | | | | | | | | (117), (119), (121), (122), (128), (131), (134),
% 111.71/16.53 | | | | | | | | | (139), (144), (146), (150), (151), (152), (156),
% 111.71/16.53 | | | | | | | | | (157), (163), (166), (170), (171), (174), (176),
% 111.71/16.53 | | | | | | | | | (178), (180), (181), (182), (184), (187), (188),
% 111.71/16.53 | | | | | | | | | (212), (213), (215), (217), (219), (236) are
% 111.71/16.53 | | | | | | | | | inconsistent by sub-proof #35.
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | Case 2:
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | (237) all_56_5 = e2
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | COMBINE_EQS: (158), (237) imply:
% 111.71/16.53 | | | | | | | | | (238) all_52_13 = e2
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | BETA: splitting (175) gives:
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | | Case 1:
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | (239) ~ (all_56_5 = e2)
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | REDUCE: (237), (239) imply:
% 111.71/16.53 | | | | | | | | | | (240) $false
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | CLOSE: (240) is inconsistent.
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | Case 2:
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | (241) ~ (all_56_12 = e0)
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | REDUCE: (34), (241) imply:
% 111.71/16.53 | | | | | | | | | | (242) ~ (all_10_2 = e0)
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | BETA: splitting (47) gives:
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | Case 1:
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | (243) all_54_10 = e3
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | COMBINE_EQS: (55), (243) imply:
% 111.71/16.53 | | | | | | | | | | | (244) all_6_2 = e3
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | REDUCE: (50), (244) imply:
% 111.71/16.53 | | | | | | | | | | | (245) ~ (all_52_2 = e3)
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | REDUCE: (205), (244) imply:
% 111.71/16.53 | | | | | | | | | | | (246) op(e1, e3) = e3
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | REF_CLOSE: (3), (20), (48), (49), (85), (104), (114), (123),
% 111.71/16.53 | | | | | | | | | | | (151), (169), (173), (219), (229), (230), (232),
% 111.71/16.53 | | | | | | | | | | | (233), (234), (242), (245), (246) are inconsistent
% 111.71/16.53 | | | | | | | | | | | by sub-proof #9.
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | Case 2:
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | (247) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | | REF_CLOSE: (17), (55), (83), (188), (215), (237), (247) are
% 111.71/16.53 | | | | | | | | | | | inconsistent by sub-proof #434.
% 111.71/16.53 | | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | | End of split
% 111.71/16.53 | | | | | | | | | |
% 111.71/16.53 | | | | | | | | | End of split
% 111.71/16.53 | | | | | | | | |
% 111.71/16.53 | | | | | | | | End of split
% 111.71/16.53 | | | | | | | |
% 111.71/16.53 | | | | | | | End of split
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | Case 2:
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | (248) all_56_12 = e2
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | | REF_CLOSE: (16), (34), (48), (179), (213), (248) are inconsistent
% 111.71/16.53 | | | | | | | by sub-proof #300.
% 111.71/16.53 | | | | | | |
% 111.71/16.53 | | | | | | End of split
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | Case 2:
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | (249) all_56_15 = e1
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | COMBINE_EQS: (119), (249) imply:
% 111.71/16.53 | | | | | | (250) all_4_2 = e1
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | SIMP: (250) implies:
% 111.71/16.53 | | | | | | (251) all_4_2 = e1
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | | REF_CLOSE: (7), (14), (17), (18), (22), (29), (47), (48), (50),
% 111.71/16.53 | | | | | | (55), (58), (64), (65), (66), (68), (71), (76), (83),
% 111.71/16.53 | | | | | | (87), (88), (99), (105), (113), (114), (120), (121),
% 111.71/16.53 | | | | | | (126), (139), (144), (150), (156), (158), (163), (164),
% 111.71/16.53 | | | | | | (168), (171), (173), (181), (188), (194), (195), (204),
% 111.71/16.53 | | | | | | (205), (215), (249), (251) are inconsistent by sub-proof
% 111.71/16.53 | | | | | | #343.
% 111.71/16.53 | | | | | |
% 111.71/16.53 | | | | | End of split
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | Case 2:
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | (252) all_56_14 = e2
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | | REF_CLOSE: (8), (15), (16), (17), (18), (21), (25), (33), (36), (39),
% 111.71/16.53 | | | | | (48), (52), (57), (61), (62), (63), (64), (66), (72), (84),
% 111.71/16.53 | | | | | (86), (88), (99), (104), (115), (118), (119), (121), (125),
% 111.71/16.53 | | | | | (131), (132), (135), (136), (139), (141), (143), (145),
% 111.71/16.53 | | | | | (147), (148), (157), (158), (176), (181), (182), (185),
% 111.71/16.53 | | | | | (187), (190), (195), (201), (204), (205), (252) are
% 111.71/16.53 | | | | | inconsistent by sub-proof #306.
% 111.71/16.53 | | | | |
% 111.71/16.53 | | | | End of split
% 111.71/16.53 | | | |
% 111.71/16.53 | | | End of split
% 111.71/16.53 | | |
% 111.71/16.53 | | End of split
% 111.71/16.53 | |
% 111.71/16.53 | Case 2:
% 111.71/16.53 | |
% 111.71/16.53 | | (253) all_32_1 = e1
% 111.71/16.53 | | (254) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 111.71/16.53 | |
% 111.71/16.53 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (12), (15), (16), (17), (18), (20),
% 111.71/16.53 | | (21), (23), (24), (25), (26), (28), (31), (33), (34), (35), (36),
% 111.71/16.53 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 111.71/16.53 | | (49), (50), (51), (52), (53), (55), (56), (57), (58), (60), (61),
% 111.71/16.53 | | (62), (63), (64), (65), (66), (69), (70), (71), (72), (73), (74),
% 111.71/16.53 | | (77), (79), (84), (85), (86), (87), (88), (89), (90), (92), (93),
% 111.71/16.53 | | (94), (95), (96), (98), (99), (102), (104), (106), (107), (108),
% 111.71/16.53 | | (109), (111), (112), (114), (115), (118), (119), (121), (124),
% 111.71/16.53 | | (125), (128), (130), (131), (132), (134), (135), (136), (139),
% 111.71/16.53 | | (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 111.71/16.53 | | (150), (151), (154), (155), (156), (157), (158), (161), (163),
% 111.71/16.53 | | (166), (167), (168), (172), (174), (175), (176), (178), (179),
% 111.71/16.53 | | (180), (181), (182), (183), (184), (185), (187), (188), (189),
% 111.71/16.53 | | (190), (195), (253), (254) are inconsistent by sub-proof #288.
% 111.71/16.53 | |
% 111.71/16.53 | End of split
% 111.71/16.53 |
% 111.71/16.53 End of proof
% 111.71/16.53
% 111.71/16.53 Sub-proof #9 shows that the following formulas are inconsistent:
% 111.71/16.53 ----------------------------------------------------------------
% 111.71/16.53 (1) ~ (all_52_2 = all_10_2)
% 111.71/16.53 (2) all_54_0 = all_10_2
% 111.71/16.54 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.54 (4) all_54_8 = all_52_2
% 111.71/16.54 (5) ~ (all_10_2 = all_4_1)
% 111.71/16.54 (6) ~ (all_10_2 = e2)
% 111.71/16.54 (7) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.71/16.54 (8) ~ (all_10_2 = e3)
% 111.71/16.54 (9) ~ (all_4_1 = e0)
% 111.71/16.54 (10) ~ (all_52_2 = e3)
% 111.71/16.54 (11) all_58_6 = all_52_2
% 111.71/16.54 (12) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 111.71/16.54 (13) ~ (all_10_2 = e0)
% 111.71/16.54 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.54 (15) ~ (all_52_2 = all_4_1)
% 111.71/16.54 (16) all_54_12 = all_4_1
% 111.71/16.54 (17) op(e1, e3) = e3
% 111.71/16.54 (18) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.54 (19) op(e1, e3) = all_52_2
% 111.71/16.54 (20) ~ (all_4_1 = e3)
% 111.71/16.54
% 111.71/16.54 Begin of proof
% 111.71/16.54 |
% 111.71/16.54 | BETA: splitting (14) gives:
% 111.71/16.54 |
% 111.71/16.54 | Case 1:
% 111.71/16.54 | |
% 111.71/16.54 | | (21) all_54_0 = e3
% 111.71/16.54 | |
% 111.71/16.54 | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #451.
% 111.71/16.54 | |
% 111.71/16.54 | Case 2:
% 111.71/16.54 | |
% 111.71/16.54 | | (22) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.54 | |
% 111.71/16.54 | | BETA: splitting (22) gives:
% 111.71/16.54 | |
% 111.71/16.54 | | Case 1:
% 111.71/16.54 | | |
% 111.71/16.54 | | | (23) all_54_0 = e2
% 111.71/16.54 | | |
% 111.71/16.54 | | | REF_CLOSE: (2), (6), (23) are inconsistent by sub-proof #450.
% 111.71/16.54 | | |
% 111.71/16.54 | | Case 2:
% 111.71/16.54 | | |
% 111.71/16.54 | | | (24) all_54_0 = e1 | all_54_0 = e0
% 111.71/16.54 | | |
% 111.71/16.54 | | | BETA: splitting (24) gives:
% 111.71/16.54 | | |
% 111.71/16.54 | | | Case 1:
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | (25) all_54_0 = e1
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | COMBINE_EQS: (2), (25) imply:
% 111.71/16.54 | | | | (26) all_10_2 = e1
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | SIMP: (26) implies:
% 111.71/16.54 | | | | (27) all_10_2 = e1
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | REDUCE: (1), (27) imply:
% 111.71/16.54 | | | | (28) ~ (all_52_2 = e1)
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | REDUCE: (5), (27) imply:
% 111.71/16.54 | | | | (29) ~ (all_4_1 = e1)
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | SIMP: (29) implies:
% 111.71/16.54 | | | | (30) ~ (all_4_1 = e1)
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | BETA: splitting (18) gives:
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | Case 1:
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | | (31) all_54_12 = e3
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | | REF_CLOSE: (16), (20), (31) are inconsistent by sub-proof #239.
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | Case 2:
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | | (32) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | | BETA: splitting (32) gives:
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | | Case 1:
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | (33) all_54_12 = e2
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | COMBINE_EQS: (16), (33) imply:
% 111.71/16.54 | | | | | | (34) all_4_1 = e2
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | REDUCE: (15), (34) imply:
% 111.71/16.54 | | | | | | (35) ~ (all_52_2 = e2)
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | BETA: splitting (7) gives:
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | Case 1:
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | | (36) all_54_8 = e3
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | | REF_CLOSE: (4), (10), (36) are inconsistent by sub-proof #399.
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | Case 2:
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | | (37) ~ (all_54_8 = e3)
% 111.71/16.54 | | | | | | | (38) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | | BETA: splitting (38) gives:
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | | Case 1:
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | | (39) all_54_8 = e2
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | | REF_CLOSE: (4), (35), (39) are inconsistent by sub-proof #382.
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | Case 2:
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | | (40) all_54_8 = e1 | all_54_8 = e0
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | | BETA: splitting (12) gives:
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | | Case 1:
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | (41) all_58_6 = e0
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | COMBINE_EQS: (11), (41) imply:
% 111.71/16.54 | | | | | | | | | (42) all_52_2 = e0
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | REDUCE: (10), (42) imply:
% 111.71/16.54 | | | | | | | | | (43) ~ (e3 = e0)
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | SIMP: (43) implies:
% 111.71/16.54 | | | | | | | | | (44) ~ (e3 = e0)
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | REDUCE: (19), (42) imply:
% 111.71/16.54 | | | | | | | | | (45) op(e1, e3) = e0
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | GROUND_INST: instantiating (3) with e0, e3, e3, e1, simplifying
% 111.71/16.54 | | | | | | | | | with (17), (45) gives:
% 111.71/16.54 | | | | | | | | | (46) e3 = e0
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | REDUCE: (44), (46) imply:
% 111.71/16.54 | | | | | | | | | (47) $false
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | CLOSE: (47) is inconsistent.
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | Case 2:
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | (48) ~ (all_58_6 = e0)
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | REDUCE: (11), (48) imply:
% 111.71/16.54 | | | | | | | | | (49) ~ (all_52_2 = e0)
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | | REF_CLOSE: (4), (28), (40), (49) are inconsistent by sub-proof
% 111.71/16.54 | | | | | | | | | #396.
% 111.71/16.54 | | | | | | | | |
% 111.71/16.54 | | | | | | | | End of split
% 111.71/16.54 | | | | | | | |
% 111.71/16.54 | | | | | | | End of split
% 111.71/16.54 | | | | | | |
% 111.71/16.54 | | | | | | End of split
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | Case 2:
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | (50) all_54_12 = e1 | all_54_12 = e0
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | | REF_CLOSE: (9), (16), (30), (50) are inconsistent by sub-proof #315.
% 111.71/16.54 | | | | | |
% 111.71/16.54 | | | | | End of split
% 111.71/16.54 | | | | |
% 111.71/16.54 | | | | End of split
% 111.71/16.54 | | | |
% 111.71/16.54 | | | Case 2:
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | (51) all_54_0 = e0
% 111.71/16.54 | | | |
% 111.71/16.54 | | | | REF_CLOSE: (2), (13), (51) are inconsistent by sub-proof #424.
% 111.71/16.54 | | | |
% 111.71/16.54 | | | End of split
% 111.71/16.54 | | |
% 111.71/16.54 | | End of split
% 111.71/16.54 | |
% 111.71/16.54 | End of split
% 111.71/16.54 |
% 111.71/16.54 End of proof
% 111.71/16.54
% 111.71/16.54 Sub-proof #10 shows that the following formulas are inconsistent:
% 111.71/16.54 ----------------------------------------------------------------
% 111.71/16.54 (1) all_20_2 = all_4_2
% 111.71/16.54 (2) ~ (all_52_8 = all_52_11)
% 111.71/16.54 (3) all_20_1 = all_4_1
% 111.71/16.54 (4) all_56_11 = all_52_11
% 111.71/16.54 (5) all_54_14 = all_52_11
% 111.71/16.54 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.54 (7) op(e3, e1) = all_52_8
% 111.71/16.54 (8) all_56_15 = e1
% 111.71/16.54 (9) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 111.71/16.54 (10) op(all_4_1, all_4_2) = e3
% 111.71/16.54 (11) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 111.71/16.54 (12) all_56_15 = all_4_2
% 111.71/16.54 (13) ~ (all_52_11 = all_4_2)
% 111.71/16.54 (14) op(e0, e1) = all_52_11
% 111.71/16.54 (15) op(e0, all_4_2) = all_4_1
% 111.71/16.54 (16) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.54
% 111.71/16.54 Begin of proof
% 111.71/16.54 |
% 111.71/16.54 | COMBINE_EQS: (8), (12) imply:
% 111.71/16.54 | (17) all_4_2 = e1
% 111.71/16.54 |
% 111.71/16.54 | SIMP: (17) implies:
% 111.71/16.54 | (18) all_4_2 = e1
% 111.71/16.54 |
% 111.71/16.54 | COMBINE_EQS: (1), (18) imply:
% 111.71/16.54 | (19) all_20_2 = e1
% 111.71/16.54 |
% 111.71/16.54 | REDUCE: (13), (18) imply:
% 111.71/16.54 | (20) ~ (all_52_11 = e1)
% 111.71/16.54 |
% 111.71/16.54 | REDUCE: (10), (18) imply:
% 111.71/16.54 | (21) op(all_4_1, e1) = e3
% 111.71/16.54 |
% 111.71/16.54 | REDUCE: (15), (18) imply:
% 111.71/16.55 | (22) op(e0, e1) = all_4_1
% 111.71/16.55 |
% 111.71/16.55 | BETA: splitting (9) gives:
% 111.71/16.55 |
% 111.71/16.55 | Case 1:
% 111.71/16.55 | |
% 111.71/16.55 | | (23) ~ (all_56_15 = e1)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (8), (23) imply:
% 111.71/16.55 | | (24) $false
% 111.71/16.55 | |
% 111.71/16.55 | | CLOSE: (24) is inconsistent.
% 111.71/16.55 | |
% 111.71/16.55 | Case 2:
% 111.71/16.55 | |
% 111.71/16.55 | | (25) ~ (all_56_11 = e0)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (4), (25) imply:
% 111.71/16.55 | | (26) ~ (all_52_11 = e0)
% 111.71/16.55 | |
% 111.71/16.55 | | REF_CLOSE: (2), (3), (5), (6), (7), (11), (14), (16), (19), (20), (21),
% 111.71/16.55 | | (22), (26) are inconsistent by sub-proof #11.
% 111.71/16.55 | |
% 111.71/16.55 | End of split
% 111.71/16.55 |
% 111.71/16.55 End of proof
% 111.71/16.55
% 111.71/16.55 Sub-proof #11 shows that the following formulas are inconsistent:
% 111.71/16.55 ----------------------------------------------------------------
% 111.71/16.55 (1) ~ (all_52_8 = all_52_11)
% 111.71/16.55 (2) all_20_1 = all_4_1
% 111.71/16.55 (3) all_54_14 = all_52_11
% 111.71/16.55 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.55 (5) op(e3, e1) = all_52_8
% 111.71/16.55 (6) ~ (all_20_1 = e2) | ~ (all_20_2 = e1)
% 111.71/16.55 (7) op(e0, e1) = all_4_1
% 111.71/16.55 (8) op(e0, e1) = all_52_11
% 111.71/16.55 (9) all_20_2 = e1
% 111.71/16.55 (10) ~ (all_52_11 = e1)
% 111.71/16.55 (11) op(all_4_1, e1) = e3
% 111.71/16.55 (12) ~ (all_52_11 = e0)
% 111.71/16.55 (13) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.55
% 111.71/16.55 Begin of proof
% 111.71/16.55 |
% 111.71/16.55 | BETA: splitting (6) gives:
% 111.71/16.55 |
% 111.71/16.55 | Case 1:
% 111.71/16.55 | |
% 111.71/16.55 | | (14) ~ (all_20_1 = e2)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (2), (14) imply:
% 111.71/16.55 | | (15) ~ (all_4_1 = e2)
% 111.71/16.55 | |
% 111.71/16.55 | | GROUND_INST: instantiating (4) with all_52_11, all_4_1, e1, e0, simplifying
% 111.71/16.55 | | with (7), (8) gives:
% 111.71/16.55 | | (16) all_52_11 = all_4_1
% 111.71/16.55 | |
% 111.71/16.55 | | COMBINE_EQS: (3), (16) imply:
% 111.71/16.55 | | (17) all_54_14 = all_4_1
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (1), (16) imply:
% 111.71/16.55 | | (18) ~ (all_52_8 = all_4_1)
% 111.71/16.55 | |
% 111.71/16.55 | | BETA: splitting (13) gives:
% 111.71/16.55 | |
% 111.71/16.55 | | Case 1:
% 111.71/16.55 | | |
% 111.71/16.55 | | | (19) all_54_14 = e3
% 111.71/16.55 | | |
% 111.71/16.55 | | | COMBINE_EQS: (17), (19) imply:
% 111.71/16.55 | | | (20) all_4_1 = e3
% 111.71/16.55 | | |
% 111.71/16.55 | | | REDUCE: (18), (20) imply:
% 111.71/16.55 | | | (21) ~ (all_52_8 = e3)
% 111.71/16.55 | | |
% 111.71/16.55 | | | REDUCE: (11), (20) imply:
% 111.71/16.55 | | | (22) op(e3, e1) = e3
% 111.71/16.55 | | |
% 111.71/16.55 | | | GROUND_INST: instantiating (4) with all_52_8, e3, e1, e3, simplifying with
% 111.71/16.55 | | | (5), (22) gives:
% 111.71/16.55 | | | (23) all_52_8 = e3
% 111.71/16.55 | | |
% 111.71/16.55 | | | REDUCE: (21), (23) imply:
% 111.71/16.55 | | | (24) $false
% 111.71/16.55 | | |
% 111.71/16.55 | | | CLOSE: (24) is inconsistent.
% 111.71/16.55 | | |
% 111.71/16.55 | | Case 2:
% 111.71/16.55 | | |
% 111.71/16.55 | | | (25) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.55 | | |
% 111.71/16.55 | | | REF_CLOSE: (3), (10), (12), (15), (17), (25) are inconsistent by sub-proof
% 111.71/16.55 | | | #138.
% 111.71/16.55 | | |
% 111.71/16.55 | | End of split
% 111.71/16.55 | |
% 111.71/16.55 | Case 2:
% 111.71/16.55 | |
% 111.71/16.55 | | (26) ~ (all_20_2 = e1)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (9), (26) imply:
% 111.71/16.55 | | (27) $false
% 111.71/16.55 | |
% 111.71/16.55 | | CLOSE: (27) is inconsistent.
% 111.71/16.55 | |
% 111.71/16.55 | End of split
% 111.71/16.55 |
% 111.71/16.55 End of proof
% 111.71/16.55
% 111.71/16.55 Sub-proof #12 shows that the following formulas are inconsistent:
% 111.71/16.55 ----------------------------------------------------------------
% 111.71/16.55 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.55 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.55 (3) ~ (all_52_2 = all_10_2)
% 111.71/16.55 (4) all_54_2 = all_52_8
% 111.71/16.55 (5) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 111.71/16.55 (6) all_56_14 = all_6_2
% 111.71/16.55 (7) all_56_3 = all_52_1
% 111.71/16.55 (8) op(e2, all_6_2) = e3
% 111.71/16.55 (9) all_54_0 = all_10_2
% 111.71/16.55 (10) all_54_3 = all_52_12
% 111.71/16.55 (11) all_50_0 = e2
% 111.71/16.55 (12) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.71/16.55 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.55 (14) ~ (all_52_12 = all_10_2)
% 111.71/16.55 (15) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 111.71/16.55 (16) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.55 (17) all_56_12 = all_10_2
% 111.71/16.55 (18) all_58_0 = all_10_2
% 111.71/16.55 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.55 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.55 (21) op(e1, all_6_2) = e2
% 111.71/16.55 (22) all_54_10 = all_6_2
% 111.71/16.55 (23) op(e3, e0) = all_52_12
% 111.71/16.55 (24) ~ (all_52_8 = all_6_2)
% 111.71/16.55 (25) all_50_1 = all_10_1
% 111.71/16.55 (26) all_56_2 = all_52_12
% 111.71/16.55 (27) all_58_3 = all_8_2
% 111.71/16.55 (28) all_58_11 = all_52_14
% 111.71/16.55 (29) op(e3, e1) = all_52_8
% 111.71/16.55 (30) op(e2, e3) = all_52_1
% 111.71/16.55 (31) all_50_2 = all_10_2
% 111.71/16.55 (32) all_58_5 = all_52_9
% 111.71/16.55 (33) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.55 (34) all_58_15 = all_4_2
% 111.71/16.55 (35) all_58_2 = all_52_1
% 111.71/16.55 (36) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.71/16.55 (37) all_18_1 = e2
% 111.71/16.55 (38) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.55 (39) ~ (all_52_12 = all_52_13)
% 111.71/16.55 (40) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 111.71/16.55 (41) ~ (all_52_1 = all_10_2)
% 111.71/16.55 (42) all_56_15 = all_4_2
% 111.71/16.55 (43) all_58_10 = all_52_13
% 111.71/16.55 (44) op(e3, all_10_2) = all_10_1
% 111.71/16.55 (45) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.71/16.55 (46) ~ (all_8_2 = e2)
% 111.71/16.55 (47) op(e1, e2) = all_52_6
% 111.71/16.55 (48) all_18_2 = all_6_2
% 111.71/16.55 (49) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.55 (50) all_56_4 = all_52_9
% 111.71/16.55 (51) all_58_9 = all_52_12
% 111.71/16.55 (52) all_56_5 = all_52_13
% 111.71/16.55 (53) op(e2, e1) = all_52_9
% 111.71/16.55 (54) ~ (all_52_6 = all_6_2)
% 111.71/16.55 (55) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.55 (56) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.55 (57) ~ (all_52_8 = all_52_9)
% 111.71/16.55 (58) op(e2, e0) = all_52_13
% 111.71/16.55 (59) op(e1, e3) = all_52_2
% 111.71/16.55 (60) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.71/16.55 (61) op(e1, e1) = all_6_2
% 111.71/16.55 (62) all_56_8 = all_52_14
% 111.71/16.55 (63) op(all_10_1, all_10_2) = e2
% 111.71/16.55 (64) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.55 (65) ~ (all_6_2 = e1)
% 111.71/16.55
% 111.71/16.55 Begin of proof
% 111.71/16.55 |
% 111.71/16.55 | BETA: splitting (15) gives:
% 111.71/16.55 |
% 111.71/16.55 | Case 1:
% 111.71/16.55 | |
% 111.71/16.55 | | (66) ~ (all_18_1 = e2)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (37), (66) imply:
% 111.71/16.55 | | (67) $false
% 111.71/16.55 | |
% 111.71/16.55 | | CLOSE: (67) is inconsistent.
% 111.71/16.55 | |
% 111.71/16.55 | Case 2:
% 111.71/16.55 | |
% 111.71/16.55 | | (68) ~ (all_18_2 = e0)
% 111.71/16.55 | |
% 111.71/16.55 | | REDUCE: (48), (68) imply:
% 111.71/16.55 | | (69) ~ (all_6_2 = e0)
% 111.71/16.55 | |
% 111.71/16.55 | | BETA: splitting (16) gives:
% 111.71/16.55 | |
% 111.71/16.55 | | Case 1:
% 111.71/16.55 | | |
% 111.71/16.55 | | | (70) ~ (all_50_0 = e2)
% 111.71/16.55 | | |
% 111.71/16.55 | | | REDUCE: (11), (70) imply:
% 111.71/16.55 | | | (71) $false
% 111.71/16.55 | | |
% 111.71/16.55 | | | CLOSE: (71) is inconsistent.
% 111.71/16.55 | | |
% 111.71/16.55 | | Case 2:
% 111.71/16.55 | | |
% 111.71/16.55 | | | (72) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.55 | | |
% 111.71/16.55 | | | BETA: splitting (40) gives:
% 111.71/16.55 | | |
% 111.71/16.55 | | | Case 1:
% 111.71/16.55 | | | |
% 111.71/16.55 | | | | (73) ~ (all_56_14 = e2)
% 111.71/16.55 | | | |
% 111.71/16.55 | | | | REDUCE: (6), (73) imply:
% 111.71/16.55 | | | | (74) ~ (all_6_2 = e2)
% 111.71/16.55 | | | |
% 111.71/16.55 | | | | BETA: splitting (19) gives:
% 111.71/16.55 | | | |
% 111.71/16.55 | | | | Case 1:
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | (75) all_54_10 = e3
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | COMBINE_EQS: (22), (75) imply:
% 111.71/16.55 | | | | | (76) all_6_2 = e3
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | SIMP: (76) implies:
% 111.71/16.55 | | | | | (77) all_6_2 = e3
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | REDUCE: (24), (77) imply:
% 111.71/16.55 | | | | | (78) ~ (all_52_8 = e3)
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | REDUCE: (8), (77) imply:
% 111.71/16.55 | | | | | (79) op(e2, e3) = e3
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | REDUCE: (21), (77) imply:
% 111.71/16.55 | | | | | (80) op(e1, e3) = e2
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | REDUCE: (61), (77) imply:
% 111.71/16.55 | | | | | (81) op(e1, e1) = e3
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | BETA: splitting (45) gives:
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | | Case 1:
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | (82) ~ (all_56_3 = e2)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | REDUCE: (7), (82) imply:
% 111.71/16.55 | | | | | | (83) ~ (all_52_1 = e2)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | GROUND_INST: instantiating (20) with all_52_2, e2, e3, e1,
% 111.71/16.55 | | | | | | simplifying with (59), (80) gives:
% 111.71/16.55 | | | | | | (84) all_52_2 = e2
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | GROUND_INST: instantiating (20) with all_52_1, e3, e3, e2,
% 111.71/16.55 | | | | | | simplifying with (30), (79) gives:
% 111.71/16.55 | | | | | | (85) all_52_1 = e3
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | REDUCE: (41), (85) imply:
% 111.71/16.55 | | | | | | (86) ~ (all_10_2 = e3)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | SIMP: (86) implies:
% 111.71/16.55 | | | | | | (87) ~ (all_10_2 = e3)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | REDUCE: (3), (84) imply:
% 111.71/16.55 | | | | | | (88) ~ (all_10_2 = e2)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | SIMP: (88) implies:
% 111.71/16.55 | | | | | | (89) ~ (all_10_2 = e2)
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | BETA: splitting (5) gives:
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | Case 1:
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | (90) all_58_0 = e0
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | COMBINE_EQS: (18), (90) imply:
% 111.71/16.55 | | | | | | | (91) all_10_2 = e0
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | REF_CLOSE: (2), (9), (10), (13), (14), (17), (20), (23), (25),
% 111.71/16.55 | | | | | | | (26), (27), (28), (31), (32), (33), (34), (35), (36),
% 111.71/16.55 | | | | | | | (38), (39), (42), (43), (44), (46), (49), (50), (51),
% 111.71/16.55 | | | | | | | (52), (56), (58), (60), (62), (63), (64), (72), (83),
% 111.71/16.55 | | | | | | | (87), (89), (91) are inconsistent by sub-proof #13.
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | Case 2:
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | (92) ~ (all_58_0 = e0)
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | REDUCE: (18), (92) imply:
% 111.71/16.55 | | | | | | | (93) ~ (all_10_2 = e0)
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | | REF_CLOSE: (1), (4), (9), (12), (20), (29), (44), (49), (53),
% 111.71/16.55 | | | | | | | (55), (57), (63), (78), (87), (89), (93) are
% 111.71/16.55 | | | | | | | inconsistent by sub-proof #144.
% 111.71/16.55 | | | | | | |
% 111.71/16.55 | | | | | | End of split
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | Case 2:
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | (94) all_56_3 = e2
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | | REF_CLOSE: (6), (20), (45), (61), (81), (94) are inconsistent by
% 111.71/16.55 | | | | | | sub-proof #121.
% 111.71/16.55 | | | | | |
% 111.71/16.55 | | | | | End of split
% 111.71/16.55 | | | | |
% 111.71/16.55 | | | | Case 2:
% 111.71/16.55 | | | | |
% 111.71/16.56 | | | | | (95) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.56 | | | | |
% 111.71/16.56 | | | | | REF_CLOSE: (22), (65), (69), (74), (95) are inconsistent by sub-proof
% 111.71/16.56 | | | | | #435.
% 111.71/16.56 | | | | |
% 111.71/16.56 | | | | End of split
% 111.71/16.56 | | | |
% 111.71/16.56 | | | Case 2:
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | (96) all_56_14 = e2
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | COMBINE_EQS: (6), (96) imply:
% 111.71/16.56 | | | | (97) all_6_2 = e2
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | REF_CLOSE: (20), (21), (47), (54), (97) are inconsistent by sub-proof
% 111.71/16.56 | | | | #39.
% 111.71/16.56 | | | |
% 111.71/16.56 | | | End of split
% 111.71/16.56 | | |
% 111.71/16.56 | | End of split
% 111.71/16.56 | |
% 111.71/16.56 | End of split
% 111.71/16.56 |
% 111.71/16.56 End of proof
% 111.71/16.56
% 111.71/16.56 Sub-proof #13 shows that the following formulas are inconsistent:
% 111.71/16.56 ----------------------------------------------------------------
% 111.71/16.56 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.56 (2) ~ (all_52_1 = e2)
% 111.71/16.56 (3) all_54_0 = all_10_2
% 111.71/16.56 (4) all_54_3 = all_52_12
% 111.71/16.56 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.56 (6) ~ (all_52_12 = all_10_2)
% 111.71/16.56 (7) all_56_12 = all_10_2
% 111.71/16.56 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.56 (9) ~ (all_10_2 = e2)
% 111.71/16.56 (10) op(e3, e0) = all_52_12
% 111.71/16.56 (11) all_50_1 = all_10_1
% 111.71/16.56 (12) all_56_2 = all_52_12
% 111.71/16.56 (13) all_58_3 = all_8_2
% 111.71/16.56 (14) all_58_11 = all_52_14
% 111.71/16.56 (15) all_50_2 = all_10_2
% 111.71/16.56 (16) all_58_5 = all_52_9
% 111.71/16.56 (17) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.56 (18) all_58_15 = all_4_2
% 111.71/16.56 (19) all_58_2 = all_52_1
% 111.71/16.56 (20) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.71/16.56 (21) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.56 (22) ~ (all_10_2 = e3)
% 111.71/16.56 (23) ~ (all_52_12 = all_52_13)
% 111.71/16.56 (24) all_56_15 = all_4_2
% 111.71/16.56 (25) all_58_10 = all_52_13
% 111.71/16.56 (26) op(e3, all_10_2) = all_10_1
% 111.71/16.56 (27) ~ (all_8_2 = e2)
% 111.71/16.56 (28) all_10_2 = e0
% 111.71/16.56 (29) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.56 (30) all_56_4 = all_52_9
% 111.71/16.56 (31) all_58_9 = all_52_12
% 111.71/16.56 (32) all_56_5 = all_52_13
% 111.71/16.56 (33) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.56 (34) op(e2, e0) = all_52_13
% 111.71/16.56 (35) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.56 (36) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.71/16.56 (37) all_56_8 = all_52_14
% 111.71/16.56 (38) op(all_10_1, all_10_2) = e2
% 111.71/16.56 (39) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.56
% 111.71/16.56 Begin of proof
% 111.71/16.56 |
% 111.71/16.56 | COMBINE_EQS: (7), (28) imply:
% 111.71/16.56 | (40) all_56_12 = e0
% 111.71/16.56 |
% 111.71/16.56 | BETA: splitting (36) gives:
% 111.71/16.56 |
% 111.71/16.56 | Case 1:
% 111.71/16.56 | |
% 111.71/16.56 | | (41) ~ (all_56_5 = e2)
% 111.71/16.56 | |
% 111.71/16.56 | | REDUCE: (32), (41) imply:
% 111.71/16.56 | | (42) ~ (all_52_13 = e2)
% 111.71/16.56 | |
% 111.71/16.56 | | BETA: splitting (39) gives:
% 111.71/16.56 | |
% 111.71/16.56 | | Case 1:
% 111.71/16.56 | | |
% 111.71/16.56 | | | (43) all_58_2 = e2
% 111.71/16.56 | | |
% 111.71/16.56 | | | COMBINE_EQS: (19), (43) imply:
% 111.71/16.56 | | | (44) all_52_1 = e2
% 111.71/16.56 | | |
% 111.71/16.56 | | | REDUCE: (2), (44) imply:
% 111.71/16.56 | | | (45) $false
% 111.71/16.56 | | |
% 111.71/16.56 | | | CLOSE: (45) is inconsistent.
% 111.71/16.56 | | |
% 111.71/16.56 | | Case 2:
% 111.71/16.56 | | |
% 111.71/16.56 | | | (46) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.56 | | |
% 111.71/16.56 | | | BETA: splitting (46) gives:
% 111.71/16.56 | | |
% 111.71/16.56 | | | Case 1:
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | (47) all_58_3 = e2
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | COMBINE_EQS: (13), (47) imply:
% 111.71/16.56 | | | | (48) all_8_2 = e2
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | REDUCE: (27), (48) imply:
% 111.71/16.56 | | | | (49) $false
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | CLOSE: (49) is inconsistent.
% 111.71/16.56 | | | |
% 111.71/16.56 | | | Case 2:
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | (50) all_58_5 = e2 | all_58_10 = e2
% 111.71/16.56 | | | |
% 111.71/16.56 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 111.71/16.56 | | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 111.71/16.56 | | | | (25), (26), (29), (30), (31), (33), (34), (35), (37), (38),
% 111.71/16.56 | | | | (42), (50) are inconsistent by sub-proof #19.
% 111.71/16.56 | | | |
% 111.71/16.56 | | | End of split
% 111.71/16.56 | | |
% 111.71/16.56 | | End of split
% 111.71/16.56 | |
% 111.71/16.56 | Case 2:
% 111.71/16.56 | |
% 111.71/16.56 | | (51) ~ (all_56_12 = e0)
% 111.71/16.56 | |
% 111.71/16.56 | | REDUCE: (40), (51) imply:
% 111.71/16.56 | | (52) $false
% 111.71/16.56 | |
% 111.71/16.56 | | CLOSE: (52) is inconsistent.
% 111.71/16.56 | |
% 111.71/16.56 | End of split
% 111.71/16.56 |
% 111.71/16.56 End of proof
% 111.71/16.56
% 111.71/16.56 Sub-proof #14 shows that the following formulas are inconsistent:
% 111.71/16.56 ----------------------------------------------------------------
% 111.71/16.56 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.56 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.56 (3) all_54_2 = all_52_8
% 111.71/16.56 (4) all_58_7 = all_52_6
% 111.71/16.56 (5) ~ (all_4_2 = e0)
% 111.71/16.56 (6) all_56_14 = all_6_2
% 111.71/16.56 (7) all_54_0 = all_10_2
% 111.71/16.56 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.71/16.56 (9) all_54_3 = all_52_12
% 111.71/16.56 (10) ~ (all_52_12 = all_52_14)
% 111.71/16.56 (11) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.71/16.56 (12) all_56_11 = all_52_11
% 111.71/16.56 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.56 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.56 (15) all_56_12 = all_10_2
% 111.71/16.56 (16) all_58_0 = all_10_2
% 111.71/16.56 (17) all_54_13 = all_52_7
% 111.71/16.56 (18) all_56_10 = all_52_7
% 111.71/16.56 (19) all_54_14 = all_52_11
% 111.71/16.56 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.57 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.57 (22) ~ (all_52_2 = all_6_2)
% 111.71/16.57 (23) op(e1, all_6_2) = e2
% 111.71/16.57 (24) all_54_10 = all_6_2
% 111.71/16.57 (25) all_58_4 = all_52_8
% 111.71/16.57 (26) ~ (all_52_4 = all_52_7)
% 111.71/16.57 (27) all_56_2 = all_52_12
% 111.71/16.57 (28) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.71/16.57 (29) all_58_3 = all_8_2
% 111.71/16.57 (30) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.57 (31) all_58_11 = all_52_14
% 111.71/16.57 (32) op(e3, e1) = all_52_8
% 111.71/16.57 (33) all_54_7 = all_52_13
% 111.71/16.57 (34) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.71/16.57 (35) ~ (all_52_11 = all_6_2)
% 111.71/16.57 (36) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.57 (37) ~ (all_6_0 = e3)
% 111.71/16.57 (38) ~ (all_52_7 = all_8_2)
% 111.71/16.57 (39) ~ (all_52_4 = all_8_2)
% 111.71/16.57 (40) all_56_15 = e1
% 111.71/16.57 (41) op(e1, e0) = all_52_14
% 111.71/16.57 (42) all_58_5 = all_52_9
% 111.71/16.57 (43) all_56_9 = all_52_3
% 111.71/16.57 (44) all_58_15 = all_4_2
% 111.71/16.57 (45) all_58_2 = all_52_1
% 111.71/16.57 (46) ~ (all_10_2 = e3)
% 111.71/16.57 (47) ~ (all_52_12 = all_52_13)
% 111.71/16.57 (48) all_58_13 = all_52_7
% 111.71/16.57 (49) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.71/16.57 (50) ~ (all_52_14 = all_4_2)
% 111.71/16.57 (51) all_58_6 = all_52_2
% 111.71/16.57 (52) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.71/16.57 (53) ~ (all_52_1 = all_10_2)
% 111.71/16.57 (54) all_54_5 = all_8_2
% 111.71/16.57 (55) all_56_15 = all_4_2
% 111.71/16.57 (56) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.57 (57) all_58_10 = all_52_13
% 111.71/16.57 (58) ~ (all_52_11 = all_4_2)
% 111.71/16.57 (59) op(e2, all_6_2) = all_6_0
% 111.71/16.57 (60) op(e3, all_10_2) = all_10_1
% 111.71/16.57 (61) ~ (all_52_6 = all_8_2)
% 111.71/16.57 (62) all_58_1 = all_52_4
% 111.71/16.57 (63) all_58_14 = all_52_11
% 111.71/16.57 (64) op(e0, e1) = all_52_11
% 111.71/16.57 (65) ~ (all_56_11 = e0)
% 111.71/16.57 (66) ~ (all_8_2 = e2)
% 111.71/16.57 (67) ~ (all_52_7 = all_52_11)
% 111.71/16.57 (68) op(e1, e2) = all_52_6
% 111.71/16.57 (69) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.57 (70) all_56_1 = all_52_8
% 111.71/16.57 (71) op(e0, all_4_2) = all_4_1
% 111.71/16.57 (72) all_58_8 = all_6_2
% 111.71/16.57 (73) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.57 (74) all_56_4 = all_52_9
% 111.71/16.57 (75) all_58_9 = all_52_12
% 111.71/16.57 (76) all_56_5 = all_52_13
% 111.71/16.57 (77) op(e2, e1) = all_52_9
% 111.71/16.57 (78) ~ (all_52_6 = all_6_2)
% 111.71/16.57 (79) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.57 (80) all_56_6 = all_52_2
% 111.71/16.57 (81) ~ (all_52_13 = all_4_2)
% 111.71/16.57 (82) all_58_12 = all_52_3
% 111.71/16.57 (83) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.57 (84) ~ (all_52_8 = all_52_9)
% 111.71/16.57 (85) op(e2, e0) = all_52_13
% 111.71/16.57 (86) ~ (all_52_12 = all_4_2)
% 111.71/16.57 (87) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.57 (88) op(all_10_1, all_10_2) = e2
% 111.71/16.57 (89) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.57 (90) all_56_0 = all_52_4
% 111.71/16.57 (91) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.57 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.71/16.57 (92) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.71/16.57 (93) ~ (all_6_2 = e1)
% 111.71/16.57 (94) ~ (all_52_6 = all_52_7)
% 111.71/16.57 (95) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.57
% 111.71/16.57 Begin of proof
% 111.71/16.57 |
% 111.71/16.57 | COMBINE_EQS: (40), (55) imply:
% 111.71/16.57 | (96) all_4_2 = e1
% 111.71/16.57 |
% 111.71/16.57 | SIMP: (96) implies:
% 111.71/16.57 | (97) all_4_2 = e1
% 111.71/16.57 |
% 111.71/16.57 | COMBINE_EQS: (44), (97) imply:
% 111.71/16.57 | (98) all_58_15 = e1
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (12), (65) imply:
% 111.71/16.57 | (99) ~ (all_52_11 = e0)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (58), (97) imply:
% 111.71/16.57 | (100) ~ (all_52_11 = e1)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (86), (97) imply:
% 111.71/16.57 | (101) ~ (all_52_12 = e1)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (81), (97) imply:
% 111.71/16.57 | (102) ~ (all_52_13 = e1)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (50), (97) imply:
% 111.71/16.57 | (103) ~ (all_52_14 = e1)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (5), (97) imply:
% 111.71/16.57 | (104) ~ (e1 = e0)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (71), (97) imply:
% 111.71/16.57 | (105) op(e0, e1) = all_4_1
% 111.71/16.57 |
% 111.71/16.57 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 111.71/16.57 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 111.71/16.57 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 111.71/16.57 | (37), (38), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 111.71/16.57 | (49), (51), (52), (53), (54), (56), (57), (59), (60), (61), (62),
% 111.71/16.57 | (63), (64), (66), (67), (68), (69), (70), (72), (73), (74), (75),
% 111.71/16.57 | (76), (77), (78), (79), (80), (82), (83), (84), (85), (87), (88),
% 111.71/16.57 | (89), (90), (91), (92), (93), (94), (95), (98), (99), (100), (101),
% 111.71/16.57 | (102), (103), (104), (105) are inconsistent by sub-proof #22.
% 111.71/16.57 |
% 111.71/16.57 End of proof
% 111.71/16.57
% 111.71/16.57 Sub-proof #15 shows that the following formulas are inconsistent:
% 111.71/16.57 ----------------------------------------------------------------
% 111.71/16.57 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.57 (2) all_54_2 = all_52_8
% 111.71/16.57 (3) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.71/16.57 (4) all_56_12 = all_10_2
% 111.71/16.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.57 (6) op(e3, e1) = all_52_8
% 111.71/16.57 (7) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.71/16.57 (8) all_56_12 = e1
% 111.71/16.57 (9) op(e3, all_10_2) = all_10_1
% 111.71/16.57 (10) all_56_1 = all_52_8
% 111.71/16.57 (11) op(e2, e1) = all_52_9
% 111.71/16.57 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.57 (13) ~ (all_52_8 = all_52_9)
% 111.71/16.57 (14) op(all_10_1, all_10_2) = e2
% 111.71/16.57
% 111.71/16.57 Begin of proof
% 111.71/16.57 |
% 111.71/16.57 | COMBINE_EQS: (4), (8) imply:
% 111.71/16.57 | (15) all_10_2 = e1
% 111.71/16.57 |
% 111.71/16.57 | SIMP: (15) implies:
% 111.71/16.57 | (16) all_10_2 = e1
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (1), (16) imply:
% 111.71/16.57 | (17) ~ (all_52_8 = e1)
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (14), (16) imply:
% 111.71/16.57 | (18) op(all_10_1, e1) = e2
% 111.71/16.57 |
% 111.71/16.57 | REDUCE: (9), (16) imply:
% 111.71/16.57 | (19) op(e3, e1) = all_10_1
% 111.71/16.57 |
% 111.71/16.57 | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (16), (17),
% 111.71/16.57 | (18), (19) are inconsistent by sub-proof #145.
% 111.71/16.57 |
% 111.71/16.57 End of proof
% 111.71/16.57
% 111.71/16.57 Sub-proof #16 shows that the following formulas are inconsistent:
% 111.71/16.57 ----------------------------------------------------------------
% 111.71/16.57 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.57 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.57 (3) all_54_0 = all_10_2
% 111.71/16.57 (4) all_54_3 = all_52_12
% 111.71/16.57 (5) ~ (all_4_2 = e1)
% 111.71/16.57 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.57 (7) ~ (all_52_12 = all_10_2)
% 111.71/16.57 (8) all_56_12 = all_10_2
% 111.71/16.57 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.57 (10) ~ (all_10_2 = e2)
% 111.71/16.57 (11) op(e3, e0) = all_52_12
% 111.71/16.57 (12) all_58_4 = all_52_8
% 111.71/16.57 (13) all_50_1 = all_10_1
% 111.71/16.57 (14) all_56_2 = all_52_12
% 111.71/16.57 (15) all_58_11 = all_52_14
% 111.71/16.57 (16) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.71/16.57 (17) all_50_2 = all_10_2
% 111.71/16.57 (18) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.57 (19) all_58_15 = all_4_2
% 111.71/16.57 (20) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.57 (21) ~ (all_52_12 = all_52_13)
% 111.71/16.57 (22) ~ (all_52_12 = e3)
% 111.71/16.57 (23) all_58_10 = all_52_13
% 111.71/16.57 (24) op(e3, all_10_2) = all_10_1
% 111.71/16.57 (25) all_58_4 = e3 | all_58_9 = e3
% 111.71/16.57 (26) all_56_1 = all_52_8
% 111.71/16.57 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.57 (28) all_58_9 = all_52_12
% 111.71/16.57 (29) op(e2, e0) = all_52_13
% 111.71/16.57 (30) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.57 (31) all_56_8 = all_52_14
% 111.71/16.57 (32) op(all_10_1, all_10_2) = e2
% 111.71/16.57
% 111.71/16.57 Begin of proof
% 111.71/16.57 |
% 111.71/16.57 | BETA: splitting (25) gives:
% 111.71/16.57 |
% 111.71/16.57 | Case 1:
% 111.71/16.57 | |
% 111.71/16.57 | | (33) all_58_4 = e3
% 111.71/16.57 | |
% 111.71/16.57 | | COMBINE_EQS: (12), (33) imply:
% 111.71/16.57 | | (34) all_52_8 = e3
% 111.71/16.57 | |
% 111.71/16.57 | | SIMP: (34) implies:
% 111.71/16.57 | | (35) all_52_8 = e3
% 111.71/16.57 | |
% 111.71/16.57 | | COMBINE_EQS: (26), (35) imply:
% 111.71/16.57 | | (36) all_56_1 = e3
% 111.71/16.57 | |
% 111.71/16.57 | | REDUCE: (1), (35) imply:
% 111.71/16.57 | | (37) ~ (all_10_2 = e3)
% 111.71/16.57 | |
% 111.71/16.57 | | SIMP: (37) implies:
% 111.71/16.57 | | (38) ~ (all_10_2 = e3)
% 111.71/16.57 | |
% 111.71/16.57 | | BETA: splitting (16) gives:
% 111.71/16.57 | |
% 111.71/16.57 | | Case 1:
% 111.71/16.57 | | |
% 111.71/16.57 | | | (39) ~ (all_56_1 = e3)
% 111.71/16.57 | | |
% 111.71/16.57 | | | REDUCE: (36), (39) imply:
% 111.71/16.57 | | | (40) $false
% 111.71/16.57 | | |
% 111.71/16.57 | | | CLOSE: (40) is inconsistent.
% 111.71/16.57 | | |
% 111.71/16.57 | | Case 2:
% 111.71/16.57 | | |
% 111.71/16.57 | | | (41) ~ (all_56_12 = e1)
% 111.71/16.57 | | |
% 111.71/16.57 | | | REDUCE: (8), (41) imply:
% 111.71/16.57 | | | (42) ~ (all_10_2 = e1)
% 111.71/16.57 | | |
% 111.71/16.57 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 111.71/16.57 | | | (15), (17), (18), (19), (20), (21), (23), (24), (27), (28),
% 111.71/16.57 | | | (29), (30), (31), (32), (38), (42) are inconsistent by
% 111.71/16.57 | | | sub-proof #168.
% 111.71/16.57 | | |
% 111.71/16.57 | | End of split
% 111.71/16.57 | |
% 111.71/16.57 | Case 2:
% 111.71/16.57 | |
% 111.71/16.57 | | (43) all_58_9 = e3
% 111.71/16.57 | |
% 111.71/16.57 | | REF_CLOSE: (22), (28), (43) are inconsistent by sub-proof #330.
% 111.71/16.57 | |
% 111.71/16.57 | End of split
% 111.71/16.57 |
% 111.71/16.57 End of proof
% 111.71/16.57
% 111.71/16.57 Sub-proof #17 shows that the following formulas are inconsistent:
% 111.71/16.57 ----------------------------------------------------------------
% 111.71/16.57 (1) all_58_7 = all_52_6
% 111.71/16.57 (2) ~ (all_52_1 = e2)
% 111.71/16.57 (3) ~ (all_4_2 = e0)
% 111.71/16.57 (4) all_56_14 = all_6_2
% 111.71/16.58 (5) op(e1, all_8_2) = all_8_0
% 111.71/16.58 (6) all_56_11 = all_52_11
% 111.71/16.58 (7) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 111.71/16.58 (8) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.71/16.58 (9) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 111.71/16.58 (10) all_54_11 = all_52_14
% 111.71/16.58 (11) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 111.71/16.58 (12) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.71/16.58 (13) ~ (all_52_14 = all_6_2)
% 111.71/16.58 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.58 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.58 (16) all_54_10 = all_6_2
% 111.71/16.58 (17) all_58_3 = all_8_2
% 111.71/16.58 (18) all_58_11 = all_52_14
% 111.71/16.58 (19) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.71/16.58 (20) ~ (all_52_11 = all_6_2)
% 111.71/16.58 (21) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 111.71/16.58 (22) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 111.71/16.58 (23) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.58 (24) op(e1, e0) = all_52_14
% 111.71/16.58 (25) all_58_5 = all_52_9
% 111.71/16.58 (26) all_56_9 = all_52_3
% 111.71/16.58 (27) all_58_15 = all_4_2
% 111.71/16.58 (28) all_58_2 = all_52_1
% 111.71/16.58 (29) ~ (all_52_1 = all_52_13)
% 111.71/16.58 (30) all_58_13 = all_52_7
% 111.71/16.58 (31) ~ (all_52_7 = e0)
% 111.71/16.58 (32) all_58_6 = all_52_2
% 111.71/16.58 (33) ~ (all_52_12 = e3)
% 111.71/16.58 (34) all_58_10 = all_52_13
% 111.71/16.58 (35) ~ (all_52_7 = e2)
% 111.71/16.58 (36) ~ (all_52_6 = all_8_2)
% 111.71/16.58 (37) all_58_14 = all_52_11
% 111.71/16.58 (38) all_56_13 = all_8_2
% 111.71/16.58 (39) ~ (all_8_2 = e2)
% 111.71/16.58 (40) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 111.71/16.58 (41) ~ (all_52_14 = e2)
% 111.71/16.58 (42) ~ (all_6_2 = e2)
% 111.71/16.58 (43) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.58 (44) ~ (all_52_1 = all_52_2)
% 111.71/16.58 (45) all_58_15 = e2
% 111.71/16.58 (46) ~ (all_52_1 = all_52_3)
% 111.71/16.58 (47) all_58_8 = all_6_2
% 111.71/16.58 (48) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.71/16.58 (49) all_56_4 = all_52_9
% 111.71/16.58 (50) all_58_9 = all_52_12
% 111.71/16.58 (51) all_56_5 = all_52_13
% 111.71/16.58 (52) ~ (all_52_6 = all_6_2)
% 111.71/16.58 (53) all_58_12 = all_52_3
% 111.71/16.58 (54) all_56_8 = all_52_14
% 111.71/16.58 (55) ~ (all_52_6 = e1)
% 111.71/16.58 (56) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.58 (57) ~ (all_8_0 = e3)
% 111.71/16.58 (58) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 111.71/16.58 (59) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.58 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.71/16.58 (60) all_54_4 = all_52_1
% 111.71/16.58 (61) ~ (all_52_11 = e3)
% 111.71/16.58 (62) ~ (all_6_2 = e1)
% 111.71/16.58 (63) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.58
% 111.71/16.58 Begin of proof
% 111.71/16.58 |
% 111.71/16.58 | BETA: splitting (63) gives:
% 111.71/16.58 |
% 111.71/16.58 | Case 1:
% 111.71/16.58 | |
% 111.71/16.58 | | (64) all_54_10 = e2
% 111.71/16.58 | |
% 111.71/16.58 | | REF_CLOSE: (16), (42), (64) are inconsistent by sub-proof #438.
% 111.71/16.58 | |
% 111.71/16.58 | Case 2:
% 111.71/16.58 | |
% 111.71/16.58 | | (65) ~ (all_54_10 = e2)
% 111.71/16.58 | | (66) all_54_10 = e1 | all_54_10 = e0
% 111.71/16.58 | |
% 111.71/16.58 | | BETA: splitting (66) gives:
% 111.71/16.58 | |
% 111.71/16.58 | | Case 1:
% 111.71/16.58 | | |
% 111.71/16.58 | | | (67) all_54_10 = e1
% 111.71/16.58 | | |
% 111.71/16.58 | | | REF_CLOSE: (16), (62), (67) are inconsistent by sub-proof #437.
% 111.71/16.58 | | |
% 111.71/16.58 | | Case 2:
% 111.71/16.58 | | |
% 111.71/16.58 | | | (68) all_54_10 = e0
% 111.71/16.58 | | |
% 111.71/16.58 | | | COMBINE_EQS: (16), (68) imply:
% 111.71/16.58 | | | (69) all_6_2 = e0
% 111.71/16.58 | | |
% 111.71/16.58 | | | SIMP: (69) implies:
% 111.71/16.58 | | | (70) all_6_2 = e0
% 111.71/16.58 | | |
% 111.71/16.58 | | | COMBINE_EQS: (4), (70) imply:
% 111.71/16.58 | | | (71) all_56_14 = e0
% 111.71/16.58 | | |
% 111.71/16.58 | | | REDUCE: (20), (70) imply:
% 111.71/16.58 | | | (72) ~ (all_52_11 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | REDUCE: (13), (70) imply:
% 111.71/16.58 | | | (73) ~ (all_52_14 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | REDUCE: (42), (70) imply:
% 111.71/16.58 | | | (74) ~ (e2 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | SIMP: (74) implies:
% 111.71/16.58 | | | (75) ~ (e2 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | REDUCE: (62), (70) imply:
% 111.71/16.58 | | | (76) ~ (e1 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | SIMP: (76) implies:
% 111.71/16.58 | | | (77) ~ (e1 = e0)
% 111.71/16.58 | | |
% 111.71/16.58 | | | BETA: splitting (8) gives:
% 111.71/16.58 | | |
% 111.71/16.58 | | | Case 1:
% 111.71/16.58 | | | |
% 111.71/16.58 | | | | (78) ~ (all_56_8 = e1)
% 111.71/16.58 | | | |
% 111.71/16.58 | | | | REDUCE: (54), (78) imply:
% 111.71/16.58 | | | | (79) ~ (all_52_14 = e1)
% 111.71/16.58 | | | |
% 111.71/16.58 | | | | BETA: splitting (48) gives:
% 111.71/16.58 | | | |
% 111.71/16.58 | | | | Case 1:
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | (80) all_54_11 = e3
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | COMBINE_EQS: (10), (80) imply:
% 111.71/16.58 | | | | | (81) all_52_14 = e3
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | REDUCE: (41), (81) imply:
% 111.71/16.58 | | | | | (82) ~ (e3 = e2)
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | REDUCE: (79), (81) imply:
% 111.71/16.58 | | | | | (83) ~ (e3 = e1)
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | REDUCE: (73), (81) imply:
% 111.71/16.58 | | | | | (84) ~ (e3 = e0)
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | REDUCE: (24), (81) imply:
% 111.71/16.58 | | | | | (85) op(e1, e0) = e3
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | BETA: splitting (59) gives:
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | Case 1:
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | (86) all_58_15 = e0
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | COMBINE_EQS: (45), (86) imply:
% 111.71/16.58 | | | | | | (87) e2 = e0
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | REDUCE: (75), (87) imply:
% 111.71/16.58 | | | | | | (88) $false
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | CLOSE: (88) is inconsistent.
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | Case 2:
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | (89) ~ (all_58_15 = e0)
% 111.71/16.58 | | | | | | (90) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.58 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | ALPHA: (90) implies:
% 111.71/16.58 | | | | | | (91) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | BETA: splitting (91) gives:
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | Case 1:
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | (92) all_58_12 = e0
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (14),
% 111.71/16.58 | | | | | | | (15), (16), (17), (19), (21), (23), (25), (26), (27),
% 111.71/16.58 | | | | | | | (28), (30), (31), (34), (35), (36), (37), (38), (39),
% 111.71/16.58 | | | | | | | (40), (45), (49), (51), (52), (53), (55), (56), (57),
% 111.71/16.58 | | | | | | | (58), (59), (61), (62), (66), (75), (77), (82), (83),
% 111.71/16.58 | | | | | | | (84), (85), (92) are inconsistent by sub-proof #52.
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | Case 2:
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | (93) all_58_13 = e0 | all_58_14 = e0
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | REF_CLOSE: (30), (31), (37), (72), (93) are inconsistent by
% 111.71/16.58 | | | | | | | sub-proof #428.
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | End of split
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | End of split
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | Case 2:
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | (94) ~ (all_54_11 = e3)
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | REDUCE: (10), (94) imply:
% 111.71/16.58 | | | | | (95) ~ (all_52_14 = e3)
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | BETA: splitting (43) gives:
% 111.71/16.58 | | | | |
% 111.71/16.58 | | | | | Case 1:
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | (96) all_58_6 = e1
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | COMBINE_EQS: (32), (96) imply:
% 111.71/16.58 | | | | | | (97) all_52_2 = e1
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | SIMP: (97) implies:
% 111.71/16.58 | | | | | | (98) all_52_2 = e1
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | REDUCE: (44), (98) imply:
% 111.71/16.58 | | | | | | (99) ~ (all_52_1 = e1)
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | BETA: splitting (22) gives:
% 111.71/16.58 | | | | | |
% 111.71/16.58 | | | | | | Case 1:
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | (100) all_58_9 = e3
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | COMBINE_EQS: (50), (100) imply:
% 111.71/16.58 | | | | | | | (101) all_52_12 = e3
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | REDUCE: (33), (101) imply:
% 111.71/16.58 | | | | | | | (102) $false
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | CLOSE: (102) is inconsistent.
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | Case 2:
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | (103) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | BETA: splitting (59) gives:
% 111.71/16.58 | | | | | | |
% 111.71/16.58 | | | | | | | Case 1:
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | (104) all_58_15 = e0
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | COMBINE_EQS: (45), (104) imply:
% 111.71/16.58 | | | | | | | | (105) e2 = e0
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | REDUCE: (75), (105) imply:
% 111.71/16.58 | | | | | | | | (106) $false
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | CLOSE: (106) is inconsistent.
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | Case 2:
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | (107) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.58 | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | ALPHA: (107) implies:
% 111.71/16.58 | | | | | | | | (108) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | BETA: splitting (108) gives:
% 111.71/16.58 | | | | | | | |
% 111.71/16.58 | | | | | | | | Case 1:
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | (109) all_58_12 = e0
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | COMBINE_EQS: (53), (109) imply:
% 111.71/16.58 | | | | | | | | | (110) all_52_3 = e0
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | SIMP: (110) implies:
% 111.71/16.58 | | | | | | | | | (111) all_52_3 = e0
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | REDUCE: (46), (111) imply:
% 111.71/16.58 | | | | | | | | | (112) ~ (all_52_1 = e0)
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | BETA: splitting (12) gives:
% 111.71/16.58 | | | | | | | | |
% 111.71/16.58 | | | | | | | | | Case 1:
% 111.71/16.58 | | | | | | | | | |
% 111.71/16.58 | | | | | | | | | | (113) all_54_4 = e3
% 111.71/16.58 | | | | | | | | | |
% 111.71/16.58 | | | | | | | | | | COMBINE_EQS: (60), (113) imply:
% 111.71/16.59 | | | | | | | | | | (114) all_52_1 = e3
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | SIMP: (114) implies:
% 111.71/16.59 | | | | | | | | | | (115) all_52_1 = e3
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | REDUCE: (29), (115) imply:
% 111.71/16.59 | | | | | | | | | | (116) ~ (all_52_13 = e3)
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | SIMP: (116) implies:
% 111.71/16.59 | | | | | | | | | | (117) ~ (all_52_13 = e3)
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | REDUCE: (2), (115) imply:
% 111.71/16.59 | | | | | | | | | | (118) ~ (e3 = e2)
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | BETA: splitting (103) gives:
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | Case 1:
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | (119) all_58_10 = e3
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | COMBINE_EQS: (34), (119) imply:
% 111.71/16.59 | | | | | | | | | | | (120) all_52_13 = e3
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | REDUCE: (117), (120) imply:
% 111.71/16.59 | | | | | | | | | | | (121) $false
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | CLOSE: (121) is inconsistent.
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | Case 2:
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | (122) all_58_11 = e3 | all_58_15 = e3
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | | REF_CLOSE: (18), (45), (95), (118), (122) are inconsistent by
% 111.71/16.59 | | | | | | | | | | | sub-proof #245.
% 111.71/16.59 | | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | End of split
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | Case 2:
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | (123) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | | REF_CLOSE: (2), (60), (99), (112), (123) are inconsistent by
% 111.71/16.59 | | | | | | | | | | sub-proof #62.
% 111.71/16.59 | | | | | | | | | |
% 111.71/16.59 | | | | | | | | | End of split
% 111.71/16.59 | | | | | | | | |
% 111.71/16.59 | | | | | | | | Case 2:
% 111.71/16.59 | | | | | | | | |
% 111.71/16.59 | | | | | | | | | (124) all_58_13 = e0 | all_58_14 = e0
% 111.71/16.59 | | | | | | | | |
% 111.71/16.59 | | | | | | | | | REF_CLOSE: (30), (31), (37), (72), (124) are inconsistent by
% 111.71/16.59 | | | | | | | | | sub-proof #428.
% 111.71/16.59 | | | | | | | | |
% 111.71/16.59 | | | | | | | | End of split
% 111.71/16.59 | | | | | | | |
% 111.71/16.59 | | | | | | | End of split
% 111.71/16.59 | | | | | | |
% 111.71/16.59 | | | | | | End of split
% 111.71/16.59 | | | | | |
% 111.71/16.59 | | | | | Case 2:
% 111.71/16.59 | | | | | |
% 111.71/16.59 | | | | | | (125) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.59 | | | | | |
% 111.71/16.59 | | | | | | REF_CLOSE: (1), (18), (47), (55), (62), (79), (125) are inconsistent
% 111.71/16.59 | | | | | | by sub-proof #354.
% 111.71/16.59 | | | | | |
% 111.71/16.59 | | | | | End of split
% 111.71/16.59 | | | | |
% 111.71/16.59 | | | | End of split
% 111.71/16.59 | | | |
% 111.71/16.59 | | | Case 2:
% 111.71/16.59 | | | |
% 111.71/16.59 | | | | (126) ~ (all_56_14 = e0)
% 111.71/16.59 | | | |
% 111.71/16.59 | | | | REDUCE: (71), (126) imply:
% 111.71/16.59 | | | | (127) $false
% 111.71/16.59 | | | |
% 111.71/16.59 | | | | CLOSE: (127) is inconsistent.
% 111.71/16.59 | | | |
% 111.71/16.59 | | | End of split
% 111.71/16.59 | | |
% 111.71/16.59 | | End of split
% 111.71/16.59 | |
% 111.71/16.59 | End of split
% 111.71/16.59 |
% 111.71/16.59 End of proof
% 111.71/16.59
% 111.71/16.59 Sub-proof #18 shows that the following formulas are inconsistent:
% 111.71/16.59 ----------------------------------------------------------------
% 111.71/16.59 (1) all_58_7 = all_52_6
% 111.71/16.59 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 111.71/16.59 (3) ~ (all_52_9 = all_8_2)
% 111.71/16.59 (4) ~ (all_52_13 = all_52_14)
% 111.71/16.59 (5) all_54_0 = all_10_2
% 111.71/16.59 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.59 (7) all_56_12 = all_10_2
% 111.71/16.59 (8) all_58_0 = all_10_2
% 111.71/16.59 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 111.71/16.59 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.59 (11) ~ (all_10_2 = all_4_1)
% 111.71/16.59 (12) all_56_12 = e2
% 111.71/16.59 (13) all_58_3 = all_8_2
% 111.71/16.59 (14) all_58_11 = all_52_14
% 111.71/16.59 (15) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 111.71/16.59 (16) all_54_7 = all_52_13
% 111.71/16.59 (17) op(e2, e3) = all_52_1
% 111.71/16.59 (18) ~ (all_10_2 = e1)
% 111.71/16.59 (19) all_58_5 = all_52_9
% 111.71/16.59 (20) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.59 (21) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 111.71/16.59 (22) all_58_2 = all_52_1
% 111.71/16.59 (23) ~ (all_10_2 = e3)
% 111.71/16.59 (24) ~ (all_4_1 = e0)
% 111.71/16.59 (25) all_58_6 = all_52_2
% 111.71/16.59 (26) ~ (all_52_2 = e1)
% 111.71/16.59 (27) ~ (all_52_1 = all_10_2)
% 111.71/16.59 (28) all_54_5 = all_8_2
% 111.71/16.59 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.59 (30) all_58_10 = all_52_13
% 111.71/16.59 (31) ~ (all_52_13 = all_8_2)
% 111.71/16.59 (32) ~ (all_8_2 = e1)
% 111.71/16.59 (33) all_56_13 = all_8_2
% 111.71/16.59 (34) ~ (all_52_1 = all_8_2)
% 111.71/16.59 (35) ~ (all_8_2 = e2)
% 111.71/16.59 (36) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.59 (37) all_56_7 = all_52_6
% 111.71/16.59 (38) all_58_8 = all_6_2
% 111.71/16.59 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.59 (40) all_56_5 = all_52_13
% 111.71/16.59 (41) all_54_12 = all_4_1
% 111.71/16.59 (42) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.59 (43) op(e2, e0) = all_52_13
% 111.71/16.59 (44) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 111.71/16.59 (45) ~ (all_52_1 = all_4_1)
% 111.71/16.59 (46) all_56_8 = all_52_14
% 111.71/16.59 (47) ~ (all_4_1 = e3)
% 111.71/16.59 (48) all_54_4 = all_52_1
% 111.71/16.59 (49) op(e2, all_8_2) = e1
% 111.71/16.59 (50) ~ (all_6_2 = e1)
% 111.71/16.59
% 111.71/16.59 Begin of proof
% 111.71/16.59 |
% 111.71/16.59 | BETA: splitting (21) gives:
% 111.71/16.59 |
% 111.71/16.59 | Case 1:
% 111.71/16.59 | |
% 111.71/16.59 | | (51) ~ (all_56_7 = e1)
% 111.71/16.59 | |
% 111.71/16.59 | | REDUCE: (37), (51) imply:
% 111.71/16.59 | | (52) ~ (all_52_6 = e1)
% 111.71/16.59 | |
% 111.71/16.59 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 111.71/16.59 | | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 111.71/16.59 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 111.71/16.59 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 111.71/16.59 | | (49), (50), (52) are inconsistent by sub-proof #61.
% 111.71/16.59 | |
% 111.71/16.59 | Case 2:
% 111.71/16.59 | |
% 111.71/16.59 | | (53) ~ (all_56_12 = e2)
% 111.71/16.59 | |
% 111.71/16.59 | | REDUCE: (12), (53) imply:
% 111.71/16.59 | | (54) $false
% 111.71/16.59 | |
% 111.71/16.59 | | CLOSE: (54) is inconsistent.
% 111.71/16.59 | |
% 111.71/16.59 | End of split
% 111.71/16.59 |
% 111.71/16.59 End of proof
% 111.71/16.59
% 111.71/16.59 Sub-proof #19 shows that the following formulas are inconsistent:
% 111.71/16.59 ----------------------------------------------------------------
% 111.71/16.59 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.59 (2) all_54_0 = all_10_2
% 111.71/16.59 (3) all_54_3 = all_52_12
% 111.71/16.59 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.59 (5) ~ (all_52_12 = all_10_2)
% 111.71/16.59 (6) all_58_5 = e2 | all_58_10 = e2
% 111.71/16.59 (7) all_56_12 = all_10_2
% 111.71/16.59 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.59 (9) ~ (all_10_2 = e2)
% 111.71/16.59 (10) op(e3, e0) = all_52_12
% 111.71/16.59 (11) all_50_1 = all_10_1
% 111.71/16.59 (12) all_56_2 = all_52_12
% 111.71/16.59 (13) all_58_11 = all_52_14
% 111.71/16.59 (14) all_50_2 = all_10_2
% 111.71/16.59 (15) all_58_5 = all_52_9
% 111.71/16.59 (16) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.59 (17) all_58_15 = all_4_2
% 111.71/16.59 (18) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.71/16.59 (19) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.59 (20) ~ (all_10_2 = e3)
% 111.71/16.59 (21) ~ (all_52_12 = all_52_13)
% 111.71/16.59 (22) ~ (all_52_13 = e2)
% 111.71/16.59 (23) all_56_15 = all_4_2
% 111.71/16.59 (24) all_58_10 = all_52_13
% 111.71/16.59 (25) op(e3, all_10_2) = all_10_1
% 111.71/16.59 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.59 (27) all_56_4 = all_52_9
% 111.71/16.59 (28) all_58_9 = all_52_12
% 111.71/16.59 (29) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.59 (30) op(e2, e0) = all_52_13
% 111.71/16.59 (31) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.59 (32) all_56_8 = all_52_14
% 111.71/16.59 (33) op(all_10_1, all_10_2) = e2
% 111.71/16.59
% 111.71/16.59 Begin of proof
% 111.71/16.59 |
% 111.71/16.59 | BETA: splitting (6) gives:
% 111.71/16.59 |
% 111.71/16.59 | Case 1:
% 111.71/16.59 | |
% 111.71/16.59 | | (34) all_58_5 = e2
% 111.71/16.59 | |
% 111.71/16.59 | | COMBINE_EQS: (15), (34) imply:
% 111.71/16.59 | | (35) all_52_9 = e2
% 111.71/16.59 | |
% 111.71/16.59 | | COMBINE_EQS: (27), (35) imply:
% 111.71/16.59 | | (36) all_56_4 = e2
% 111.71/16.59 | |
% 111.71/16.59 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 111.71/16.59 | | (14), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 111.71/16.59 | | (28), (29), (30), (31), (32), (33), (36) are inconsistent by
% 111.71/16.59 | | sub-proof #167.
% 111.71/16.59 | |
% 111.71/16.59 | Case 2:
% 111.71/16.59 | |
% 111.71/16.59 | | (37) all_58_10 = e2
% 111.71/16.59 | |
% 111.71/16.59 | | COMBINE_EQS: (24), (37) imply:
% 111.71/16.59 | | (38) all_52_13 = e2
% 111.71/16.59 | |
% 111.71/16.59 | | REDUCE: (22), (38) imply:
% 111.71/16.59 | | (39) $false
% 111.71/16.59 | |
% 111.71/16.59 | | CLOSE: (39) is inconsistent.
% 111.71/16.59 | |
% 111.71/16.59 | End of split
% 111.71/16.59 |
% 111.71/16.59 End of proof
% 111.71/16.59
% 111.71/16.59 Sub-proof #20 shows that the following formulas are inconsistent:
% 111.71/16.59 ----------------------------------------------------------------
% 111.71/16.59 (1) ~ (all_52_3 = e0)
% 111.71/16.59 (2) ~ (all_52_3 = e3)
% 111.71/16.59 (3) all_54_0 = all_10_2
% 111.71/16.59 (4) ~ (all_52_3 = e2)
% 111.71/16.59 (5) all_58_0 = all_10_2
% 111.71/16.59 (6) ~ (all_10_2 = e2)
% 111.71/16.59 (7) ~ (all_10_2 = e3)
% 111.71/16.59 (8) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.59 (9) ~ (all_58_0 = e0)
% 111.71/16.59 (10) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.59 (11) ~ (all_52_3 = all_10_2)
% 111.71/16.59 (12) all_54_12 = all_52_3
% 111.71/16.59
% 111.71/16.59 Begin of proof
% 111.71/16.59 |
% 111.71/16.59 | REDUCE: (5), (9) imply:
% 111.71/16.59 | (13) ~ (all_10_2 = e0)
% 111.71/16.59 |
% 111.71/16.59 | BETA: splitting (10) gives:
% 111.71/16.59 |
% 111.71/16.59 | Case 1:
% 111.71/16.59 | |
% 111.71/16.59 | | (14) all_54_12 = e3
% 111.71/16.59 | |
% 111.71/16.59 | | REF_CLOSE: (2), (12), (14) are inconsistent by sub-proof #410.
% 111.71/16.59 | |
% 111.71/16.59 | Case 2:
% 111.71/16.59 | |
% 111.71/16.59 | | (15) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.59 | |
% 111.71/16.59 | | BETA: splitting (15) gives:
% 111.71/16.59 | |
% 111.71/16.59 | | Case 1:
% 111.71/16.59 | | |
% 111.71/16.59 | | | (16) all_54_12 = e2
% 111.71/16.59 | | |
% 111.71/16.59 | | | REF_CLOSE: (4), (12), (16) are inconsistent by sub-proof #409.
% 111.71/16.59 | | |
% 111.71/16.59 | | Case 2:
% 111.71/16.59 | | |
% 111.71/16.60 | | | (17) all_54_12 = e1 | all_54_12 = e0
% 111.71/16.60 | | |
% 111.71/16.60 | | | REF_CLOSE: (1), (3), (6), (7), (8), (11), (12), (13), (17) are
% 111.71/16.60 | | | inconsistent by sub-proof #32.
% 111.71/16.60 | | |
% 111.71/16.60 | | End of split
% 111.71/16.60 | |
% 111.71/16.60 | End of split
% 111.71/16.60 |
% 111.71/16.60 End of proof
% 111.71/16.60
% 111.71/16.60 Sub-proof #21 shows that the following formulas are inconsistent:
% 111.71/16.60 ----------------------------------------------------------------
% 111.71/16.60 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.60 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.60 (3) ~ (all_52_2 = all_10_2)
% 111.71/16.60 (4) ~ (all_52_6 = all_52_14)
% 111.71/16.60 (5) all_54_2 = all_52_8
% 111.71/16.60 (6) all_58_7 = all_52_6
% 111.71/16.60 (7) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 111.71/16.60 (8) ~ (all_52_9 = all_8_2)
% 111.71/16.60 (9) ~ (all_52_13 = all_52_14)
% 111.71/16.60 (10) ~ (all_4_2 = e0)
% 111.71/16.60 (11) op(e3, e2) = all_52_4
% 111.71/16.60 (12) all_56_14 = all_6_2
% 111.71/16.60 (13) all_56_3 = all_52_1
% 111.71/16.60 (14) all_54_0 = all_10_2
% 111.71/16.60 (15) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.71/16.60 (16) all_54_3 = all_52_12
% 111.71/16.60 (17) ~ (all_52_12 = all_52_14)
% 111.71/16.60 (18) op(e0, e2) = all_52_7
% 111.71/16.60 (19) ~ (all_52_7 = all_4_2)
% 111.71/16.60 (20) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.71/16.60 (21) all_56_11 = all_52_11
% 111.71/16.60 (22) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 111.71/16.60 (23) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.60 (24) ~ (all_52_4 = all_52_8)
% 111.71/16.60 (25) ~ (all_52_12 = all_10_2)
% 111.71/16.60 (26) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 111.71/16.60 (27) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.60 (28) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.60 (29) all_56_12 = all_10_2
% 111.71/16.60 (30) all_58_0 = all_10_2
% 111.71/16.60 (31) all_54_11 = all_52_14
% 111.71/16.60 (32) all_54_13 = all_52_7
% 111.71/16.60 (33) ~ (all_52_14 = all_6_2)
% 111.71/16.60 (34) all_56_10 = all_52_7
% 111.71/16.60 (35) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 111.71/16.60 (36) all_54_14 = all_52_11
% 111.71/16.60 (37) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.60 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.60 (39) all_54_8 = all_52_2
% 111.71/16.60 (40) ~ (all_52_2 = all_6_2)
% 111.71/16.60 (41) ~ (all_52_1 = all_52_9)
% 111.71/16.60 (42) op(e1, all_6_2) = e2
% 111.71/16.60 (43) all_54_10 = all_6_2
% 111.71/16.60 (44) op(e3, e0) = all_52_12
% 111.71/16.60 (45) ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 111.71/16.60 (46) ~ (all_52_8 = all_6_2)
% 111.71/16.60 (47) all_58_4 = all_52_8
% 111.71/16.60 (48) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.71/16.60 (49) all_50_1 = all_10_1
% 111.71/16.60 (50) ~ (all_52_4 = all_52_7)
% 111.71/16.60 (51) all_56_2 = all_52_12
% 111.71/16.60 (52) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.71/16.60 (53) all_58_3 = all_8_2
% 111.71/16.60 (54) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.60 (55) all_10_0 = e2
% 111.71/16.60 (56) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 111.71/16.60 (57) all_58_11 = all_52_14
% 111.71/16.60 (58) all_54_9 = all_52_6
% 111.71/16.60 (59) op(e3, e1) = all_52_8
% 111.71/16.60 (60) ~ (all_52_2 = all_52_3)
% 111.71/16.60 (61) all_54_7 = all_52_13
% 111.71/16.60 (62) op(all_10_1, all_10_2) = all_10_0
% 111.71/16.60 (63) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.71/16.60 (64) ~ (all_52_11 = all_6_2)
% 111.71/16.60 (65) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 111.71/16.60 (66) op(e2, e3) = all_52_1
% 111.71/16.60 (67) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 111.71/16.60 (68) all_50_2 = all_10_2
% 111.71/16.60 (69) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.60 (70) ~ (all_52_7 = all_8_2)
% 111.71/16.60 (71) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.71/16.60 (72) ~ (all_52_4 = all_8_2)
% 111.71/16.60 (73) op(e1, e0) = all_52_14
% 111.71/16.60 (74) all_58_5 = all_52_9
% 111.71/16.60 (75) ~ (all_52_9 = all_52_13)
% 111.71/16.60 (76) all_56_9 = all_52_3
% 111.71/16.60 (77) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 111.71/16.60 (78) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 111.71/16.60 (79) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 111.71/16.60 (80) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 111.71/16.60 (81) all_58_15 = all_4_2
% 111.71/16.60 (82) all_58_2 = all_52_1
% 111.71/16.60 (83) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 111.71/16.60 (84) ~ (all_52_1 = all_52_13)
% 111.71/16.60 (85) all_18_1 = e2
% 111.71/16.60 (86) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 111.71/16.60 (87) ~ (all_10_2 = e3)
% 111.71/16.60 (88) ~ (all_52_12 = all_52_13)
% 111.71/16.60 (89) all_58_13 = all_52_7
% 111.71/16.60 (90) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 111.71/16.60 (91) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 111.71/16.60 (92) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.71/16.60 (93) ~ (all_52_14 = all_4_2)
% 111.71/16.60 (94) all_58_6 = all_52_2
% 111.71/16.60 (95) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.71/16.60 (96) ~ (all_52_1 = all_10_2)
% 111.71/16.60 (97) all_54_5 = all_8_2
% 111.71/16.60 (98) all_56_15 = all_4_2
% 111.71/16.60 (99) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.60 (100) all_58_10 = all_52_13
% 111.71/16.60 (101) ~ (all_52_13 = all_8_2)
% 111.71/16.60 (102) op(e2, all_8_2) = all_8_1
% 111.71/16.60 (103) ~ (all_52_11 = all_4_2)
% 111.71/16.60 (104) op(e2, all_6_2) = all_6_0
% 111.71/16.60 (105) op(e3, all_10_2) = all_10_1
% 111.71/16.60 (106) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 111.71/16.60 (107) ~ (all_52_6 = all_8_2)
% 111.71/16.60 (108) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 111.71/16.60 (109) all_58_1 = all_52_4
% 111.71/16.60 (110) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 111.71/16.60 (111) all_58_14 = all_52_11
% 111.71/16.60 (112) all_54_1 = all_52_4
% 111.71/16.60 (113) all_56_13 = all_8_2
% 111.71/16.60 (114) op(e0, e1) = all_52_11
% 111.71/16.60 (115) ~ (all_52_1 = all_8_2)
% 111.71/16.60 (116) ~ (all_8_2 = e2)
% 111.71/16.60 (117) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 111.71/16.61 (118) ~ (all_52_7 = all_52_11)
% 111.71/16.61 (119) op(e1, e2) = all_52_6
% 111.71/16.61 (120) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.61 (121) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 111.71/16.61 (122) all_56_7 = all_52_6
% 111.71/16.61 (123) ~ (all_52_4 = all_52_6)
% 111.71/16.61 (124) ~ (all_52_1 = all_52_2)
% 111.71/16.61 (125) ~ (all_52_4 = all_52_12)
% 111.71/16.61 (126) ~ (all_52_1 = all_52_3)
% 111.71/16.61 (127) all_56_1 = all_52_8
% 111.71/16.61 (128) op(e0, all_4_2) = all_4_1
% 111.71/16.61 (129) all_58_8 = all_6_2
% 111.71/16.61 (130) all_18_2 = all_6_2
% 111.71/16.61 (131) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.61 (132) all_50_0 = all_10_0
% 111.71/16.61 (133) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 111.71/16.61 (134) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.71/16.61 (135) all_56_4 = all_52_9
% 111.71/16.61 (136) all_58_9 = all_52_12
% 111.71/16.61 (137) all_56_5 = all_52_13
% 111.71/16.61 (138) op(e2, e1) = all_52_9
% 111.71/16.61 (139) ~ (all_52_3 = all_4_2)
% 111.71/16.61 (140) ~ (all_52_6 = all_6_2)
% 111.71/16.61 (141) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.61 (142) all_56_6 = all_52_2
% 111.71/16.61 (143) ~ (all_52_13 = all_4_2)
% 111.71/16.61 (144) all_58_12 = all_52_3
% 111.71/16.61 (145) ~ (all_52_2 = all_52_14)
% 111.71/16.61 (146) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.61 (147) ~ (all_52_8 = all_52_9)
% 111.71/16.61 (148) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 111.71/16.61 (149) op(e2, e0) = all_52_13
% 111.71/16.61 (150) ~ (all_52_12 = all_4_2)
% 111.71/16.61 (151) ~ (all_52_3 = all_10_2)
% 111.71/16.61 (152) op(e1, e3) = all_52_2
% 111.71/16.61 (153) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 111.71/16.61 (154) op(e1, e1) = all_6_2
% 111.71/16.61 (155) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.61 (156) ~ (all_8_1 = e1)
% 111.71/16.61 (157) ~ (all_52_8 = all_52_12)
% 111.71/16.61 (158) all_56_8 = all_52_14
% 111.71/16.61 (159) ~ (all_52_4 = all_10_2)
% 111.71/16.61 (160) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 111.71/16.61 (161) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.61 (162) all_56_0 = all_52_4
% 111.71/16.61 (163) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 111.71/16.61 (164) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.61 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.71/16.61 (165) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.71/16.61 (166) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 111.71/16.61 (167) all_54_15 = all_4_2
% 111.71/16.61 (168) ~ (all_6_2 = e1)
% 111.71/16.61 (169) ~ (all_52_6 = all_52_7)
% 111.71/16.61 (170) ~ (all_52_3 = all_52_11)
% 111.71/16.61 (171) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.61 (172) all_18_0 = all_6_0
% 111.71/16.61 (173) all_54_12 = all_52_3
% 111.71/16.61
% 111.71/16.61 Begin of proof
% 111.71/16.61 |
% 111.71/16.61 | COMBINE_EQS: (55), (132) imply:
% 111.71/16.61 | (174) all_50_0 = e2
% 111.71/16.61 |
% 111.71/16.61 | REDUCE: (55), (62) imply:
% 111.71/16.61 | (175) op(all_10_1, all_10_2) = e2
% 111.71/16.61 |
% 111.71/16.61 | BETA: splitting (45) gives:
% 111.71/16.61 |
% 111.71/16.61 | Case 1:
% 111.71/16.61 | |
% 111.71/16.61 | | (176) ~ (all_18_0 = e3)
% 111.71/16.61 | |
% 111.71/16.61 | | REDUCE: (172), (176) imply:
% 111.71/16.61 | | (177) ~ (all_6_0 = e3)
% 111.71/16.61 | |
% 111.71/16.61 | | BETA: splitting (27) gives:
% 111.71/16.61 | |
% 111.71/16.61 | | Case 1:
% 111.71/16.61 | | |
% 111.71/16.61 | | | (178) ~ (all_50_0 = e2)
% 111.71/16.61 | | |
% 111.71/16.61 | | | REDUCE: (174), (178) imply:
% 111.71/16.61 | | | (179) $false
% 111.71/16.61 | | |
% 111.71/16.61 | | | CLOSE: (179) is inconsistent.
% 111.71/16.61 | | |
% 111.71/16.61 | | Case 2:
% 111.71/16.61 | | |
% 111.71/16.61 | | | (180) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 111.71/16.61 | | |
% 111.71/16.61 | | | BETA: splitting (77) gives:
% 111.71/16.61 | | |
% 111.71/16.61 | | | Case 1:
% 111.71/16.61 | | | |
% 111.71/16.61 | | | | (181) ~ (all_56_15 = e1)
% 111.71/16.61 | | | |
% 111.71/16.61 | | | | REDUCE: (98), (181) imply:
% 111.71/16.61 | | | | (182) ~ (all_4_2 = e1)
% 111.71/16.61 | | | |
% 111.71/16.61 | | | | BETA: splitting (91) gives:
% 111.71/16.61 | | | |
% 111.71/16.61 | | | | Case 1:
% 111.71/16.61 | | | | |
% 111.71/16.61 | | | | | (183) ~ (all_56_14 = e2)
% 111.71/16.61 | | | | |
% 111.71/16.61 | | | | | REDUCE: (12), (183) imply:
% 111.71/16.61 | | | | | (184) ~ (all_6_2 = e2)
% 111.71/16.61 | | | | |
% 111.71/16.61 | | | | | BETA: splitting (92) gives:
% 111.71/16.61 | | | | |
% 111.71/16.61 | | | | | Case 1:
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | (185) ~ (all_56_12 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (29), (185) imply:
% 111.71/16.61 | | | | | | (186) ~ (all_10_2 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REF_CLOSE: (2), (5), (10), (14), (16), (23), (25), (29), (35), (38),
% 111.71/16.61 | | | | | | (44), (47), (48), (49), (51), (57), (59), (67), (68),
% 111.71/16.61 | | | | | | (74), (76), (78), (81), (83), (86), (87), (88), (98),
% 111.71/16.61 | | | | | | (100), (103), (105), (111), (127), (129), (131), (133),
% 111.71/16.61 | | | | | | (135), (136), (138), (139), (141), (147), (148), (149),
% 111.71/16.61 | | | | | | (151), (158), (160), (167), (170), (173), (175), (180),
% 111.71/16.61 | | | | | | (182), (184), (186) are inconsistent by sub-proof #155.
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | Case 2:
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | (187) all_56_12 = e2
% 111.71/16.61 | | | | | | (188) ~ (all_56_10 = e0)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | COMBINE_EQS: (29), (187) imply:
% 111.71/16.61 | | | | | | (189) all_10_2 = e2
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | SIMP: (189) implies:
% 111.71/16.61 | | | | | | (190) all_10_2 = e2
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | COMBINE_EQS: (30), (190) imply:
% 111.71/16.61 | | | | | | (191) all_58_0 = e2
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (34), (188) imply:
% 111.71/16.61 | | | | | | (192) ~ (all_52_7 = e0)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (96), (190) imply:
% 111.71/16.61 | | | | | | (193) ~ (all_52_1 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (3), (190) imply:
% 111.71/16.61 | | | | | | (194) ~ (all_52_2 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (159), (190) imply:
% 111.71/16.61 | | | | | | (195) ~ (all_52_4 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (87), (190) imply:
% 111.71/16.61 | | | | | | (196) ~ (e3 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | SIMP: (196) implies:
% 111.71/16.61 | | | | | | (197) ~ (e3 = e2)
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (175), (190) imply:
% 111.71/16.61 | | | | | | (198) op(all_10_1, e2) = e2
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | REDUCE: (105), (190) imply:
% 111.71/16.61 | | | | | | (199) op(e3, e2) = all_10_1
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | BETA: splitting (166) gives:
% 111.71/16.61 | | | | | |
% 111.71/16.61 | | | | | | Case 1:
% 111.71/16.61 | | | | | | |
% 111.71/16.61 | | | | | | | (200) ~ (all_56_0 = e3)
% 111.71/16.61 | | | | | | |
% 111.71/16.61 | | | | | | | REDUCE: (162), (200) imply:
% 111.71/16.61 | | | | | | | (201) ~ (all_52_4 = e3)
% 111.71/16.61 | | | | | | |
% 111.71/16.61 | | | | | | | BETA: splitting (79) gives:
% 111.71/16.61 | | | | | | |
% 111.71/16.61 | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | (202) ~ (all_56_7 = e1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (122), (202) imply:
% 111.71/16.61 | | | | | | | | (203) ~ (all_52_6 = e1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | GROUND_INST: instantiating (38) with all_52_4, all_10_1, e2, e3,
% 111.71/16.61 | | | | | | | | simplifying with (11), (199) gives:
% 111.71/16.61 | | | | | | | | (204) all_52_4 = all_10_1
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | COMBINE_EQS: (112), (204) imply:
% 111.71/16.61 | | | | | | | | (205) all_54_1 = all_10_1
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | COMBINE_EQS: (109), (204) imply:
% 111.71/16.61 | | | | | | | | (206) all_58_1 = all_10_1
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (123), (204) imply:
% 111.71/16.61 | | | | | | | | (207) ~ (all_52_6 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | SIMP: (207) implies:
% 111.71/16.61 | | | | | | | | (208) ~ (all_52_6 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (50), (204) imply:
% 111.71/16.61 | | | | | | | | (209) ~ (all_52_7 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | SIMP: (209) implies:
% 111.71/16.61 | | | | | | | | (210) ~ (all_52_7 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (24), (204) imply:
% 111.71/16.61 | | | | | | | | (211) ~ (all_52_8 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | SIMP: (211) implies:
% 111.71/16.61 | | | | | | | | (212) ~ (all_52_8 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (125), (204) imply:
% 111.71/16.61 | | | | | | | | (213) ~ (all_52_12 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | SIMP: (213) implies:
% 111.71/16.61 | | | | | | | | (214) ~ (all_52_12 = all_10_1)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (201), (204) imply:
% 111.71/16.61 | | | | | | | | (215) ~ (all_10_1 = e3)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | REDUCE: (195), (204) imply:
% 111.71/16.61 | | | | | | | | (216) ~ (all_10_1 = e2)
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | BETA: splitting (110) gives:
% 111.71/16.61 | | | | | | | |
% 111.71/16.61 | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | |
% 111.71/16.61 | | | | | | | | | (217) ~ (all_56_2 = e3)
% 111.71/16.61 | | | | | | | | |
% 111.71/16.61 | | | | | | | | | REDUCE: (51), (217) imply:
% 111.71/16.61 | | | | | | | | | (218) ~ (all_52_12 = e3)
% 111.71/16.61 | | | | | | | | |
% 111.71/16.61 | | | | | | | | | BETA: splitting (155) gives:
% 111.71/16.61 | | | | | | | | |
% 111.71/16.61 | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | (219) all_58_0 = e3
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | REF_CLOSE: (191), (197), (219) are inconsistent by sub-proof
% 111.71/16.61 | | | | | | | | | | #154.
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | Case 2:
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | (220) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | BETA: splitting (220) gives:
% 111.71/16.61 | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | (221) all_58_1 = e3
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | COMBINE_EQS: (206), (221) imply:
% 111.71/16.61 | | | | | | | | | | | (222) all_10_1 = e3
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | REDUCE: (215), (222) imply:
% 111.71/16.61 | | | | | | | | | | | (223) $false
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | Case 2:
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | (224) all_58_4 = e3 | all_58_9 = e3
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | BETA: splitting (224) gives:
% 111.71/16.61 | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | (225) all_58_4 = e3
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | COMBINE_EQS: (47), (225) imply:
% 111.71/16.61 | | | | | | | | | | | | (226) all_52_8 = e3
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | REDUCE: (147), (226) imply:
% 111.71/16.61 | | | | | | | | | | | | (227) ~ (all_52_9 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | SIMP: (227) implies:
% 111.71/16.61 | | | | | | | | | | | | (228) ~ (all_52_9 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | REDUCE: (157), (226) imply:
% 111.71/16.61 | | | | | | | | | | | | (229) ~ (all_52_12 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | REDUCE: (212), (226) imply:
% 111.71/16.61 | | | | | | | | | | | | (230) ~ (all_10_1 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | REDUCE: (46), (226) imply:
% 111.71/16.61 | | | | | | | | | | | | (231) ~ (all_6_2 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | SIMP: (231) implies:
% 111.71/16.61 | | | | | | | | | | | | (232) ~ (all_6_2 = e3)
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | BETA: splitting (37) gives:
% 111.71/16.61 | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | (233) all_54_10 = e3
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | COMBINE_EQS: (43), (233) imply:
% 111.71/16.61 | | | | | | | | | | | | | (234) all_6_2 = e3
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | REDUCE: (232), (234) imply:
% 111.71/16.61 | | | | | | | | | | | | | (235) $false
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | Case 2:
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | (236) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | BETA: splitting (161) gives:
% 111.71/16.61 | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | (237) all_58_2 = e2
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | REF_CLOSE: (82), (193), (237) are inconsistent by sub-proof
% 111.71/16.61 | | | | | | | | | | | | | | #335.
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | Case 2:
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | (238) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 111.71/16.61 | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | (239) all_58_3 = e2
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | COMBINE_EQS: (53), (239) imply:
% 111.71/16.61 | | | | | | | | | | | | | | | (240) all_8_2 = e2
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | REDUCE: (116), (240) imply:
% 111.71/16.61 | | | | | | | | | | | | | | | (241) $false
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | Case 2:
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | (242) all_58_5 = e2 | all_58_10 = e2
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 111.71/16.61 | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | Case 1:
% 111.71/16.61 | | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | | (243) all_58_5 = e2
% 111.71/16.61 | | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (243) imply:
% 111.71/16.61 | | | | | | | | | | | | | | | | (244) all_52_9 = e2
% 111.71/16.61 | | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 111.71/16.61 | | | | | | | | | | | | | | | | (245) all_52_9 = e2
% 111.71/16.61 | | | | | | | | | | | | | | | |
% 111.71/16.61 | | | | | | | | | | | | | | | | REDUCE: (75), (245) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | (246) ~ (all_52_13 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | SIMP: (246) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | (247) ~ (all_52_13 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | REDUCE: (8), (245) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | (248) ~ (all_8_2 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | (249) all_58_6 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (249) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (250) all_52_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | SIMP: (250) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (251) all_52_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (251) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (252) all_56_6 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REDUCE: (124), (251) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (253) ~ (all_52_1 = e1)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REDUCE: (194), (251) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (254) ~ (e2 = e1)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (255) ~ (e2 = e1)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (256) ~ (all_56_6 = e1)
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | REDUCE: (252), (256) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (257) $false
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (258) ~ (all_56_13 = e3)
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | REDUCE: (113), (258) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (259) ~ (all_8_2 = e3)
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (260) all_54_5 = e3
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (259), (260) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | #339.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (261) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (262) all_54_5 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (116), (262) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | #338.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (263) all_54_5 = e1 | all_54_5 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (264) all_58_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (264) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (265) all_52_1 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (265) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (266) $false
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (267) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (268) all_58_3 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (268) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (269) all_8_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (21), (26), (37), (43), (53), (63),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (65), (69), (74), (76), (81), (82), (89), (100),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (111), (113), (135), (137), (144), (161), (164),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (168), (184), (192), (193), (255), (269) are
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #426.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (270) all_58_5 = e1 | all_58_10 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_5 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (271) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (272) e2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (272) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (273) $false
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_10 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (274) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (275) all_52_13 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (275) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (276) op(e2, e0) = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (277) all_54_5 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (277) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (278) all_8_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (278) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (279) all_8_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (21), (26), (37), (43), (53), (63),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (65), (69), (74), (76), (81), (82), (89), (100),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (111), (113), (135), (137), (144), (161), (164),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (168), (184), (192), (193), (255), (279) are
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #426.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (280) all_54_5 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (280) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (281) all_8_2 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (281) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (282) all_8_2 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (282) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | (283) op(e2, e0) = all_8_1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (156), (276), (283) are inconsistent by
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #152.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | (284) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (22), (33), (37), (43), (46), (47),
% 111.71/16.62 | | | | | | | | | | | | | | | | | (57), (129), (136), (155), (158), (168), (184),
% 111.71/16.62 | | | | | | | | | | | | | | | | | (191), (197), (203), (206), (215), (218), (284)
% 111.71/16.62 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #151.
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | (285) all_58_10 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (43), (69), (100), (137), (168), (184),
% 111.71/16.62 | | | | | | | | | | | | | | | | (236), (285) are inconsistent by sub-proof #51.
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | (286) all_58_9 = e3
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | COMBINE_EQS: (136), (286) imply:
% 111.71/16.62 | | | | | | | | | | | | (287) all_52_12 = e3
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | REDUCE: (218), (287) imply:
% 111.71/16.62 | | | | | | | | | | | | (288) $false
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | CLOSE: (288) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | End of split
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | (289) all_56_2 = e3
% 111.71/16.62 | | | | | | | | | (290) ~ (all_56_13 = e0)
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | COMBINE_EQS: (51), (289) imply:
% 111.71/16.62 | | | | | | | | | (291) all_52_12 = e3
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | COMBINE_EQS: (136), (291) imply:
% 111.71/16.62 | | | | | | | | | (292) all_58_9 = e3
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | REDUCE: (113), (290) imply:
% 111.71/16.62 | | | | | | | | | (293) ~ (all_8_2 = e0)
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | REDUCE: (214), (291) imply:
% 111.71/16.62 | | | | | | | | | (294) ~ (all_10_1 = e3)
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | REDUCE: (150), (291) imply:
% 111.71/16.62 | | | | | | | | | (295) ~ (all_4_2 = e3)
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | SIMP: (295) implies:
% 111.71/16.62 | | | | | | | | | (296) ~ (all_4_2 = e3)
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | BETA: splitting (48) gives:
% 111.71/16.62 | | | | | | | | |
% 111.71/16.62 | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | (297) all_54_15 = e3
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | REF_CLOSE: (167), (296), (297) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | #312.
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | (298) ~ (all_54_15 = e3)
% 111.71/16.62 | | | | | | | | | | (299) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | BETA: splitting (54) gives:
% 111.71/16.62 | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | (300) ~ (all_56_2 = e3)
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | REDUCE: (289), (300) imply:
% 111.71/16.62 | | | | | | | | | | | (301) $false
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | (302) ~ (all_56_14 = e0)
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | REDUCE: (12), (302) imply:
% 111.71/16.62 | | | | | | | | | | | (303) ~ (all_6_2 = e0)
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | BETA: splitting (37) gives:
% 111.71/16.62 | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | (304) all_54_10 = e3
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | COMBINE_EQS: (43), (304) imply:
% 111.71/16.62 | | | | | | | | | | | | (305) all_6_2 = e3
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | COMBINE_EQS: (12), (305) imply:
% 111.71/16.62 | | | | | | | | | | | | (306) all_56_14 = e3
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | REDUCE: (40), (305) imply:
% 111.71/16.62 | | | | | | | | | | | | (307) ~ (all_52_2 = e3)
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | REDUCE: (140), (305) imply:
% 111.71/16.62 | | | | | | | | | | | | (308) ~ (all_52_6 = e3)
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | REDUCE: (33), (305) imply:
% 111.71/16.62 | | | | | | | | | | | | (309) ~ (all_52_14 = e3)
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | BETA: splitting (63) gives:
% 111.71/16.62 | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | (310) ~ (all_56_14 = e3)
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | REDUCE: (306), (310) imply:
% 111.71/16.62 | | | | | | | | | | | | | (311) $false
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | CLOSE: (311) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | (312) ~ (all_56_9 = e0)
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | REDUCE: (76), (312) imply:
% 111.71/16.62 | | | | | | | | | | | | | (313) ~ (all_52_3 = e0)
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | BETA: splitting (164) gives:
% 111.71/16.62 | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | (314) all_58_15 = e0
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | COMBINE_EQS: (81), (314) imply:
% 111.71/16.62 | | | | | | | | | | | | | | (315) all_4_2 = e0
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | REDUCE: (10), (315) imply:
% 111.71/16.62 | | | | | | | | | | | | | | (316) $false
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | CLOSE: (316) is inconsistent.
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | (317) ~ (all_58_15 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | (318) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 111.71/16.62 | | | | | | | | | | | | | | e0)
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | ALPHA: (318) implies:
% 111.71/16.62 | | | | | | | | | | | | | | (319) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 111.71/16.62 | | | | | | | | | | | | | | (320) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 111.71/16.62 | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | (321) all_58_12 = e0
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | REF_CLOSE: (144), (313), (321) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | #362.
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | (322) all_58_13 = e0 | all_58_14 = e0
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 111.71/16.62 | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | (323) all_54_8 = e3
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (307), (323) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | #399.
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | (324) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | (325) all_54_15 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (325) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (326) all_4_2 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | SIMP: (326) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (327) all_4_2 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REDUCE: (19), (327) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (328) ~ (all_52_7 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REDUCE: (93), (327) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (329) ~ (all_52_14 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | REDUCE: (182), (327) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | (330) ~ (e2 = e1)
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (331) all_54_8 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (331) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | | | #382.
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | (332) all_54_8 = e1 | all_54_8 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (333) all_54_8 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (333) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (334) all_52_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | SIMP: (334) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (335) all_52_2 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (335) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (336) all_56_6 = e1
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (37), (43), (52), (64), (89), (111), (168),
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (184), (192), (322), (336) are inconsistent by
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | sub-proof #304.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (337) all_54_8 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (337) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (338) all_52_2 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (339) all_52_2 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | REDUCE: (145), (339) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (340) ~ (all_52_14 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | SIMP: (340) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | (341) ~ (all_52_14 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (342) all_58_1 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (342) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (343) all_10_1 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (343) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (344) ~ (all_52_6 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (343) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (345) ~ (e3 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (346) ~ (e3 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (216), (343) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (347) ~ (e2 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | SIMP: (347) implies:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (348) ~ (e2 = e0)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (343) imply:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | (349) op(e0, e2) = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (350) all_54_11 = e3
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (309), (350) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | #388.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_54_11 = e3)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | (352) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (353) all_54_11 = e2
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (329), (353) are inconsistent by sub-proof
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | #387.
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_54_11 = e2)
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | (355) all_54_11 = e1 | all_54_11 = e0
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.62 | | | | | | | | | | | | | | | | | | | | | | | (356) all_54_11 = e1
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (356) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (357) all_52_14 = e1
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (357) implies:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (358) all_52_14 = e1
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (358) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_11 = e1
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (358) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_52_13 = e1)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (358) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (361) ~ (e3 = e1)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (361) implies:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (362) ~ (e3 = e1)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (358) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (363) ~ (e2 = e1)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (341), (358) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (364) ~ (e1 = e0)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | (365) all_54_9 = e3
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (365) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | (366) all_52_6 = e3
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (366) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | (367) $false
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (367) is inconsistent.
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | (368) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_54_9 = e2
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (369) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_52_6 = e2
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (370) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_58_7 = e2
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (18), (19), (21), (26), (32), (37),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (38), (43), (53), (63), (65), (69), (74), (76),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (89), (90), (100), (111), (113),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (116), (128), (135), (137), (143), (144), (161),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (168), (184), (192), (193), (197),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (292), (320), (330), (342), (346), (348), (349),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (359), (360), (362), (364), (371) are inconsistent
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #161.
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_54_9 = e1 | all_54_9 = e0
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (203), (344), (372) are inconsistent by
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159.
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | (373) all_54_11 = e0
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (341), (373) are inconsistent by sub-proof
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | | #384.
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (374) ~ (all_58_1 = e0)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (374) imply:
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (375) ~ (all_10_1 = e0)
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (15), (21), (26), (28), (32), (37),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (43), (53), (63), (65), (69), (70), (74), (76),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (81), (82), (89), (97), (100), (111), (113),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (116), (121), (135), (137), (144), (161), (164),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (168), (184), (192), (193), (205), (210), (215),
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | (216), (293), (328), (330), (375) are inconsistent
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | | by sub-proof #160.
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | (376) all_54_15 = e1 | all_54_15 = e0
% 111.71/16.63 | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (167), (182), (376) are inconsistent by
% 111.71/16.63 | | | | | | | | | | | | | | | | | sub-proof #418.
% 111.71/16.63 | | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | (377) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.63 | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | | REF_CLOSE: (43), (168), (184), (303), (377) are inconsistent
% 111.71/16.63 | | | | | | | | | | | | by sub-proof #435.
% 111.71/16.63 | | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | | |
% 111.71/16.63 | | | | | | | | | End of split
% 111.71/16.63 | | | | | | | | |
% 111.71/16.63 | | | | | | | | End of split
% 111.71/16.63 | | | | | | | |
% 111.71/16.63 | | | | | | | Case 2:
% 111.71/16.63 | | | | | | | |
% 111.71/16.63 | | | | | | | | (378) ~ (all_56_12 = e2)
% 111.71/16.63 | | | | | | | |
% 111.71/16.63 | | | | | | | | REDUCE: (187), (378) imply:
% 111.71/16.63 | | | | | | | | (379) $false
% 111.71/16.63 | | | | | | | |
% 111.71/16.63 | | | | | | | | CLOSE: (379) is inconsistent.
% 111.71/16.63 | | | | | | | |
% 111.71/16.63 | | | | | | | End of split
% 111.71/16.63 | | | | | | |
% 111.71/16.63 | | | | | | Case 2:
% 111.71/16.63 | | | | | | |
% 111.71/16.63 | | | | | | | (380) ~ (all_56_12 = e2)
% 111.71/16.63 | | | | | | |
% 111.71/16.63 | | | | | | | REDUCE: (187), (380) imply:
% 111.71/16.63 | | | | | | | (381) $false
% 111.71/16.63 | | | | | | |
% 111.71/16.63 | | | | | | | CLOSE: (381) is inconsistent.
% 111.71/16.63 | | | | | | |
% 111.71/16.63 | | | | | | End of split
% 111.71/16.63 | | | | | |
% 111.71/16.63 | | | | | End of split
% 111.71/16.63 | | | | |
% 111.71/16.63 | | | | Case 2:
% 111.71/16.63 | | | | |
% 111.71/16.63 | | | | | (382) all_56_14 = e2
% 111.71/16.63 | | | | |
% 111.71/16.63 | | | | | COMBINE_EQS: (12), (382) imply:
% 111.71/16.63 | | | | | (383) all_6_2 = e2
% 111.71/16.63 | | | | |
% 111.71/16.63 | | | | | REF_CLOSE: (38), (42), (119), (140), (383) are inconsistent by
% 111.71/16.63 | | | | | sub-proof #39.
% 111.71/16.63 | | | | |
% 111.71/16.63 | | | | End of split
% 111.71/16.63 | | | |
% 111.71/16.63 | | | Case 2:
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | (384) all_56_15 = e1
% 111.71/16.63 | | | | (385) ~ (all_56_11 = e0)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | COMBINE_EQS: (98), (384) imply:
% 111.71/16.63 | | | | (386) all_4_2 = e1
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | SIMP: (386) implies:
% 111.71/16.63 | | | | (387) all_4_2 = e1
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | COMBINE_EQS: (81), (387) imply:
% 111.71/16.63 | | | | (388) all_58_15 = e1
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (21), (385) imply:
% 111.71/16.63 | | | | (389) ~ (all_52_11 = e0)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (103), (387) imply:
% 111.71/16.63 | | | | (390) ~ (all_52_11 = e1)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (150), (387) imply:
% 111.71/16.63 | | | | (391) ~ (all_52_12 = e1)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (143), (387) imply:
% 111.71/16.63 | | | | (392) ~ (all_52_13 = e1)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (93), (387) imply:
% 111.71/16.63 | | | | (393) ~ (all_52_14 = e1)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (10), (387) imply:
% 111.71/16.63 | | | | (394) ~ (e1 = e0)
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REDUCE: (128), (387) imply:
% 111.71/16.63 | | | | (395) op(e0, e1) = all_4_1
% 111.71/16.63 | | | |
% 111.71/16.63 | | | | REF_CLOSE: (1), (2), (5), (6), (12), (14), (15), (16), (17), (20), (23),
% 111.71/16.63 | | | | (28), (29), (30), (32), (34), (36), (37), (38), (40), (42),
% 111.71/16.63 | | | | (43), (47), (50), (51), (52), (53), (54), (57), (59), (61),
% 111.71/16.63 | | | | (63), (64), (69), (70), (72), (73), (74), (76), (82), (87),
% 111.71/16.63 | | | | (88), (89), (92), (94), (95), (96), (97), (99), (100), (104),
% 111.71/16.63 | | | | (105), (107), (109), (111), (114), (116), (118), (119),
% 111.71/16.63 | | | | (120), (127), (129), (131), (135), (136), (137), (138),
% 111.71/16.63 | | | | (140), (141), (142), (144), (146), (147), (149), (155),
% 111.71/16.63 | | | | (161), (162), (164), (165), (168), (169), (171), (175),
% 111.71/16.63 | | | | (177), (384), (388), (389), (390), (391), (392), (393),
% 111.71/16.63 | | | | (394), (395) are inconsistent by sub-proof #22.
% 111.71/16.63 | | | |
% 111.71/16.63 | | | End of split
% 111.71/16.63 | | |
% 111.71/16.63 | | End of split
% 111.71/16.63 | |
% 111.71/16.63 | Case 2:
% 111.71/16.63 | |
% 111.71/16.63 | | (396) all_18_0 = e3
% 111.71/16.63 | | (397) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 111.71/16.63 | |
% 111.71/16.63 | | REF_CLOSE: (3), (7), (12), (13), (14), (26), (28), (29), (30), (37), (38),
% 111.71/16.63 | | (42), (43), (53), (60), (61), (63), (66), (74), (76), (82), (84),
% 111.71/16.63 | | (85), (91), (96), (97), (99), (100), (101), (102), (104), (108),
% 111.71/16.63 | | (113), (115), (116), (119), (126), (130), (131), (135), (137),
% 111.71/16.63 | | (140), (148), (149), (151), (152), (153), (154), (156), (161),
% 111.71/16.63 | | (168), (172), (173), (396), (397) are inconsistent by sub-proof
% 111.71/16.63 | | #29.
% 111.71/16.63 | |
% 111.71/16.63 | End of split
% 111.71/16.63 |
% 111.71/16.63 End of proof
% 111.71/16.63
% 111.71/16.63 Sub-proof #22 shows that the following formulas are inconsistent:
% 111.71/16.63 ----------------------------------------------------------------
% 111.71/16.63 (1) ~ (all_52_8 = all_10_2)
% 111.71/16.63 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 111.71/16.63 (3) all_54_2 = all_52_8
% 111.71/16.63 (4) all_58_7 = all_52_6
% 111.71/16.63 (5) all_56_14 = all_6_2
% 111.71/16.63 (6) all_54_0 = all_10_2
% 111.71/16.63 (7) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.71/16.63 (8) all_54_3 = all_52_12
% 111.71/16.63 (9) ~ (all_52_12 = all_52_14)
% 111.71/16.63 (10) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 111.71/16.63 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.63 (12) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.63 (13) all_56_12 = all_10_2
% 111.71/16.63 (14) all_58_0 = all_10_2
% 111.71/16.63 (15) all_54_13 = all_52_7
% 111.71/16.63 (16) all_56_10 = all_52_7
% 111.71/16.63 (17) all_54_14 = all_52_11
% 111.71/16.63 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.63 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.63 (20) ~ (all_52_2 = all_6_2)
% 111.71/16.63 (21) op(e1, all_6_2) = e2
% 111.71/16.63 (22) all_54_10 = all_6_2
% 111.71/16.63 (23) ~ (all_52_14 = e1)
% 111.71/16.63 (24) all_58_4 = all_52_8
% 111.71/16.63 (25) ~ (all_52_4 = all_52_7)
% 111.71/16.63 (26) all_56_2 = all_52_12
% 111.71/16.63 (27) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 111.71/16.63 (28) ~ (all_52_12 = e1)
% 111.71/16.63 (29) all_58_3 = all_8_2
% 111.71/16.63 (30) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.63 (31) all_58_11 = all_52_14
% 111.71/16.63 (32) op(e3, e1) = all_52_8
% 111.71/16.63 (33) all_58_15 = e1
% 111.71/16.63 (34) all_54_7 = all_52_13
% 111.71/16.63 (35) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 111.71/16.63 (36) ~ (all_52_11 = all_6_2)
% 111.71/16.63 (37) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.63 (38) ~ (all_6_0 = e3)
% 111.71/16.63 (39) ~ (all_52_7 = all_8_2)
% 111.71/16.63 (40) ~ (all_52_4 = all_8_2)
% 111.71/16.63 (41) all_56_15 = e1
% 111.71/16.64 (42) op(e1, e0) = all_52_14
% 111.71/16.64 (43) all_58_5 = all_52_9
% 111.71/16.64 (44) all_56_9 = all_52_3
% 111.71/16.64 (45) all_58_2 = all_52_1
% 111.71/16.64 (46) ~ (all_10_2 = e3)
% 111.71/16.64 (47) ~ (all_52_12 = all_52_13)
% 111.71/16.64 (48) all_58_13 = all_52_7
% 111.71/16.64 (49) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 111.71/16.64 (50) all_58_6 = all_52_2
% 111.71/16.64 (51) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 111.71/16.64 (52) ~ (all_52_1 = all_10_2)
% 111.71/16.64 (53) ~ (all_52_13 = e1)
% 111.71/16.64 (54) all_54_5 = all_8_2
% 111.71/16.64 (55) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.64 (56) all_58_10 = all_52_13
% 111.71/16.64 (57) op(e2, all_6_2) = all_6_0
% 111.71/16.64 (58) op(e3, all_10_2) = all_10_1
% 111.71/16.64 (59) ~ (all_52_6 = all_8_2)
% 111.71/16.64 (60) all_58_1 = all_52_4
% 111.71/16.64 (61) all_58_14 = all_52_11
% 111.71/16.64 (62) op(e0, e1) = all_4_1
% 111.71/16.64 (63) op(e0, e1) = all_52_11
% 111.71/16.64 (64) ~ (all_8_2 = e2)
% 111.71/16.64 (65) ~ (all_52_7 = all_52_11)
% 111.71/16.64 (66) op(e1, e2) = all_52_6
% 111.71/16.64 (67) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.64 (68) all_56_1 = all_52_8
% 111.71/16.64 (69) all_58_8 = all_6_2
% 111.71/16.64 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 111.71/16.64 (71) all_56_4 = all_52_9
% 111.71/16.64 (72) all_58_9 = all_52_12
% 111.71/16.64 (73) all_56_5 = all_52_13
% 111.71/16.64 (74) op(e2, e1) = all_52_9
% 111.71/16.64 (75) ~ (all_52_6 = all_6_2)
% 111.71/16.64 (76) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 111.71/16.64 (77) all_56_6 = all_52_2
% 111.71/16.64 (78) all_58_12 = all_52_3
% 111.71/16.64 (79) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 111.71/16.64 (80) ~ (all_52_8 = all_52_9)
% 111.71/16.64 (81) op(e2, e0) = all_52_13
% 111.71/16.64 (82) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 111.71/16.64 (83) op(all_10_1, all_10_2) = e2
% 111.71/16.64 (84) ~ (all_52_11 = e1)
% 111.71/16.64 (85) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.64 (86) all_56_0 = all_52_4
% 111.71/16.64 (87) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.64 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 111.71/16.64 (88) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 111.71/16.64 (89) ~ (all_52_11 = e0)
% 111.71/16.64 (90) ~ (all_6_2 = e1)
% 111.71/16.64 (91) ~ (all_52_6 = all_52_7)
% 111.71/16.64 (92) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 111.71/16.64 (93) ~ (e1 = e0)
% 111.71/16.64
% 111.71/16.64 Begin of proof
% 111.71/16.64 |
% 111.71/16.64 | BETA: splitting (51) gives:
% 111.71/16.64 |
% 111.71/16.64 | Case 1:
% 111.71/16.64 | |
% 111.71/16.64 | | (94) ~ (all_56_1 = e3)
% 111.71/16.64 | |
% 111.71/16.64 | | REDUCE: (68), (94) imply:
% 111.71/16.64 | | (95) ~ (all_52_8 = e3)
% 111.71/16.64 | |
% 111.71/16.64 | | BETA: splitting (79) gives:
% 111.71/16.64 | |
% 111.71/16.64 | | Case 1:
% 111.71/16.64 | | |
% 111.71/16.64 | | | (96) ~ (all_56_4 = e2)
% 111.71/16.64 | | |
% 111.71/16.64 | | | REDUCE: (71), (96) imply:
% 111.71/16.64 | | | (97) ~ (all_52_9 = e2)
% 111.71/16.64 | | |
% 111.71/16.64 | | | GROUND_INST: instantiating (19) with all_52_11, all_4_1, e1, e0,
% 111.71/16.64 | | | simplifying with (62), (63) gives:
% 111.71/16.64 | | | (98) all_52_11 = all_4_1
% 111.71/16.64 | | |
% 111.71/16.64 | | | COMBINE_EQS: (17), (98) imply:
% 111.71/16.64 | | | (99) all_54_14 = all_4_1
% 111.71/16.64 | | |
% 111.71/16.64 | | | REDUCE: (65), (98) imply:
% 111.71/16.64 | | | (100) ~ (all_52_7 = all_4_1)
% 111.71/16.64 | | |
% 111.71/16.64 | | | REDUCE: (36), (98) imply:
% 111.71/16.64 | | | (101) ~ (all_6_2 = all_4_1)
% 111.71/16.64 | | |
% 111.71/16.64 | | | SIMP: (101) implies:
% 111.71/16.64 | | | (102) ~ (all_6_2 = all_4_1)
% 111.71/16.64 | | |
% 111.71/16.64 | | | BETA: splitting (49) gives:
% 111.71/16.64 | | |
% 111.71/16.64 | | | Case 1:
% 111.71/16.64 | | | |
% 111.71/16.64 | | | | (103) ~ (all_56_12 = e2)
% 111.71/16.64 | | | |
% 111.71/16.64 | | | | REDUCE: (13), (103) imply:
% 111.71/16.64 | | | | (104) ~ (all_10_2 = e2)
% 111.71/16.64 | | | |
% 111.71/16.64 | | | | BETA: splitting (88) gives:
% 111.71/16.64 | | | |
% 111.71/16.64 | | | | Case 1:
% 111.71/16.64 | | | | |
% 111.71/16.64 | | | | | (105) ~ (all_56_0 = e3)
% 111.71/16.64 | | | | |
% 111.71/16.64 | | | | | REDUCE: (86), (105) imply:
% 111.71/16.68 | | | | | (106) ~ (all_52_4 = e3)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | REF_CLOSE: (1), (2), (3), (6), (10), (13), (14), (19), (24), (26),
% 111.71/16.68 | | | | | (32), (46), (58), (60), (70), (72), (74), (76), (80), (82),
% 111.71/16.68 | | | | | (83), (95), (104), (106) are inconsistent by sub-proof
% 111.71/16.68 | | | | | #142.
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | Case 2:
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | (107) all_56_0 = e3
% 111.71/16.68 | | | | | (108) ~ (all_56_14 = e2)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | COMBINE_EQS: (86), (107) imply:
% 111.71/16.68 | | | | | (109) all_52_4 = e3
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | REDUCE: (5), (108) imply:
% 111.71/16.68 | | | | | (110) ~ (all_6_2 = e2)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | REDUCE: (25), (109) imply:
% 111.71/16.68 | | | | | (111) ~ (all_52_7 = e3)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | SIMP: (111) implies:
% 111.71/16.68 | | | | | (112) ~ (all_52_7 = e3)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | REDUCE: (40), (109) imply:
% 111.71/16.68 | | | | | (113) ~ (all_8_2 = e3)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | SIMP: (113) implies:
% 111.71/16.68 | | | | | (114) ~ (all_8_2 = e3)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | BETA: splitting (27) gives:
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | Case 1:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | (115) ~ (all_56_6 = e1)
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | REDUCE: (77), (115) imply:
% 111.71/16.68 | | | | | | (116) ~ (all_52_2 = e1)
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | BETA: splitting (67) gives:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | Case 1:
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | (117) all_58_6 = e1
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | REF_CLOSE: (50), (116), (117) are inconsistent by sub-proof #452.
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | Case 2:
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | (118) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | BETA: splitting (118) gives:
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | Case 1:
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | | (119) all_58_7 = e1
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (11), (12), (15), (17),
% 111.71/16.68 | | | | | | | | (18), (19), (21), (22), (26), (28), (30), (34), (37),
% 111.71/16.68 | | | | | | | | (38), (39), (42), (47), (53), (54), (55), (57), (59),
% 111.71/16.68 | | | | | | | | (64), (73), (75), (81), (84), (89), (91), (92), (99),
% 111.71/16.68 | | | | | | | | (100), (102), (110), (112), (114), (119) are
% 111.71/16.68 | | | | | | | | inconsistent by sub-proof #25.
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | Case 2:
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | | (120) all_58_8 = e1 | all_58_11 = e1
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | | REF_CLOSE: (23), (31), (69), (90), (120) are inconsistent by
% 111.71/16.68 | | | | | | | | sub-proof #445.
% 111.71/16.68 | | | | | | | |
% 111.71/16.68 | | | | | | | End of split
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | End of split
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | Case 2:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | (121) all_56_6 = e1
% 111.71/16.68 | | | | | | (122) ~ (all_56_14 = e3)
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | REF_CLOSE: (5), (8), (9), (11), (18), (19), (20), (21), (22), (26),
% 111.71/16.68 | | | | | | (28), (30), (34), (37), (38), (42), (47), (53), (55),
% 111.71/16.68 | | | | | | (57), (73), (77), (81), (110), (121), (122) are
% 111.71/16.68 | | | | | | inconsistent by sub-proof #24.
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | End of split
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | End of split
% 111.71/16.68 | | | |
% 111.71/16.68 | | | Case 2:
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | (123) all_56_12 = e2
% 111.71/16.68 | | | | (124) ~ (all_56_10 = e0)
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | COMBINE_EQS: (13), (123) imply:
% 111.71/16.68 | | | | (125) all_10_2 = e2
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | SIMP: (125) implies:
% 111.71/16.68 | | | | (126) all_10_2 = e2
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | REDUCE: (16), (124) imply:
% 111.71/16.68 | | | | (127) ~ (all_52_7 = e0)
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | REDUCE: (52), (126) imply:
% 111.71/16.68 | | | | (128) ~ (all_52_1 = e2)
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | BETA: splitting (87) gives:
% 111.71/16.68 | | | |
% 111.71/16.68 | | | | Case 1:
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | (129) all_58_15 = e0
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | COMBINE_EQS: (33), (129) imply:
% 111.71/16.68 | | | | | (130) e1 = e0
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | REDUCE: (93), (130) imply:
% 111.71/16.68 | | | | | (131) $false
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | CLOSE: (131) is inconsistent.
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | Case 2:
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | (132) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 111.71/16.68 | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | ALPHA: (132) implies:
% 111.71/16.68 | | | | | (133) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | BETA: splitting (133) gives:
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | | Case 1:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | (134) all_58_12 = e0
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | COMBINE_EQS: (78), (134) imply:
% 111.71/16.68 | | | | | | (135) all_52_3 = e0
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | SIMP: (135) implies:
% 111.71/16.68 | | | | | | (136) all_52_3 = e0
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | COMBINE_EQS: (44), (136) imply:
% 111.71/16.68 | | | | | | (137) all_56_9 = e0
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | BETA: splitting (35) gives:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | Case 1:
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | (138) ~ (all_56_14 = e3)
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | REF_CLOSE: (5), (18), (19), (21), (22), (29), (37), (43), (45),
% 111.71/16.68 | | | | | | | (56), (64), (66), (73), (75), (85), (90), (97), (128),
% 111.71/16.68 | | | | | | | (138) are inconsistent by sub-proof #23.
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | Case 2:
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | (139) ~ (all_56_9 = e0)
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | REDUCE: (137), (139) imply:
% 111.71/16.68 | | | | | | | (140) $false
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | | CLOSE: (140) is inconsistent.
% 111.71/16.68 | | | | | | |
% 111.71/16.68 | | | | | | End of split
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | Case 2:
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | (141) all_58_13 = e0 | all_58_14 = e0
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | | REF_CLOSE: (48), (61), (89), (127), (141) are inconsistent by
% 111.71/16.68 | | | | | | sub-proof #428.
% 111.71/16.68 | | | | | |
% 111.71/16.68 | | | | | End of split
% 111.71/16.68 | | | | |
% 111.71/16.68 | | | | End of split
% 111.71/16.68 | | | |
% 111.71/16.68 | | | End of split
% 111.71/16.68 | | |
% 111.71/16.68 | | Case 2:
% 111.71/16.68 | | |
% 111.71/16.68 | | | (142) ~ (all_56_15 = e1)
% 111.71/16.68 | | |
% 111.71/16.68 | | | REDUCE: (41), (142) imply:
% 111.71/16.68 | | | (143) $false
% 111.71/16.68 | | |
% 111.71/16.68 | | | CLOSE: (143) is inconsistent.
% 111.71/16.68 | | |
% 111.71/16.68 | | End of split
% 111.71/16.68 | |
% 111.71/16.68 | Case 2:
% 111.71/16.68 | |
% 111.71/16.68 | | (144) ~ (all_56_15 = e1)
% 111.71/16.68 | |
% 111.71/16.68 | | REDUCE: (41), (144) imply:
% 111.71/16.68 | | (145) $false
% 111.71/16.68 | |
% 111.71/16.68 | | CLOSE: (145) is inconsistent.
% 111.71/16.68 | |
% 111.71/16.68 | End of split
% 111.71/16.68 |
% 111.71/16.68 End of proof
% 111.71/16.68
% 111.71/16.68 Sub-proof #23 shows that the following formulas are inconsistent:
% 111.71/16.68 ----------------------------------------------------------------
% 111.71/16.68 (1) ~ (all_52_9 = e2)
% 111.71/16.68 (2) ~ (all_52_1 = e2)
% 111.71/16.68 (3) all_56_14 = all_6_2
% 111.71/16.68 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.68 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.69 (6) op(e1, all_6_2) = e2
% 111.71/16.69 (7) all_54_10 = all_6_2
% 111.71/16.69 (8) all_58_3 = all_8_2
% 111.71/16.69 (9) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.69 (10) all_58_5 = all_52_9
% 111.71/16.69 (11) all_58_2 = all_52_1
% 111.71/16.69 (12) all_58_10 = all_52_13
% 111.71/16.69 (13) ~ (all_8_2 = e2)
% 111.71/16.69 (14) op(e1, e2) = all_52_6
% 111.71/16.69 (15) all_56_5 = all_52_13
% 111.71/16.69 (16) ~ (all_52_6 = all_6_2)
% 111.71/16.69 (17) ~ (all_56_14 = e3)
% 111.71/16.69 (18) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.69 (19) ~ (all_6_2 = e1)
% 111.71/16.69
% 111.71/16.69 Begin of proof
% 111.71/16.69 |
% 111.71/16.69 | REDUCE: (3), (17) imply:
% 111.71/16.69 | (20) ~ (all_6_2 = e3)
% 111.71/16.69 |
% 111.71/16.69 | BETA: splitting (18) gives:
% 111.71/16.69 |
% 111.71/16.69 | Case 1:
% 111.71/16.69 | |
% 111.71/16.69 | | (21) all_58_2 = e2
% 111.71/16.69 | |
% 111.71/16.69 | | COMBINE_EQS: (11), (21) imply:
% 111.71/16.69 | | (22) all_52_1 = e2
% 111.71/16.69 | |
% 111.71/16.69 | | REDUCE: (2), (22) imply:
% 111.71/16.69 | | (23) $false
% 111.71/16.69 | |
% 111.71/16.69 | | CLOSE: (23) is inconsistent.
% 111.71/16.69 | |
% 111.71/16.69 | Case 2:
% 111.71/16.69 | |
% 111.71/16.69 | | (24) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 111.71/16.69 | |
% 111.71/16.69 | | BETA: splitting (24) gives:
% 111.71/16.69 | |
% 111.71/16.69 | | Case 1:
% 111.71/16.69 | | |
% 111.71/16.69 | | | (25) all_58_3 = e2
% 111.71/16.69 | | |
% 111.71/16.69 | | | COMBINE_EQS: (8), (25) imply:
% 111.71/16.69 | | | (26) all_8_2 = e2
% 111.71/16.69 | | |
% 111.71/16.69 | | | REDUCE: (13), (26) imply:
% 111.71/16.69 | | | (27) $false
% 111.71/16.69 | | |
% 111.71/16.69 | | | CLOSE: (27) is inconsistent.
% 111.71/16.69 | | |
% 111.71/16.69 | | Case 2:
% 111.71/16.69 | | |
% 111.71/16.69 | | | (28) all_58_5 = e2 | all_58_10 = e2
% 111.71/16.69 | | |
% 111.71/16.69 | | | BETA: splitting (28) gives:
% 111.71/16.69 | | |
% 111.71/16.69 | | | Case 1:
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | (29) all_58_5 = e2
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | COMBINE_EQS: (10), (29) imply:
% 111.71/16.69 | | | | (30) all_52_9 = e2
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | REDUCE: (1), (30) imply:
% 111.71/16.69 | | | | (31) $false
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | CLOSE: (31) is inconsistent.
% 111.71/16.69 | | | |
% 111.71/16.69 | | | Case 2:
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | (32) all_58_10 = e2
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | COMBINE_EQS: (12), (32) imply:
% 111.71/16.69 | | | | (33) all_52_13 = e2
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | COMBINE_EQS: (15), (33) imply:
% 111.71/16.69 | | | | (34) all_56_5 = e2
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | BETA: splitting (9) gives:
% 111.71/16.69 | | | |
% 111.71/16.69 | | | | Case 1:
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | (35) ~ (all_56_5 = e2)
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | REDUCE: (34), (35) imply:
% 111.71/16.69 | | | | | (36) $false
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | CLOSE: (36) is inconsistent.
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | Case 2:
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | (37) ~ (all_56_14 = e0)
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | REDUCE: (3), (37) imply:
% 111.71/16.69 | | | | | (38) ~ (all_6_2 = e0)
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | BETA: splitting (4) gives:
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | | Case 1:
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | | (39) all_54_10 = e3
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | | REF_CLOSE: (7), (20), (39) are inconsistent by sub-proof #352.
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | Case 2:
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | | (40) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | | BETA: splitting (40) gives:
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | | Case 1:
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | | (41) all_54_10 = e2
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | | COMBINE_EQS: (7), (41) imply:
% 111.71/16.69 | | | | | | | (42) all_6_2 = e2
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | | REF_CLOSE: (5), (6), (14), (16), (42) are inconsistent by
% 111.71/16.69 | | | | | | | sub-proof #39.
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | Case 2:
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | | (43) all_54_10 = e1 | all_54_10 = e0
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | | REF_CLOSE: (7), (19), (38), (43) are inconsistent by sub-proof
% 111.71/16.69 | | | | | | | #436.
% 111.71/16.69 | | | | | | |
% 111.71/16.69 | | | | | | End of split
% 111.71/16.69 | | | | | |
% 111.71/16.69 | | | | | End of split
% 111.71/16.69 | | | | |
% 111.71/16.69 | | | | End of split
% 111.71/16.69 | | | |
% 111.71/16.69 | | | End of split
% 111.71/16.69 | | |
% 111.71/16.69 | | End of split
% 111.71/16.69 | |
% 111.71/16.69 | End of split
% 111.71/16.69 |
% 111.71/16.69 End of proof
% 111.71/16.69
% 111.71/16.69 Sub-proof #24 shows that the following formulas are inconsistent:
% 111.71/16.69 ----------------------------------------------------------------
% 111.71/16.69 (1) all_56_14 = all_6_2
% 111.71/16.69 (2) all_54_3 = all_52_12
% 111.71/16.69 (3) ~ (all_52_12 = all_52_14)
% 111.71/16.69 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.69 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.70 (7) ~ (all_52_2 = all_6_2)
% 111.71/16.70 (8) op(e1, all_6_2) = e2
% 111.71/16.70 (9) all_54_10 = all_6_2
% 111.71/16.70 (10) all_56_2 = all_52_12
% 111.71/16.70 (11) ~ (all_52_12 = e1)
% 111.71/16.70 (12) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.70 (13) all_56_6 = e1
% 111.71/16.70 (14) all_54_7 = all_52_13
% 111.71/16.70 (15) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 111.71/16.70 (16) ~ (all_6_0 = e3)
% 111.71/16.70 (17) op(e1, e0) = all_52_14
% 111.71/16.70 (18) ~ (all_52_12 = all_52_13)
% 111.71/16.70 (19) ~ (all_52_13 = e1)
% 111.71/16.70 (20) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 111.71/16.70 (21) op(e2, all_6_2) = all_6_0
% 111.71/16.70 (22) ~ (all_6_2 = e2)
% 111.71/16.70 (23) all_56_5 = all_52_13
% 111.71/16.70 (24) all_56_6 = all_52_2
% 111.71/16.70 (25) op(e2, e0) = all_52_13
% 111.71/16.70 (26) ~ (all_56_14 = e3)
% 111.71/16.70
% 111.71/16.70 Begin of proof
% 111.71/16.70 |
% 111.71/16.70 | COMBINE_EQS: (13), (24) imply:
% 111.71/16.70 | (27) all_52_2 = e1
% 111.71/16.70 |
% 111.71/16.70 | REDUCE: (1), (26) imply:
% 111.71/16.70 | (28) ~ (all_6_2 = e3)
% 111.71/16.70 |
% 111.71/16.70 | REDUCE: (7), (27) imply:
% 111.71/16.70 | (29) ~ (all_6_2 = e1)
% 111.71/16.70 |
% 111.71/16.70 | SIMP: (29) implies:
% 111.71/16.70 | (30) ~ (all_6_2 = e1)
% 111.71/16.70 |
% 111.71/16.70 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 111.71/16.70 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (28),
% 111.71/16.70 | (30) are inconsistent by sub-proof #43.
% 111.71/16.70 |
% 111.71/16.70 End of proof
% 111.71/16.70
% 111.71/16.70 Sub-proof #25 shows that the following formulas are inconsistent:
% 111.71/16.70 ----------------------------------------------------------------
% 111.71/16.70 (1) all_58_7 = all_52_6
% 111.71/16.70 (2) all_58_7 = e1
% 111.71/16.70 (3) all_56_14 = all_6_2
% 111.71/16.70 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 111.71/16.70 (5) all_54_3 = all_52_12
% 111.71/16.70 (6) ~ (all_52_12 = all_52_14)
% 111.71/16.70 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 111.71/16.70 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 111.71/16.70 (9) all_54_13 = all_52_7
% 111.71/16.70 (10) all_54_14 = all_52_11
% 111.71/16.70 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 111.71/16.70 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 111.71/16.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 111.71/16.70 (13) op(e1, all_6_2) = e2
% 111.71/16.70 (14) ~ (all_52_7 = e3)
% 111.71/16.70 (15) all_54_10 = all_6_2
% 111.71/16.70 (16) all_56_2 = all_52_12
% 111.71/16.70 (17) ~ (all_52_12 = e1)
% 111.71/16.70 (18) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 111.71/16.70 (19) all_54_7 = all_52_13
% 111.71/16.70 (20) ~ (all_8_2 = e3)
% 111.71/16.70 (21) ~ (all_52_7 = all_4_1)
% 111.71/16.70 (22) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.44/16.70 (23) ~ (all_6_0 = e3)
% 112.44/16.70 (24) ~ (all_52_7 = all_8_2)
% 112.44/16.70 (25) op(e1, e0) = all_52_14
% 112.44/16.70 (26) ~ (all_6_2 = all_4_1)
% 112.44/16.70 (27) ~ (all_52_12 = all_52_13)
% 112.44/16.70 (28) ~ (all_52_13 = e1)
% 112.44/16.70 (29) all_54_5 = all_8_2
% 112.44/16.70 (30) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.44/16.70 (31) op(e2, all_6_2) = all_6_0
% 112.44/16.70 (32) ~ (all_52_6 = all_8_2)
% 112.44/16.70 (33) ~ (all_8_2 = e2)
% 112.44/16.70 (34) ~ (all_6_2 = e2)
% 112.44/16.70 (35) all_56_5 = all_52_13
% 112.44/16.70 (36) ~ (all_52_6 = all_6_2)
% 112.44/16.70 (37) all_54_14 = all_4_1
% 112.44/16.70 (38) op(e2, e0) = all_52_13
% 112.44/16.70 (39) ~ (all_52_11 = e1)
% 112.44/16.70 (40) ~ (all_52_11 = e0)
% 112.44/16.70 (41) ~ (all_52_6 = all_52_7)
% 112.44/16.70 (42) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.44/16.70
% 112.44/16.70 Begin of proof
% 112.44/16.70 |
% 112.44/16.70 | COMBINE_EQS: (1), (2) imply:
% 112.44/16.70 | (43) all_52_6 = e1
% 112.44/16.70 |
% 112.44/16.70 | REDUCE: (41), (43) imply:
% 112.44/16.70 | (44) ~ (all_52_7 = e1)
% 112.44/16.70 |
% 112.44/16.70 | SIMP: (44) implies:
% 112.44/16.70 | (45) ~ (all_52_7 = e1)
% 112.44/16.70 |
% 112.44/16.70 | REDUCE: (32), (43) imply:
% 112.44/16.70 | (46) ~ (all_8_2 = e1)
% 112.44/16.70 |
% 112.44/16.70 | SIMP: (46) implies:
% 112.44/16.70 | (47) ~ (all_8_2 = e1)
% 112.44/16.71 |
% 112.44/16.71 | REDUCE: (36), (43) imply:
% 112.44/16.71 | (48) ~ (all_6_2 = e1)
% 112.44/16.71 |
% 112.44/16.71 | SIMP: (48) implies:
% 112.44/16.71 | (49) ~ (all_6_2 = e1)
% 112.44/16.71 |
% 112.44/16.71 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 112.44/16.71 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 112.44/16.71 | (26), (27), (28), (29), (30), (31), (33), (34), (35), (37), (38),
% 112.44/16.71 | (39), (40), (42), (45), (47), (49) are inconsistent by sub-proof
% 112.44/16.71 | #42.
% 112.44/16.71 |
% 112.44/16.71 End of proof
% 112.44/16.71
% 112.44/16.71 Sub-proof #26 shows that the following formulas are inconsistent:
% 112.44/16.71 ----------------------------------------------------------------
% 112.44/16.71 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.44/16.71 (2) ~ (all_52_2 = all_10_2)
% 112.44/16.71 (3) all_58_7 = all_52_6
% 112.44/16.71 (4) ~ (all_4_2 = e0)
% 112.44/16.71 (5) op(e3, e2) = all_52_4
% 112.44/16.71 (6) all_56_14 = all_6_2
% 112.44/16.71 (7) all_56_3 = all_52_1
% 112.44/16.71 (8) all_24_0 = e1
% 112.44/16.71 (9) all_54_0 = all_10_2
% 112.44/16.71 (10) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 112.44/16.71 (11) all_54_3 = all_52_12
% 112.44/16.71 (12) ~ (all_52_12 = all_52_14)
% 112.44/16.71 (13) ~ (all_52_7 = all_4_2)
% 112.44/16.71 (14) all_56_11 = all_52_11
% 112.44/16.71 (15) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 112.44/16.71 (16) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.44/16.71 (17) ~ (all_52_4 = all_52_8)
% 112.44/16.71 (18) ~ (all_18_0 = e3)
% 112.44/16.71 (19) ~ (all_52_12 = all_10_2)
% 112.44/16.71 (20) ~ (e3 = e1)
% 112.44/16.71 (21) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 112.44/16.71 (22) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.44/16.71 (23) all_56_12 = all_10_2
% 112.44/16.71 (24) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.44/16.71 (25) all_58_0 = all_10_2
% 112.44/16.71 (26) all_54_13 = all_52_7
% 112.44/16.71 (27) op(all_10_1, all_10_2) = e1
% 112.44/16.71 (28) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 112.44/16.71 (29) all_56_10 = all_52_7
% 112.44/16.71 (30) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.44/16.71 (31) all_54_14 = all_52_11
% 112.44/16.71 (32) op(all_4_1, all_4_2) = all_4_0
% 112.44/16.71 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.49/16.71 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.49/16.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.49/16.71 (35) ~ (all_52_2 = all_6_2)
% 112.49/16.71 (36) op(e1, all_6_2) = e2
% 112.49/16.71 (37) all_54_10 = all_6_2
% 112.49/16.71 (38) op(e3, e0) = all_52_12
% 112.49/16.71 (39) ~ (all_52_8 = all_6_2)
% 112.49/16.71 (40) all_58_4 = all_52_8
% 112.49/16.71 (41) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.49/16.71 (42) ~ (all_52_4 = all_52_7)
% 112.49/16.71 (43) all_56_2 = all_52_12
% 112.49/16.71 (44) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.49/16.71 (45) all_58_3 = all_8_2
% 112.49/16.71 (46) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.49/16.71 (47) all_58_11 = all_52_14
% 112.49/16.71 (48) all_54_7 = all_52_13
% 112.49/16.71 (49) all_16_1 = all_10_1
% 112.49/16.71 (50) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.49/16.71 (51) ~ (all_52_11 = all_6_2)
% 112.49/16.71 (52) op(e2, e3) = all_52_1
% 112.49/16.71 (53) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.49/16.71 (54) ~ (all_52_7 = all_8_2)
% 112.49/16.71 (55) ~ (all_52_4 = all_8_2)
% 112.49/16.71 (56) op(e1, e0) = all_52_14
% 112.49/16.71 (57) all_58_5 = all_52_9
% 112.49/16.71 (58) ~ (all_4_0 = e3)
% 112.49/16.71 (59) all_56_9 = all_52_3
% 112.49/16.71 (60) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 112.49/16.71 (61) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 112.49/16.71 (62) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.49/16.71 (63) all_58_15 = all_4_2
% 112.49/16.71 (64) all_58_2 = all_52_1
% 112.49/16.71 (65) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.49/16.71 (66) op(e0, e3) = all_52_3
% 112.49/16.71 (67) ~ (all_10_2 = e3)
% 112.49/16.71 (68) ~ (all_52_12 = all_52_13)
% 112.49/16.71 (69) all_58_13 = all_52_7
% 112.49/16.71 (70) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 112.49/16.71 (71) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 112.49/16.71 (72) ~ (all_52_14 = all_4_2)
% 112.49/16.71 (73) all_58_6 = all_52_2
% 112.49/16.71 (74) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 112.49/16.71 (75) ~ (all_52_1 = all_10_2)
% 112.49/16.71 (76) all_54_5 = all_8_2
% 112.49/16.71 (77) all_56_15 = all_4_2
% 112.49/16.71 (78) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.49/16.71 (79) all_58_10 = all_52_13
% 112.49/16.71 (80) ~ (all_52_13 = all_8_2)
% 112.49/16.72 (81) op(e2, all_8_2) = all_8_1
% 112.49/16.72 (82) ~ (all_52_11 = all_4_2)
% 112.49/16.72 (83) op(e2, all_6_2) = all_6_0
% 112.49/16.72 (84) op(e3, all_10_2) = all_10_1
% 112.49/16.72 (85) ~ (all_52_6 = all_8_2)
% 112.49/16.72 (86) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.49/16.72 (87) all_58_1 = all_52_4
% 112.49/16.72 (88) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 112.49/16.72 (89) all_58_14 = all_52_11
% 112.49/16.72 (90) all_54_1 = all_52_4
% 112.49/16.72 (91) all_56_13 = all_8_2
% 112.49/16.72 (92) op(e0, e1) = all_52_11
% 112.49/16.72 (93) ~ (all_52_1 = all_8_2)
% 112.49/16.72 (94) ~ (all_8_2 = e2)
% 112.49/16.72 (95) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 112.49/16.72 (96) ~ (all_52_7 = all_52_11)
% 112.49/16.72 (97) op(e1, e2) = all_52_6
% 112.49/16.72 (98) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.49/16.72 (99) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 112.49/16.72 (100) all_56_7 = all_52_6
% 112.49/16.72 (101) ~ (all_52_4 = all_52_6)
% 112.49/16.72 (102) all_56_1 = all_52_8
% 112.49/16.72 (103) op(e0, all_4_2) = all_4_1
% 112.49/16.72 (104) all_58_8 = all_6_2
% 112.49/16.72 (105) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.49/16.72 (106) all_16_2 = all_10_2
% 112.49/16.72 (107) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 112.49/16.72 (108) all_56_4 = all_52_9
% 112.49/16.72 (109) all_58_9 = all_52_12
% 112.49/16.72 (110) all_56_5 = all_52_13
% 112.49/16.72 (111) ~ (all_52_3 = all_4_2)
% 112.49/16.72 (112) ~ (all_52_6 = all_6_2)
% 112.49/16.72 (113) all_56_6 = all_52_2
% 112.49/16.72 (114) ~ (all_52_13 = all_4_2)
% 112.49/16.72 (115) all_58_12 = all_52_3
% 112.49/16.72 (116) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 112.49/16.72 (117) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.49/16.72 (118) op(e2, e0) = all_52_13
% 112.49/16.72 (119) ~ (all_52_12 = all_4_2)
% 112.49/16.72 (120) ~ (all_52_3 = all_10_2)
% 112.49/16.72 (121) all_24_1 = all_10_1
% 112.49/16.72 (122) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.49/16.72 (123) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 112.49/16.72 (124) all_24_2 = all_10_2
% 112.49/16.72 (125) op(e1, e1) = all_6_2
% 112.49/16.72 (126) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.49/16.72 (127) ~ (all_52_8 = all_52_12)
% 112.49/16.72 (128) all_56_8 = all_52_14
% 112.49/16.72 (129) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 112.49/16.72 (130) ~ (all_52_4 = all_10_2)
% 112.49/16.72 (131) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.49/16.72 (132) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.49/16.72 (133) all_56_0 = all_52_4
% 112.49/16.72 (134) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.49/16.72 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.49/16.72 (135) all_54_4 = all_52_1
% 112.49/16.72 (136) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 112.49/16.72 (137) all_54_15 = all_4_2
% 112.49/16.72 (138) ~ (all_6_2 = e1)
% 112.49/16.72 (139) ~ (all_52_3 = all_52_11)
% 112.49/16.72 (140) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.49/16.72 (141) all_18_0 = all_6_0
% 112.49/16.72 (142) all_54_12 = all_52_3
% 112.49/16.72
% 112.49/16.72 Begin of proof
% 112.49/16.72 |
% 112.49/16.72 | REDUCE: (18), (141) imply:
% 112.49/16.72 | (143) ~ (all_6_0 = e3)
% 112.49/16.72 |
% 112.49/16.72 | BETA: splitting (129) gives:
% 112.49/16.72 |
% 112.49/16.72 | Case 1:
% 112.49/16.72 | |
% 112.49/16.72 | | (144) ~ (all_24_0 = e1)
% 112.49/16.72 | |
% 112.49/16.72 | | REDUCE: (8), (144) imply:
% 112.49/16.72 | | (145) $false
% 112.49/16.72 | |
% 112.49/16.72 | | CLOSE: (145) is inconsistent.
% 112.49/16.72 | |
% 112.49/16.72 | Case 2:
% 112.49/16.72 | |
% 112.49/16.72 | | (146) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 112.49/16.72 | |
% 112.49/16.72 | | BETA: splitting (70) gives:
% 112.49/16.72 | |
% 112.49/16.72 | | Case 1:
% 112.49/16.72 | | |
% 112.49/16.72 | | | (147) ~ (all_56_14 = e2)
% 112.49/16.72 | | |
% 112.49/16.72 | | | REDUCE: (6), (147) imply:
% 112.49/16.72 | | | (148) ~ (all_6_2 = e2)
% 112.49/16.72 | | |
% 112.49/16.72 | | | BETA: splitting (71) gives:
% 112.49/16.72 | | |
% 112.49/16.72 | | | Case 1:
% 112.49/16.72 | | | |
% 112.49/16.72 | | | | (149) ~ (all_56_12 = e2)
% 112.49/16.72 | | | |
% 112.49/16.72 | | | | REDUCE: (23), (149) imply:
% 112.49/16.72 | | | | (150) ~ (all_10_2 = e2)
% 112.49/16.72 | | | |
% 112.49/16.72 | | | | BETA: splitting (107) gives:
% 112.49/16.72 | | | |
% 112.49/16.72 | | | | Case 1:
% 112.49/16.72 | | | | |
% 112.49/16.72 | | | | | (151) ~ (all_56_15 = e3)
% 112.49/16.72 | | | | |
% 112.49/16.72 | | | | | REDUCE: (77), (151) imply:
% 112.49/16.72 | | | | | (152) ~ (all_4_2 = e3)
% 112.49/16.72 | | | | |
% 112.49/16.72 | | | | | BETA: splitting (24) gives:
% 112.49/16.72 | | | | |
% 112.49/16.72 | | | | | Case 1:
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | (153) ~ (all_56_7 = e1)
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (11), (14), (15), (16),
% 112.49/16.72 | | | | | | (19), (20), (23), (27), (29), (33), (34), (37), (38),
% 112.49/16.72 | | | | | | (41), (43), (44), (47), (49), (50), (56), (59), (61),
% 112.49/16.72 | | | | | | (62), (63), (67), (69), (72), (73), (77), (84), (89),
% 112.49/16.72 | | | | | | (98), (100), (104), (105), (106), (113), (115), (122),
% 112.49/16.72 | | | | | | (128), (131), (134), (137), (138), (148), (150), (152),
% 112.49/16.72 | | | | | | (153) are inconsistent by sub-proof #191.
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | Case 2:
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | (154) all_56_7 = e1
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | COMBINE_EQS: (100), (154) imply:
% 112.49/16.72 | | | | | | (155) all_52_6 = e1
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | REDUCE: (85), (155) imply:
% 112.49/16.72 | | | | | | (156) ~ (all_8_2 = e1)
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | SIMP: (156) implies:
% 112.49/16.72 | | | | | | (157) ~ (all_8_2 = e1)
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | REDUCE: (112), (155) imply:
% 112.49/16.72 | | | | | | (158) ~ (all_6_2 = e1)
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | BETA: splitting (41) gives:
% 112.49/16.72 | | | | | |
% 112.49/16.72 | | | | | | Case 1:
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | (159) all_54_15 = e3
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | COMBINE_EQS: (137), (159) imply:
% 112.49/16.72 | | | | | | | (160) all_4_2 = e3
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | REDUCE: (152), (160) imply:
% 112.49/16.72 | | | | | | | (161) $false
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | CLOSE: (161) is inconsistent.
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | Case 2:
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | (162) ~ (all_54_15 = e3)
% 112.49/16.72 | | | | | | | (163) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | BETA: splitting (163) gives:
% 112.49/16.72 | | | | | | |
% 112.49/16.72 | | | | | | | Case 1:
% 112.49/16.72 | | | | | | | |
% 112.49/16.72 | | | | | | | | (164) all_54_15 = e2
% 112.49/16.72 | | | | | | | |
% 112.49/16.72 | | | | | | | | COMBINE_EQS: (137), (164) imply:
% 112.49/16.72 | | | | | | | | (165) all_4_2 = e2
% 112.49/16.72 | | | | | | | |
% 112.49/16.72 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (11), (14), (15), (16),
% 112.49/16.72 | | | | | | | | (19), (20), (23), (24), (27), (29), (33), (34), (37),
% 112.49/16.72 | | | | | | | | (38), (41), (43), (44), (47), (49), (50), (56), (59),
% 112.49/16.72 | | | | | | | | (61), (62), (63), (67), (69), (72), (73), (77), (84),
% 112.49/16.72 | | | | | | | | (89), (98), (100), (104), (105), (106), (113), (115),
% 112.49/16.72 | | | | | | | | (122), (128), (131), (134), (137), (138), (148),
% 112.49/16.72 | | | | | | | | (150), (152), (165) are inconsistent by sub-proof
% 112.49/16.72 | | | | | | | | #27.
% 112.49/16.72 | | | | | | | |
% 112.49/16.72 | | | | | | | Case 2:
% 112.49/16.72 | | | | | | | |
% 112.49/16.73 | | | | | | | | (166) all_54_15 = e1 | all_54_15 = e0
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | BETA: splitting (166) gives:
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | (167) all_54_15 = e1
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | COMBINE_EQS: (137), (167) imply:
% 112.49/16.73 | | | | | | | | | (168) all_4_2 = e1
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | COMBINE_EQS: (77), (168) imply:
% 112.49/16.73 | | | | | | | | | (169) all_56_15 = e1
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (13), (168) imply:
% 112.49/16.73 | | | | | | | | | (170) ~ (all_52_7 = e1)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (82), (168) imply:
% 112.49/16.73 | | | | | | | | | (171) ~ (all_52_11 = e1)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (119), (168) imply:
% 112.49/16.73 | | | | | | | | | (172) ~ (all_52_12 = e1)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (114), (168) imply:
% 112.49/16.73 | | | | | | | | | (173) ~ (all_52_13 = e1)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (103), (168) imply:
% 112.49/16.73 | | | | | | | | | (174) op(e0, e1) = all_4_1
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | BETA: splitting (60) gives:
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | (175) ~ (all_56_15 = e1)
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | REDUCE: (169), (175) imply:
% 112.49/16.73 | | | | | | | | | | (176) $false
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | CLOSE: (176) is inconsistent.
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | Case 2:
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | (177) ~ (all_56_11 = e0)
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | REDUCE: (14), (177) imply:
% 112.49/16.73 | | | | | | | | | | (178) ~ (all_52_11 = e0)
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | BETA: splitting (74) gives:
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | (179) ~ (all_56_1 = e3)
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | REDUCE: (102), (179) imply:
% 112.49/16.73 | | | | | | | | | | | (180) ~ (all_52_8 = e3)
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | BETA: splitting (116) gives:
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | | (181) ~ (all_56_4 = e2)
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | | REDUCE: (108), (181) imply:
% 112.49/16.73 | | | | | | | | | | | | (182) ~ (all_52_9 = e2)
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (9), (10), (11), (12), (16), (19),
% 112.49/16.73 | | | | | | | | | | | | (22), (23), (25), (26), (28), (31), (33), (34),
% 112.49/16.73 | | | | | | | | | | | | (36), (37), (40), (42), (43), (45), (46), (48),
% 112.49/16.73 | | | | | | | | | | | | (51), (52), (53), (54), (55), (56), (57), (64),
% 112.49/16.73 | | | | | | | | | | | | (67), (68), (75), (76), (78), (79), (81), (83),
% 112.49/16.73 | | | | | | | | | | | | (86), (87), (88), (91), (92), (93), (94), (95),
% 112.49/16.73 | | | | | | | | | | | | (96), (105), (109), (110), (118), (123), (125),
% 112.49/16.73 | | | | | | | | | | | | (126), (132), (135), (138), (140), (143), (148),
% 112.49/16.73 | | | | | | | | | | | | (150), (157), (170), (171), (172), (173), (174),
% 112.49/16.73 | | | | | | | | | | | | (178), (180), (182) are inconsistent by sub-proof
% 112.49/16.73 | | | | | | | | | | | | #41.
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | Case 2:
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | | (183) all_56_4 = e2
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | | REF_CLOSE: (1), (9), (11), (16), (19), (23), (27), (34),
% 112.49/16.73 | | | | | | | | | | | | (38), (43), (49), (56), (61), (62), (65), (67),
% 112.49/16.73 | | | | | | | | | | | | (84), (105), (106), (128), (150), (183) are
% 112.49/16.73 | | | | | | | | | | | | inconsistent by sub-proof #190.
% 112.49/16.73 | | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | End of split
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | Case 2:
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | (184) ~ (all_56_15 = e1)
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | REDUCE: (169), (184) imply:
% 112.49/16.73 | | | | | | | | | | | (185) $false
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 112.49/16.73 | | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | End of split
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | End of split
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | Case 2:
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | (186) all_54_15 = e0
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | COMBINE_EQS: (137), (186) imply:
% 112.49/16.73 | | | | | | | | | (187) all_4_2 = e0
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (4), (187) imply:
% 112.49/16.73 | | | | | | | | | (188) $false
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | CLOSE: (188) is inconsistent.
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | End of split
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | End of split
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | End of split
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | End of split
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | Case 2:
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | (189) all_56_15 = e3
% 112.49/16.73 | | | | | (190) ~ (all_56_9 = e0)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | COMBINE_EQS: (77), (189) imply:
% 112.49/16.73 | | | | | (191) all_4_2 = e3
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | SIMP: (191) implies:
% 112.49/16.73 | | | | | (192) all_4_2 = e3
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | COMBINE_EQS: (63), (192) imply:
% 112.49/16.73 | | | | | (193) all_58_15 = e3
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (59), (190) imply:
% 112.49/16.73 | | | | | (194) ~ (all_52_3 = e0)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (111), (192) imply:
% 112.49/16.73 | | | | | (195) ~ (all_52_3 = e3)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (119), (192) imply:
% 112.49/16.73 | | | | | (196) ~ (all_52_12 = e3)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (114), (192) imply:
% 112.49/16.73 | | | | | (197) ~ (all_52_13 = e3)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (4), (192) imply:
% 112.49/16.73 | | | | | (198) ~ (e3 = e0)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (32), (192) imply:
% 112.49/16.73 | | | | | (199) op(all_4_1, e3) = all_4_0
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (103), (192) imply:
% 112.49/16.73 | | | | | (200) op(e0, e3) = all_4_1
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | GROUND_INST: instantiating (34) with all_52_3, all_4_1, e3, e0,
% 112.49/16.73 | | | | | simplifying with (66), (200) gives:
% 112.49/16.73 | | | | | (201) all_52_3 = all_4_1
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | COMBINE_EQS: (142), (201) imply:
% 112.49/16.73 | | | | | (202) all_54_12 = all_4_1
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | COMBINE_EQS: (115), (201) imply:
% 112.49/16.73 | | | | | (203) all_58_12 = all_4_1
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (139), (201) imply:
% 112.49/16.73 | | | | | (204) ~ (all_52_11 = all_4_1)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | SIMP: (204) implies:
% 112.49/16.73 | | | | | (205) ~ (all_52_11 = all_4_1)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (120), (201) imply:
% 112.49/16.73 | | | | | (206) ~ (all_10_2 = all_4_1)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | SIMP: (206) implies:
% 112.49/16.73 | | | | | (207) ~ (all_10_2 = all_4_1)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (195), (201) imply:
% 112.49/16.73 | | | | | (208) ~ (all_4_1 = e3)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | REDUCE: (194), (201) imply:
% 112.49/16.73 | | | | | (209) ~ (all_4_1 = e0)
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | BETA: splitting (131) gives:
% 112.49/16.73 | | | | |
% 112.49/16.73 | | | | | Case 1:
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | (210) ~ (all_56_12 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REDUCE: (23), (210) imply:
% 112.49/16.73 | | | | | | (211) ~ (all_10_2 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REF_CLOSE: (1), (9), (11), (16), (19), (23), (27), (34), (38), (43),
% 112.49/16.73 | | | | | | (49), (56), (61), (62), (67), (84), (105), (106), (128),
% 112.49/16.73 | | | | | | (150), (211) are inconsistent by sub-proof #193.
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | Case 2:
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | (212) all_56_12 = e1
% 112.49/16.73 | | | | | | (213) ~ (all_56_11 = e0)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | COMBINE_EQS: (23), (212) imply:
% 112.49/16.73 | | | | | | (214) all_10_2 = e1
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | SIMP: (214) implies:
% 112.49/16.73 | | | | | | (215) all_10_2 = e1
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | COMBINE_EQS: (25), (215) imply:
% 112.49/16.73 | | | | | | (216) all_58_0 = e1
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REDUCE: (14), (213) imply:
% 112.49/16.73 | | | | | | (217) ~ (all_52_11 = e0)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REDUCE: (130), (215) imply:
% 112.49/16.73 | | | | | | (218) ~ (all_52_4 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REDUCE: (19), (215) imply:
% 112.49/16.73 | | | | | | (219) ~ (all_52_12 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | REDUCE: (207), (215) imply:
% 112.49/16.73 | | | | | | (220) ~ (all_4_1 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | SIMP: (220) implies:
% 112.49/16.73 | | | | | | (221) ~ (all_4_1 = e1)
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | BETA: splitting (117) gives:
% 112.49/16.73 | | | | | |
% 112.49/16.73 | | | | | | Case 1:
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | (222) all_54_12 = e3
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | COMBINE_EQS: (202), (222) imply:
% 112.49/16.73 | | | | | | | (223) all_4_1 = e3
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | REDUCE: (208), (223) imply:
% 112.49/16.73 | | | | | | | (224) $false
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | CLOSE: (224) is inconsistent.
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | Case 2:
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | (225) ~ (all_54_12 = e3)
% 112.49/16.73 | | | | | | | (226) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | BETA: splitting (65) gives:
% 112.49/16.73 | | | | | | |
% 112.49/16.73 | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | (227) ~ (all_56_4 = e2)
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | REDUCE: (108), (227) imply:
% 112.49/16.73 | | | | | | | | (228) ~ (all_52_9 = e2)
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | BETA: splitting (226) gives:
% 112.49/16.73 | | | | | | | |
% 112.49/16.73 | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | (229) all_54_12 = e2
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | COMBINE_EQS: (202), (229) imply:
% 112.49/16.73 | | | | | | | | | (230) all_4_1 = e2
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | COMBINE_EQS: (203), (230) imply:
% 112.49/16.73 | | | | | | | | | (231) all_58_12 = e2
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (205), (230) imply:
% 112.49/16.73 | | | | | | | | | (232) ~ (all_52_11 = e2)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (209), (230) imply:
% 112.49/16.73 | | | | | | | | | (233) ~ (e2 = e0)
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | REDUCE: (199), (230) imply:
% 112.49/16.73 | | | | | | | | | (234) op(e2, e3) = all_4_0
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | BETA: splitting (134) gives:
% 112.49/16.73 | | | | | | | | |
% 112.49/16.73 | | | | | | | | | Case 1:
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | (235) all_58_15 = e0
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | COMBINE_EQS: (193), (235) imply:
% 112.49/16.73 | | | | | | | | | | (236) e3 = e0
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | REDUCE: (198), (236) imply:
% 112.49/16.73 | | | | | | | | | | (237) $false
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | | CLOSE: (237) is inconsistent.
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.73 | | | | | | | | | Case 2:
% 112.49/16.73 | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | (238) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.49/16.74 | | | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 112.49/16.74 | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | ALPHA: (238) implies:
% 112.49/16.74 | | | | | | | | | | (239) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 112.49/16.74 | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | BETA: splitting (30) gives:
% 112.49/16.74 | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | (240) all_58_4 = e2
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | COMBINE_EQS: (40), (240) imply:
% 112.49/16.74 | | | | | | | | | | | (241) all_52_8 = e2
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | REDUCE: (17), (241) imply:
% 112.49/16.74 | | | | | | | | | | | (242) ~ (all_52_4 = e2)
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | REDUCE: (127), (241) imply:
% 112.49/16.74 | | | | | | | | | | | (243) ~ (all_52_12 = e2)
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | SIMP: (243) implies:
% 112.49/16.74 | | | | | | | | | | | (244) ~ (all_52_12 = e2)
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | REDUCE: (39), (241) imply:
% 112.49/16.74 | | | | | | | | | | | (245) ~ (all_6_2 = e2)
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | BETA: splitting (16) gives:
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | (246) all_54_3 = e3
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | REF_CLOSE: (11), (196), (246) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | #224.
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | (247) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | BETA: splitting (247) gives:
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | (248) all_54_3 = e2
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | REF_CLOSE: (11), (244), (248) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | #285.
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | (249) all_54_3 = e1 | all_54_3 = e0
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | BETA: splitting (239) gives:
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | (250) all_58_12 = e0
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | COMBINE_EQS: (231), (250) imply:
% 112.49/16.74 | | | | | | | | | | | | | | (251) e2 = e0
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | SIMP: (251) implies:
% 112.49/16.74 | | | | | | | | | | | | | | (252) e2 = e0
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | REDUCE: (233), (252) imply:
% 112.49/16.74 | | | | | | | | | | | | | | (253) $false
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | (254) all_58_13 = e0 | all_58_14 = e0
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | (255) all_58_13 = e0
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | COMBINE_EQS: (69), (255) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | (256) all_52_7 = e0
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | SIMP: (256) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | (257) all_52_7 = e0
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | REDUCE: (42), (257) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | (258) ~ (all_52_4 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | REDUCE: (54), (257) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | (259) ~ (all_8_2 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | SIMP: (259) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | (260) ~ (all_8_2 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | (261) all_54_1 = e3
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (261) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | (262) all_52_4 = e3
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | (263) all_52_4 = e3
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | REDUCE: (55), (263) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | (264) ~ (all_8_2 = e3)
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | SIMP: (264) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | (265) ~ (all_8_2 = e3)
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | (266) all_54_5 = e3
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (265), (266) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | #339.
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | (267) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (268) all_54_3 = e1
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (219), (268) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | #284.
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (269) all_54_3 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (269) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (270) all_52_12 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (271) all_52_12 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | REDUCE: (68), (271) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (272) ~ (all_52_13 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | (273) ~ (all_52_13 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | (274) all_54_5 = e2
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (94), (274) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | #338.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | (275) all_54_5 = e1 | all_54_5 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | (276) all_54_5 = e1
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (276) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | (277) all_8_2 = e1
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | (278) all_8_2 = e1
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (278) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | (279) ~ (all_52_13 = e1)
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | (280) all_54_7 = e3
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (197), (280) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | #350.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | (281) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | (282) all_54_7 = e2
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (282) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | (283) all_52_13 = e2
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | (284) all_52_13 = e2
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (284) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | (285) all_56_5 = e2
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_56_5 = e2)
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (285), (286) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (287) $false
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (288) ~ (all_56_14 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (288) imply:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (289) ~ (all_6_2 = e0)
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (34), (35), (37), (52), (58), (64),
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (73), (138), (148), (203), (208), (216), (234),
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (289) are inconsistent by sub-proof #316.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | (290) all_54_7 = e1 | all_54_7 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (291) all_54_7 = e1
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (279), (291) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | #349.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | (292) all_54_7 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (273), (292) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | | #130.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | (293) all_54_5 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (260), (293) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | | #311.
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | (294) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | | REF_CLOSE: (90), (218), (242), (258), (294) are inconsistent
% 112.49/16.74 | | | | | | | | | | | | | | | | by sub-proof #101.
% 112.49/16.74 | | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | (295) all_58_14 = e0
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | | REF_CLOSE: (89), (217), (295) are inconsistent by sub-proof
% 112.49/16.74 | | | | | | | | | | | | | | | #429.
% 112.49/16.74 | | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | (296) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | BETA: splitting (296) gives:
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | Case 1:
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | (297) all_58_5 = e2
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | COMBINE_EQS: (57), (297) imply:
% 112.49/16.74 | | | | | | | | | | | | (298) all_52_9 = e2
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | REDUCE: (228), (298) imply:
% 112.49/16.74 | | | | | | | | | | | | (299) $false
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | (300) all_58_8 = e2 | all_58_14 = e2
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | | REF_CLOSE: (89), (104), (148), (232), (300) are inconsistent
% 112.49/16.74 | | | | | | | | | | | | by sub-proof #294.
% 112.49/16.74 | | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | | |
% 112.49/16.74 | | | | | | | | | End of split
% 112.49/16.74 | | | | | | | | |
% 112.49/16.74 | | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | | |
% 112.49/16.74 | | | | | | | | | (301) all_54_12 = e1 | all_54_12 = e0
% 112.49/16.74 | | | | | | | | |
% 112.49/16.74 | | | | | | | | | REF_CLOSE: (202), (209), (221), (301) are inconsistent by
% 112.49/16.74 | | | | | | | | | sub-proof #315.
% 112.49/16.74 | | | | | | | | |
% 112.49/16.74 | | | | | | | | End of split
% 112.49/16.74 | | | | | | | |
% 112.49/16.74 | | | | | | | Case 2:
% 112.49/16.74 | | | | | | | |
% 112.49/16.74 | | | | | | | | (302) all_56_4 = e2
% 112.49/16.74 | | | | | | | |
% 112.49/16.74 | | | | | | | | REF_CLOSE: (1), (9), (11), (16), (19), (23), (27), (34), (38),
% 112.49/16.74 | | | | | | | | (43), (49), (56), (61), (62), (65), (67), (84),
% 112.49/16.74 | | | | | | | | (105), (106), (128), (150), (302) are inconsistent by
% 112.49/16.74 | | | | | | | | sub-proof #190.
% 112.49/16.74 | | | | | | | |
% 112.49/16.74 | | | | | | | End of split
% 112.49/16.74 | | | | | | |
% 112.49/16.74 | | | | | | End of split
% 112.49/16.74 | | | | | |
% 112.49/16.74 | | | | | End of split
% 112.49/16.74 | | | | |
% 112.49/16.74 | | | | End of split
% 112.49/16.74 | | | |
% 112.49/16.74 | | | Case 2:
% 112.49/16.74 | | | |
% 112.49/16.74 | | | | (303) all_56_12 = e2
% 112.49/16.74 | | | |
% 112.49/16.75 | | | | REF_CLOSE: (5), (23), (27), (34), (84), (90), (97), (99), (101), (121),
% 112.49/16.75 | | | | (124), (130), (133), (136), (146), (303) are inconsistent by
% 112.49/16.75 | | | | sub-proof #195.
% 112.49/16.75 | | | |
% 112.49/16.75 | | | End of split
% 112.49/16.75 | | |
% 112.49/16.75 | | Case 2:
% 112.49/16.75 | | |
% 112.49/16.75 | | | (304) all_56_14 = e2
% 112.49/16.75 | | |
% 112.49/16.75 | | | COMBINE_EQS: (6), (304) imply:
% 112.49/16.75 | | | (305) all_6_2 = e2
% 112.49/16.75 | | |
% 112.49/16.75 | | | REF_CLOSE: (34), (36), (97), (112), (305) are inconsistent by sub-proof
% 112.49/16.75 | | | #39.
% 112.49/16.75 | | |
% 112.49/16.75 | | End of split
% 112.49/16.75 | |
% 112.49/16.75 | End of split
% 112.49/16.75 |
% 112.49/16.75 End of proof
% 112.49/16.75
% 112.49/16.75 Sub-proof #27 shows that the following formulas are inconsistent:
% 112.49/16.75 ----------------------------------------------------------------
% 112.49/16.75 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.49/16.75 (2) ~ (all_52_2 = all_10_2)
% 112.49/16.75 (3) all_58_7 = all_52_6
% 112.49/16.75 (4) ~ (all_4_2 = e0)
% 112.49/16.75 (5) all_56_14 = all_6_2
% 112.49/16.75 (6) all_54_0 = all_10_2
% 112.49/16.75 (7) all_54_3 = all_52_12
% 112.49/16.75 (8) all_56_11 = all_52_11
% 112.49/16.75 (9) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 112.49/16.75 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.49/16.75 (11) ~ (all_52_12 = all_10_2)
% 112.49/16.75 (12) ~ (e3 = e1)
% 112.49/16.75 (13) all_56_12 = all_10_2
% 112.49/16.75 (14) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.49/16.75 (15) op(all_10_1, all_10_2) = e1
% 112.49/16.75 (16) all_56_10 = all_52_7
% 112.49/16.75 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.49/16.75 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.49/16.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.49/16.75 (19) ~ (all_10_2 = e2)
% 112.49/16.75 (20) all_54_10 = all_6_2
% 112.49/16.75 (21) op(e3, e0) = all_52_12
% 112.49/16.75 (22) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.49/16.75 (23) all_56_2 = all_52_12
% 112.49/16.75 (24) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.49/16.75 (25) all_58_11 = all_52_14
% 112.49/16.75 (26) all_16_1 = all_10_1
% 112.49/16.75 (27) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.49/16.75 (28) ~ (all_4_2 = e3)
% 112.49/16.75 (29) op(e1, e0) = all_52_14
% 112.49/16.75 (30) all_56_9 = all_52_3
% 112.49/16.75 (31) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 112.49/16.75 (32) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.49/16.75 (33) all_58_15 = all_4_2
% 112.49/16.75 (34) ~ (all_10_2 = e3)
% 112.49/16.75 (35) all_58_13 = all_52_7
% 112.49/16.75 (36) ~ (all_52_14 = all_4_2)
% 112.49/16.75 (37) all_58_6 = all_52_2
% 112.49/16.75 (38) all_56_15 = all_4_2
% 112.49/16.75 (39) op(e3, all_10_2) = all_10_1
% 112.49/16.75 (40) all_58_14 = all_52_11
% 112.49/16.75 (41) ~ (all_6_2 = e2)
% 112.49/16.75 (42) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.49/16.75 (43) all_56_7 = all_52_6
% 112.49/16.75 (44) all_58_8 = all_6_2
% 112.49/16.75 (45) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.49/16.75 (46) all_16_2 = all_10_2
% 112.49/16.75 (47) all_56_6 = all_52_2
% 112.49/16.75 (48) all_58_12 = all_52_3
% 112.49/16.75 (49) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.49/16.75 (50) all_4_2 = e2
% 112.49/16.75 (51) all_56_8 = all_52_14
% 112.49/16.75 (52) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.49/16.75 (53) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.49/16.75 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.49/16.75 (54) all_54_15 = all_4_2
% 112.49/16.75 (55) ~ (all_6_2 = e1)
% 112.49/16.75
% 112.49/16.75 Begin of proof
% 112.49/16.75 |
% 112.49/16.75 | COMBINE_EQS: (38), (50) imply:
% 112.49/16.75 | (56) all_56_15 = e2
% 112.49/16.75 |
% 112.49/16.75 | BETA: splitting (14) gives:
% 112.49/16.75 |
% 112.49/16.75 | Case 1:
% 112.49/16.75 | |
% 112.49/16.75 | | (57) ~ (all_56_7 = e1)
% 112.49/16.75 | |
% 112.49/16.75 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 112.49/16.75 | | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 112.49/16.75 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 112.49/16.75 | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 112.49/16.75 | | (47), (48), (49), (51), (52), (53), (54), (55), (57) are
% 112.49/16.75 | | inconsistent by sub-proof #191.
% 112.49/16.75 | |
% 112.49/16.75 | Case 2:
% 112.49/16.75 | |
% 112.49/16.75 | | (58) ~ (all_56_15 = e2)
% 112.49/16.75 | |
% 112.49/16.75 | | REDUCE: (56), (58) imply:
% 112.49/16.75 | | (59) $false
% 112.49/16.75 | |
% 112.49/16.75 | | CLOSE: (59) is inconsistent.
% 112.49/16.75 | |
% 112.49/16.75 | End of split
% 112.49/16.75 |
% 112.49/16.75 End of proof
% 112.49/16.75
% 112.49/16.75 Sub-proof #28 shows that the following formulas are inconsistent:
% 112.49/16.75 ----------------------------------------------------------------
% 112.61/16.75 (1) ~ (all_52_8 = all_10_2)
% 112.61/16.75 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.61/16.75 (3) ~ (all_52_2 = all_10_2)
% 112.61/16.75 (4) all_54_2 = all_52_8
% 112.61/16.75 (5) all_58_7 = all_52_6
% 112.61/16.75 (6) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 112.61/16.75 (7) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 112.61/16.75 (8) ~ (all_52_8 = all_52_11)
% 112.61/16.75 (9) ~ (all_52_9 = all_8_2)
% 112.61/16.76 (10) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 112.61/16.76 (11) ~ (all_4_2 = e0)
% 112.61/16.76 (12) op(e3, e2) = all_52_4
% 112.61/16.76 (13) all_56_14 = all_6_2
% 112.61/16.76 (14) all_56_3 = all_52_1
% 112.61/16.76 (15) all_38_1 = all_10_1
% 112.61/16.76 (16) all_54_0 = all_10_2
% 112.61/16.76 (17) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 112.61/16.76 (18) all_54_3 = all_52_12
% 112.61/16.76 (19) ~ (all_52_2 = all_52_6)
% 112.61/16.76 (20) ~ (all_52_12 = all_52_14)
% 112.61/16.76 (21) op(e0, e2) = all_52_7
% 112.61/16.76 (22) ~ (all_52_7 = all_4_2)
% 112.61/16.76 (23) all_56_11 = all_52_11
% 112.61/16.76 (24) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 112.61/16.76 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.61/16.76 (26) ~ (all_52_12 = all_10_2)
% 112.61/16.76 (27) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.61/16.76 (28) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.61/16.76 (29) all_56_12 = all_10_2
% 112.61/16.76 (30) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.61/16.76 (31) all_58_0 = all_10_2
% 112.61/16.76 (32) all_54_13 = all_52_7
% 112.61/16.76 (33) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 112.61/16.76 (34) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 112.61/16.76 (35) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 112.61/16.76 (36) all_56_10 = all_52_7
% 112.61/16.76 (37) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.61/16.76 (38) all_54_14 = all_52_11
% 112.61/16.76 (39) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.76 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.76 (41) all_54_8 = all_52_2
% 112.61/16.76 (42) ~ (all_52_2 = all_6_2)
% 112.61/16.76 (43) all_32_2 = all_10_2
% 112.61/16.76 (44) op(e1, all_6_2) = e2
% 112.61/16.76 (45) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 112.61/16.76 (46) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 112.61/16.76 (47) all_54_10 = all_6_2
% 112.61/16.76 (48) ~ (e2 = e1)
% 112.61/16.76 (49) op(e3, e0) = all_52_12
% 112.61/16.76 (50) ~ (all_18_0 = e3) | ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 112.61/16.76 (51) ~ (all_52_8 = all_6_2)
% 112.61/16.76 (52) all_58_4 = all_52_8
% 112.61/16.76 (53) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.61/16.76 (54) ~ (all_52_4 = all_52_7)
% 112.61/16.76 (55) all_56_2 = all_52_12
% 112.61/16.76 (56) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.61/16.76 (57) all_58_3 = all_8_2
% 112.61/16.76 (58) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.61/16.76 (59) ~ (all_10_0 = e2)
% 112.61/16.76 (60) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 112.61/16.76 (61) all_58_11 = all_52_14
% 112.61/16.76 (62) all_54_9 = all_52_6
% 112.61/16.76 (63) op(e3, e1) = all_52_8
% 112.61/16.76 (64) ~ (all_52_2 = all_52_3)
% 112.61/16.76 (65) all_54_7 = all_52_13
% 112.61/16.76 (66) op(all_10_1, all_10_2) = all_10_0
% 112.61/16.76 (67) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.61/16.76 (68) ~ (all_52_11 = all_6_2)
% 112.61/16.77 (69) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 112.61/16.77 (70) op(e2, e3) = all_52_1
% 112.61/16.77 (71) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 112.61/16.77 (72) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 112.61/16.77 (73) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.61/16.77 (74) ~ (all_52_7 = all_8_2)
% 112.61/16.77 (75) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 112.61/16.77 (76) ~ (all_52_4 = all_8_2)
% 112.61/16.77 (77) op(e1, e0) = all_52_14
% 112.61/16.77 (78) all_58_5 = all_52_9
% 112.61/16.77 (79) all_56_9 = all_52_3
% 112.61/16.77 (80) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 112.61/16.77 (81) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.61/16.77 (82) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 112.61/16.77 (83) all_32_0 = all_10_0
% 112.61/16.77 (84) all_58_15 = all_4_2
% 112.61/16.77 (85) all_58_2 = all_52_1
% 112.61/16.77 (86) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.61/16.77 (87) ~ (all_52_1 = all_52_13)
% 112.61/16.77 (88) all_18_1 = e2
% 112.61/16.77 (89) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 112.61/16.77 (90) ~ (all_10_2 = e3)
% 112.61/16.77 (91) ~ (all_52_12 = all_52_13)
% 112.61/16.77 (92) all_58_13 = all_52_7
% 112.61/16.77 (93) all_32_1 = all_10_1
% 112.61/16.77 (94) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 112.61/16.77 (95) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 112.61/16.77 (96) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 112.61/16.77 (97) ~ (all_52_14 = all_4_2)
% 112.61/16.77 (98) all_58_6 = all_52_2
% 112.61/16.77 (99) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 112.61/16.77 (100) ~ (all_52_1 = all_10_2)
% 112.61/16.77 (101) all_54_5 = all_8_2
% 112.61/16.77 (102) all_56_15 = all_4_2
% 112.61/16.77 (103) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.61/16.77 (104) all_58_10 = all_52_13
% 112.61/16.77 (105) ~ (all_52_13 = all_8_2)
% 112.61/16.77 (106) op(e2, all_8_2) = all_8_1
% 112.61/16.77 (107) ~ (all_52_11 = all_4_2)
% 112.61/16.77 (108) op(e2, all_6_2) = all_6_0
% 112.61/16.77 (109) op(e3, all_10_2) = all_10_1
% 112.61/16.77 (110) ~ (all_52_6 = all_8_2)
% 112.61/16.77 (111) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.61/16.77 (112) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 112.61/16.77 (113) all_58_1 = all_52_4
% 112.61/16.77 (114) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 112.61/16.77 (115) ~ (all_52_9 = all_52_11)
% 112.61/16.77 (116) all_58_14 = all_52_11
% 112.61/16.77 (117) all_54_1 = all_52_4
% 112.61/16.77 (118) all_56_13 = all_8_2
% 112.61/16.77 (119) op(e0, e1) = all_52_11
% 112.61/16.77 (120) ~ (all_52_1 = all_8_2)
% 112.61/16.77 (121) ~ (all_8_2 = e2)
% 112.61/16.77 (122) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 112.61/16.77 (123) ~ (all_52_7 = all_52_11)
% 112.61/16.77 (124) op(e1, e2) = all_52_6
% 112.61/16.77 (125) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.61/16.77 (126) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 112.61/16.77 (127) all_56_7 = all_52_6
% 112.61/16.77 (128) ~ (all_52_9 = all_6_2)
% 112.61/16.77 (129) ~ (all_52_1 = all_52_3)
% 112.61/16.77 (130) all_56_1 = all_52_8
% 112.61/16.77 (131) op(e0, all_4_2) = all_4_1
% 112.61/16.77 (132) all_58_8 = all_6_2
% 112.61/16.77 (133) all_18_2 = all_6_2
% 112.61/16.77 (134) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.77 (135) ~ (all_10_0 = e1)
% 112.61/16.77 (136) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 112.61/16.77 (137) all_56_4 = all_52_9
% 112.61/16.77 (138) all_58_9 = all_52_12
% 112.61/16.77 (139) all_56_5 = all_52_13
% 112.61/16.77 (140) ~ (all_52_3 = all_4_2)
% 112.61/16.77 (141) ~ (all_52_6 = all_6_2)
% 112.61/16.77 (142) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 112.61/16.77 (143) all_56_6 = all_52_2
% 112.61/16.77 (144) ~ (all_52_13 = all_4_2)
% 112.61/16.77 (145) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 112.61/16.77 (146) all_58_12 = all_52_3
% 112.61/16.78 (147) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 112.61/16.78 (148) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.61/16.78 (149) op(e2, e0) = all_52_13
% 112.61/16.78 (150) ~ (all_52_12 = all_4_2)
% 112.61/16.78 (151) ~ (all_52_3 = all_10_2)
% 112.61/16.78 (152) op(e1, e3) = all_52_2
% 112.61/16.78 (153) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.61/16.78 (154) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 112.61/16.78 (155) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 112.61/16.78 (156) op(e1, e1) = all_6_2
% 112.61/16.78 (157) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.61/16.78 (158) ~ (all_8_1 = e1)
% 112.61/16.78 (159) ~ (all_52_8 = all_52_12)
% 112.61/16.78 (160) all_56_8 = all_52_14
% 112.61/16.78 (161) ~ (all_52_4 = all_10_2)
% 112.61/16.78 (162) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.61/16.78 (163) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.61/16.78 (164) all_56_0 = all_52_4
% 112.61/16.78 (165) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 112.61/16.78 (166) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.61/16.78 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.61/16.78 (167) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 112.61/16.78 (168) all_54_4 = all_52_1
% 112.61/16.78 (169) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 112.61/16.78 (170) all_54_15 = all_4_2
% 112.61/16.78 (171) ~ (all_6_2 = e1)
% 112.61/16.78 (172) ~ (all_52_6 = all_52_7)
% 112.61/16.78 (173) ~ (all_52_3 = all_52_11)
% 112.61/16.78 (174) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.61/16.78 (175) all_18_0 = all_6_0
% 112.61/16.78 (176) all_54_12 = all_52_3
% 112.61/16.78
% 112.61/16.78 Begin of proof
% 112.61/16.78 |
% 112.61/16.78 | BETA: splitting (50) gives:
% 112.61/16.78 |
% 112.61/16.78 | Case 1:
% 112.61/16.78 | |
% 112.61/16.78 | | (177) ~ (all_18_0 = e3)
% 112.61/16.78 | |
% 112.61/16.78 | | REDUCE: (175), (177) imply:
% 112.61/16.78 | | (178) ~ (all_6_0 = e3)
% 112.61/16.78 | |
% 112.61/16.78 | | BETA: splitting (7) gives:
% 112.61/16.78 | |
% 112.61/16.78 | | Case 1:
% 112.61/16.78 | | |
% 112.61/16.78 | | | (179) ~ (all_32_1 = e1)
% 112.61/16.78 | | |
% 112.61/16.78 | | | REDUCE: (93), (179) imply:
% 112.61/16.78 | | | (180) ~ (all_10_1 = e1)
% 112.61/16.78 | | |
% 112.61/16.78 | | | BETA: splitting (46) gives:
% 112.61/16.78 | | |
% 112.61/16.78 | | | Case 1:
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | (181) ~ (all_38_1 = e2)
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | REDUCE: (15), (181) imply:
% 112.61/16.78 | | | | (182) ~ (all_10_1 = e2)
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (13), (14),
% 112.61/16.78 | | | | (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 112.61/16.78 | | | | (27), (28), (29), (31), (32), (33), (34), (35), (36), (38),
% 112.61/16.78 | | | | (39), (40), (44), (47), (49), (51), (52), (53), (54), (55),
% 112.61/16.78 | | | | (56), (57), (58), (59), (61), (63), (65), (66), (67), (68),
% 112.61/16.78 | | | | (69), (70), (71), (72), (73), (74), (76), (77), (78), (79),
% 112.61/16.78 | | | | (80), (82), (84), (85), (86), (90), (91), (92), (95), (96),
% 112.61/16.78 | | | | (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 112.61/16.78 | | | | (107), (108), (109), (110), (111), (113), (114), (115),
% 112.61/16.78 | | | | (116), (117), (118), (119), (120), (121), (122), (123),
% 112.61/16.78 | | | | (124), (125), (126), (127), (130), (131), (132), (134),
% 112.61/16.78 | | | | (135), (137), (138), (139), (140), (141), (142), (143),
% 112.61/16.78 | | | | (144), (146), (148), (149), (150), (151), (154), (156),
% 112.61/16.78 | | | | (157), (159), (161), (162), (163), (164), (165), (166),
% 112.61/16.78 | | | | (167), (168), (169), (170), (171), (173), (174), (176),
% 112.61/16.78 | | | | (178), (180), (182) are inconsistent by sub-proof #38.
% 112.61/16.78 | | | |
% 112.61/16.78 | | | Case 2:
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | (183) all_38_1 = e2
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | COMBINE_EQS: (15), (183) imply:
% 112.61/16.78 | | | | (184) all_10_1 = e2
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | REDUCE: (66), (184) imply:
% 112.61/16.78 | | | | (185) op(e2, all_10_2) = all_10_0
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | REDUCE: (109), (184) imply:
% 112.61/16.78 | | | | (186) op(e3, all_10_2) = e2
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | BETA: splitting (95) gives:
% 112.61/16.78 | | | |
% 112.61/16.78 | | | | Case 1:
% 112.61/16.78 | | | | |
% 112.61/16.78 | | | | | (187) ~ (all_56_14 = e2)
% 112.61/16.78 | | | | |
% 112.61/16.78 | | | | | REDUCE: (13), (187) imply:
% 112.61/16.78 | | | | | (188) ~ (all_6_2 = e2)
% 112.61/16.78 | | | | |
% 112.61/16.78 | | | | | BETA: splitting (96) gives:
% 112.61/16.78 | | | | |
% 112.61/16.78 | | | | | Case 1:
% 112.61/16.78 | | | | | |
% 112.61/16.78 | | | | | | (189) ~ (all_56_12 = e2)
% 112.61/16.78 | | | | | |
% 112.61/16.78 | | | | | | REDUCE: (29), (189) imply:
% 112.61/16.78 | | | | | | (190) ~ (all_10_2 = e2)
% 112.61/16.78 | | | | | |
% 112.61/16.78 | | | | | | BETA: splitting (80) gives:
% 112.61/16.78 | | | | | |
% 112.61/16.78 | | | | | | Case 1:
% 112.61/16.78 | | | | | | |
% 112.61/16.78 | | | | | | | (191) ~ (all_56_15 = e1)
% 112.61/16.78 | | | | | | |
% 112.61/16.78 | | | | | | | REDUCE: (102), (191) imply:
% 112.61/16.78 | | | | | | | (192) ~ (all_4_2 = e1)
% 112.61/16.78 | | | | | | |
% 112.61/16.78 | | | | | | | BETA: splitting (155) gives:
% 112.61/16.78 | | | | | | |
% 112.61/16.78 | | | | | | | Case 1:
% 112.61/16.78 | | | | | | | |
% 112.61/16.78 | | | | | | | | (193) ~ (all_56_5 = e2)
% 112.61/16.78 | | | | | | | |
% 112.61/16.78 | | | | | | | | REDUCE: (139), (193) imply:
% 112.61/16.78 | | | | | | | | (194) ~ (all_52_13 = e2)
% 112.61/16.78 | | | | | | | |
% 112.61/16.78 | | | | | | | | REF_CLOSE: (1), (2), (5), (11), (13), (14), (16), (23), (26),
% 112.61/16.78 | | | | | | | | (27), (29), (30), (31), (36), (37), (39), (40), (45),
% 112.61/16.78 | | | | | | | | (47), (48), (49), (52), (53), (55), (56), (57), (58),
% 112.61/16.78 | | | | | | | | (61), (67), (78), (79), (81), (84), (85), (86), (89),
% 112.61/16.78 | | | | | | | | (90), (92), (97), (98), (100), (102), (104), (107),
% 112.61/16.78 | | | | | | | | (112), (113), (116), (121), (125), (127), (132),
% 112.61/16.78 | | | | | | | | (134), (135), (137), (138), (143), (146), (149),
% 112.61/16.78 | | | | | | | | (150), (153), (157), (160), (162), (163), (164),
% 112.61/16.78 | | | | | | | | (166), (170), (171), (185), (186), (188), (190),
% 112.61/16.78 | | | | | | | | (192), (194) are inconsistent by sub-proof #35.
% 112.61/16.78 | | | | | | | |
% 112.61/16.78 | | | | | | | Case 2:
% 112.61/16.78 | | | | | | | |
% 112.61/16.78 | | | | | | | | (195) all_56_5 = e2
% 112.61/16.78 | | | | | | | |
% 112.61/16.79 | | | | | | | | COMBINE_EQS: (139), (195) imply:
% 112.61/16.79 | | | | | | | | (196) all_52_13 = e2
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | COMBINE_EQS: (104), (196) imply:
% 112.61/16.79 | | | | | | | | (197) all_58_10 = e2
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | REDUCE: (105), (196) imply:
% 112.61/16.79 | | | | | | | | (198) ~ (all_8_2 = e2)
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | REDUCE: (144), (196) imply:
% 112.61/16.79 | | | | | | | | (199) ~ (all_4_2 = e2)
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | SIMP: (199) implies:
% 112.61/16.79 | | | | | | | | (200) ~ (all_4_2 = e2)
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | BETA: splitting (73) gives:
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | (201) ~ (all_56_5 = e2)
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | REDUCE: (195), (201) imply:
% 112.61/16.79 | | | | | | | | | (202) $false
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | CLOSE: (202) is inconsistent.
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | (203) ~ (all_56_14 = e0)
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | REDUCE: (13), (203) imply:
% 112.61/16.79 | | | | | | | | | (204) ~ (all_6_2 = e0)
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | BETA: splitting (39) gives:
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | (205) all_54_10 = e3
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | COMBINE_EQS: (47), (205) imply:
% 112.61/16.79 | | | | | | | | | | (206) all_6_2 = e3
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | SIMP: (206) implies:
% 112.61/16.79 | | | | | | | | | | (207) all_6_2 = e3
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | REDUCE: (51), (207) imply:
% 112.61/16.79 | | | | | | | | | | (208) ~ (all_52_8 = e3)
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | REDUCE: (128), (207) imply:
% 112.61/16.79 | | | | | | | | | | (209) ~ (all_52_9 = e3)
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | REDUCE: (44), (207) imply:
% 112.61/16.79 | | | | | | | | | | (210) op(e1, e3) = e2
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | REDUCE: (156), (207) imply:
% 112.61/16.79 | | | | | | | | | | (211) op(e1, e1) = e3
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | BETA: splitting (53) gives:
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | (212) all_54_15 = e3
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | COMBINE_EQS: (170), (212) imply:
% 112.61/16.79 | | | | | | | | | | | (213) all_4_2 = e3
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | COMBINE_EQS: (102), (213) imply:
% 112.61/16.79 | | | | | | | | | | | (214) all_56_15 = e3
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | REDUCE: (150), (213) imply:
% 112.61/16.79 | | | | | | | | | | | (215) ~ (all_52_12 = e3)
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | REDUCE: (200), (213) imply:
% 112.61/16.79 | | | | | | | | | | | (216) ~ (e3 = e2)
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | BETA: splitting (136) gives:
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | (217) ~ (all_56_15 = e3)
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | REDUCE: (214), (217) imply:
% 112.61/16.79 | | | | | | | | | | | | (218) $false
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | (219) ~ (all_56_9 = e0)
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | REDUCE: (79), (219) imply:
% 112.61/16.79 | | | | | | | | | | | | (220) ~ (all_52_3 = e0)
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | BETA: splitting (157) gives:
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | (221) all_58_0 = e3
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | COMBINE_EQS: (31), (221) imply:
% 112.61/16.79 | | | | | | | | | | | | | (222) all_10_2 = e3
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | REDUCE: (90), (222) imply:
% 112.61/16.79 | | | | | | | | | | | | | (223) $false
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | (224) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | BETA: splitting (224) gives:
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | (225) all_58_1 = e3
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | COMBINE_EQS: (113), (225) imply:
% 112.61/16.79 | | | | | | | | | | | | | | (226) all_52_4 = e3
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | REDUCE: (76), (226) imply:
% 112.61/16.79 | | | | | | | | | | | | | | (227) ~ (all_8_2 = e3)
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | SIMP: (227) implies:
% 112.61/16.79 | | | | | | | | | | | | | | (228) ~ (all_8_2 = e3)
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | Case 1:
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | (229) all_58_2 = e3
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | COMBINE_EQS: (85), (229) imply:
% 112.61/16.79 | | | | | | | | | | | | | | | (230) all_52_1 = e3
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | REDUCE: (70), (230) imply:
% 112.61/16.79 | | | | | | | | | | | | | | | (231) op(e2, e3) = e3
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (13), (14), (16), (27), (28), (29),
% 112.61/16.79 | | | | | | | | | | | | | | | (31), (40), (57), (64), (65), (70), (78), (85),
% 112.61/16.79 | | | | | | | | | | | | | | | (87), (100), (101), (103), (104), (105), (106),
% 112.61/16.79 | | | | | | | | | | | | | | | (111), (118), (120), (121), (129), (134), (137),
% 112.61/16.79 | | | | | | | | | | | | | | | (139), (148), (149), (151), (152), (155), (156),
% 112.61/16.79 | | | | | | | | | | | | | | | (158), (163), (176), (210), (211), (220), (231)
% 112.61/16.79 | | | | | | | | | | | | | | | are inconsistent by sub-proof #31.
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | (232) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | | REF_CLOSE: (57), (78), (197), (209), (216), (228), (232) are
% 112.61/16.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 112.61/16.79 | | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | (233) all_58_4 = e3 | all_58_9 = e3
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | | REF_CLOSE: (52), (138), (208), (215), (233) are inconsistent
% 112.61/16.79 | | | | | | | | | | | | | | by sub-proof #184.
% 112.61/16.79 | | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | (234) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | | REF_CLOSE: (11), (170), (192), (200), (234) are inconsistent
% 112.61/16.79 | | | | | | | | | | | by sub-proof #417.
% 112.61/16.79 | | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | Case 2:
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | (235) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | | REF_CLOSE: (47), (171), (188), (204), (235) are inconsistent
% 112.61/16.79 | | | | | | | | | | by sub-proof #435.
% 112.61/16.79 | | | | | | | | | |
% 112.61/16.79 | | | | | | | | | End of split
% 112.61/16.79 | | | | | | | | |
% 112.61/16.79 | | | | | | | | End of split
% 112.61/16.79 | | | | | | | |
% 112.61/16.79 | | | | | | | End of split
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | Case 2:
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | (236) all_56_15 = e1
% 112.61/16.79 | | | | | | | (237) ~ (all_56_11 = e0)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | COMBINE_EQS: (102), (236) imply:
% 112.61/16.79 | | | | | | | (238) all_4_2 = e1
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | SIMP: (238) implies:
% 112.61/16.79 | | | | | | | (239) all_4_2 = e1
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | COMBINE_EQS: (84), (239) imply:
% 112.61/16.79 | | | | | | | (240) all_58_15 = e1
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (23), (237) imply:
% 112.61/16.79 | | | | | | | (241) ~ (all_52_11 = e0)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (140), (239) imply:
% 112.61/16.79 | | | | | | | (242) ~ (all_52_3 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (22), (239) imply:
% 112.61/16.79 | | | | | | | (243) ~ (all_52_7 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (107), (239) imply:
% 112.61/16.79 | | | | | | | (244) ~ (all_52_11 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (150), (239) imply:
% 112.61/16.79 | | | | | | | (245) ~ (all_52_12 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (144), (239) imply:
% 112.61/16.79 | | | | | | | (246) ~ (all_52_13 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (97), (239) imply:
% 112.61/16.79 | | | | | | | (247) ~ (all_52_14 = e1)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (11), (239) imply:
% 112.61/16.79 | | | | | | | (248) ~ (e1 = e0)
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REDUCE: (131), (239) imply:
% 112.61/16.79 | | | | | | | (249) op(e0, e1) = all_4_1
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | | REF_CLOSE: (2), (3), (5), (11), (12), (13), (14), (16), (17),
% 112.61/16.79 | | | | | | | (18), (20), (21), (23), (25), (26), (27), (28), (29),
% 112.61/16.79 | | | | | | | (31), (32), (33), (34), (35), (36), (38), (39), (40),
% 112.61/16.79 | | | | | | | (44), (47), (51), (52), (54), (55), (56), (57), (58),
% 112.61/16.79 | | | | | | | (59), (61), (65), (66), (67), (68), (69), (70), (73),
% 112.61/16.79 | | | | | | | (74), (76), (77), (78), (79), (82), (84), (85), (90),
% 112.61/16.79 | | | | | | | (91), (92), (96), (98), (99), (100), (101), (103),
% 112.61/16.79 | | | | | | | (104), (106), (108), (109), (110), (111), (113), (114),
% 112.61/16.79 | | | | | | | (115), (116), (117), (118), (119), (120), (121), (122),
% 112.61/16.79 | | | | | | | (123), (125), (126), (127), (130), (132), (134), (135),
% 112.61/16.79 | | | | | | | (137), (138), (139), (141), (143), (146), (148), (149),
% 112.61/16.79 | | | | | | | (151), (154), (156), (157), (161), (163), (164), (165),
% 112.61/16.79 | | | | | | | (166), (167), (168), (169), (171), (173), (174), (176),
% 112.61/16.79 | | | | | | | (178), (180), (188), (236), (240), (241), (242), (243),
% 112.61/16.79 | | | | | | | (244), (245), (246), (247), (248), (249) are
% 112.61/16.79 | | | | | | | inconsistent by sub-proof #40.
% 112.61/16.79 | | | | | | |
% 112.61/16.79 | | | | | | End of split
% 112.61/16.79 | | | | | |
% 112.61/16.79 | | | | | Case 2:
% 112.61/16.79 | | | | | |
% 112.61/16.79 | | | | | | (250) all_56_12 = e2
% 112.61/16.79 | | | | | |
% 112.61/16.79 | | | | | | REF_CLOSE: (12), (29), (40), (161), (186), (250) are inconsistent by
% 112.61/16.79 | | | | | | sub-proof #300.
% 112.61/16.79 | | | | | |
% 112.61/16.79 | | | | | End of split
% 112.61/16.79 | | | | |
% 112.61/16.79 | | | | Case 2:
% 112.61/16.79 | | | | |
% 112.61/16.79 | | | | | (251) all_56_14 = e2
% 112.61/16.79 | | | | |
% 112.61/16.79 | | | | | COMBINE_EQS: (13), (251) imply:
% 112.61/16.79 | | | | | (252) all_6_2 = e2
% 112.61/16.79 | | | | |
% 112.61/16.79 | | | | | REF_CLOSE: (40), (44), (124), (141), (252) are inconsistent by
% 112.61/16.79 | | | | | sub-proof #39.
% 112.61/16.79 | | | | |
% 112.61/16.79 | | | | End of split
% 112.61/16.79 | | | |
% 112.61/16.79 | | | End of split
% 112.61/16.79 | | |
% 112.61/16.79 | | Case 2:
% 112.61/16.79 | | |
% 112.61/16.79 | | | (253) all_32_1 = e1
% 112.61/16.80 | | | (254) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 112.61/16.80 | | |
% 112.61/16.80 | | | COMBINE_EQS: (93), (253) imply:
% 112.61/16.80 | | | (255) all_10_1 = e1
% 112.61/16.80 | | |
% 112.61/16.80 | | | REF_CLOSE: (1), (3), (5), (10), (11), (12), (13), (16), (19), (22), (29),
% 112.61/16.80 | | | (30), (33), (36), (37), (39), (40), (41), (42), (43), (44),
% 112.61/16.80 | | | (47), (48), (49), (52), (53), (56), (57), (59), (60), (61),
% 112.61/16.80 | | | (62), (63), (66), (68), (75), (77), (78), (81), (82), (83),
% 112.61/16.80 | | | (84), (90), (92), (94), (95), (96), (98), (102), (104), (109),
% 112.61/16.80 | | | (113), (116), (121), (123), (124), (125), (127), (128), (132),
% 112.61/16.80 | | | (134), (137), (138), (139), (141), (143), (146), (147), (151),
% 112.61/16.80 | | | (153), (155), (160), (161), (162), (166), (170), (171), (172),
% 112.61/16.80 | | | (254), (255) are inconsistent by sub-proof #30.
% 112.61/16.80 | | |
% 112.61/16.80 | | End of split
% 112.61/16.80 | |
% 112.61/16.80 | Case 2:
% 112.61/16.80 | |
% 112.61/16.80 | | (256) all_18_0 = e3
% 112.61/16.80 | | (257) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 112.61/16.80 | |
% 112.61/16.80 | | REF_CLOSE: (3), (6), (13), (14), (16), (27), (28), (29), (31), (39), (40),
% 112.61/16.80 | | (44), (47), (57), (64), (65), (67), (70), (78), (79), (85), (87),
% 112.61/16.80 | | (88), (95), (100), (101), (103), (104), (105), (106), (108),
% 112.61/16.80 | | (111), (118), (120), (121), (124), (129), (133), (134), (137),
% 112.61/16.80 | | (139), (141), (148), (149), (151), (152), (155), (156), (158),
% 112.61/16.80 | | (163), (171), (175), (176), (256), (257) are inconsistent by
% 112.61/16.80 | | sub-proof #29.
% 112.61/16.80 | |
% 112.61/16.80 | End of split
% 112.61/16.80 |
% 112.61/16.80 End of proof
% 112.61/16.80
% 112.61/16.80 Sub-proof #29 shows that the following formulas are inconsistent:
% 112.61/16.80 ----------------------------------------------------------------
% 112.61/16.80 (1) ~ (all_52_2 = all_10_2)
% 112.61/16.80 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 112.61/16.80 (3) all_56_14 = all_6_2
% 112.61/16.80 (4) all_56_3 = all_52_1
% 112.61/16.80 (5) all_54_0 = all_10_2
% 112.61/16.80 (6) all_18_0 = e3
% 112.61/16.80 (7) ~ (all_18_1 = e2) | ~ (all_18_2 = e0)
% 112.61/16.80 (8) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.61/16.80 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.61/16.80 (10) all_56_12 = all_10_2
% 112.61/16.80 (11) all_58_0 = all_10_2
% 112.61/16.80 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.80 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.80 (14) op(e1, all_6_2) = e2
% 112.61/16.80 (15) all_54_10 = all_6_2
% 112.61/16.80 (16) all_58_3 = all_8_2
% 112.61/16.80 (17) ~ (all_52_2 = all_52_3)
% 112.61/16.80 (18) all_54_7 = all_52_13
% 112.61/16.80 (19) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.61/16.80 (20) op(e2, e3) = all_52_1
% 112.61/16.80 (21) all_58_5 = all_52_9
% 112.61/16.80 (22) all_56_9 = all_52_3
% 112.61/16.80 (23) all_58_2 = all_52_1
% 112.61/16.80 (24) ~ (all_52_1 = all_52_13)
% 112.61/16.80 (25) all_18_1 = e2
% 112.61/16.80 (26) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 112.61/16.80 (27) ~ (all_52_1 = all_10_2)
% 112.61/16.80 (28) all_54_5 = all_8_2
% 112.61/16.80 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.61/16.80 (30) all_58_10 = all_52_13
% 112.61/16.80 (31) ~ (all_52_13 = all_8_2)
% 112.61/16.80 (32) op(e2, all_8_2) = all_8_1
% 112.61/16.80 (33) op(e2, all_6_2) = all_6_0
% 112.61/16.80 (34) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.61/16.80 (35) all_56_13 = all_8_2
% 112.61/16.80 (36) ~ (all_52_1 = all_8_2)
% 112.61/16.80 (37) ~ (all_8_2 = e2)
% 112.61/16.80 (38) op(e1, e2) = all_52_6
% 112.61/16.80 (39) ~ (all_52_1 = all_52_3)
% 112.61/16.80 (40) all_18_2 = all_6_2
% 112.61/16.80 (41) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.80 (42) all_56_4 = all_52_9
% 112.61/16.80 (43) all_56_5 = all_52_13
% 112.61/16.80 (44) ~ (all_52_6 = all_6_2)
% 112.61/16.80 (45) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.61/16.80 (46) op(e2, e0) = all_52_13
% 112.61/16.80 (47) ~ (all_52_3 = all_10_2)
% 112.61/16.80 (48) op(e1, e3) = all_52_2
% 112.61/16.80 (49) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 112.61/16.80 (50) op(e1, e1) = all_6_2
% 112.61/16.80 (51) ~ (all_8_1 = e1)
% 112.61/16.80 (52) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.61/16.80 (53) ~ (all_6_2 = e1)
% 112.61/16.80 (54) all_18_0 = all_6_0
% 112.61/16.80 (55) all_54_12 = all_52_3
% 112.61/16.80
% 112.61/16.80 Begin of proof
% 112.61/16.80 |
% 112.61/16.80 | COMBINE_EQS: (6), (54) imply:
% 112.61/16.80 | (56) all_6_0 = e3
% 112.61/16.80 |
% 112.61/16.80 | SIMP: (56) implies:
% 112.61/16.80 | (57) all_6_0 = e3
% 112.61/16.80 |
% 112.61/16.80 | REDUCE: (33), (57) imply:
% 112.61/16.80 | (58) op(e2, all_6_2) = e3
% 112.61/16.80 |
% 112.61/16.80 | BETA: splitting (7) gives:
% 112.61/16.80 |
% 112.61/16.80 | Case 1:
% 112.61/16.80 | |
% 112.61/16.80 | | (59) ~ (all_18_1 = e2)
% 112.61/16.80 | |
% 112.61/16.80 | | REDUCE: (25), (59) imply:
% 112.61/16.80 | | (60) $false
% 112.61/16.80 | |
% 112.61/16.80 | | CLOSE: (60) is inconsistent.
% 112.61/16.80 | |
% 112.61/16.80 | Case 2:
% 112.61/16.80 | |
% 112.61/16.80 | | (61) ~ (all_18_2 = e0)
% 112.61/16.80 | |
% 112.61/16.80 | | REDUCE: (40), (61) imply:
% 112.61/16.80 | | (62) ~ (all_6_2 = e0)
% 112.61/16.80 | |
% 112.61/16.80 | | BETA: splitting (26) gives:
% 112.61/16.80 | |
% 112.61/16.80 | | Case 1:
% 112.61/16.80 | | |
% 112.61/16.80 | | | (63) ~ (all_56_14 = e2)
% 112.61/16.80 | | |
% 112.61/16.80 | | | REDUCE: (3), (63) imply:
% 112.61/16.80 | | | (64) ~ (all_6_2 = e2)
% 112.61/16.80 | | |
% 112.61/16.80 | | | BETA: splitting (12) gives:
% 112.61/16.80 | | |
% 112.61/16.80 | | | Case 1:
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | (65) all_54_10 = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | COMBINE_EQS: (15), (65) imply:
% 112.61/16.80 | | | | (66) all_6_2 = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | SIMP: (66) implies:
% 112.61/16.80 | | | | (67) all_6_2 = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | COMBINE_EQS: (3), (67) imply:
% 112.61/16.80 | | | | (68) all_56_14 = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | REDUCE: (58), (67) imply:
% 112.61/16.80 | | | | (69) op(e2, e3) = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | REDUCE: (14), (67) imply:
% 112.61/16.80 | | | | (70) op(e1, e3) = e2
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | REDUCE: (50), (67) imply:
% 112.61/16.80 | | | | (71) op(e1, e1) = e3
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | BETA: splitting (19) gives:
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | Case 1:
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | (72) ~ (all_56_14 = e3)
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | REDUCE: (68), (72) imply:
% 112.61/16.80 | | | | | (73) $false
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | CLOSE: (73) is inconsistent.
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | Case 2:
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | (74) ~ (all_56_9 = e0)
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | REDUCE: (22), (74) imply:
% 112.61/16.80 | | | | | (75) ~ (all_52_3 = e0)
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13), (16),
% 112.61/16.80 | | | | | (17), (18), (20), (21), (23), (24), (27), (28), (29), (30),
% 112.61/16.80 | | | | | (31), (32), (34), (35), (36), (37), (39), (41), (42), (43),
% 112.61/16.80 | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (55), (69),
% 112.61/16.80 | | | | | (70), (71), (75) are inconsistent by sub-proof #31.
% 112.61/16.80 | | | | |
% 112.61/16.80 | | | | End of split
% 112.61/16.80 | | | |
% 112.61/16.80 | | | Case 2:
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | (76) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.80 | | | |
% 112.61/16.80 | | | | REF_CLOSE: (15), (53), (62), (64), (76) are inconsistent by sub-proof
% 112.61/16.80 | | | | #435.
% 112.61/16.80 | | | |
% 112.61/16.80 | | | End of split
% 112.61/16.80 | | |
% 112.61/16.80 | | Case 2:
% 112.61/16.80 | | |
% 112.61/16.80 | | | (77) all_56_14 = e2
% 112.61/16.80 | | |
% 112.61/16.80 | | | COMBINE_EQS: (3), (77) imply:
% 112.61/16.80 | | | (78) all_6_2 = e2
% 112.61/16.80 | | |
% 112.61/16.80 | | | REF_CLOSE: (13), (14), (38), (44), (78) are inconsistent by sub-proof #39.
% 112.61/16.80 | | |
% 112.61/16.80 | | End of split
% 112.61/16.80 | |
% 112.61/16.80 | End of split
% 112.61/16.80 |
% 112.61/16.80 End of proof
% 112.61/16.80
% 112.61/16.80 Sub-proof #30 shows that the following formulas are inconsistent:
% 112.61/16.80 ----------------------------------------------------------------
% 112.61/16.80 (1) ~ (all_52_8 = all_10_2)
% 112.61/16.80 (2) ~ (all_52_2 = all_10_2)
% 112.61/16.80 (3) all_58_7 = all_52_6
% 112.61/16.80 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 112.61/16.81 (5) ~ (all_4_2 = e0)
% 112.61/16.81 (6) op(e3, e2) = all_52_4
% 112.61/16.81 (7) all_56_14 = all_6_2
% 112.61/16.81 (8) all_54_0 = all_10_2
% 112.61/16.81 (9) ~ (all_52_2 = all_52_6)
% 112.61/16.81 (10) ~ (all_52_7 = all_4_2)
% 112.61/16.81 (11) all_56_12 = all_10_2
% 112.61/16.81 (12) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.61/16.81 (13) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 112.61/16.81 (14) all_56_10 = all_52_7
% 112.61/16.81 (15) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.61/16.81 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.81 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.81 (18) all_54_8 = all_52_2
% 112.61/16.81 (19) ~ (all_52_2 = all_6_2)
% 112.61/16.81 (20) all_32_2 = all_10_2
% 112.61/16.81 (21) op(e1, all_6_2) = e2
% 112.61/16.81 (22) all_54_10 = all_6_2
% 112.61/16.81 (23) ~ (e2 = e1)
% 112.61/16.81 (24) op(e3, e0) = all_52_12
% 112.61/16.81 (25) all_58_4 = all_52_8
% 112.61/16.81 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.61/16.81 (27) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.61/16.81 (28) all_58_3 = all_8_2
% 112.61/16.81 (29) ~ (all_10_0 = e2)
% 112.61/16.81 (30) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 112.61/16.81 (31) all_58_11 = all_52_14
% 112.61/16.81 (32) all_54_9 = all_52_6
% 112.61/16.81 (33) op(e3, e1) = all_52_8
% 112.61/16.81 (34) op(all_10_1, all_10_2) = all_10_0
% 112.61/16.81 (35) ~ (all_52_11 = all_6_2)
% 112.61/16.81 (36) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 112.61/16.81 (37) op(e1, e0) = all_52_14
% 112.61/16.81 (38) all_58_5 = all_52_9
% 112.61/16.81 (39) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.61/16.81 (40) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 112.61/16.81 (41) all_32_0 = all_10_0
% 112.61/16.81 (42) all_58_15 = all_4_2
% 112.61/16.81 (43) ~ (all_10_2 = e3)
% 112.61/16.81 (44) all_58_13 = all_52_7
% 112.61/16.81 (45) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 112.61/16.81 (46) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 112.61/16.81 (47) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 112.61/16.81 (48) all_58_6 = all_52_2
% 112.61/16.81 (49) all_56_15 = all_4_2
% 112.61/16.81 (50) all_58_10 = all_52_13
% 112.61/16.81 (51) op(e3, all_10_2) = all_10_1
% 112.61/16.81 (52) all_58_1 = all_52_4
% 112.61/16.81 (53) all_58_14 = all_52_11
% 112.61/16.81 (54) ~ (all_8_2 = e2)
% 112.61/16.81 (55) ~ (all_52_7 = all_52_11)
% 112.61/16.81 (56) op(e1, e2) = all_52_6
% 112.61/16.81 (57) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.61/16.81 (58) all_56_7 = all_52_6
% 112.61/16.81 (59) ~ (all_52_9 = all_6_2)
% 112.61/16.81 (60) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 112.61/16.81 (61) all_58_8 = all_6_2
% 112.61/16.81 (62) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.81 (63) all_56_4 = all_52_9
% 112.61/16.81 (64) all_58_9 = all_52_12
% 112.61/16.81 (65) all_56_5 = all_52_13
% 112.61/16.81 (66) ~ (all_52_6 = all_6_2)
% 112.61/16.81 (67) all_56_6 = all_52_2
% 112.61/16.81 (68) all_58_12 = all_52_3
% 112.61/16.81 (69) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 112.61/16.81 (70) ~ (all_52_3 = all_10_2)
% 112.61/16.81 (71) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.61/16.81 (72) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 112.61/16.81 (73) all_56_8 = all_52_14
% 112.61/16.81 (74) ~ (all_52_4 = all_10_2)
% 112.61/16.81 (75) all_10_1 = e1
% 112.61/16.81 (76) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.61/16.81 (77) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.61/16.81 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.61/16.81 (78) all_54_15 = all_4_2
% 112.61/16.81 (79) ~ (all_6_2 = e1)
% 112.61/16.81 (80) ~ (all_52_6 = all_52_7)
% 112.61/16.81
% 112.61/16.81 Begin of proof
% 112.61/16.81 |
% 112.61/16.81 | REDUCE: (34), (75) imply:
% 112.61/16.81 | (81) op(e1, all_10_2) = all_10_0
% 112.61/16.81 |
% 112.61/16.81 | REDUCE: (51), (75) imply:
% 112.61/16.81 | (82) op(e3, all_10_2) = e1
% 112.61/16.81 |
% 112.61/16.81 | BETA: splitting (46) gives:
% 112.61/16.81 |
% 112.61/16.81 | Case 1:
% 112.61/16.81 | |
% 112.61/16.81 | | (83) ~ (all_56_14 = e2)
% 112.61/16.81 | |
% 112.61/16.81 | | REDUCE: (7), (83) imply:
% 112.61/16.81 | | (84) ~ (all_6_2 = e2)
% 112.61/16.81 | |
% 112.61/16.81 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 112.61/16.81 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 112.61/16.81 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 112.61/16.81 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 112.61/16.81 | | (49), (50), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 112.61/16.81 | | (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 112.61/16.81 | | (72), (73), (74), (76), (77), (78), (79), (80), (81), (82), (84)
% 112.61/16.81 | | are inconsistent by sub-proof #289.
% 112.61/16.81 | |
% 112.61/16.81 | Case 2:
% 112.61/16.81 | |
% 112.61/16.81 | | (85) all_56_14 = e2
% 112.61/16.81 | |
% 112.61/16.81 | | COMBINE_EQS: (7), (85) imply:
% 112.61/16.81 | | (86) all_6_2 = e2
% 112.61/16.81 | |
% 112.61/16.81 | | REF_CLOSE: (17), (21), (56), (66), (86) are inconsistent by sub-proof #39.
% 112.61/16.81 | |
% 112.61/16.81 | End of split
% 112.61/16.81 |
% 112.61/16.81 End of proof
% 112.61/16.81
% 112.61/16.81 Sub-proof #31 shows that the following formulas are inconsistent:
% 112.61/16.81 ----------------------------------------------------------------
% 112.61/16.81 (1) op(e1, e3) = e2
% 112.61/16.81 (2) ~ (all_52_2 = all_10_2)
% 112.61/16.81 (3) ~ (all_52_3 = e0)
% 112.61/16.81 (4) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 112.61/16.81 (5) all_56_14 = all_6_2
% 112.61/16.81 (6) all_56_3 = all_52_1
% 112.61/16.82 (7) all_54_0 = all_10_2
% 112.61/16.82 (8) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.61/16.82 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.61/16.82 (10) all_56_12 = all_10_2
% 112.61/16.82 (11) all_58_0 = all_10_2
% 112.61/16.82 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.82 (13) all_58_3 = all_8_2
% 112.61/16.82 (14) ~ (all_52_2 = all_52_3)
% 112.61/16.82 (15) all_54_7 = all_52_13
% 112.61/16.82 (16) op(e2, e3) = all_52_1
% 112.61/16.82 (17) all_58_5 = all_52_9
% 112.61/16.82 (18) all_58_2 = all_52_1
% 112.61/16.82 (19) ~ (all_52_1 = all_52_13)
% 112.61/16.82 (20) ~ (all_52_1 = all_10_2)
% 112.61/16.82 (21) all_54_5 = all_8_2
% 112.61/16.82 (22) op(e1, e1) = e3
% 112.61/16.82 (23) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.61/16.82 (24) all_58_10 = all_52_13
% 112.61/16.82 (25) ~ (all_52_13 = all_8_2)
% 112.61/16.82 (26) op(e2, all_8_2) = all_8_1
% 112.61/16.82 (27) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.61/16.82 (28) all_56_13 = all_8_2
% 112.61/16.82 (29) ~ (all_52_1 = all_8_2)
% 112.61/16.82 (30) ~ (all_8_2 = e2)
% 112.61/16.82 (31) ~ (all_52_1 = all_52_3)
% 112.61/16.82 (32) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.82 (33) all_56_4 = all_52_9
% 112.61/16.82 (34) all_56_5 = all_52_13
% 112.61/16.82 (35) op(e2, e3) = e3
% 112.61/16.82 (36) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.61/16.82 (37) op(e2, e0) = all_52_13
% 112.61/16.82 (38) ~ (all_52_3 = all_10_2)
% 112.61/16.82 (39) op(e1, e3) = all_52_2
% 112.61/16.82 (40) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 112.61/16.82 (41) op(e1, e1) = all_6_2
% 112.61/16.82 (42) ~ (all_8_1 = e1)
% 112.61/16.82 (43) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.61/16.82 (44) all_54_12 = all_52_3
% 112.61/16.82
% 112.61/16.82 Begin of proof
% 112.61/16.82 |
% 112.61/16.82 | GROUND_INST: instantiating (12) with all_52_2, e2, e3, e1, simplifying with
% 112.61/16.82 | (1), (39) gives:
% 112.61/16.82 | (45) all_52_2 = e2
% 112.61/16.82 |
% 112.61/16.82 | GROUND_INST: instantiating (12) with all_52_1, e3, e3, e2, simplifying with
% 112.61/16.82 | (16), (35) gives:
% 112.61/16.82 | (46) all_52_1 = e3
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (31), (46) imply:
% 112.61/16.82 | (47) ~ (all_52_3 = e3)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (47) implies:
% 112.61/16.82 | (48) ~ (all_52_3 = e3)
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (19), (46) imply:
% 112.61/16.82 | (49) ~ (all_52_13 = e3)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (49) implies:
% 112.61/16.82 | (50) ~ (all_52_13 = e3)
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (20), (46) imply:
% 112.61/16.82 | (51) ~ (all_10_2 = e3)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (51) implies:
% 112.61/16.82 | (52) ~ (all_10_2 = e3)
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (29), (46) imply:
% 112.61/16.82 | (53) ~ (all_8_2 = e3)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (53) implies:
% 112.61/16.82 | (54) ~ (all_8_2 = e3)
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (14), (45) imply:
% 112.61/16.82 | (55) ~ (all_52_3 = e2)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (55) implies:
% 112.61/16.82 | (56) ~ (all_52_3 = e2)
% 112.61/16.82 |
% 112.61/16.82 | REDUCE: (2), (45) imply:
% 112.61/16.82 | (57) ~ (all_10_2 = e2)
% 112.61/16.82 |
% 112.61/16.82 | SIMP: (57) implies:
% 112.61/16.82 | (58) ~ (all_10_2 = e2)
% 112.61/16.82 |
% 112.61/16.82 | BETA: splitting (36) gives:
% 112.61/16.82 |
% 112.61/16.82 | Case 1:
% 112.61/16.82 | |
% 112.61/16.82 | | (59) all_54_12 = e3
% 112.61/16.82 | |
% 112.61/16.82 | | REF_CLOSE: (44), (48), (59) are inconsistent by sub-proof #410.
% 112.61/16.82 | |
% 112.61/16.82 | Case 2:
% 112.61/16.82 | |
% 112.61/16.82 | | (60) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.61/16.82 | |
% 112.61/16.82 | | BETA: splitting (60) gives:
% 112.61/16.82 | |
% 112.61/16.82 | | Case 1:
% 112.61/16.82 | | |
% 112.61/16.82 | | | (61) all_54_12 = e2
% 112.61/16.82 | | |
% 112.61/16.82 | | | REF_CLOSE: (44), (56), (61) are inconsistent by sub-proof #409.
% 112.61/16.82 | | |
% 112.61/16.82 | | Case 2:
% 112.61/16.82 | | |
% 112.61/16.82 | | | (62) all_54_12 = e1 | all_54_12 = e0
% 112.61/16.82 | | |
% 112.61/16.82 | | | BETA: splitting (4) gives:
% 112.61/16.82 | | |
% 112.61/16.82 | | | Case 1:
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | (63) all_58_0 = e0
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | COMBINE_EQS: (11), (63) imply:
% 112.61/16.82 | | | | (64) all_10_2 = e0
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | COMBINE_EQS: (10), (64) imply:
% 112.61/16.82 | | | | (65) all_56_12 = e0
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | BETA: splitting (40) gives:
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | Case 1:
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | (66) ~ (all_56_5 = e2)
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | REDUCE: (34), (66) imply:
% 112.61/16.82 | | | | | (67) ~ (all_52_13 = e2)
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | BETA: splitting (23) gives:
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | Case 1:
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | | (68) all_54_7 = e3
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | | REF_CLOSE: (15), (50), (68) are inconsistent by sub-proof #350.
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | Case 2:
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | | (69) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | | BETA: splitting (9) gives:
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | | Case 1:
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | | (70) all_54_5 = e3
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | | REF_CLOSE: (21), (54), (70) are inconsistent by sub-proof #339.
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | Case 2:
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | | (71) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | | BETA: splitting (71) gives:
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | | Case 1:
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | | (72) all_54_5 = e2
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | | REF_CLOSE: (21), (30), (72) are inconsistent by sub-proof #338.
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | Case 2:
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | | (73) ~ (all_54_5 = e2)
% 112.61/16.82 | | | | | | | | (74) all_54_5 = e1 | all_54_5 = e0
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | | BETA: splitting (69) gives:
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | | Case 1:
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | | (75) all_54_7 = e2
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | | REF_CLOSE: (15), (67), (75) are inconsistent by sub-proof #34.
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | Case 2:
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | | (76) ~ (all_54_7 = e2)
% 112.61/16.82 | | | | | | | | | (77) all_54_7 = e1 | all_54_7 = e0
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | | BETA: splitting (74) gives:
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | | Case 1:
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | (78) all_54_5 = e1
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | REF_CLOSE: (5), (6), (8), (12), (13), (17), (18), (21), (22),
% 112.61/16.82 | | | | | | | | | | (24), (27), (28), (30), (33), (41), (43), (67),
% 112.61/16.82 | | | | | | | | | | (78) are inconsistent by sub-proof #102.
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | Case 2:
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | (79) all_54_5 = e0
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | COMBINE_EQS: (21), (79) imply:
% 112.61/16.82 | | | | | | | | | | (80) all_8_2 = e0
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | SIMP: (80) implies:
% 112.61/16.82 | | | | | | | | | | (81) all_8_2 = e0
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | REDUCE: (25), (81) imply:
% 112.61/16.82 | | | | | | | | | | (82) ~ (all_52_13 = e0)
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | REDUCE: (26), (81) imply:
% 112.61/16.82 | | | | | | | | | | (83) op(e2, e0) = all_8_1
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | | REF_CLOSE: (12), (15), (37), (42), (77), (82), (83) are
% 112.61/16.82 | | | | | | | | | | inconsistent by sub-proof #33.
% 112.61/16.82 | | | | | | | | | |
% 112.61/16.82 | | | | | | | | | End of split
% 112.61/16.82 | | | | | | | | |
% 112.61/16.82 | | | | | | | | End of split
% 112.61/16.82 | | | | | | | |
% 112.61/16.82 | | | | | | | End of split
% 112.61/16.82 | | | | | | |
% 112.61/16.82 | | | | | | End of split
% 112.61/16.82 | | | | | |
% 112.61/16.82 | | | | | End of split
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | Case 2:
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | (84) ~ (all_56_12 = e0)
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | REDUCE: (65), (84) imply:
% 112.61/16.82 | | | | | (85) $false
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | | CLOSE: (85) is inconsistent.
% 112.61/16.82 | | | | |
% 112.61/16.82 | | | | End of split
% 112.61/16.82 | | | |
% 112.61/16.82 | | | Case 2:
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | (86) ~ (all_58_0 = e0)
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | REDUCE: (11), (86) imply:
% 112.61/16.82 | | | | (87) ~ (all_10_2 = e0)
% 112.61/16.82 | | | |
% 112.61/16.82 | | | | REF_CLOSE: (3), (7), (32), (38), (44), (52), (58), (62), (87) are
% 112.61/16.82 | | | | inconsistent by sub-proof #32.
% 112.61/16.82 | | | |
% 112.61/16.82 | | | End of split
% 112.61/16.82 | | |
% 112.61/16.82 | | End of split
% 112.61/16.82 | |
% 112.61/16.82 | End of split
% 112.61/16.82 |
% 112.61/16.82 End of proof
% 112.61/16.82
% 112.61/16.82 Sub-proof #32 shows that the following formulas are inconsistent:
% 112.61/16.82 ----------------------------------------------------------------
% 112.61/16.82 (1) ~ (all_52_3 = e0)
% 112.61/16.82 (2) all_54_0 = all_10_2
% 112.61/16.82 (3) ~ (all_10_2 = e2)
% 112.61/16.82 (4) all_54_12 = e1 | all_54_12 = e0
% 112.61/16.82 (5) ~ (all_10_2 = e3)
% 112.61/16.82 (6) ~ (all_10_2 = e0)
% 112.61/16.83 (7) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.83 (8) ~ (all_52_3 = all_10_2)
% 112.61/16.83 (9) all_54_12 = all_52_3
% 112.61/16.83
% 112.61/16.83 Begin of proof
% 112.61/16.83 |
% 112.61/16.83 | BETA: splitting (4) gives:
% 112.61/16.83 |
% 112.61/16.83 | Case 1:
% 112.61/16.83 | |
% 112.61/16.83 | | (10) all_54_12 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | COMBINE_EQS: (9), (10) imply:
% 112.61/16.83 | | (11) all_52_3 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | SIMP: (11) implies:
% 112.61/16.83 | | (12) all_52_3 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | REDUCE: (8), (12) imply:
% 112.61/16.83 | | (13) ~ (all_10_2 = e1)
% 112.61/16.83 | |
% 112.61/16.83 | | SIMP: (13) implies:
% 112.61/16.83 | | (14) ~ (all_10_2 = e1)
% 112.61/16.83 | |
% 112.61/16.83 | | REF_CLOSE: (2), (3), (5), (6), (7), (14) are inconsistent by sub-proof #256.
% 112.61/16.83 | |
% 112.61/16.83 | Case 2:
% 112.61/16.83 | |
% 112.61/16.83 | | (15) all_54_12 = e0
% 112.61/16.83 | |
% 112.61/16.83 | | REF_CLOSE: (1), (9), (15) are inconsistent by sub-proof #407.
% 112.61/16.83 | |
% 112.61/16.83 | End of split
% 112.61/16.83 |
% 112.61/16.83 End of proof
% 112.61/16.83
% 112.61/16.83 Sub-proof #33 shows that the following formulas are inconsistent:
% 112.61/16.83 ----------------------------------------------------------------
% 112.61/16.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.83 (2) all_54_7 = all_52_13
% 112.61/16.83 (3) all_54_7 = e1 | all_54_7 = e0
% 112.61/16.83 (4) op(e2, e0) = all_8_1
% 112.61/16.83 (5) op(e2, e0) = all_52_13
% 112.61/16.83 (6) ~ (all_8_1 = e1)
% 112.61/16.83 (7) ~ (all_52_13 = e0)
% 112.61/16.83
% 112.61/16.83 Begin of proof
% 112.61/16.83 |
% 112.61/16.83 | BETA: splitting (3) gives:
% 112.61/16.83 |
% 112.61/16.83 | Case 1:
% 112.61/16.83 | |
% 112.61/16.83 | | (8) all_54_7 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | COMBINE_EQS: (2), (8) imply:
% 112.61/16.83 | | (9) all_52_13 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | SIMP: (9) implies:
% 112.61/16.83 | | (10) all_52_13 = e1
% 112.61/16.83 | |
% 112.61/16.83 | | REDUCE: (5), (10) imply:
% 112.61/16.83 | | (11) op(e2, e0) = e1
% 112.61/16.83 | |
% 112.61/16.83 | | REF_CLOSE: (1), (4), (6), (11) are inconsistent by sub-proof #152.
% 112.61/16.83 | |
% 112.61/16.83 | Case 2:
% 112.61/16.83 | |
% 112.61/16.83 | | (12) all_54_7 = e0
% 112.61/16.83 | |
% 112.61/16.83 | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #130.
% 112.61/16.83 | |
% 112.61/16.83 | End of split
% 112.61/16.83 |
% 112.61/16.83 End of proof
% 112.61/16.83
% 112.61/16.83 Sub-proof #34 shows that the following formulas are inconsistent:
% 112.61/16.83 ----------------------------------------------------------------
% 112.61/16.83 (1) all_54_7 = all_52_13
% 112.61/16.83 (2) all_54_7 = e2
% 112.61/16.83 (3) ~ (all_52_13 = e2)
% 112.61/16.83
% 112.61/16.83 Begin of proof
% 112.61/16.83 |
% 112.61/16.83 | COMBINE_EQS: (1), (2) imply:
% 112.61/16.83 | (4) all_52_13 = e2
% 112.61/16.83 |
% 112.61/16.83 | SIMP: (4) implies:
% 112.61/16.83 | (5) all_52_13 = e2
% 112.61/16.83 |
% 112.61/16.83 | REDUCE: (3), (5) imply:
% 112.61/16.83 | (6) $false
% 112.61/16.83 |
% 112.61/16.83 | CLOSE: (6) is inconsistent.
% 112.61/16.83 |
% 112.61/16.83 End of proof
% 112.61/16.83
% 112.61/16.83 Sub-proof #35 shows that the following formulas are inconsistent:
% 112.61/16.83 ----------------------------------------------------------------
% 112.61/16.83 (1) ~ (all_52_8 = all_10_2)
% 112.61/16.83 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.61/16.83 (3) all_58_7 = all_52_6
% 112.61/16.83 (4) ~ (all_4_2 = e0)
% 112.61/16.83 (5) all_56_14 = all_6_2
% 112.61/16.83 (6) all_56_3 = all_52_1
% 112.61/16.83 (7) all_54_0 = all_10_2
% 112.61/16.83 (8) ~ (all_4_2 = e1)
% 112.61/16.83 (9) all_56_11 = all_52_11
% 112.61/16.83 (10) ~ (all_52_12 = all_10_2)
% 112.61/16.83 (11) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.61/16.83 (12) all_56_12 = all_10_2
% 112.61/16.83 (13) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.61/16.83 (14) all_58_0 = all_10_2
% 112.61/16.83 (15) all_56_10 = all_52_7
% 112.61/16.83 (16) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.61/16.83 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.83 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.83 (19) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 112.61/16.83 (20) ~ (all_10_2 = e2)
% 112.61/16.83 (21) all_54_10 = all_6_2
% 112.61/16.83 (22) ~ (e2 = e1)
% 112.61/16.83 (23) op(e3, e0) = all_52_12
% 112.61/16.83 (24) all_58_4 = all_52_8
% 112.61/16.83 (25) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.61/16.83 (26) all_56_2 = all_52_12
% 112.61/16.83 (27) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.61/16.83 (28) all_58_3 = all_8_2
% 112.61/16.83 (29) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.61/16.83 (30) all_58_11 = all_52_14
% 112.61/16.83 (31) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.61/16.83 (32) all_58_5 = all_52_9
% 112.61/16.83 (33) all_56_9 = all_52_3
% 112.61/16.83 (34) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.61/16.83 (35) all_58_15 = all_4_2
% 112.61/16.83 (36) all_58_2 = all_52_1
% 112.61/16.83 (37) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.61/16.83 (38) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 112.61/16.83 (39) ~ (all_10_2 = e3)
% 112.61/16.83 (40) all_58_13 = all_52_7
% 112.61/16.83 (41) op(e2, all_10_2) = all_10_0
% 112.61/16.83 (42) ~ (all_52_14 = all_4_2)
% 112.61/16.83 (43) all_58_6 = all_52_2
% 112.61/16.83 (44) ~ (all_52_1 = all_10_2)
% 112.61/16.83 (45) ~ (all_52_13 = e2)
% 112.61/16.83 (46) all_56_15 = all_4_2
% 112.61/16.83 (47) all_58_10 = all_52_13
% 112.61/16.83 (48) ~ (all_52_11 = all_4_2)
% 112.61/16.83 (49) op(e3, all_10_2) = e2
% 112.61/16.83 (50) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 112.61/16.83 (51) all_58_1 = all_52_4
% 112.61/16.83 (52) all_58_14 = all_52_11
% 112.61/16.83 (53) ~ (all_8_2 = e2)
% 112.61/16.83 (54) ~ (all_6_2 = e2)
% 112.61/16.83 (55) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.61/16.83 (56) all_56_7 = all_52_6
% 112.61/16.83 (57) all_58_8 = all_6_2
% 112.61/16.83 (58) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.61/16.83 (59) ~ (all_10_0 = e1)
% 112.61/16.83 (60) all_56_4 = all_52_9
% 112.61/16.83 (61) all_58_9 = all_52_12
% 112.61/16.83 (62) all_56_6 = all_52_2
% 112.61/16.83 (63) all_58_12 = all_52_3
% 112.61/16.83 (64) op(e2, e0) = all_52_13
% 112.61/16.83 (65) ~ (all_52_12 = all_4_2)
% 112.61/16.83 (66) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.61/16.83 (67) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.61/16.83 (68) all_56_8 = all_52_14
% 112.61/16.83 (69) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.61/16.83 (70) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.61/16.83 (71) all_56_0 = all_52_4
% 112.61/16.83 (72) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.61/16.83 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.61/16.83 (73) all_54_15 = all_4_2
% 112.61/16.83 (74) ~ (all_6_2 = e1)
% 112.61/16.83
% 112.61/16.83 Begin of proof
% 112.61/16.83 |
% 112.61/16.83 | BETA: splitting (11) gives:
% 112.61/16.83 |
% 112.61/16.83 | Case 1:
% 112.61/16.83 | |
% 112.61/16.83 | | (75) ~ (all_56_4 = e2)
% 112.61/16.83 | |
% 112.61/16.83 | | REDUCE: (60), (75) imply:
% 112.61/16.84 | | (76) ~ (all_52_9 = e2)
% 112.61/16.84 | |
% 112.61/16.84 | | BETA: splitting (70) gives:
% 112.61/16.84 | |
% 112.61/16.84 | | Case 1:
% 112.61/16.84 | | |
% 112.61/16.84 | | | (77) all_58_2 = e2
% 112.61/16.84 | | |
% 112.61/16.84 | | | COMBINE_EQS: (36), (77) imply:
% 112.61/16.84 | | | (78) all_52_1 = e2
% 112.61/16.84 | | |
% 112.61/16.84 | | | COMBINE_EQS: (6), (78) imply:
% 112.61/16.84 | | | (79) all_56_3 = e2
% 112.61/16.84 | | |
% 112.61/16.84 | | | REDUCE: (44), (78) imply:
% 112.61/16.84 | | | (80) ~ (all_10_2 = e2)
% 112.61/16.84 | | |
% 112.61/16.84 | | | BETA: splitting (19) gives:
% 112.61/16.84 | | |
% 112.61/16.84 | | | Case 1:
% 112.61/16.84 | | | |
% 112.61/16.84 | | | | (81) ~ (all_56_3 = e2)
% 112.61/16.84 | | | |
% 112.61/16.84 | | | | REDUCE: (79), (81) imply:
% 112.61/16.84 | | | | (82) $false
% 112.61/16.84 | | | |
% 112.61/16.84 | | | | CLOSE: (82) is inconsistent.
% 112.61/16.84 | | | |
% 112.61/16.84 | | | Case 2:
% 112.61/16.84 | | | |
% 112.61/16.84 | | | | (83) ~ (all_56_15 = e3)
% 112.61/16.84 | | | |
% 112.61/16.84 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13),
% 112.61/16.84 | | | | (14), (15), (16), (17), (18), (20), (21), (23), (24), (25),
% 112.61/16.84 | | | | (26), (27), (29), (30), (31), (32), (33), (34), (35), (37),
% 112.61/16.84 | | | | (38), (39), (40), (41), (42), (43), (46), (47), (48), (49),
% 112.61/16.84 | | | | (50), (51), (52), (54), (55), (56), (57), (58), (59), (60),
% 112.61/16.84 | | | | (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 112.61/16.84 | | | | (72), (73), (74), (83) are inconsistent by sub-proof #36.
% 112.61/16.84 | | | |
% 112.61/16.84 | | | End of split
% 112.61/16.84 | | |
% 112.61/16.84 | | Case 2:
% 112.61/16.84 | | |
% 112.61/16.84 | | | (84) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.61/16.84 | | |
% 112.61/16.84 | | | REF_CLOSE: (28), (32), (45), (47), (53), (76), (84) are inconsistent by
% 112.61/16.84 | | | sub-proof #401.
% 112.61/16.84 | | |
% 112.61/16.84 | | End of split
% 112.61/16.84 | |
% 112.61/16.84 | Case 2:
% 112.61/16.84 | |
% 112.61/16.84 | | (85) all_56_4 = e2
% 112.61/16.84 | |
% 112.61/16.84 | | REF_CLOSE: (4), (7), (8), (12), (18), (20), (22), (23), (25), (30), (34),
% 112.61/16.84 | | (35), (37), (38), (39), (41), (47), (49), (58), (59), (61), (64),
% 112.61/16.84 | | (65), (68), (73), (85) are inconsistent by sub-proof #37.
% 112.61/16.84 | |
% 112.61/16.84 | End of split
% 112.61/16.84 |
% 112.61/16.84 End of proof
% 112.61/16.84
% 112.61/16.84 Sub-proof #36 shows that the following formulas are inconsistent:
% 112.61/16.84 ----------------------------------------------------------------
% 112.61/16.84 (1) ~ (all_52_8 = all_10_2)
% 112.61/16.84 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.61/16.84 (3) all_58_7 = all_52_6
% 112.61/16.84 (4) ~ (all_4_2 = e0)
% 112.61/16.84 (5) all_56_14 = all_6_2
% 112.61/16.84 (6) all_54_0 = all_10_2
% 112.61/16.84 (7) ~ (all_4_2 = e1)
% 112.61/16.84 (8) all_56_11 = all_52_11
% 112.61/16.84 (9) ~ (all_52_12 = all_10_2)
% 112.61/16.84 (10) all_56_12 = all_10_2
% 112.61/16.84 (11) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 112.61/16.84 (12) all_58_0 = all_10_2
% 112.61/16.84 (13) all_56_10 = all_52_7
% 112.61/16.84 (14) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.61/16.84 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.61/16.84 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.61/16.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.61/16.84 (17) ~ (all_10_2 = e2)
% 112.61/16.84 (18) all_54_10 = all_6_2
% 112.61/16.84 (19) op(e3, e0) = all_52_12
% 112.61/16.84 (20) all_58_4 = all_52_8
% 112.61/16.84 (21) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.61/16.84 (22) all_56_2 = all_52_12
% 112.61/16.84 (23) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.61/16.84 (24) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.61/16.84 (25) all_58_11 = all_52_14
% 112.61/16.84 (26) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.61/16.84 (27) all_58_5 = all_52_9
% 112.61/16.84 (28) all_56_9 = all_52_3
% 112.61/16.84 (29) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.61/16.84 (30) all_58_15 = all_4_2
% 112.61/16.84 (31) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.61/16.84 (32) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 112.61/16.84 (33) ~ (all_10_2 = e3)
% 112.61/16.84 (34) all_58_13 = all_52_7
% 112.61/16.84 (35) op(e2, all_10_2) = all_10_0
% 112.61/16.84 (36) ~ (all_52_14 = all_4_2)
% 112.61/16.84 (37) all_58_6 = all_52_2
% 112.61/16.84 (38) all_56_15 = all_4_2
% 112.61/16.84 (39) all_58_10 = all_52_13
% 112.61/16.84 (40) ~ (all_52_11 = all_4_2)
% 112.61/16.84 (41) op(e3, all_10_2) = e2
% 112.61/16.84 (42) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 112.61/16.84 (43) all_58_1 = all_52_4
% 112.61/16.84 (44) all_58_14 = all_52_11
% 112.61/16.84 (45) ~ (all_6_2 = e2)
% 112.61/16.84 (46) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.61/16.84 (47) all_56_7 = all_52_6
% 112.61/16.84 (48) all_58_8 = all_6_2
% 112.61/16.84 (49) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.86/16.84 (50) ~ (all_10_0 = e1)
% 112.86/16.84 (51) all_56_4 = all_52_9
% 112.86/16.84 (52) all_58_9 = all_52_12
% 112.86/16.84 (53) all_56_6 = all_52_2
% 112.86/16.84 (54) all_58_12 = all_52_3
% 112.86/16.84 (55) op(e2, e0) = all_52_13
% 112.86/16.84 (56) ~ (all_52_12 = all_4_2)
% 112.86/16.84 (57) ~ (all_56_15 = e3)
% 112.86/16.84 (58) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 112.86/16.84 (59) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.86/16.84 (60) all_56_8 = all_52_14
% 112.86/16.84 (61) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.86/16.84 (62) all_56_0 = all_52_4
% 112.86/16.84 (63) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.86/16.84 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.86/16.84 (64) all_54_15 = all_4_2
% 112.86/16.84 (65) ~ (all_6_2 = e1)
% 112.86/16.84
% 112.86/16.84 Begin of proof
% 112.86/16.84 |
% 112.86/16.84 | REDUCE: (38), (57) imply:
% 112.86/16.84 | (66) ~ (all_4_2 = e3)
% 112.86/16.84 |
% 112.86/16.84 | BETA: splitting (21) gives:
% 112.86/16.84 |
% 112.86/16.84 | Case 1:
% 112.86/16.84 | |
% 112.86/16.84 | | (67) all_54_15 = e3
% 112.86/16.84 | |
% 112.86/16.84 | | COMBINE_EQS: (64), (67) imply:
% 112.86/16.84 | | (68) all_4_2 = e3
% 112.86/16.84 | |
% 112.86/16.84 | | REDUCE: (66), (68) imply:
% 112.86/16.84 | | (69) $false
% 112.86/16.84 | |
% 112.86/16.84 | | CLOSE: (69) is inconsistent.
% 112.86/16.84 | |
% 112.86/16.84 | Case 2:
% 112.86/16.84 | |
% 112.86/16.84 | | (70) ~ (all_54_15 = e3)
% 112.86/16.84 | | (71) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.86/16.84 | |
% 112.86/16.84 | | BETA: splitting (71) gives:
% 112.86/16.84 | |
% 112.86/16.84 | | Case 1:
% 112.86/16.84 | | |
% 112.86/16.84 | | | (72) all_54_15 = e2
% 112.86/16.84 | | |
% 112.86/16.84 | | | COMBINE_EQS: (64), (72) imply:
% 112.86/16.84 | | | (73) all_4_2 = e2
% 112.86/16.84 | | |
% 112.86/16.84 | | | COMBINE_EQS: (38), (73) imply:
% 112.86/16.84 | | | (74) all_56_15 = e2
% 112.86/16.84 | | |
% 112.86/16.84 | | | REDUCE: (40), (73) imply:
% 112.86/16.84 | | | (75) ~ (all_52_11 = e2)
% 112.86/16.84 | | |
% 112.86/16.84 | | | REDUCE: (66), (73) imply:
% 112.86/16.84 | | | (76) ~ (e3 = e2)
% 112.86/16.84 | | |
% 112.86/16.84 | | | SIMP: (76) implies:
% 112.86/16.84 | | | (77) ~ (e3 = e2)
% 112.86/16.84 | | |
% 112.86/16.84 | | | REDUCE: (7), (73) imply:
% 112.86/16.84 | | | (78) ~ (e2 = e1)
% 112.86/16.84 | | |
% 112.86/16.84 | | | BETA: splitting (11) gives:
% 112.86/16.84 | | |
% 112.86/16.84 | | | Case 1:
% 112.86/16.84 | | | |
% 112.86/16.84 | | | | (79) ~ (all_56_7 = e1)
% 112.86/16.84 | | | |
% 112.86/16.84 | | | | REDUCE: (47), (79) imply:
% 112.86/16.84 | | | | (80) ~ (all_52_6 = e1)
% 112.86/16.84 | | | |
% 112.86/16.84 | | | | BETA: splitting (42) gives:
% 112.86/16.84 | | | |
% 112.86/16.84 | | | | Case 1:
% 112.86/16.84 | | | | |
% 112.86/16.84 | | | | | (81) ~ (all_56_0 = e3)
% 112.86/16.84 | | | | |
% 112.86/16.84 | | | | | REDUCE: (62), (81) imply:
% 112.86/16.84 | | | | | (82) ~ (all_52_4 = e3)
% 112.86/16.84 | | | | |
% 112.86/16.84 | | | | | BETA: splitting (2) gives:
% 112.86/16.84 | | | | |
% 112.86/16.84 | | | | | Case 1:
% 112.86/16.84 | | | | | |
% 112.86/16.84 | | | | | | (83) ~ (all_56_2 = e3)
% 112.86/16.84 | | | | | |
% 112.86/16.84 | | | | | | REDUCE: (22), (83) imply:
% 112.86/16.84 | | | | | | (84) ~ (all_52_12 = e3)
% 112.86/16.84 | | | | | |
% 112.86/16.84 | | | | | | BETA: splitting (59) gives:
% 112.86/16.84 | | | | | |
% 112.86/16.84 | | | | | | Case 1:
% 112.86/16.84 | | | | | | |
% 112.86/16.84 | | | | | | | (85) all_58_0 = e3
% 112.86/16.84 | | | | | | |
% 112.86/16.84 | | | | | | | COMBINE_EQS: (12), (85) imply:
% 112.86/16.85 | | | | | | | (86) all_10_2 = e3
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | REDUCE: (33), (86) imply:
% 112.86/16.85 | | | | | | | (87) $false
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | CLOSE: (87) is inconsistent.
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | Case 2:
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | (88) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | BETA: splitting (88) gives:
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | Case 1:
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | (89) all_58_1 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | COMBINE_EQS: (43), (89) imply:
% 112.86/16.85 | | | | | | | | (90) all_52_4 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | REDUCE: (82), (90) imply:
% 112.86/16.85 | | | | | | | | (91) $false
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | CLOSE: (91) is inconsistent.
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | Case 2:
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | (92) all_58_4 = e3 | all_58_9 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | BETA: splitting (92) gives:
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | Case 1:
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | (93) all_58_4 = e3
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | COMBINE_EQS: (20), (93) imply:
% 112.86/16.85 | | | | | | | | | (94) all_52_8 = e3
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | REDUCE: (1), (94) imply:
% 112.86/16.85 | | | | | | | | | (95) ~ (all_10_2 = e3)
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | BETA: splitting (14) gives:
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | Case 1:
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | (96) all_58_4 = e2
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | COMBINE_EQS: (93), (96) imply:
% 112.86/16.85 | | | | | | | | | | (97) e3 = e2
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | REDUCE: (77), (97) imply:
% 112.86/16.85 | | | | | | | | | | (98) $false
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | CLOSE: (98) is inconsistent.
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | Case 2:
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | (99) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | BETA: splitting (99) gives:
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | Case 1:
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | (100) all_58_5 = e2
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | COMBINE_EQS: (27), (100) imply:
% 112.86/16.85 | | | | | | | | | | | (101) all_52_9 = e2
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | COMBINE_EQS: (51), (101) imply:
% 112.86/16.85 | | | | | | | | | | | (102) all_56_4 = e2
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (16), (17), (19), (21), (25),
% 112.86/16.85 | | | | | | | | | | | (29), (30), (31), (32), (33), (35), (39), (41),
% 112.86/16.85 | | | | | | | | | | | (49), (50), (52), (55), (56), (60), (64), (78),
% 112.86/16.85 | | | | | | | | | | | (102) are inconsistent by sub-proof #37.
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | Case 2:
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | (103) all_58_8 = e2 | all_58_14 = e2
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | | REF_CLOSE: (44), (45), (48), (75), (103) are inconsistent by
% 112.86/16.85 | | | | | | | | | | | sub-proof #294.
% 112.86/16.85 | | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | | End of split
% 112.86/16.85 | | | | | | | | | |
% 112.86/16.85 | | | | | | | | | End of split
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | Case 2:
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | (104) all_58_9 = e3
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | COMBINE_EQS: (52), (104) imply:
% 112.86/16.85 | | | | | | | | | (105) all_52_12 = e3
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | REDUCE: (84), (105) imply:
% 112.86/16.85 | | | | | | | | | (106) $false
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | | CLOSE: (106) is inconsistent.
% 112.86/16.85 | | | | | | | | |
% 112.86/16.85 | | | | | | | | End of split
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | End of split
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | End of split
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | Case 2:
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | | (107) all_56_2 = e3
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | | COMBINE_EQS: (22), (107) imply:
% 112.86/16.85 | | | | | | (108) all_52_12 = e3
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | | REDUCE: (9), (108) imply:
% 112.86/16.85 | | | | | | (109) ~ (all_10_2 = e3)
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | | BETA: splitting (24) gives:
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | | Case 1:
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | (110) ~ (all_56_2 = e3)
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | REDUCE: (107), (110) imply:
% 112.86/16.85 | | | | | | | (111) $false
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | CLOSE: (111) is inconsistent.
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | Case 2:
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | (112) ~ (all_56_14 = e0)
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | REDUCE: (5), (112) imply:
% 112.86/16.85 | | | | | | | (113) ~ (all_6_2 = e0)
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | BETA: splitting (15) gives:
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | | Case 1:
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | (114) all_54_10 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | COMBINE_EQS: (18), (114) imply:
% 112.86/16.85 | | | | | | | | (115) all_6_2 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | SIMP: (115) implies:
% 112.86/16.85 | | | | | | | | (116) all_6_2 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | COMBINE_EQS: (5), (116) imply:
% 112.86/16.85 | | | | | | | | (117) all_56_14 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | COMBINE_EQS: (48), (116) imply:
% 112.86/16.85 | | | | | | | | (118) all_58_8 = e3
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | REDUCE: (65), (116) imply:
% 112.86/16.85 | | | | | | | | (119) ~ (e3 = e1)
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (10), (13), (17), (21), (23),
% 112.86/16.85 | | | | | | | | (25), (26), (28), (29), (30), (33), (34), (36), (37),
% 112.86/16.85 | | | | | | | | (38), (44), (46), (49), (53), (54), (58), (60), (61),
% 112.86/16.85 | | | | | | | | (63), (64), (66), (80), (117), (118), (119) are
% 112.86/16.85 | | | | | | | | inconsistent by sub-proof #358.
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | Case 2:
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | (120) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | | REF_CLOSE: (18), (45), (65), (113), (120) are inconsistent by
% 112.86/16.85 | | | | | | | | sub-proof #435.
% 112.86/16.85 | | | | | | | |
% 112.86/16.85 | | | | | | | End of split
% 112.86/16.85 | | | | | | |
% 112.86/16.85 | | | | | | End of split
% 112.86/16.85 | | | | | |
% 112.86/16.85 | | | | | End of split
% 112.86/16.85 | | | | |
% 112.86/16.85 | | | | Case 2:
% 112.86/16.85 | | | | |
% 112.86/16.85 | | | | | (121) ~ (all_56_15 = e2)
% 112.86/16.85 | | | | |
% 112.86/16.85 | | | | | REDUCE: (74), (121) imply:
% 112.86/16.85 | | | | | (122) $false
% 112.86/16.85 | | | | |
% 112.86/16.85 | | | | | CLOSE: (122) is inconsistent.
% 112.86/16.85 | | | | |
% 112.86/16.85 | | | | End of split
% 112.86/16.85 | | | |
% 112.86/16.85 | | | Case 2:
% 112.86/16.85 | | | |
% 112.86/16.85 | | | | (123) ~ (all_56_15 = e2)
% 112.86/16.85 | | | |
% 112.86/16.85 | | | | REDUCE: (74), (123) imply:
% 112.86/16.85 | | | | (124) $false
% 112.86/16.85 | | | |
% 112.86/16.85 | | | | CLOSE: (124) is inconsistent.
% 112.86/16.85 | | | |
% 112.86/16.85 | | | End of split
% 112.86/16.85 | | |
% 112.86/16.85 | | Case 2:
% 112.86/16.85 | | |
% 112.86/16.85 | | | (125) all_54_15 = e1 | all_54_15 = e0
% 112.86/16.85 | | |
% 112.86/16.85 | | | REF_CLOSE: (4), (7), (64), (125) are inconsistent by sub-proof #418.
% 112.86/16.85 | | |
% 112.86/16.85 | | End of split
% 112.86/16.85 | |
% 112.86/16.85 | End of split
% 112.86/16.85 |
% 112.86/16.85 End of proof
% 112.86/16.85
% 112.86/16.85 Sub-proof #37 shows that the following formulas are inconsistent:
% 112.86/16.85 ----------------------------------------------------------------
% 112.86/16.85 (1) ~ (all_4_2 = e0)
% 112.86/16.85 (2) all_54_0 = all_10_2
% 112.86/16.85 (3) ~ (all_4_2 = e1)
% 112.86/16.85 (4) all_56_12 = all_10_2
% 112.86/16.85 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.86/16.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.86/16.85 (6) ~ (all_10_2 = e2)
% 112.86/16.85 (7) ~ (e2 = e1)
% 112.86/16.85 (8) op(e3, e0) = all_52_12
% 112.86/16.85 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.86/16.85 (10) all_58_11 = all_52_14
% 112.86/16.85 (11) all_56_4 = e2
% 112.86/16.85 (12) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 112.86/16.85 (13) all_58_15 = all_4_2
% 112.86/16.85 (14) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.86/16.85 (15) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 112.86/16.85 (16) ~ (all_10_2 = e3)
% 112.86/16.85 (17) op(e2, all_10_2) = all_10_0
% 112.86/16.85 (18) all_58_10 = all_52_13
% 112.86/16.85 (19) op(e3, all_10_2) = e2
% 112.86/16.85 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.86/16.85 (21) ~ (all_10_0 = e1)
% 112.86/16.85 (22) all_58_9 = all_52_12
% 112.86/16.85 (23) op(e2, e0) = all_52_13
% 112.86/16.85 (24) ~ (all_52_12 = all_4_2)
% 112.86/16.85 (25) all_56_8 = all_52_14
% 112.86/16.85 (26) all_54_15 = all_4_2
% 112.86/16.85
% 112.86/16.85 Begin of proof
% 112.86/16.85 |
% 112.86/16.85 | BETA: splitting (14) gives:
% 112.86/16.85 |
% 112.86/16.85 | Case 1:
% 112.86/16.85 | |
% 112.86/16.85 | | (27) ~ (all_56_4 = e2)
% 112.86/16.85 | |
% 112.86/16.85 | | REDUCE: (11), (27) imply:
% 112.86/16.85 | | (28) $false
% 112.86/16.85 | |
% 112.86/16.85 | | CLOSE: (28) is inconsistent.
% 112.86/16.85 | |
% 112.86/16.85 | Case 2:
% 112.86/16.85 | |
% 112.86/16.85 | | (29) ~ (all_56_12 = e1)
% 112.86/16.85 | |
% 112.86/16.85 | | REDUCE: (4), (29) imply:
% 112.86/16.85 | | (30) ~ (all_10_2 = e1)
% 112.86/16.85 | |
% 112.86/16.85 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 112.86/16.85 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 112.86/16.85 | | (26), (30) are inconsistent by sub-proof #367.
% 112.86/16.85 | |
% 112.86/16.85 | End of split
% 112.86/16.85 |
% 112.86/16.85 End of proof
% 112.86/16.85
% 112.86/16.85 Sub-proof #38 shows that the following formulas are inconsistent:
% 112.86/16.85 ----------------------------------------------------------------
% 112.86/16.85 (1) ~ (all_52_8 = all_10_2)
% 112.86/16.85 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.86/16.85 (3) ~ (all_52_2 = all_10_2)
% 112.86/16.85 (4) all_54_2 = all_52_8
% 112.86/16.85 (5) all_58_7 = all_52_6
% 112.86/16.85 (6) ~ (all_52_8 = all_52_11)
% 112.86/16.85 (7) ~ (all_52_9 = all_8_2)
% 112.86/16.85 (8) ~ (all_4_2 = e0)
% 112.86/16.85 (9) op(e3, e2) = all_52_4
% 112.86/16.85 (10) all_56_14 = all_6_2
% 112.86/16.85 (11) all_56_3 = all_52_1
% 112.86/16.85 (12) all_54_0 = all_10_2
% 112.86/16.85 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 112.86/16.85 (14) all_54_3 = all_52_12
% 112.86/16.85 (15) ~ (all_52_12 = all_52_14)
% 112.86/16.86 (16) op(e0, e2) = all_52_7
% 112.86/16.86 (17) ~ (all_52_7 = all_4_2)
% 112.86/16.86 (18) all_56_11 = all_52_11
% 112.86/16.86 (19) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 112.86/16.86 (20) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.86/16.86 (21) ~ (all_52_12 = all_10_2)
% 112.86/16.86 (22) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.86/16.86 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.86/16.86 (24) all_56_12 = all_10_2
% 112.86/16.86 (25) all_58_0 = all_10_2
% 112.86/16.86 (26) all_54_13 = all_52_7
% 112.86/16.86 (27) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 112.86/16.86 (28) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 112.86/16.86 (29) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 112.86/16.86 (30) all_56_10 = all_52_7
% 112.86/16.86 (31) all_54_14 = all_52_11
% 112.86/16.86 (32) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.86/16.86 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.86/16.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.86/16.86 (34) op(e1, all_6_2) = e2
% 112.86/16.86 (35) all_54_10 = all_6_2
% 112.86/16.86 (36) op(e3, e0) = all_52_12
% 112.86/16.86 (37) ~ (all_52_8 = all_6_2)
% 112.86/16.86 (38) all_58_4 = all_52_8
% 112.86/16.86 (39) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 112.86/16.86 (40) ~ (all_52_4 = all_52_7)
% 112.86/16.86 (41) all_56_2 = all_52_12
% 112.86/16.86 (42) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.86/16.86 (43) all_58_3 = all_8_2
% 112.86/16.86 (44) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.86/16.86 (45) ~ (all_10_0 = e2)
% 112.86/16.86 (46) all_58_11 = all_52_14
% 112.86/16.86 (47) op(e3, e1) = all_52_8
% 112.86/16.86 (48) all_54_7 = all_52_13
% 112.86/16.86 (49) op(all_10_1, all_10_2) = all_10_0
% 112.86/16.86 (50) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.86/16.86 (51) ~ (all_52_11 = all_6_2)
% 112.86/16.86 (52) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 112.86/16.86 (53) op(e2, e3) = all_52_1
% 112.86/16.86 (54) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 112.86/16.86 (55) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 112.86/16.86 (56) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.86/16.86 (57) ~ (all_6_0 = e3)
% 112.86/16.86 (58) ~ (all_52_7 = all_8_2)
% 112.86/16.86 (59) ~ (all_52_4 = all_8_2)
% 112.86/16.86 (60) op(e1, e0) = all_52_14
% 112.86/16.86 (61) all_58_5 = all_52_9
% 112.86/16.86 (62) all_56_9 = all_52_3
% 112.86/16.86 (63) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 112.86/16.86 (64) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 112.86/16.86 (65) all_58_15 = all_4_2
% 112.86/16.86 (66) all_58_2 = all_52_1
% 112.86/16.86 (67) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 112.86/16.86 (68) ~ (all_10_2 = e3)
% 112.86/16.86 (69) ~ (all_52_12 = all_52_13)
% 112.86/16.86 (70) all_58_13 = all_52_7
% 112.86/16.86 (71) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 112.86/16.86 (72) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 112.86/16.86 (73) ~ (all_52_14 = all_4_2)
% 112.86/16.86 (74) all_58_6 = all_52_2
% 112.86/16.86 (75) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 112.86/16.86 (76) ~ (all_52_1 = all_10_2)
% 112.86/16.86 (77) all_54_5 = all_8_2
% 112.86/16.86 (78) all_56_15 = all_4_2
% 112.86/16.86 (79) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.86/16.86 (80) all_58_10 = all_52_13
% 112.86/16.86 (81) op(e2, all_8_2) = all_8_1
% 112.86/16.86 (82) ~ (all_52_11 = all_4_2)
% 112.86/16.86 (83) op(e2, all_6_2) = all_6_0
% 112.86/16.86 (84) op(e3, all_10_2) = all_10_1
% 112.86/16.86 (85) ~ (all_52_6 = all_8_2)
% 112.86/16.86 (86) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.86/16.86 (87) ~ (all_10_1 = e2)
% 112.86/16.86 (88) all_58_1 = all_52_4
% 112.86/16.86 (89) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 112.86/16.86 (90) ~ (all_52_9 = all_52_11)
% 112.86/16.86 (91) all_58_14 = all_52_11
% 112.86/16.86 (92) all_54_1 = all_52_4
% 112.86/16.86 (93) all_56_13 = all_8_2
% 112.86/16.86 (94) op(e0, e1) = all_52_11
% 112.86/16.86 (95) ~ (all_52_1 = all_8_2)
% 112.86/16.86 (96) ~ (all_8_2 = e2)
% 112.86/16.86 (97) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 112.86/16.86 (98) ~ (all_52_7 = all_52_11)
% 112.86/16.86 (99) op(e1, e2) = all_52_6
% 112.86/16.86 (100) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.86/16.86 (101) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 112.86/16.86 (102) all_56_7 = all_52_6
% 112.86/16.86 (103) all_56_1 = all_52_8
% 112.86/16.86 (104) op(e0, all_4_2) = all_4_1
% 112.86/16.86 (105) all_58_8 = all_6_2
% 112.86/16.86 (106) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.86/16.86 (107) ~ (all_10_0 = e1)
% 112.86/16.86 (108) all_56_4 = all_52_9
% 112.86/16.86 (109) all_58_9 = all_52_12
% 112.86/16.86 (110) all_56_5 = all_52_13
% 112.86/16.86 (111) ~ (all_52_3 = all_4_2)
% 112.86/16.86 (112) ~ (all_52_6 = all_6_2)
% 112.86/16.86 (113) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 112.86/16.86 (114) all_56_6 = all_52_2
% 112.86/16.86 (115) ~ (all_52_13 = all_4_2)
% 112.86/16.86 (116) all_58_12 = all_52_3
% 112.86/16.86 (117) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.86/16.86 (118) op(e2, e0) = all_52_13
% 112.86/16.86 (119) ~ (all_52_12 = all_4_2)
% 112.86/16.86 (120) ~ (all_52_3 = all_10_2)
% 112.86/16.86 (121) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 112.86/16.86 (122) op(e1, e1) = all_6_2
% 112.86/16.86 (123) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.86/16.86 (124) ~ (all_52_8 = all_52_12)
% 112.86/16.86 (125) ~ (all_52_4 = all_10_2)
% 112.86/16.86 (126) ~ (all_10_1 = e1)
% 112.86/16.86 (127) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 112.86/16.86 (128) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.86/16.86 (129) all_56_0 = all_52_4
% 112.86/16.86 (130) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 112.86/16.86 (131) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.86/16.86 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.86/16.86 (132) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 112.86/16.86 (133) all_54_4 = all_52_1
% 112.86/16.86 (134) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 112.86/16.86 (135) all_54_15 = all_4_2
% 112.86/16.86 (136) ~ (all_6_2 = e1)
% 112.86/16.86 (137) ~ (all_52_3 = all_52_11)
% 112.86/16.86 (138) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.86/16.86 (139) all_54_12 = all_52_3
% 112.86/16.86
% 112.86/16.86 Begin of proof
% 112.86/16.86 |
% 112.86/16.86 | BETA: splitting (71) gives:
% 112.86/16.86 |
% 112.86/16.86 | Case 1:
% 112.86/16.86 | |
% 112.86/16.86 | | (140) ~ (all_56_14 = e2)
% 112.86/16.86 | |
% 112.86/16.86 | | REDUCE: (10), (140) imply:
% 112.86/16.86 | | (141) ~ (all_6_2 = e2)
% 112.86/16.86 | |
% 112.86/16.86 | | BETA: splitting (63) gives:
% 112.86/16.86 | |
% 112.86/16.86 | | Case 1:
% 112.86/16.86 | | |
% 112.86/16.86 | | | (142) ~ (all_56_15 = e1)
% 112.86/16.86 | | |
% 112.86/16.86 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 112.86/16.86 | | | (16), (18), (19), (20), (21), (22), (23), (24), (27), (31),
% 112.86/16.86 | | | (32), (33), (35), (36), (38), (39), (40), (41), (43), (45),
% 112.86/16.86 | | | (47), (49), (50), (52), (54), (55), (56), (61), (62), (64),
% 112.86/16.86 | | | (65), (66), (67), (68), (70), (72), (76), (77), (78), (80),
% 112.86/16.86 | | | (82), (84), (87), (88), (89), (90), (91), (92), (93), (94),
% 112.86/16.86 | | | (95), (96), (101), (102), (103), (105), (106), (107), (108),
% 112.86/16.86 | | | (110), (112), (113), (115), (116), (119), (124), (125), (126),
% 112.86/16.86 | | | (127), (128), (129), (130), (131), (134), (135), (136), (138),
% 112.86/16.86 | | | (142) are inconsistent by sub-proof #46.
% 112.86/16.86 | | |
% 112.86/16.86 | | Case 2:
% 112.86/16.86 | | |
% 112.86/16.86 | | | (143) all_56_15 = e1
% 112.86/16.86 | | | (144) ~ (all_56_11 = e0)
% 112.86/16.87 | | |
% 112.86/16.87 | | | COMBINE_EQS: (78), (143) imply:
% 112.86/16.87 | | | (145) all_4_2 = e1
% 112.86/16.87 | | |
% 112.86/16.87 | | | SIMP: (145) implies:
% 112.86/16.87 | | | (146) all_4_2 = e1
% 112.86/16.87 | | |
% 112.86/16.87 | | | COMBINE_EQS: (65), (146) imply:
% 112.86/16.87 | | | (147) all_58_15 = e1
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (18), (144) imply:
% 112.86/16.87 | | | (148) ~ (all_52_11 = e0)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (111), (146) imply:
% 112.86/16.87 | | | (149) ~ (all_52_3 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (17), (146) imply:
% 112.86/16.87 | | | (150) ~ (all_52_7 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (82), (146) imply:
% 112.86/16.87 | | | (151) ~ (all_52_11 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (119), (146) imply:
% 112.86/16.87 | | | (152) ~ (all_52_12 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (115), (146) imply:
% 112.86/16.87 | | | (153) ~ (all_52_13 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (73), (146) imply:
% 112.86/16.87 | | | (154) ~ (all_52_14 = e1)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (8), (146) imply:
% 112.86/16.87 | | | (155) ~ (e1 = e0)
% 112.86/16.87 | | |
% 112.86/16.87 | | | REDUCE: (104), (146) imply:
% 112.86/16.87 | | | (156) op(e0, e1) = all_4_1
% 112.86/16.87 | | |
% 112.86/16.87 | | | REF_CLOSE: (2), (3), (5), (8), (9), (10), (11), (12), (13), (14), (15),
% 112.86/16.87 | | | (16), (18), (20), (21), (22), (23), (24), (25), (26), (27),
% 112.86/16.87 | | | (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 112.86/16.87 | | | (40), (41), (42), (43), (44), (45), (46), (48), (49), (50),
% 112.86/16.87 | | | (51), (52), (53), (56), (57), (58), (59), (60), (61), (62),
% 112.86/16.87 | | | (64), (65), (66), (68), (69), (70), (72), (74), (75), (76),
% 112.86/16.87 | | | (77), (79), (80), (81), (83), (84), (85), (86), (88), (89),
% 112.86/16.87 | | | (90), (91), (92), (93), (94), (95), (96), (97), (98), (100),
% 112.86/16.87 | | | (101), (102), (103), (105), (106), (107), (108), (109), (110),
% 112.86/16.87 | | | (112), (114), (116), (117), (118), (120), (121), (122), (123),
% 112.86/16.87 | | | (125), (126), (128), (129), (130), (131), (132), (133), (134),
% 112.86/16.87 | | | (136), (137), (138), (139), (141), (143), (147), (148), (149),
% 112.86/16.87 | | | (150), (151), (152), (153), (154), (155), (156) are
% 112.86/16.87 | | | inconsistent by sub-proof #40.
% 112.86/16.87 | | |
% 112.86/16.87 | | End of split
% 112.86/16.87 | |
% 112.86/16.87 | Case 2:
% 112.86/16.87 | |
% 112.86/16.87 | | (157) all_56_14 = e2
% 112.86/16.87 | |
% 112.86/16.87 | | COMBINE_EQS: (10), (157) imply:
% 112.86/16.87 | | (158) all_6_2 = e2
% 112.86/16.87 | |
% 112.86/16.87 | | REF_CLOSE: (33), (34), (99), (112), (158) are inconsistent by sub-proof #39.
% 112.86/16.87 | |
% 112.86/16.87 | End of split
% 112.86/16.87 |
% 112.86/16.87 End of proof
% 112.86/16.87
% 112.86/16.87 Sub-proof #39 shows that the following formulas are inconsistent:
% 112.86/16.87 ----------------------------------------------------------------
% 112.86/16.87 (1) all_6_2 = e2
% 112.86/16.87 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.86/16.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.86/16.87 (3) op(e1, all_6_2) = e2
% 112.86/16.87 (4) op(e1, e2) = all_52_6
% 112.86/16.87 (5) ~ (all_52_6 = all_6_2)
% 112.86/16.87
% 112.86/16.87 Begin of proof
% 112.86/16.87 |
% 112.86/16.87 | SIMP: (1) implies:
% 112.86/16.87 | (6) all_6_2 = e2
% 112.86/16.87 |
% 112.86/16.87 | REDUCE: (5), (6) imply:
% 112.86/16.87 | (7) ~ (all_52_6 = e2)
% 112.86/16.87 |
% 112.86/16.87 | REDUCE: (3), (6) imply:
% 112.86/16.87 | (8) op(e1, e2) = e2
% 112.86/16.87 |
% 112.86/16.87 | GROUND_INST: instantiating (2) with all_52_6, e2, e2, e1, simplifying with
% 112.86/16.87 | (4), (8) gives:
% 112.86/16.87 | (9) all_52_6 = e2
% 112.86/16.87 |
% 112.86/16.87 | REDUCE: (7), (9) imply:
% 112.86/16.87 | (10) $false
% 112.86/16.87 |
% 112.86/16.87 | CLOSE: (10) is inconsistent.
% 112.86/16.87 |
% 112.86/16.87 End of proof
% 112.86/16.87
% 112.86/16.87 Sub-proof #40 shows that the following formulas are inconsistent:
% 112.86/16.87 ----------------------------------------------------------------
% 112.86/16.87 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.86/16.87 (2) ~ (all_52_2 = all_10_2)
% 112.86/16.87 (3) all_58_7 = all_52_6
% 112.86/16.87 (4) ~ (all_4_2 = e0)
% 112.86/16.87 (5) op(e3, e2) = all_52_4
% 112.86/16.87 (6) all_56_14 = all_6_2
% 112.86/16.87 (7) all_56_3 = all_52_1
% 112.86/16.87 (8) all_54_0 = all_10_2
% 112.86/16.87 (9) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 112.86/16.87 (10) all_54_3 = all_52_12
% 112.86/16.87 (11) ~ (all_52_12 = all_52_14)
% 112.86/16.87 (12) op(e0, e2) = all_52_7
% 112.86/16.87 (13) all_56_11 = all_52_11
% 112.86/16.87 (14) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.86/16.87 (15) ~ (all_52_12 = all_10_2)
% 112.86/16.87 (16) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 112.86/16.87 (17) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.86/16.87 (18) all_56_12 = all_10_2
% 112.86/16.87 (19) all_58_0 = all_10_2
% 112.86/16.87 (20) all_54_13 = all_52_7
% 112.86/16.87 (21) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 112.86/16.87 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 112.86/16.87 (23) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 112.86/16.87 (24) all_56_10 = all_52_7
% 112.86/16.87 (25) all_54_14 = all_52_11
% 112.86/16.87 (26) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.86/16.87 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.86/16.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.86/16.87 (28) op(e1, all_6_2) = e2
% 112.86/16.87 (29) all_54_10 = all_6_2
% 112.86/16.87 (30) ~ (all_52_14 = e1)
% 112.86/16.87 (31) ~ (all_52_8 = all_6_2)
% 112.86/16.87 (32) all_58_4 = all_52_8
% 112.86/16.87 (33) ~ (all_52_4 = all_52_7)
% 112.86/16.87 (34) all_56_2 = all_52_12
% 112.86/16.87 (35) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 112.86/16.87 (36) ~ (all_52_12 = e1)
% 112.86/16.87 (37) all_58_3 = all_8_2
% 112.86/16.87 (38) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.86/16.87 (39) ~ (all_10_0 = e2)
% 112.86/16.87 (40) all_58_11 = all_52_14
% 112.86/16.87 (41) all_58_15 = e1
% 112.86/16.87 (42) all_54_7 = all_52_13
% 112.86/16.87 (43) op(all_10_1, all_10_2) = all_10_0
% 112.86/16.87 (44) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 112.86/16.87 (45) ~ (all_52_11 = all_6_2)
% 112.86/16.87 (46) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 112.86/16.87 (47) op(e2, e3) = all_52_1
% 112.86/16.87 (48) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.86/16.87 (49) ~ (all_6_0 = e3)
% 112.86/16.87 (50) ~ (all_52_7 = all_8_2)
% 112.86/16.87 (51) ~ (all_52_4 = all_8_2)
% 112.86/16.87 (52) all_56_15 = e1
% 112.86/16.87 (53) op(e1, e0) = all_52_14
% 112.86/16.87 (54) all_58_5 = all_52_9
% 112.86/16.87 (55) all_56_9 = all_52_3
% 112.86/16.87 (56) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 112.86/16.87 (57) all_58_15 = all_4_2
% 112.86/16.87 (58) all_58_2 = all_52_1
% 112.86/16.87 (59) ~ (all_10_2 = e3)
% 112.86/16.87 (60) ~ (all_52_12 = all_52_13)
% 112.86/16.87 (61) all_58_13 = all_52_7
% 112.86/16.87 (62) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 112.86/16.87 (63) all_58_6 = all_52_2
% 112.86/16.87 (64) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 112.86/16.87 (65) ~ (all_52_1 = all_10_2)
% 112.86/16.87 (66) ~ (all_52_13 = e1)
% 112.86/16.87 (67) all_54_5 = all_8_2
% 112.86/16.87 (68) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 112.86/16.87 (69) all_58_10 = all_52_13
% 112.86/16.87 (70) op(e2, all_8_2) = all_8_1
% 112.86/16.87 (71) op(e2, all_6_2) = all_6_0
% 112.86/16.87 (72) op(e3, all_10_2) = all_10_1
% 112.86/16.87 (73) ~ (all_52_6 = all_8_2)
% 112.86/16.87 (74) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 112.86/16.87 (75) all_58_1 = all_52_4
% 112.86/16.87 (76) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 112.86/16.87 (77) ~ (all_52_9 = all_52_11)
% 112.86/16.87 (78) all_58_14 = all_52_11
% 112.86/16.87 (79) all_54_1 = all_52_4
% 112.86/16.87 (80) op(e0, e1) = all_4_1
% 112.86/16.87 (81) all_56_13 = all_8_2
% 112.86/16.87 (82) op(e0, e1) = all_52_11
% 112.86/16.87 (83) ~ (all_52_1 = all_8_2)
% 112.86/16.87 (84) ~ (all_8_2 = e2)
% 112.86/16.87 (85) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 112.86/16.87 (86) ~ (all_6_2 = e2)
% 112.86/16.87 (87) ~ (all_52_7 = all_52_11)
% 112.86/16.87 (88) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.86/16.87 (89) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 112.86/16.87 (90) all_56_7 = all_52_6
% 112.86/16.87 (91) all_56_1 = all_52_8
% 112.86/16.87 (92) all_58_8 = all_6_2
% 112.86/16.87 (93) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 112.86/16.87 (94) ~ (all_10_0 = e1)
% 112.86/16.87 (95) all_56_4 = all_52_9
% 112.86/16.87 (96) all_58_9 = all_52_12
% 112.86/16.87 (97) all_56_5 = all_52_13
% 112.86/16.87 (98) ~ (all_52_6 = all_6_2)
% 112.86/16.87 (99) all_56_6 = all_52_2
% 112.86/16.87 (100) all_58_12 = all_52_3
% 112.86/16.87 (101) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.86/16.87 (102) op(e2, e0) = all_52_13
% 112.86/16.87 (103) ~ (all_52_3 = all_10_2)
% 112.86/16.87 (104) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 112.86/16.87 (105) ~ (all_52_3 = e1)
% 112.86/16.87 (106) op(e1, e1) = all_6_2
% 112.86/16.87 (107) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 112.86/16.87 (108) ~ (all_52_7 = e1)
% 112.86/16.87 (109) ~ (all_52_4 = all_10_2)
% 112.86/16.87 (110) ~ (all_10_1 = e1)
% 112.86/16.87 (111) ~ (all_52_11 = e1)
% 112.86/16.87 (112) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.86/16.87 (113) all_56_0 = all_52_4
% 112.86/16.87 (114) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 112.86/16.87 (115) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.86/16.87 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 112.86/16.87 (116) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 112.86/16.87 (117) ~ (all_52_11 = e0)
% 112.86/16.87 (118) all_54_4 = all_52_1
% 112.86/16.87 (119) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 112.86/16.87 (120) ~ (all_6_2 = e1)
% 112.86/16.87 (121) ~ (all_52_3 = all_52_11)
% 112.86/16.87 (122) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.86/16.87 (123) all_54_12 = all_52_3
% 112.86/16.87 (124) ~ (e1 = e0)
% 112.86/16.87
% 112.86/16.87 Begin of proof
% 112.86/16.87 |
% 112.86/16.87 | BETA: splitting (64) gives:
% 112.86/16.87 |
% 112.86/16.87 | Case 1:
% 112.86/16.87 | |
% 112.86/16.87 | | (125) ~ (all_56_1 = e3)
% 112.86/16.87 | |
% 112.86/16.87 | | REDUCE: (91), (125) imply:
% 112.86/16.87 | | (126) ~ (all_52_8 = e3)
% 112.86/16.87 | |
% 112.86/16.87 | | GROUND_INST: instantiating (27) with all_52_11, all_4_1, e1, e0, simplifying
% 112.86/16.87 | | with (80), (82) gives:
% 112.86/16.87 | | (127) all_52_11 = all_4_1
% 112.86/16.87 | |
% 112.86/16.87 | | COMBINE_EQS: (25), (127) imply:
% 112.86/16.87 | | (128) all_54_14 = all_4_1
% 112.86/16.87 | |
% 112.86/16.87 | | COMBINE_EQS: (78), (127) imply:
% 112.86/16.88 | | (129) all_58_14 = all_4_1
% 112.86/16.88 | |
% 112.86/16.88 | | REDUCE: (121), (127) imply:
% 112.86/16.88 | | (130) ~ (all_52_3 = all_4_1)
% 112.86/16.88 | |
% 112.86/16.88 | | REDUCE: (77), (127) imply:
% 112.86/16.88 | | (131) ~ (all_52_9 = all_4_1)
% 112.86/16.88 | |
% 112.86/16.88 | | REDUCE: (45), (127) imply:
% 112.86/16.88 | | (132) ~ (all_6_2 = all_4_1)
% 112.86/16.88 | |
% 112.86/16.88 | | SIMP: (132) implies:
% 112.86/16.88 | | (133) ~ (all_6_2 = all_4_1)
% 112.86/16.88 | |
% 112.86/16.88 | | REDUCE: (117), (127) imply:
% 112.86/16.88 | | (134) ~ (all_4_1 = e0)
% 112.86/16.88 | |
% 112.86/16.88 | | BETA: splitting (44) gives:
% 112.86/16.88 | |
% 112.86/16.88 | | Case 1:
% 112.86/16.88 | | |
% 112.86/16.88 | | | (135) ~ (all_56_14 = e3)
% 112.86/16.88 | | |
% 112.86/16.88 | | | REDUCE: (6), (135) imply:
% 112.86/16.88 | | | (136) ~ (all_6_2 = e3)
% 112.86/16.88 | | |
% 112.86/16.88 | | | BETA: splitting (26) gives:
% 112.86/16.88 | | |
% 112.86/16.88 | | | Case 1:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | (137) all_54_10 = e3
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | COMBINE_EQS: (29), (137) imply:
% 112.86/16.88 | | | | (138) all_6_2 = e3
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | REDUCE: (136), (138) imply:
% 112.86/16.88 | | | | (139) $false
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | CLOSE: (139) is inconsistent.
% 112.86/16.88 | | | |
% 112.86/16.88 | | | Case 2:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | (140) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | BETA: splitting (140) gives:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | Case 1:
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | (141) all_54_10 = e2
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | COMBINE_EQS: (29), (141) imply:
% 112.86/16.88 | | | | | (142) all_6_2 = e2
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | COMBINE_EQS: (6), (142) imply:
% 112.86/16.88 | | | | | (143) all_56_14 = e2
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (12), (13), (15), (16),
% 112.86/16.88 | | | | | (18), (19), (21), (23), (26), (27), (29), (30), (32), (33),
% 112.86/16.88 | | | | | (34), (37), (39), (40), (43), (44), (46), (48), (54), (55),
% 112.86/16.88 | | | | | (56), (57), (58), (59), (61), (63), (65), (69), (72), (75),
% 112.86/16.88 | | | | | (78), (79), (81), (84), (88), (89), (90), (92), (93), (94),
% 112.86/16.88 | | | | | (95), (96), (97), (98), (100), (107), (109), (110), (112),
% 112.86/16.88 | | | | | (113), (114), (115), (116), (119), (120), (126), (143) are
% 112.86/16.88 | | | | | inconsistent by sub-proof #87.
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | Case 2:
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | (144) ~ (all_54_10 = e2)
% 112.86/16.88 | | | | | (145) all_54_10 = e1 | all_54_10 = e0
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | REF_CLOSE: (6), (10), (11), (14), (27), (28), (29), (34), (36), (38),
% 112.86/16.88 | | | | | (42), (48), (49), (53), (60), (66), (68), (71), (86), (97),
% 112.86/16.88 | | | | | (102), (120), (140), (145) are inconsistent by sub-proof
% 112.86/16.88 | | | | | #45.
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | End of split
% 112.86/16.88 | | | |
% 112.86/16.88 | | | End of split
% 112.86/16.88 | | |
% 112.86/16.88 | | Case 2:
% 112.86/16.88 | | |
% 112.86/16.88 | | | (146) all_56_14 = e3
% 112.86/16.88 | | | (147) ~ (all_56_9 = e0)
% 112.86/16.88 | | |
% 112.86/16.88 | | | COMBINE_EQS: (6), (146) imply:
% 112.86/16.88 | | | (148) all_6_2 = e3
% 112.86/16.88 | | |
% 112.86/16.88 | | | SIMP: (148) implies:
% 112.86/16.88 | | | (149) all_6_2 = e3
% 112.86/16.88 | | |
% 112.86/16.88 | | | REDUCE: (55), (147) imply:
% 112.86/16.88 | | | (150) ~ (all_52_3 = e0)
% 112.86/16.88 | | |
% 112.86/16.88 | | | REDUCE: (133), (149) imply:
% 112.86/16.88 | | | (151) ~ (all_4_1 = e3)
% 112.86/16.88 | | |
% 112.86/16.88 | | | SIMP: (151) implies:
% 112.86/16.88 | | | (152) ~ (all_4_1 = e3)
% 112.86/16.88 | | |
% 112.86/16.88 | | | REDUCE: (106), (149) imply:
% 112.86/16.88 | | | (153) op(e1, e1) = e3
% 112.86/16.88 | | |
% 112.86/16.88 | | | BETA: splitting (122) gives:
% 112.86/16.88 | | |
% 112.86/16.88 | | | Case 1:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | (154) all_54_14 = e3
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | COMBINE_EQS: (128), (154) imply:
% 112.86/16.88 | | | | (155) all_4_1 = e3
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | SIMP: (155) implies:
% 112.86/16.88 | | | | (156) all_4_1 = e3
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | REDUCE: (152), (156) imply:
% 112.86/16.88 | | | | (157) $false
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | CLOSE: (157) is inconsistent.
% 112.86/16.88 | | | |
% 112.86/16.88 | | | Case 2:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | (158) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | BETA: splitting (115) gives:
% 112.86/16.88 | | | |
% 112.86/16.88 | | | | Case 1:
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | (159) all_58_15 = e0
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | COMBINE_EQS: (41), (159) imply:
% 112.86/16.88 | | | | | (160) e1 = e0
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | REDUCE: (124), (160) imply:
% 112.86/16.88 | | | | | (161) $false
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | CLOSE: (161) is inconsistent.
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | Case 2:
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | (162) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 112.86/16.88 | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | ALPHA: (162) implies:
% 112.86/16.88 | | | | | (163) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | BETA: splitting (35) gives:
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | | Case 1:
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | (164) ~ (all_56_6 = e1)
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | REDUCE: (99), (164) imply:
% 112.86/16.88 | | | | | | (165) ~ (all_52_2 = e1)
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | BETA: splitting (88) gives:
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | Case 1:
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | | (166) all_58_6 = e1
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | | REF_CLOSE: (63), (165), (166) are inconsistent by sub-proof #452.
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | Case 2:
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | | (167) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | | BETA: splitting (158) gives:
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | (168) all_54_14 = e2
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | COMBINE_EQS: (128), (168) imply:
% 112.86/16.88 | | | | | | | | (169) all_4_1 = e2
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | SIMP: (169) implies:
% 112.86/16.88 | | | | | | | | (170) all_4_1 = e2
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | COMBINE_EQS: (129), (170) imply:
% 112.86/16.88 | | | | | | | | (171) all_58_14 = e2
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | REDUCE: (130), (170) imply:
% 112.86/16.88 | | | | | | | | (172) ~ (all_52_3 = e2)
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | REDUCE: (131), (170) imply:
% 112.86/16.88 | | | | | | | | (173) ~ (all_52_9 = e2)
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | REDUCE: (134), (170) imply:
% 112.86/16.88 | | | | | | | | (174) ~ (e2 = e0)
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | BETA: splitting (112) gives:
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | (175) all_58_2 = e2
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | COMBINE_EQS: (58), (175) imply:
% 112.86/16.88 | | | | | | | | | (176) all_52_1 = e2
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | REF_CLOSE: (6), (7), (27), (74), (106), (153), (176) are
% 112.86/16.88 | | | | | | | | | inconsistent by sub-proof #44.
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | (177) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | BETA: splitting (177) gives:
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | (178) all_58_3 = e2
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | COMBINE_EQS: (37), (178) imply:
% 112.86/16.88 | | | | | | | | | | (179) all_8_2 = e2
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | REDUCE: (84), (179) imply:
% 112.86/16.88 | | | | | | | | | | (180) $false
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | CLOSE: (180) is inconsistent.
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | (181) ~ (all_58_3 = e2)
% 112.86/16.88 | | | | | | | | | | (182) all_58_5 = e2 | all_58_10 = e2
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | BETA: splitting (101) gives:
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | (183) all_54_12 = e3
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | COMBINE_EQS: (123), (183) imply:
% 112.86/16.88 | | | | | | | | | | | (184) all_52_3 = e3
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | SIMP: (184) implies:
% 112.86/16.88 | | | | | | | | | | | (185) all_52_3 = e3
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | COMBINE_EQS: (55), (185) imply:
% 112.86/16.88 | | | | | | | | | | | (186) all_56_9 = e3
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | COMBINE_EQS: (100), (185) imply:
% 112.86/16.88 | | | | | | | | | | | (187) all_58_12 = e3
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | REDUCE: (103), (185) imply:
% 112.86/16.88 | | | | | | | | | | | (188) ~ (all_10_2 = e3)
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | BETA: splitting (163) gives:
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | (189) all_58_12 = e0
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | COMBINE_EQS: (187), (189) imply:
% 112.86/16.88 | | | | | | | | | | | | (190) e3 = e0
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | SIMP: (190) implies:
% 112.86/16.88 | | | | | | | | | | | | (191) e3 = e0
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | COMBINE_EQS: (186), (191) imply:
% 112.86/16.88 | | | | | | | | | | | | (192) all_56_9 = e0
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | REF_CLOSE: (6), (26), (29), (44), (48), (54), (69), (86),
% 112.86/16.88 | | | | | | | | | | | | (97), (120), (173), (182), (192) are inconsistent
% 112.86/16.88 | | | | | | | | | | | | by sub-proof #431.
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | (193) all_58_13 = e0 | all_58_14 = e0
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | BETA: splitting (193) gives:
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | (194) all_58_13 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | COMBINE_EQS: (61), (194) imply:
% 112.86/16.88 | | | | | | | | | | | | | (195) all_52_7 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | SIMP: (195) implies:
% 112.86/16.88 | | | | | | | | | | | | | (196) all_52_7 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | COMBINE_EQS: (24), (196) imply:
% 112.86/16.88 | | | | | | | | | | | | | (197) all_56_10 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | BETA: splitting (167) gives:
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | (198) all_58_7 = e1
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | COMBINE_EQS: (3), (198) imply:
% 112.86/16.88 | | | | | | | | | | | | | | (199) all_52_6 = e1
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | REDUCE: (73), (199) imply:
% 112.86/16.88 | | | | | | | | | | | | | | (200) ~ (all_8_2 = e1)
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | SIMP: (200) implies:
% 112.86/16.88 | | | | | | | | | | | | | | (201) ~ (all_8_2 = e1)
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | Case 1:
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | (202) ~ (all_56_12 = e2)
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | REDUCE: (18), (202) imply:
% 112.86/16.88 | | | | | | | | | | | | | | | (203) ~ (all_10_2 = e2)
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (14), (15),
% 112.86/16.88 | | | | | | | | | | | | | | | (17), (18), (19), (20), (22), (25), (26), (27),
% 112.86/16.88 | | | | | | | | | | | | | | | (28), (29), (32), (33), (34), (36), (37), (38),
% 112.86/16.88 | | | | | | | | | | | | | | | (42), (45), (47), (48), (49), (50), (51), (53),
% 112.86/16.88 | | | | | | | | | | | | | | | (54), (58), (59), (60), (65), (66), (67), (68),
% 112.86/16.88 | | | | | | | | | | | | | | | (69), (70), (71), (74), (75), (76), (80), (81),
% 112.86/16.88 | | | | | | | | | | | | | | | (82), (83), (84), (85), (86), (87), (93), (96),
% 112.86/16.88 | | | | | | | | | | | | | | | (97), (102), (104), (106), (107), (108), (111),
% 112.86/16.88 | | | | | | | | | | | | | | | (112), (117), (118), (120), (122), (126), (173),
% 112.86/16.88 | | | | | | | | | | | | | | | (201), (203) are inconsistent by sub-proof #41.
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | (204) ~ (all_56_10 = e0)
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | REDUCE: (197), (204) imply:
% 112.86/16.88 | | | | | | | | | | | | | | | (205) $false
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 112.86/16.88 | | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | (206) all_58_8 = e1 | all_58_11 = e1
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | | REF_CLOSE: (30), (40), (92), (120), (206) are inconsistent by
% 112.86/16.88 | | | | | | | | | | | | | | sub-proof #445.
% 112.86/16.88 | | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | (207) all_58_14 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | COMBINE_EQS: (171), (207) imply:
% 112.86/16.88 | | | | | | | | | | | | | (208) e2 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | SIMP: (208) implies:
% 112.86/16.88 | | | | | | | | | | | | | (209) e2 = e0
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | REDUCE: (174), (209) imply:
% 112.86/16.88 | | | | | | | | | | | | | (210) $false
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 112.86/16.88 | | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | (211) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | | REF_CLOSE: (105), (123), (150), (172), (211) are inconsistent
% 112.86/16.88 | | | | | | | | | | | by sub-proof #406.
% 112.86/16.88 | | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | | |
% 112.86/16.88 | | | | | | | | | End of split
% 112.86/16.88 | | | | | | | | |
% 112.86/16.88 | | | | | | | | End of split
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | Case 2:
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | (212) all_54_14 = e1 | all_54_14 = e0
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | | REF_CLOSE: (25), (111), (117), (212) are inconsistent by
% 112.86/16.88 | | | | | | | | sub-proof #139.
% 112.86/16.88 | | | | | | | |
% 112.86/16.88 | | | | | | | End of split
% 112.86/16.88 | | | | | | |
% 112.86/16.88 | | | | | | End of split
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | Case 2:
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | (213) ~ (all_56_14 = e3)
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | REDUCE: (146), (213) imply:
% 112.86/16.88 | | | | | | (214) $false
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | | CLOSE: (214) is inconsistent.
% 112.86/16.88 | | | | | |
% 112.86/16.88 | | | | | End of split
% 112.86/16.88 | | | | |
% 112.86/16.88 | | | | End of split
% 112.86/16.88 | | | |
% 112.86/16.88 | | | End of split
% 112.86/16.88 | | |
% 112.86/16.88 | | End of split
% 112.86/16.88 | |
% 112.86/16.88 | Case 2:
% 112.86/16.88 | |
% 112.86/16.88 | | (215) ~ (all_56_15 = e1)
% 112.86/16.88 | |
% 112.86/16.88 | | REDUCE: (52), (215) imply:
% 112.86/16.88 | | (216) $false
% 112.86/16.88 | |
% 112.86/16.88 | | CLOSE: (216) is inconsistent.
% 112.86/16.88 | |
% 112.86/16.88 | End of split
% 112.86/16.88 |
% 112.86/16.88 End of proof
% 112.86/16.88
% 112.86/16.88 Sub-proof #41 shows that the following formulas are inconsistent:
% 112.86/16.88 ----------------------------------------------------------------
% 112.86/16.88 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 112.86/16.88 (2) ~ (all_52_9 = e2)
% 112.86/16.88 (3) all_56_14 = all_6_2
% 112.86/16.88 (4) all_56_3 = all_52_1
% 112.86/16.88 (5) all_54_0 = all_10_2
% 112.86/16.88 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 112.86/16.88 (7) all_54_3 = all_52_12
% 112.86/16.88 (8) ~ (all_52_12 = all_52_14)
% 112.86/16.88 (9) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 112.86/16.88 (10) ~ (all_52_12 = all_10_2)
% 112.86/16.88 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 112.86/16.88 (12) all_56_12 = all_10_2
% 112.86/16.88 (13) all_58_0 = all_10_2
% 112.86/16.88 (14) all_54_13 = all_52_7
% 112.86/16.88 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 112.86/16.88 (16) all_54_14 = all_52_11
% 112.86/16.88 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 112.86/16.88 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 112.86/16.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 112.86/16.88 (19) op(e1, all_6_2) = e2
% 112.86/16.88 (20) ~ (all_10_2 = e2)
% 112.86/16.88 (21) all_54_10 = all_6_2
% 112.86/16.88 (22) all_58_4 = all_52_8
% 112.86/16.88 (23) ~ (all_52_4 = all_52_7)
% 112.86/16.88 (24) all_56_2 = all_52_12
% 112.86/16.88 (25) ~ (all_52_12 = e1)
% 112.86/16.88 (26) all_58_3 = all_8_2
% 112.86/16.88 (27) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 112.86/16.88 (28) all_54_7 = all_52_13
% 112.86/16.88 (29) ~ (all_52_11 = all_6_2)
% 112.86/16.88 (30) op(e2, e3) = all_52_1
% 112.86/16.88 (31) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 112.86/16.88 (32) ~ (all_6_0 = e3)
% 112.86/16.88 (33) ~ (all_52_7 = all_8_2)
% 112.86/16.88 (34) ~ (all_52_4 = all_8_2)
% 112.86/16.88 (35) op(e1, e0) = all_52_14
% 113.01/16.88 (36) all_58_5 = all_52_9
% 113.01/16.88 (37) all_58_2 = all_52_1
% 113.01/16.88 (38) ~ (all_10_2 = e3)
% 113.01/16.88 (39) ~ (all_52_12 = all_52_13)
% 113.01/16.88 (40) ~ (all_52_1 = all_10_2)
% 113.01/16.88 (41) ~ (all_52_13 = e1)
% 113.01/16.88 (42) all_54_5 = all_8_2
% 113.01/16.88 (43) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.01/16.88 (44) all_58_10 = all_52_13
% 113.01/16.89 (45) op(e2, all_8_2) = all_8_1
% 113.01/16.89 (46) op(e2, all_6_2) = all_6_0
% 113.01/16.89 (47) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.01/16.89 (48) all_58_1 = all_52_4
% 113.01/16.89 (49) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.01/16.89 (50) ~ (all_8_2 = e1)
% 113.01/16.89 (51) op(e0, e1) = all_4_1
% 113.01/16.89 (52) all_56_13 = all_8_2
% 113.01/16.89 (53) ~ (all_52_8 = e3)
% 113.01/16.89 (54) op(e0, e1) = all_52_11
% 113.01/16.89 (55) ~ (all_52_1 = all_8_2)
% 113.01/16.89 (56) ~ (all_8_2 = e2)
% 113.01/16.89 (57) ~ (all_6_0 = e0) | ~ (all_6_2 = e3)
% 113.01/16.89 (58) ~ (all_6_2 = e2)
% 113.01/16.89 (59) ~ (all_52_7 = all_52_11)
% 113.01/16.89 (60) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.01/16.89 (61) all_58_9 = all_52_12
% 113.01/16.89 (62) all_56_5 = all_52_13
% 113.01/16.89 (63) op(e2, e0) = all_52_13
% 113.01/16.89 (64) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.01/16.89 (65) op(e1, e1) = all_6_2
% 113.01/16.89 (66) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.01/16.89 (67) ~ (all_52_7 = e1)
% 113.01/16.89 (68) ~ (all_52_11 = e1)
% 113.01/16.89 (69) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.01/16.89 (70) ~ (all_52_11 = e0)
% 113.01/16.89 (71) all_54_4 = all_52_1
% 113.01/16.89 (72) ~ (all_6_2 = e1)
% 113.01/16.89 (73) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.01/16.89
% 113.01/16.89 Begin of proof
% 113.01/16.89 |
% 113.01/16.89 | GROUND_INST: instantiating (18) with all_52_11, all_4_1, e1, e0, simplifying
% 113.01/16.89 | with (51), (54) gives:
% 113.01/16.89 | (74) all_52_11 = all_4_1
% 113.01/16.89 |
% 113.01/16.89 | COMBINE_EQS: (16), (74) imply:
% 113.01/16.89 | (75) all_54_14 = all_4_1
% 113.01/16.89 |
% 113.01/16.89 | REDUCE: (59), (74) imply:
% 113.01/16.89 | (76) ~ (all_52_7 = all_4_1)
% 113.01/16.89 |
% 113.01/16.89 | REDUCE: (29), (74) imply:
% 113.01/16.89 | (77) ~ (all_6_2 = all_4_1)
% 113.01/16.89 |
% 113.01/16.89 | SIMP: (77) implies:
% 113.01/16.89 | (78) ~ (all_6_2 = all_4_1)
% 113.01/16.89 |
% 113.01/16.89 | BETA: splitting (49) gives:
% 113.01/16.89 |
% 113.01/16.89 | Case 1:
% 113.01/16.89 | |
% 113.01/16.89 | | (79) ~ (all_56_2 = e3)
% 113.01/16.89 | |
% 113.01/16.89 | | REDUCE: (24), (79) imply:
% 113.01/16.89 | | (80) ~ (all_52_12 = e3)
% 113.01/16.89 | |
% 113.01/16.89 | | BETA: splitting (66) gives:
% 113.01/16.89 | |
% 113.01/16.89 | | Case 1:
% 113.01/16.89 | | |
% 113.01/16.89 | | | (81) all_58_0 = e3
% 113.01/16.89 | | |
% 113.01/16.89 | | | COMBINE_EQS: (13), (81) imply:
% 113.01/16.89 | | | (82) all_10_2 = e3
% 113.01/16.89 | | |
% 113.01/16.89 | | | REDUCE: (38), (82) imply:
% 113.01/16.89 | | | (83) $false
% 113.01/16.89 | | |
% 113.01/16.89 | | | CLOSE: (83) is inconsistent.
% 113.01/16.89 | | |
% 113.01/16.89 | | Case 2:
% 113.01/16.89 | | |
% 113.01/16.89 | | | (84) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.01/16.89 | | |
% 113.01/16.89 | | | BETA: splitting (84) gives:
% 113.01/16.89 | | |
% 113.01/16.89 | | | Case 1:
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | (85) all_58_1 = e3
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | COMBINE_EQS: (48), (85) imply:
% 113.01/16.89 | | | | (86) all_52_4 = e3
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | REDUCE: (23), (86) imply:
% 113.01/16.89 | | | | (87) ~ (all_52_7 = e3)
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | SIMP: (87) implies:
% 113.01/16.89 | | | | (88) ~ (all_52_7 = e3)
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | REDUCE: (34), (86) imply:
% 113.01/16.89 | | | | (89) ~ (all_8_2 = e3)
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | SIMP: (89) implies:
% 113.01/16.89 | | | | (90) ~ (all_8_2 = e3)
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (14), (16), (17), (18), (19),
% 113.01/16.89 | | | | (21), (24), (25), (27), (28), (31), (32), (33), (35), (39),
% 113.01/16.89 | | | | (41), (42), (43), (46), (50), (56), (58), (62), (63), (67),
% 113.01/16.89 | | | | (68), (70), (72), (73), (75), (76), (78), (88), (90) are
% 113.01/16.89 | | | | inconsistent by sub-proof #42.
% 113.01/16.89 | | | |
% 113.01/16.89 | | | Case 2:
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | (91) all_58_4 = e3 | all_58_9 = e3
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | REF_CLOSE: (22), (53), (61), (80), (91) are inconsistent by sub-proof
% 113.01/16.89 | | | | #184.
% 113.01/16.89 | | | |
% 113.01/16.89 | | | End of split
% 113.01/16.89 | | |
% 113.01/16.89 | | End of split
% 113.01/16.89 | |
% 113.01/16.89 | Case 2:
% 113.01/16.89 | |
% 113.01/16.89 | | (92) all_56_2 = e3
% 113.01/16.89 | | (93) ~ (all_56_13 = e0)
% 113.01/16.89 | |
% 113.01/16.89 | | COMBINE_EQS: (24), (92) imply:
% 113.01/16.89 | | (94) all_52_12 = e3
% 113.01/16.89 | |
% 113.01/16.89 | | REDUCE: (52), (93) imply:
% 113.01/16.89 | | (95) ~ (all_8_2 = e0)
% 113.01/16.89 | |
% 113.01/16.89 | | REDUCE: (10), (94) imply:
% 113.01/16.89 | | (96) ~ (all_10_2 = e3)
% 113.01/16.89 | |
% 113.01/16.89 | | BETA: splitting (1) gives:
% 113.01/16.89 | |
% 113.01/16.89 | | Case 1:
% 113.01/16.89 | | |
% 113.01/16.89 | | | (97) ~ (all_56_2 = e3)
% 113.01/16.89 | | |
% 113.01/16.89 | | | REDUCE: (92), (97) imply:
% 113.01/16.89 | | | (98) $false
% 113.01/16.89 | | |
% 113.01/16.89 | | | CLOSE: (98) is inconsistent.
% 113.01/16.89 | | |
% 113.01/16.89 | | Case 2:
% 113.01/16.89 | | |
% 113.01/16.89 | | | (99) ~ (all_56_12 = e0)
% 113.01/16.89 | | |
% 113.01/16.89 | | | REDUCE: (12), (99) imply:
% 113.01/16.89 | | | (100) ~ (all_10_2 = e0)
% 113.01/16.89 | | |
% 113.01/16.89 | | | BETA: splitting (60) gives:
% 113.01/16.89 | | |
% 113.01/16.89 | | | Case 1:
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | (101) all_54_0 = e3
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | REF_CLOSE: (5), (38), (101) are inconsistent by sub-proof #451.
% 113.01/16.89 | | | |
% 113.01/16.89 | | | Case 2:
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | (102) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | BETA: splitting (11) gives:
% 113.01/16.89 | | | |
% 113.01/16.89 | | | | Case 1:
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | (103) all_54_5 = e3
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | COMBINE_EQS: (42), (103) imply:
% 113.01/16.89 | | | | | (104) all_8_2 = e3
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | SIMP: (104) implies:
% 113.01/16.89 | | | | | (105) all_8_2 = e3
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | COMBINE_EQS: (26), (105) imply:
% 113.01/16.89 | | | | | (106) all_58_3 = e3
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | REDUCE: (55), (105) imply:
% 113.01/16.89 | | | | | (107) ~ (all_52_1 = e3)
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | REDUCE: (45), (105) imply:
% 113.01/16.89 | | | | | (108) op(e2, e3) = all_8_1
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | BETA: splitting (27) gives:
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | Case 1:
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | (109) ~ (all_56_2 = e3)
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | REDUCE: (92), (109) imply:
% 113.01/16.89 | | | | | | (110) $false
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | CLOSE: (110) is inconsistent.
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | Case 2:
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | (111) ~ (all_56_14 = e0)
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | REDUCE: (3), (111) imply:
% 113.01/16.89 | | | | | | (112) ~ (all_6_2 = e0)
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | BETA: splitting (102) gives:
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | | Case 1:
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | | (113) all_54_0 = e2
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | | REF_CLOSE: (5), (20), (113) are inconsistent by sub-proof #450.
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | Case 2:
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | | (114) all_54_0 = e1 | all_54_0 = e0
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | | BETA: splitting (17) gives:
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | (115) all_54_10 = e3
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | COMBINE_EQS: (21), (115) imply:
% 113.01/16.89 | | | | | | | | (116) all_6_2 = e3
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | REDUCE: (58), (116) imply:
% 113.01/16.89 | | | | | | | | (117) ~ (e3 = e2)
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | REDUCE: (46), (116) imply:
% 113.01/16.89 | | | | | | | | (118) op(e2, e3) = all_6_0
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | REDUCE: (65), (116) imply:
% 113.01/16.89 | | | | | | | | (119) op(e1, e1) = e3
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | BETA: splitting (114) gives:
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | (120) all_54_0 = e1
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | COMBINE_EQS: (5), (120) imply:
% 113.01/16.89 | | | | | | | | | (121) all_10_2 = e1
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | SIMP: (121) implies:
% 113.01/16.89 | | | | | | | | | (122) all_10_2 = e1
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | REDUCE: (40), (122) imply:
% 113.01/16.89 | | | | | | | | | (123) ~ (all_52_1 = e1)
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | BETA: splitting (69) gives:
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | (124) all_58_2 = e2
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | COMBINE_EQS: (37), (124) imply:
% 113.01/16.89 | | | | | | | | | | (125) all_52_1 = e2
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | REF_CLOSE: (3), (4), (18), (47), (65), (119), (125) are
% 113.01/16.89 | | | | | | | | | | inconsistent by sub-proof #44.
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | (126) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | BETA: splitting (15) gives:
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | (127) all_54_4 = e3
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | REF_CLOSE: (71), (107), (127) are inconsistent by sub-proof
% 113.01/16.89 | | | | | | | | | | | #329.
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | (128) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | BETA: splitting (126) gives:
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | (129) all_58_3 = e2
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | COMBINE_EQS: (106), (129) imply:
% 113.01/16.89 | | | | | | | | | | | | (130) e3 = e2
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | REDUCE: (117), (130) imply:
% 113.01/16.89 | | | | | | | | | | | | (131) $false
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | (132) all_58_5 = e2 | all_58_10 = e2
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | BETA: splitting (128) gives:
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | (133) all_54_4 = e2
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | COMBINE_EQS: (71), (133) imply:
% 113.01/16.89 | | | | | | | | | | | | | (134) all_52_1 = e2
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (18), (47), (65), (119), (134) are
% 113.01/16.89 | | | | | | | | | | | | | inconsistent by sub-proof #44.
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | (135) all_54_4 = e1 | all_54_4 = e0
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | BETA: splitting (64) gives:
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | (136) all_58_2 = e0
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | COMBINE_EQS: (37), (136) imply:
% 113.01/16.89 | | | | | | | | | | | | | | (137) all_52_1 = e0
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | REDUCE: (30), (137) imply:
% 113.01/16.89 | | | | | | | | | | | | | | (138) op(e2, e3) = e0
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | Case 1:
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | (139) ~ (all_6_2 = e3)
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (17), (21), (31), (36), (44), (58),
% 113.01/16.89 | | | | | | | | | | | | | | | (62), (72), (132), (139) are inconsistent by
% 113.01/16.89 | | | | | | | | | | | | | | | sub-proof #432.
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | (140) ~ (all_6_0 = e0)
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_6_0, all_8_1, e3, e2,
% 113.01/16.89 | | | | | | | | | | | | | | | simplifying with (108), (118) gives:
% 113.01/16.89 | | | | | | | | | | | | | | | (141) all_8_1 = all_6_0
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with e0, all_8_1, e3, e2,
% 113.01/16.89 | | | | | | | | | | | | | | | simplifying with (108), (138) gives:
% 113.01/16.89 | | | | | | | | | | | | | | | (142) all_8_1 = e0
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | COMBINE_EQS: (141), (142) imply:
% 113.01/16.89 | | | | | | | | | | | | | | | (143) all_6_0 = e0
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | SIMP: (143) implies:
% 113.01/16.89 | | | | | | | | | | | | | | | (144) all_6_0 = e0
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | REDUCE: (140), (144) imply:
% 113.01/16.89 | | | | | | | | | | | | | | | (145) $false
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 113.01/16.89 | | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | (146) ~ (all_58_2 = e0)
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | REDUCE: (37), (146) imply:
% 113.01/16.89 | | | | | | | | | | | | | | (147) ~ (all_52_1 = e0)
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | | REF_CLOSE: (71), (123), (135), (147) are inconsistent by
% 113.01/16.89 | | | | | | | | | | | | | | sub-proof #147.
% 113.01/16.89 | | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | | |
% 113.01/16.89 | | | | | | | | | End of split
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | (148) all_54_0 = e0
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | | REF_CLOSE: (5), (100), (148) are inconsistent by sub-proof
% 113.01/16.89 | | | | | | | | | #424.
% 113.01/16.89 | | | | | | | | |
% 113.01/16.89 | | | | | | | | End of split
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | Case 2:
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | (149) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | | REF_CLOSE: (21), (58), (72), (112), (149) are inconsistent by
% 113.01/16.89 | | | | | | | | sub-proof #435.
% 113.01/16.89 | | | | | | | |
% 113.01/16.89 | | | | | | | End of split
% 113.01/16.89 | | | | | | |
% 113.01/16.89 | | | | | | End of split
% 113.01/16.89 | | | | | |
% 113.01/16.89 | | | | | End of split
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | Case 2:
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | (150) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | | REF_CLOSE: (42), (50), (56), (95), (150) are inconsistent by sub-proof
% 113.01/16.89 | | | | | #310.
% 113.01/16.89 | | | | |
% 113.01/16.89 | | | | End of split
% 113.01/16.89 | | | |
% 113.01/16.89 | | | End of split
% 113.01/16.89 | | |
% 113.01/16.89 | | End of split
% 113.01/16.89 | |
% 113.01/16.89 | End of split
% 113.01/16.89 |
% 113.01/16.89 End of proof
% 113.01/16.89
% 113.01/16.89 Sub-proof #42 shows that the following formulas are inconsistent:
% 113.01/16.89 ----------------------------------------------------------------
% 113.01/16.89 (1) all_56_14 = all_6_2
% 113.01/16.89 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.01/16.89 (3) all_54_3 = all_52_12
% 113.01/16.89 (4) ~ (all_52_12 = all_52_14)
% 113.01/16.89 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.89 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.89 (7) all_54_13 = all_52_7
% 113.01/16.89 (8) all_54_14 = all_52_11
% 113.01/16.89 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.89 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.89 (11) op(e1, all_6_2) = e2
% 113.01/16.89 (12) ~ (all_52_7 = e3)
% 113.01/16.89 (13) all_54_10 = all_6_2
% 113.01/16.89 (14) all_56_2 = all_52_12
% 113.01/16.89 (15) ~ (all_52_12 = e1)
% 113.01/16.89 (16) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.01/16.89 (17) all_54_7 = all_52_13
% 113.01/16.89 (18) ~ (all_8_2 = e3)
% 113.01/16.89 (19) ~ (all_52_7 = all_4_1)
% 113.01/16.89 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.89 (21) ~ (all_6_0 = e3)
% 113.01/16.89 (22) ~ (all_52_7 = all_8_2)
% 113.01/16.89 (23) op(e1, e0) = all_52_14
% 113.01/16.89 (24) ~ (all_6_2 = all_4_1)
% 113.01/16.89 (25) ~ (all_52_12 = all_52_13)
% 113.01/16.89 (26) ~ (all_52_13 = e1)
% 113.01/16.90 (27) all_54_5 = all_8_2
% 113.01/16.90 (28) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.01/16.90 (29) op(e2, all_6_2) = all_6_0
% 113.01/16.90 (30) ~ (all_8_2 = e1)
% 113.01/16.90 (31) ~ (all_8_2 = e2)
% 113.01/16.90 (32) ~ (all_6_2 = e2)
% 113.01/16.90 (33) all_56_5 = all_52_13
% 113.01/16.90 (34) all_54_14 = all_4_1
% 113.01/16.90 (35) op(e2, e0) = all_52_13
% 113.01/16.90 (36) ~ (all_52_7 = e1)
% 113.01/16.90 (37) ~ (all_52_11 = e1)
% 113.01/16.90 (38) ~ (all_52_11 = e0)
% 113.01/16.90 (39) ~ (all_6_2 = e1)
% 113.01/16.90 (40) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.01/16.90
% 113.01/16.90 Begin of proof
% 113.01/16.90 |
% 113.01/16.90 | BETA: splitting (6) gives:
% 113.01/16.90 |
% 113.01/16.90 | Case 1:
% 113.01/16.90 | |
% 113.01/16.90 | | (41) all_54_5 = e3
% 113.01/16.90 | |
% 113.01/16.90 | | REF_CLOSE: (18), (27), (41) are inconsistent by sub-proof #339.
% 113.01/16.90 | |
% 113.01/16.90 | Case 2:
% 113.01/16.90 | |
% 113.01/16.90 | | (42) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.90 | |
% 113.01/16.90 | | BETA: splitting (2) gives:
% 113.01/16.90 | |
% 113.01/16.90 | | Case 1:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (43) all_54_13 = e3
% 113.01/16.90 | | |
% 113.01/16.90 | | | COMBINE_EQS: (7), (43) imply:
% 113.01/16.90 | | | (44) all_52_7 = e3
% 113.01/16.90 | | |
% 113.01/16.90 | | | REDUCE: (12), (44) imply:
% 113.01/16.90 | | | (45) $false
% 113.01/16.90 | | |
% 113.01/16.90 | | | CLOSE: (45) is inconsistent.
% 113.01/16.90 | | |
% 113.01/16.90 | | Case 2:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (46) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.01/16.90 | | |
% 113.01/16.90 | | | BETA: splitting (46) gives:
% 113.01/16.90 | | |
% 113.01/16.90 | | | Case 1:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | (47) all_54_13 = e2
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | COMBINE_EQS: (7), (47) imply:
% 113.01/16.90 | | | | (48) all_52_7 = e2
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | REDUCE: (19), (48) imply:
% 113.01/16.90 | | | | (49) ~ (all_4_1 = e2)
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | SIMP: (49) implies:
% 113.01/16.90 | | | | (50) ~ (all_4_1 = e2)
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | BETA: splitting (40) gives:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | Case 1:
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | (51) all_54_14 = e3
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | COMBINE_EQS: (34), (51) imply:
% 113.01/16.90 | | | | | (52) all_4_1 = e3
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | REDUCE: (24), (52) imply:
% 113.01/16.90 | | | | | (53) ~ (all_6_2 = e3)
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (13), (14), (15),
% 113.01/16.90 | | | | | (16), (17), (20), (21), (23), (25), (26), (28), (29), (32),
% 113.01/16.90 | | | | | (33), (35), (39), (53) are inconsistent by sub-proof #43.
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | Case 2:
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | (54) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | REF_CLOSE: (8), (34), (37), (38), (50), (54) are inconsistent by
% 113.01/16.90 | | | | | sub-proof #138.
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | End of split
% 113.01/16.90 | | | |
% 113.01/16.90 | | | Case 2:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | (55) all_54_13 = e1 | all_54_13 = e0
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | REF_CLOSE: (7), (22), (27), (30), (31), (36), (42), (55) are
% 113.01/16.90 | | | | inconsistent by sub-proof #309.
% 113.01/16.90 | | | |
% 113.01/16.90 | | | End of split
% 113.01/16.90 | | |
% 113.01/16.90 | | End of split
% 113.01/16.90 | |
% 113.01/16.90 | End of split
% 113.01/16.90 |
% 113.01/16.90 End of proof
% 113.01/16.90
% 113.01/16.90 Sub-proof #43 shows that the following formulas are inconsistent:
% 113.01/16.90 ----------------------------------------------------------------
% 113.01/16.90 (1) all_56_14 = all_6_2
% 113.01/16.90 (2) all_54_3 = all_52_12
% 113.01/16.90 (3) ~ (all_52_12 = all_52_14)
% 113.01/16.90 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.90 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.90 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.90 (7) op(e1, all_6_2) = e2
% 113.01/16.90 (8) all_54_10 = all_6_2
% 113.01/16.90 (9) all_56_2 = all_52_12
% 113.01/16.90 (10) ~ (all_52_12 = e1)
% 113.01/16.90 (11) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.01/16.90 (12) all_54_7 = all_52_13
% 113.01/16.90 (13) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.90 (14) ~ (all_6_0 = e3)
% 113.01/16.90 (15) op(e1, e0) = all_52_14
% 113.01/16.90 (16) ~ (all_52_12 = all_52_13)
% 113.01/16.90 (17) ~ (all_52_13 = e1)
% 113.01/16.90 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.01/16.90 (19) op(e2, all_6_2) = all_6_0
% 113.01/16.90 (20) ~ (all_6_2 = e2)
% 113.01/16.90 (21) all_56_5 = all_52_13
% 113.01/16.90 (22) op(e2, e0) = all_52_13
% 113.01/16.90 (23) ~ (all_6_2 = e3)
% 113.01/16.90 (24) ~ (all_6_2 = e1)
% 113.01/16.90
% 113.01/16.90 Begin of proof
% 113.01/16.90 |
% 113.01/16.90 | BETA: splitting (5) gives:
% 113.01/16.90 |
% 113.01/16.90 | Case 1:
% 113.01/16.90 | |
% 113.01/16.90 | | (25) all_54_10 = e3
% 113.01/16.90 | |
% 113.01/16.90 | | COMBINE_EQS: (8), (25) imply:
% 113.01/16.90 | | (26) all_6_2 = e3
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (23), (26) imply:
% 113.01/16.90 | | (27) $false
% 113.01/16.90 | |
% 113.01/16.90 | | CLOSE: (27) is inconsistent.
% 113.01/16.90 | |
% 113.01/16.90 | Case 2:
% 113.01/16.90 | |
% 113.01/16.90 | | (28) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.90 | |
% 113.01/16.90 | | BETA: splitting (28) gives:
% 113.01/16.90 | |
% 113.01/16.90 | | Case 1:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (29) all_54_10 = e2
% 113.01/16.90 | | |
% 113.01/16.90 | | | COMBINE_EQS: (8), (29) imply:
% 113.01/16.90 | | | (30) all_6_2 = e2
% 113.01/16.90 | | |
% 113.01/16.90 | | | REDUCE: (20), (30) imply:
% 113.01/16.90 | | | (31) $false
% 113.01/16.90 | | |
% 113.01/16.90 | | | CLOSE: (31) is inconsistent.
% 113.01/16.90 | | |
% 113.01/16.90 | | Case 2:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (32) all_54_10 = e1 | all_54_10 = e0
% 113.01/16.90 | | |
% 113.01/16.90 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 113.01/16.90 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 113.01/16.90 | | | (28), (32) are inconsistent by sub-proof #45.
% 113.01/16.90 | | |
% 113.01/16.90 | | End of split
% 113.01/16.90 | |
% 113.01/16.90 | End of split
% 113.01/16.90 |
% 113.01/16.90 End of proof
% 113.01/16.90
% 113.01/16.90 Sub-proof #44 shows that the following formulas are inconsistent:
% 113.01/16.90 ----------------------------------------------------------------
% 113.01/16.90 (1) all_56_14 = all_6_2
% 113.01/16.90 (2) all_56_3 = all_52_1
% 113.01/16.90 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.90 (4) op(e1, e1) = e3
% 113.01/16.90 (5) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.01/16.90 (6) op(e1, e1) = all_6_2
% 113.01/16.90 (7) all_52_1 = e2
% 113.01/16.90
% 113.01/16.90 Begin of proof
% 113.01/16.90 |
% 113.01/16.90 | SIMP: (7) implies:
% 113.01/16.90 | (8) all_52_1 = e2
% 113.01/16.90 |
% 113.01/16.90 | COMBINE_EQS: (2), (8) imply:
% 113.01/16.90 | (9) all_56_3 = e2
% 113.01/16.90 |
% 113.01/16.90 | REF_CLOSE: (1), (3), (4), (5), (6), (9) are inconsistent by sub-proof #121.
% 113.01/16.90 |
% 113.01/16.90 End of proof
% 113.01/16.90
% 113.01/16.90 Sub-proof #45 shows that the following formulas are inconsistent:
% 113.01/16.90 ----------------------------------------------------------------
% 113.01/16.90 (1) all_56_14 = all_6_2
% 113.01/16.90 (2) all_54_3 = all_52_12
% 113.01/16.90 (3) ~ (all_52_12 = all_52_14)
% 113.01/16.90 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.90 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.90 (6) op(e1, all_6_2) = e2
% 113.01/16.90 (7) all_54_10 = all_6_2
% 113.01/16.90 (8) all_56_2 = all_52_12
% 113.01/16.90 (9) ~ (all_52_12 = e1)
% 113.01/16.90 (10) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.01/16.90 (11) all_54_7 = all_52_13
% 113.01/16.90 (12) all_54_10 = e1 | all_54_10 = e0
% 113.01/16.90 (13) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.90 (14) ~ (all_6_0 = e3)
% 113.01/16.90 (15) op(e1, e0) = all_52_14
% 113.01/16.90 (16) ~ (all_52_12 = all_52_13)
% 113.01/16.90 (17) ~ (all_52_13 = e1)
% 113.01/16.90 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.01/16.90 (19) op(e2, all_6_2) = all_6_0
% 113.01/16.90 (20) ~ (all_6_2 = e2)
% 113.01/16.90 (21) all_56_5 = all_52_13
% 113.01/16.90 (22) op(e2, e0) = all_52_13
% 113.01/16.90 (23) ~ (all_6_2 = e1)
% 113.01/16.90 (24) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.90
% 113.01/16.90 Begin of proof
% 113.01/16.90 |
% 113.01/16.90 | BETA: splitting (12) gives:
% 113.01/16.90 |
% 113.01/16.90 | Case 1:
% 113.01/16.90 | |
% 113.01/16.90 | | (25) all_54_10 = e1
% 113.01/16.90 | |
% 113.01/16.90 | | COMBINE_EQS: (7), (25) imply:
% 113.01/16.90 | | (26) all_6_2 = e1
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (23), (26) imply:
% 113.01/16.90 | | (27) $false
% 113.01/16.90 | |
% 113.01/16.90 | | CLOSE: (27) is inconsistent.
% 113.01/16.90 | |
% 113.01/16.90 | Case 2:
% 113.01/16.90 | |
% 113.01/16.90 | | (28) all_54_10 = e0
% 113.01/16.90 | |
% 113.01/16.90 | | COMBINE_EQS: (7), (28) imply:
% 113.01/16.90 | | (29) all_6_2 = e0
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (19), (29) imply:
% 113.01/16.90 | | (30) op(e2, e0) = all_6_0
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (6), (29) imply:
% 113.01/16.90 | | (31) op(e1, e0) = e2
% 113.01/16.90 | |
% 113.01/16.90 | | GROUND_INST: instantiating (5) with all_52_14, e2, e0, e1, simplifying with
% 113.01/16.90 | | (15), (31) gives:
% 113.01/16.90 | | (32) all_52_14 = e2
% 113.01/16.90 | |
% 113.01/16.90 | | GROUND_INST: instantiating (5) with all_52_13, all_6_0, e0, e2, simplifying
% 113.01/16.90 | | with (22), (30) gives:
% 113.01/16.90 | | (33) all_52_13 = all_6_0
% 113.01/16.90 | |
% 113.01/16.90 | | COMBINE_EQS: (11), (33) imply:
% 113.01/16.90 | | (34) all_54_7 = all_6_0
% 113.01/16.90 | |
% 113.01/16.90 | | COMBINE_EQS: (21), (33) imply:
% 113.01/16.90 | | (35) all_56_5 = all_6_0
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (16), (33) imply:
% 113.01/16.90 | | (36) ~ (all_52_12 = all_6_0)
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (3), (32) imply:
% 113.01/16.90 | | (37) ~ (all_52_12 = e2)
% 113.01/16.90 | |
% 113.01/16.90 | | REDUCE: (17), (33) imply:
% 113.01/16.90 | | (38) ~ (all_6_0 = e1)
% 113.01/16.90 | |
% 113.01/16.90 | | BETA: splitting (18) gives:
% 113.01/16.90 | |
% 113.01/16.90 | | Case 1:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (39) all_54_7 = e3
% 113.01/16.90 | | |
% 113.01/16.90 | | | COMBINE_EQS: (34), (39) imply:
% 113.01/16.90 | | | (40) all_6_0 = e3
% 113.01/16.90 | | |
% 113.01/16.90 | | | SIMP: (40) implies:
% 113.01/16.90 | | | (41) all_6_0 = e3
% 113.01/16.90 | | |
% 113.01/16.90 | | | REDUCE: (14), (41) imply:
% 113.01/16.90 | | | (42) $false
% 113.01/16.90 | | |
% 113.01/16.90 | | | CLOSE: (42) is inconsistent.
% 113.01/16.90 | | |
% 113.01/16.90 | | Case 2:
% 113.01/16.90 | | |
% 113.01/16.90 | | | (43) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.01/16.90 | | |
% 113.01/16.90 | | | BETA: splitting (4) gives:
% 113.01/16.90 | | |
% 113.01/16.90 | | | Case 1:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | (44) all_54_3 = e3
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | COMBINE_EQS: (2), (44) imply:
% 113.01/16.90 | | | | (45) all_52_12 = e3
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | SIMP: (45) implies:
% 113.01/16.90 | | | | (46) all_52_12 = e3
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | COMBINE_EQS: (8), (46) imply:
% 113.01/16.90 | | | | (47) all_56_2 = e3
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | REF_CLOSE: (1), (7), (10), (20), (23), (24), (47) are inconsistent by
% 113.01/16.90 | | | | sub-proof #351.
% 113.01/16.90 | | | |
% 113.01/16.90 | | | Case 2:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | (48) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | BETA: splitting (48) gives:
% 113.01/16.90 | | | |
% 113.01/16.90 | | | | Case 1:
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | (49) all_54_3 = e2
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | REF_CLOSE: (2), (37), (49) are inconsistent by sub-proof #285.
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | Case 2:
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | (50) all_54_3 = e1 | all_54_3 = e0
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | BETA: splitting (50) gives:
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | | Case 1:
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | (51) all_54_3 = e1
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | REF_CLOSE: (2), (9), (51) are inconsistent by sub-proof #284.
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | Case 2:
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | (52) all_54_3 = e0
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | COMBINE_EQS: (2), (52) imply:
% 113.01/16.90 | | | | | | (53) all_52_12 = e0
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | SIMP: (53) implies:
% 113.01/16.90 | | | | | | (54) all_52_12 = e0
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | REDUCE: (36), (54) imply:
% 113.01/16.90 | | | | | | (55) ~ (all_6_0 = e0)
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | SIMP: (55) implies:
% 113.01/16.90 | | | | | | (56) ~ (all_6_0 = e0)
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | BETA: splitting (43) gives:
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | | Case 1:
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | (57) all_54_7 = e2
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | COMBINE_EQS: (34), (57) imply:
% 113.01/16.90 | | | | | | | (58) all_6_0 = e2
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | SIMP: (58) implies:
% 113.01/16.90 | | | | | | | (59) all_6_0 = e2
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | COMBINE_EQS: (35), (59) imply:
% 113.01/16.90 | | | | | | | (60) all_56_5 = e2
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | REF_CLOSE: (1), (7), (13), (20), (23), (24), (60) are inconsistent
% 113.01/16.90 | | | | | | | by sub-proof #434.
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | Case 2:
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | (61) all_54_7 = e1 | all_54_7 = e0
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | BETA: splitting (61) gives:
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | | Case 1:
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | (62) all_54_7 = e1
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | COMBINE_EQS: (34), (62) imply:
% 113.01/16.90 | | | | | | | | (63) all_6_0 = e1
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | SIMP: (63) implies:
% 113.01/16.90 | | | | | | | | (64) all_6_0 = e1
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | REDUCE: (38), (64) imply:
% 113.01/16.90 | | | | | | | | (65) $false
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | CLOSE: (65) is inconsistent.
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | Case 2:
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | (66) all_54_7 = e0
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | COMBINE_EQS: (34), (66) imply:
% 113.01/16.90 | | | | | | | | (67) all_6_0 = e0
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | SIMP: (67) implies:
% 113.01/16.90 | | | | | | | | (68) all_6_0 = e0
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | REDUCE: (56), (68) imply:
% 113.01/16.90 | | | | | | | | (69) $false
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | | CLOSE: (69) is inconsistent.
% 113.01/16.90 | | | | | | | |
% 113.01/16.90 | | | | | | | End of split
% 113.01/16.90 | | | | | | |
% 113.01/16.90 | | | | | | End of split
% 113.01/16.90 | | | | | |
% 113.01/16.90 | | | | | End of split
% 113.01/16.90 | | | | |
% 113.01/16.90 | | | | End of split
% 113.01/16.90 | | | |
% 113.01/16.90 | | | End of split
% 113.01/16.90 | | |
% 113.01/16.90 | | End of split
% 113.01/16.90 | |
% 113.01/16.90 | End of split
% 113.01/16.90 |
% 113.01/16.90 End of proof
% 113.01/16.90
% 113.01/16.90 Sub-proof #46 shows that the following formulas are inconsistent:
% 113.01/16.90 ----------------------------------------------------------------
% 113.01/16.91 (1) ~ (all_52_8 = all_10_2)
% 113.01/16.91 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.01/16.91 (3) all_54_2 = all_52_8
% 113.01/16.91 (4) all_58_7 = all_52_6
% 113.01/16.91 (5) ~ (all_52_8 = all_52_11)
% 113.01/16.91 (6) ~ (all_52_9 = all_8_2)
% 113.01/16.91 (7) ~ (all_4_2 = e0)
% 113.01/16.91 (8) op(e3, e2) = all_52_4
% 113.01/16.91 (9) all_56_14 = all_6_2
% 113.01/16.91 (10) all_56_3 = all_52_1
% 113.01/16.91 (11) all_54_0 = all_10_2
% 113.01/16.91 (12) all_54_3 = all_52_12
% 113.01/16.91 (13) op(e0, e2) = all_52_7
% 113.01/16.91 (14) all_56_11 = all_52_11
% 113.01/16.91 (15) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.01/16.91 (16) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.91 (17) ~ (all_52_12 = all_10_2)
% 113.01/16.91 (18) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.01/16.91 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.91 (20) all_56_12 = all_10_2
% 113.01/16.91 (21) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.01/16.91 (22) all_54_14 = all_52_11
% 113.01/16.91 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.91 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.91 (25) all_54_10 = all_6_2
% 113.01/16.91 (26) op(e3, e0) = all_52_12
% 113.01/16.91 (27) all_58_4 = all_52_8
% 113.01/16.91 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.01/16.91 (29) ~ (all_52_4 = all_52_7)
% 113.01/16.91 (30) all_56_2 = all_52_12
% 113.01/16.91 (31) all_58_3 = all_8_2
% 113.01/16.91 (32) ~ (all_10_0 = e2)
% 113.01/16.91 (33) op(e3, e1) = all_52_8
% 113.01/16.91 (34) op(all_10_1, all_10_2) = all_10_0
% 113.01/16.91 (35) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.01/16.91 (36) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.01/16.91 (37) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.01/16.91 (38) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.01/16.91 (39) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.91 (40) ~ (all_56_15 = e1)
% 113.01/16.91 (41) all_58_5 = all_52_9
% 113.01/16.91 (42) all_56_9 = all_52_3
% 113.01/16.91 (43) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.01/16.91 (44) all_58_15 = all_4_2
% 113.01/16.91 (45) all_58_2 = all_52_1
% 113.01/16.91 (46) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.01/16.91 (47) ~ (all_10_2 = e3)
% 113.01/16.91 (48) all_58_13 = all_52_7
% 113.01/16.91 (49) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.01/16.91 (50) ~ (all_52_1 = all_10_2)
% 113.01/16.91 (51) all_54_5 = all_8_2
% 113.01/16.91 (52) all_56_15 = all_4_2
% 113.01/16.91 (53) all_58_10 = all_52_13
% 113.01/16.91 (54) ~ (all_52_11 = all_4_2)
% 113.01/16.91 (55) op(e3, all_10_2) = all_10_1
% 113.01/16.91 (56) ~ (all_10_1 = e2)
% 113.01/16.91 (57) all_58_1 = all_52_4
% 113.01/16.91 (58) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.01/16.91 (59) ~ (all_52_9 = all_52_11)
% 113.01/16.91 (60) all_58_14 = all_52_11
% 113.01/16.91 (61) all_54_1 = all_52_4
% 113.01/16.91 (62) all_56_13 = all_8_2
% 113.01/16.91 (63) op(e0, e1) = all_52_11
% 113.01/16.91 (64) ~ (all_52_1 = all_8_2)
% 113.01/16.91 (65) ~ (all_8_2 = e2)
% 113.01/16.91 (66) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.01/16.91 (67) all_56_7 = all_52_6
% 113.01/16.91 (68) all_56_1 = all_52_8
% 113.01/16.91 (69) all_58_8 = all_6_2
% 113.01/16.91 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.01/16.91 (71) ~ (all_10_0 = e1)
% 113.01/16.91 (72) all_56_4 = all_52_9
% 113.01/16.91 (73) all_56_5 = all_52_13
% 113.01/16.91 (74) ~ (all_52_6 = all_6_2)
% 113.01/16.91 (75) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.01/16.91 (76) ~ (all_52_13 = all_4_2)
% 113.01/16.91 (77) all_58_12 = all_52_3
% 113.01/16.91 (78) ~ (all_52_12 = all_4_2)
% 113.01/16.91 (79) ~ (all_52_8 = all_52_12)
% 113.01/16.91 (80) ~ (all_52_4 = all_10_2)
% 113.01/16.91 (81) ~ (all_10_1 = e1)
% 113.01/16.91 (82) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.01/16.91 (83) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.01/16.91 (84) all_56_0 = all_52_4
% 113.01/16.91 (85) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 113.01/16.91 (86) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.01/16.91 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.01/16.91 (87) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.01/16.91 (88) all_54_15 = all_4_2
% 113.01/16.91 (89) ~ (all_6_2 = e1)
% 113.01/16.91 (90) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.01/16.91
% 113.01/16.91 Begin of proof
% 113.01/16.91 |
% 113.01/16.91 | REDUCE: (40), (52) imply:
% 113.01/16.91 | (91) ~ (all_4_2 = e1)
% 113.01/16.91 |
% 113.01/16.91 | BETA: splitting (49) gives:
% 113.01/16.91 |
% 113.01/16.91 | Case 1:
% 113.01/16.91 | |
% 113.01/16.91 | | (92) ~ (all_56_12 = e2)
% 113.01/16.91 | |
% 113.01/16.91 | | REDUCE: (20), (92) imply:
% 113.01/16.91 | | (93) ~ (all_10_2 = e2)
% 113.01/16.91 | |
% 113.01/16.91 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 113.01/16.91 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 113.01/16.91 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 113.01/16.91 | | (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 113.01/16.91 | | (47), (48), (50), (51), (53), (54), (55), (56), (57), (58), (59),
% 113.01/16.91 | | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 113.01/16.91 | | (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 113.01/16.91 | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (93)
% 113.01/16.91 | | are inconsistent by sub-proof #280.
% 113.01/16.91 | |
% 113.01/16.91 | Case 2:
% 113.01/16.91 | |
% 113.01/16.91 | | (94) all_56_12 = e2
% 113.01/16.91 | |
% 113.01/16.91 | | COMBINE_EQS: (20), (94) imply:
% 113.01/16.91 | | (95) all_10_2 = e2
% 113.01/16.91 | |
% 113.01/16.91 | | SIMP: (95) implies:
% 113.01/16.91 | | (96) all_10_2 = e2
% 113.01/16.91 | |
% 113.01/16.91 | | REF_CLOSE: (4), (7), (8), (9), (13), (14), (18), (21), (23), (24), (25),
% 113.01/16.91 | | (29), (31), (32), (34), (35), (36), (39), (41), (42), (43), (44),
% 113.01/16.91 | | (45), (48), (50), (53), (55), (57), (60), (61), (62), (65), (66),
% 113.01/16.91 | | (67), (71), (72), (73), (74), (77), (80), (81), (83), (84), (85),
% 113.01/16.91 | | (86), (87), (89), (94), (96) are inconsistent by sub-proof #425.
% 113.01/16.91 | |
% 113.01/16.91 | End of split
% 113.01/16.91 |
% 113.01/16.91 End of proof
% 113.01/16.91
% 113.01/16.91 Sub-proof #47 shows that the following formulas are inconsistent:
% 113.01/16.91 ----------------------------------------------------------------
% 113.01/16.91 (1) ~ (all_52_8 = all_10_2)
% 113.01/16.91 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.01/16.91 (3) ~ (all_52_2 = all_10_2)
% 113.01/16.91 (4) ~ (all_52_6 = all_52_14)
% 113.01/16.91 (5) all_54_2 = all_52_8
% 113.01/16.91 (6) all_58_7 = all_52_6
% 113.01/16.91 (7) ~ (all_52_8 = all_52_11)
% 113.01/16.91 (8) ~ (all_52_9 = all_8_2)
% 113.01/16.91 (9) all_28_1 = all_6_1
% 113.01/16.91 (10) ~ (all_4_2 = e0)
% 113.01/16.91 (11) op(e3, e2) = all_52_4
% 113.01/16.91 (12) all_56_14 = all_6_2
% 113.01/16.91 (13) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 113.01/16.91 (14) all_56_3 = all_52_1
% 113.01/16.91 (15) all_54_0 = all_10_2
% 113.01/16.91 (16) all_54_3 = all_52_12
% 113.01/16.91 (17) op(e0, e2) = all_52_7
% 113.01/16.91 (18) all_50_0 = e2
% 113.01/16.91 (19) all_56_11 = all_52_11
% 113.01/16.91 (20) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.01/16.91 (21) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.01/16.91 (22) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.01/16.91 (23) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.91 (24) ~ (all_52_12 = all_10_2)
% 113.01/16.91 (25) ~ (e3 = e1)
% 113.01/16.91 (26) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.01/16.91 (27) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 113.01/16.91 (28) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.91 (29) all_56_12 = all_10_2
% 113.01/16.91 (30) all_58_0 = all_10_2
% 113.01/16.91 (31) all_54_11 = all_52_14
% 113.01/16.91 (32) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.01/16.91 (33) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.01/16.91 (34) ~ (all_52_14 = all_6_2)
% 113.01/16.91 (35) all_56_10 = all_52_7
% 113.01/16.91 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.91 (37) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.01/16.91 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.91 (39) all_54_8 = all_52_2
% 113.01/16.91 (40) ~ (all_52_2 = all_6_2)
% 113.01/16.91 (41) ~ (all_52_1 = all_52_9)
% 113.01/16.91 (42) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.01/16.91 (43) all_54_10 = all_6_2
% 113.01/16.91 (44) op(e3, e0) = all_52_12
% 113.01/16.91 (45) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.01/16.91 (46) ~ (all_52_8 = all_6_2)
% 113.01/16.91 (47) all_58_4 = all_52_8
% 113.01/16.91 (48) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.01/16.91 (49) all_50_1 = all_10_1
% 113.01/16.91 (50) ~ (all_52_4 = all_52_7)
% 113.01/16.91 (51) all_56_2 = all_52_12
% 113.01/16.91 (52) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.01/16.91 (53) all_58_3 = all_8_2
% 113.01/16.91 (54) all_58_11 = all_52_14
% 113.01/16.91 (55) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.01/16.91 (56) ~ (all_52_2 = all_52_3)
% 113.01/16.91 (57) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.01/16.91 (58) ~ (all_52_11 = all_6_2)
% 113.01/16.91 (59) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.01/16.91 (60) op(e2, e3) = all_52_1
% 113.01/16.91 (61) all_28_2 = all_6_2
% 113.01/16.91 (62) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.01/16.91 (63) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.01/16.91 (64) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.01/16.91 (65) all_50_2 = all_10_2
% 113.01/16.91 (66) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.91 (67) ~ (all_52_7 = all_8_2)
% 113.01/16.91 (68) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.01/16.91 (69) ~ (all_52_4 = all_8_2)
% 113.01/16.91 (70) op(e1, e0) = all_52_14
% 113.01/16.91 (71) all_58_5 = all_52_9
% 113.01/16.91 (72) all_56_9 = all_52_3
% 113.01/16.91 (73) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.01/16.91 (74) op(e1, all_6_2) = all_6_1
% 113.01/16.91 (75) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.01/16.92 (76) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.01/16.92 (77) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.01/16.92 (78) all_58_15 = all_4_2
% 113.01/16.92 (79) all_58_2 = all_52_1
% 113.01/16.92 (80) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.01/16.92 (81) ~ (all_52_1 = all_52_13)
% 113.01/16.92 (82) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.01/16.92 (83) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.01/16.92 (84) ~ (all_10_2 = e3)
% 113.01/16.92 (85) ~ (all_52_12 = all_52_13)
% 113.01/16.92 (86) all_58_13 = all_52_7
% 113.01/16.92 (87) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.01/16.92 (88) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.01/16.92 (89) ~ (all_52_14 = all_4_2)
% 113.01/16.92 (90) all_58_6 = all_52_2
% 113.01/16.92 (91) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.01/16.92 (92) ~ (all_52_1 = all_10_2)
% 113.01/16.92 (93) all_54_5 = all_8_2
% 113.01/16.92 (94) all_56_15 = all_4_2
% 113.01/16.92 (95) all_58_10 = all_52_13
% 113.01/16.92 (96) ~ (all_52_13 = all_8_2)
% 113.01/16.92 (97) ~ (all_52_11 = all_4_2)
% 113.01/16.92 (98) op(e3, all_10_2) = all_10_1
% 113.01/16.92 (99) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.01/16.92 (100) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.01/16.92 (101) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 113.01/16.92 (102) all_58_1 = all_52_4
% 113.01/16.92 (103) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.01/16.92 (104) ~ (all_52_9 = all_52_11)
% 113.01/16.92 (105) all_58_14 = all_52_11
% 113.01/16.92 (106) all_56_13 = all_8_2
% 113.01/16.92 (107) ~ (all_52_1 = all_8_2)
% 113.01/16.92 (108) ~ (all_8_2 = e2)
% 113.01/16.92 (109) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.01/16.92 (110) ~ (all_52_7 = all_52_11)
% 113.01/16.92 (111) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.01/16.92 (112) all_56_7 = all_52_6
% 113.01/16.92 (113) ~ (all_52_9 = all_6_2)
% 113.01/16.92 (114) ~ (all_52_1 = all_52_2)
% 113.01/16.92 (115) ~ (all_52_1 = all_52_3)
% 113.01/16.92 (116) all_56_1 = all_52_8
% 113.01/16.92 (117) op(e0, all_4_2) = all_4_1
% 113.01/16.92 (118) all_58_8 = all_6_2
% 113.01/16.92 (119) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.01/16.92 (120) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.01/16.92 (121) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.01/16.92 (122) all_56_4 = all_52_9
% 113.01/16.92 (123) all_58_9 = all_52_12
% 113.01/16.92 (124) all_56_5 = all_52_13
% 113.01/16.92 (125) op(e2, e1) = all_52_9
% 113.01/16.92 (126) ~ (all_52_3 = all_4_2)
% 113.01/16.92 (127) ~ (all_52_6 = all_6_2)
% 113.01/16.92 (128) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.01/16.92 (129) all_56_6 = all_52_2
% 113.01/16.92 (130) ~ (all_52_13 = all_4_2)
% 113.01/16.92 (131) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.01/16.92 (132) all_58_12 = all_52_3
% 113.01/16.92 (133) ~ (all_52_2 = all_52_14)
% 113.01/16.92 (134) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.01/16.92 (135) ~ (all_52_8 = all_52_9)
% 113.01/16.92 (136) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.01/16.92 (137) op(e2, e0) = all_52_13
% 113.01/16.92 (138) ~ (all_52_12 = all_4_2)
% 113.01/16.92 (139) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.01/16.92 (140) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.01/16.92 (141) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.01/16.92 (142) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.01/16.92 (143) all_56_8 = all_52_14
% 113.01/16.92 (144) op(all_10_1, all_10_2) = e2
% 113.01/16.92 (145) ~ (all_52_4 = all_10_2)
% 113.01/16.92 (146) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.01/16.92 (147) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.01/16.92 (148) all_56_0 = all_52_4
% 113.01/16.92 (149) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.01/16.92 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.01/16.92 (150) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 113.01/16.92 (151) all_54_4 = all_52_1
% 113.01/16.92 (152) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.01/16.92 (153) all_54_15 = all_4_2
% 113.01/16.92 (154) op(e2, all_8_2) = e1
% 113.01/16.92 (155) ~ (all_6_2 = e1)
% 113.01/16.92 (156) ~ (all_6_1 = e2)
% 113.01/16.92 (157) ~ (all_52_6 = all_52_7)
% 113.01/16.92 (158) all_54_12 = all_52_3
% 113.01/16.92 (159) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.01/16.92 (160) ~ (e1 = e0)
% 113.01/16.92
% 113.01/16.92 Begin of proof
% 113.01/16.92 |
% 113.01/16.92 | BETA: splitting (27) gives:
% 113.01/16.92 |
% 113.01/16.92 | Case 1:
% 113.01/16.92 | |
% 113.01/16.92 | | (161) ~ (all_50_0 = e2)
% 113.01/16.92 | |
% 113.01/16.92 | | REDUCE: (18), (161) imply:
% 113.01/16.92 | | (162) $false
% 113.01/16.92 | |
% 113.01/16.92 | | CLOSE: (162) is inconsistent.
% 113.01/16.92 | |
% 113.01/16.92 | Case 2:
% 113.01/16.92 | |
% 113.01/16.92 | | (163) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 113.01/16.92 | |
% 113.01/16.92 | | BETA: splitting (87) gives:
% 113.01/16.92 | |
% 113.01/16.92 | | Case 1:
% 113.01/16.92 | | |
% 113.01/16.92 | | | (164) ~ (all_56_14 = e2)
% 113.01/16.92 | | |
% 113.01/16.92 | | | REDUCE: (12), (164) imply:
% 113.01/16.92 | | | (165) ~ (all_6_2 = e2)
% 113.01/16.92 | | |
% 113.01/16.92 | | | BETA: splitting (88) gives:
% 113.01/16.92 | | |
% 113.01/16.92 | | | Case 1:
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | (166) ~ (all_56_12 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (29), (166) imply:
% 113.01/16.92 | | | | (167) ~ (all_10_2 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | BETA: splitting (73) gives:
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | Case 1:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | (168) ~ (all_56_15 = e1)
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | REDUCE: (94), (168) imply:
% 113.01/16.92 | | | | | (169) ~ (all_4_2 = e1)
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | BETA: splitting (146) gives:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | Case 1:
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | (170) ~ (all_56_12 = e1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (29), (170) imply:
% 113.01/16.92 | | | | | | (171) ~ (all_10_2 = e1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REF_CLOSE: (2), (15), (16), (23), (24), (29), (38), (44), (49),
% 113.01/16.92 | | | | | | (51), (54), (65), (75), (78), (82), (84), (85), (95),
% 113.01/16.92 | | | | | | (98), (119), (123), (137), (143), (144), (163), (167),
% 113.01/16.92 | | | | | | (169), (171) are inconsistent by sub-proof #168.
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | Case 2:
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | (172) all_56_12 = e1
% 113.01/16.92 | | | | | | (173) ~ (all_56_11 = e0)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | COMBINE_EQS: (29), (172) imply:
% 113.01/16.92 | | | | | | (174) all_10_2 = e1
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | SIMP: (174) implies:
% 113.01/16.92 | | | | | | (175) all_10_2 = e1
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REF_CLOSE: (8), (10), (14), (19), (21), (28), (30), (35), (37),
% 113.01/16.92 | | | | | | (38), (42), (47), (48), (51), (53), (55), (59), (60),
% 113.01/16.92 | | | | | | (63), (67), (69), (71), (72), (78), (79), (80), (83),
% 113.01/16.92 | | | | | | (84), (86), (91), (93), (94), (95), (96), (97), (101),
% 113.01/16.92 | | | | | | (102), (103), (104), (105), (106), (107), (108), (116),
% 113.01/16.92 | | | | | | (120), (122), (123), (124), (125), (130), (131), (132),
% 113.01/16.92 | | | | | | (135), (137), (138), (139), (140), (142), (147), (148),
% 113.01/16.92 | | | | | | (149), (153), (154), (160), (169), (172), (173), (175)
% 113.01/16.92 | | | | | | are inconsistent by sub-proof #74.
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | End of split
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | Case 2:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | (176) all_56_15 = e1
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | REF_CLOSE: (1), (6), (8), (9), (12), (13), (14), (15), (28), (29),
% 113.01/16.92 | | | | | (30), (31), (33), (34), (36), (38), (41), (43), (47), (52),
% 113.01/16.92 | | | | | (53), (54), (55), (60), (61), (62), (66), (70), (71), (74),
% 113.01/16.92 | | | | | (76), (79), (81), (84), (89), (90), (92), (93), (94), (95),
% 113.01/16.92 | | | | | (96), (97), (100), (105), (106), (107), (108), (111),
% 113.01/16.92 | | | | | (112), (118), (119), (121), (122), (124), (129), (134),
% 113.01/16.92 | | | | | (140), (141), (142), (147), (151), (154), (155), (156),
% 113.01/16.92 | | | | | (165), (176) are inconsistent by sub-proof #64.
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | End of split
% 113.01/16.92 | | | |
% 113.01/16.92 | | | Case 2:
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | (177) all_56_12 = e2
% 113.01/16.92 | | | | (178) ~ (all_56_10 = e0)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | COMBINE_EQS: (29), (177) imply:
% 113.01/16.92 | | | | (179) all_10_2 = e2
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | SIMP: (179) implies:
% 113.01/16.92 | | | | (180) all_10_2 = e2
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | COMBINE_EQS: (30), (180) imply:
% 113.01/16.92 | | | | (181) all_58_0 = e2
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (35), (178) imply:
% 113.01/16.92 | | | | (182) ~ (all_52_7 = e0)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (92), (180) imply:
% 113.01/16.92 | | | | (183) ~ (all_52_1 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (3), (180) imply:
% 113.01/16.92 | | | | (184) ~ (all_52_2 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (145), (180) imply:
% 113.01/16.92 | | | | (185) ~ (all_52_4 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (1), (180) imply:
% 113.01/16.92 | | | | (186) ~ (all_52_8 = e2)
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (144), (180) imply:
% 113.01/16.92 | | | | (187) op(all_10_1, e2) = e2
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | REDUCE: (98), (180) imply:
% 113.01/16.92 | | | | (188) op(e3, e2) = all_10_1
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | BETA: splitting (152) gives:
% 113.01/16.92 | | | |
% 113.01/16.92 | | | | Case 1:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | (189) ~ (all_56_0 = e3)
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | REDUCE: (148), (189) imply:
% 113.01/16.92 | | | | | (190) ~ (all_52_4 = e3)
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | BETA: splitting (76) gives:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | Case 1:
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | (191) ~ (all_56_7 = e1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (112), (191) imply:
% 113.01/16.92 | | | | | | (192) ~ (all_52_6 = e1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | GROUND_INST: instantiating (38) with all_52_4, all_10_1, e2, e3,
% 113.01/16.92 | | | | | | simplifying with (11), (188) gives:
% 113.01/16.92 | | | | | | (193) all_52_4 = all_10_1
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | COMBINE_EQS: (102), (193) imply:
% 113.01/16.92 | | | | | | (194) all_58_1 = all_10_1
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (50), (193) imply:
% 113.01/16.92 | | | | | | (195) ~ (all_52_7 = all_10_1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | SIMP: (195) implies:
% 113.01/16.92 | | | | | | (196) ~ (all_52_7 = all_10_1)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (69), (193) imply:
% 113.01/16.92 | | | | | | (197) ~ (all_10_1 = all_8_2)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (185), (193) imply:
% 113.01/16.92 | | | | | | (198) ~ (all_10_1 = e2)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | BETA: splitting (83) gives:
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | Case 1:
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | (199) ~ (all_56_13 = e3)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | REDUCE: (106), (199) imply:
% 113.01/16.92 | | | | | | | (200) ~ (all_8_2 = e3)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | BETA: splitting (103) gives:
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | Case 1:
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | | (201) ~ (all_56_2 = e3)
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | | REDUCE: (51), (201) imply:
% 113.01/16.92 | | | | | | | | (202) ~ (all_52_12 = e3)
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | | REF_CLOSE: (1), (9), (12), (13), (22), (30), (31), (34), (36),
% 113.01/16.92 | | | | | | | | (38), (43), (46), (47), (61), (70), (74), (84),
% 113.01/16.92 | | | | | | | | (102), (121), (123), (142), (143), (155), (156),
% 113.01/16.92 | | | | | | | | (165), (190), (202) are inconsistent by sub-proof
% 113.01/16.92 | | | | | | | | #251.
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | Case 2:
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | | (203) all_56_2 = e3
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | | REF_CLOSE: (8), (28), (38), (93), (103), (106), (108), (125),
% 113.01/16.92 | | | | | | | | (154), (200), (203) are inconsistent by sub-proof
% 113.01/16.92 | | | | | | | | #107.
% 113.01/16.92 | | | | | | | |
% 113.01/16.92 | | | | | | | End of split
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | Case 2:
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | (204) all_56_13 = e3
% 113.01/16.92 | | | | | | | (205) ~ (all_56_9 = e0)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | COMBINE_EQS: (106), (204) imply:
% 113.01/16.92 | | | | | | | (206) all_8_2 = e3
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | SIMP: (206) implies:
% 113.01/16.92 | | | | | | | (207) all_8_2 = e3
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | COMBINE_EQS: (53), (207) imply:
% 113.01/16.92 | | | | | | | (208) all_58_3 = e3
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | REDUCE: (72), (205) imply:
% 113.01/16.92 | | | | | | | (209) ~ (all_52_3 = e0)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | REDUCE: (107), (207) imply:
% 113.01/16.92 | | | | | | | (210) ~ (all_52_1 = e3)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | REDUCE: (197), (207) imply:
% 113.01/16.92 | | | | | | | (211) ~ (all_10_1 = e3)
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (12), (17), (19), (20),
% 113.01/16.92 | | | | | | | (26), (28), (32), (33), (36), (38), (39), (40), (43),
% 113.01/16.92 | | | | | | | (45), (46), (47), (48), (51), (53), (54), (56), (57),
% 113.01/16.92 | | | | | | | (58), (59), (64), (66), (68), (71), (72), (73), (77),
% 113.01/16.92 | | | | | | | (78), (79), (82), (83), (86), (89), (90), (93), (94),
% 113.01/16.92 | | | | | | | (95), (97), (99), (103), (105), (106), (108), (109),
% 113.01/16.92 | | | | | | | (110), (114), (115), (117), (118), (122), (123), (124),
% 113.01/16.92 | | | | | | | (125), (126), (127), (128), (129), (130), (132), (133),
% 113.01/16.92 | | | | | | | (136), (138), (142), (147), (149), (151), (153), (154),
% 113.01/16.92 | | | | | | | (155), (157), (158), (159), (165), (181), (182), (183),
% 113.01/16.92 | | | | | | | (184), (186), (187), (192), (194), (196), (198), (204),
% 113.01/16.92 | | | | | | | (208), (209), (210), (211) are inconsistent by
% 113.01/16.92 | | | | | | | sub-proof #50.
% 113.01/16.92 | | | | | | |
% 113.01/16.92 | | | | | | End of split
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | Case 2:
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | (212) ~ (all_56_12 = e2)
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | REDUCE: (177), (212) imply:
% 113.01/16.92 | | | | | | (213) $false
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | | CLOSE: (213) is inconsistent.
% 113.01/16.92 | | | | | |
% 113.01/16.92 | | | | | End of split
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | Case 2:
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | (214) ~ (all_56_12 = e2)
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | REDUCE: (177), (214) imply:
% 113.01/16.92 | | | | | (215) $false
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | | CLOSE: (215) is inconsistent.
% 113.01/16.92 | | | | |
% 113.01/16.92 | | | | End of split
% 113.01/16.92 | | | |
% 113.01/16.93 | | | End of split
% 113.01/16.93 | | |
% 113.01/16.93 | | Case 2:
% 113.01/16.93 | | |
% 113.01/16.93 | | | (216) all_56_14 = e2
% 113.01/16.93 | | | (217) ~ (all_56_10 = e0)
% 113.01/16.93 | | |
% 113.01/16.93 | | | REF_CLOSE: (8), (10), (12), (14), (19), (21), (25), (28), (30), (35),
% 113.01/16.93 | | | (37), (38), (42), (47), (48), (51), (53), (55), (58), (59),
% 113.01/16.93 | | | (60), (71), (72), (78), (79), (83), (84), (86), (91), (93),
% 113.01/16.93 | | | (94), (95), (96), (102), (103), (104), (105), (106), (107),
% 113.01/16.93 | | | (108), (113), (116), (120), (123), (124), (125), (130), (131),
% 113.01/16.93 | | | (132), (135), (137), (140), (142), (147), (148), (149), (150),
% 113.01/16.93 | | | (153), (154), (160), (216), (217) are inconsistent by sub-proof
% 113.01/16.93 | | | #104.
% 113.01/16.93 | | |
% 113.01/16.93 | | End of split
% 113.01/16.93 | |
% 113.01/16.93 | End of split
% 113.01/16.93 |
% 113.01/16.93 End of proof
% 113.01/16.93
% 113.01/16.93 Sub-proof #48 shows that the following formulas are inconsistent:
% 113.01/16.93 ----------------------------------------------------------------
% 113.01/16.93 (1) ~ (all_52_8 = all_10_2)
% 113.01/16.93 (2) ~ (all_52_2 = all_10_2)
% 113.01/16.93 (3) ~ (all_52_6 = all_52_14)
% 113.01/16.93 (4) all_54_2 = all_52_8
% 113.01/16.93 (5) all_58_7 = all_52_6
% 113.01/16.93 (6) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.01/16.93 (7) ~ (all_52_8 = all_52_11)
% 113.01/16.93 (8) ~ (all_52_9 = all_8_2)
% 113.01/16.93 (9) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 113.01/16.93 (10) ~ (all_52_13 = all_52_14)
% 113.01/16.93 (11) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 113.01/16.93 (12) ~ (all_4_2 = e0)
% 113.01/16.93 (13) op(e3, e2) = all_52_4
% 113.01/16.93 (14) all_56_14 = all_6_2
% 113.01/16.93 (15) all_56_3 = all_52_1
% 113.01/16.93 (16) all_54_0 = all_10_2
% 113.01/16.93 (17) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.01/16.93 (18) all_54_3 = all_52_12
% 113.01/16.93 (19) ~ (all_52_2 = all_52_6)
% 113.01/16.93 (20) ~ (all_52_12 = all_52_14)
% 113.01/16.93 (21) op(e0, e2) = all_52_7
% 113.01/16.93 (22) ~ (all_52_7 = all_4_2)
% 113.01/16.93 (23) all_56_11 = all_52_11
% 113.01/16.93 (24) ~ (all_4_0 = e1)
% 113.01/16.93 (25) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.01/16.93 (26) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.01/16.93 (27) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.01/16.93 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.01/16.93 (29) ~ (all_52_12 = all_10_2)
% 113.01/16.93 (30) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 113.01/16.93 (31) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.01/16.93 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.01/16.93 (33) all_56_12 = all_10_2
% 113.01/16.93 (34) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.01/16.93 (35) all_58_0 = all_10_2
% 113.01/16.93 (36) all_54_11 = all_52_14
% 113.01/16.93 (37) all_54_13 = all_52_7
% 113.01/16.93 (38) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.01/16.93 (39) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.01/16.93 (40) ~ (all_52_14 = all_6_2)
% 113.01/16.93 (41) all_56_10 = all_52_7
% 113.01/16.93 (42) all_54_14 = all_52_11
% 113.01/16.93 (43) op(all_4_1, all_4_2) = all_4_0
% 113.01/16.93 (44) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.01/16.93 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.01/16.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.01/16.93 (46) all_54_8 = all_52_2
% 113.01/16.93 (47) ~ (all_52_2 = all_6_2)
% 113.01/16.93 (48) ~ (all_52_1 = all_52_9)
% 113.01/16.93 (49) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.01/16.93 (50) all_54_10 = all_6_2
% 113.01/16.93 (51) ~ (e2 = e1)
% 113.01/16.93 (52) op(e1, all_8_2) = e3
% 113.01/16.93 (53) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.01/16.93 (54) ~ (all_52_8 = all_6_2)
% 113.01/16.93 (55) all_58_4 = all_52_8
% 113.01/16.93 (56) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.01/16.93 (57) ~ (all_52_4 = all_52_7)
% 113.01/16.93 (58) all_56_2 = all_52_12
% 113.01/16.93 (59) all_58_3 = all_8_2
% 113.01/16.93 (60) all_54_6 = all_52_9
% 113.01/16.93 (61) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 113.01/16.93 (62) all_58_11 = all_52_14
% 113.01/16.93 (63) ~ (all_52_2 = all_52_3)
% 113.01/16.93 (64) ~ (all_8_2 = e0)
% 113.01/16.93 (65) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.01/16.93 (66) ~ (all_52_11 = all_6_2)
% 113.01/16.93 (67) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.01/16.93 (68) op(e2, e3) = all_52_1
% 113.01/16.93 (69) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.01/16.93 (70) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.01/16.93 (71) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.01/16.93 (72) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.01/16.93 (73) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.01/16.93 (74) ~ (all_52_7 = all_8_2)
% 113.01/16.93 (75) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.01/16.93 (76) ~ (all_52_4 = all_8_2)
% 113.01/16.93 (77) all_58_5 = all_52_9
% 113.01/16.93 (78) ~ (all_52_9 = all_52_13)
% 113.01/16.93 (79) all_56_9 = all_52_3
% 113.01/16.93 (80) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.01/16.93 (81) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.01/16.93 (82) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.01/16.93 (83) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.01/16.93 (84) all_58_15 = all_4_2
% 113.01/16.93 (85) all_58_2 = all_52_1
% 113.01/16.93 (86) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.01/16.93 (87) ~ (all_52_1 = all_52_13)
% 113.01/16.93 (88) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.01/16.93 (89) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.01/16.93 (90) op(e0, e3) = all_52_3
% 113.01/16.93 (91) ~ (all_10_2 = e3)
% 113.01/16.93 (92) all_58_13 = all_52_7
% 113.01/16.93 (93) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.01/16.93 (94) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.01/16.93 (95) ~ (all_52_14 = all_4_2)
% 113.01/16.93 (96) all_58_6 = all_52_2
% 113.01/16.93 (97) ~ (all_52_1 = all_10_2)
% 113.01/16.93 (98) all_54_5 = all_8_2
% 113.01/16.93 (99) all_56_15 = all_4_2
% 113.01/16.93 (100) all_58_10 = all_52_13
% 113.01/16.93 (101) ~ (all_52_13 = all_8_2)
% 113.01/16.93 (102) ~ (all_52_11 = all_4_2)
% 113.01/16.93 (103) op(e3, all_10_2) = all_10_1
% 113.01/16.93 (104) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.01/16.93 (105) ~ (all_52_6 = all_8_2)
% 113.01/16.93 (106) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.01/16.93 (107) all_58_1 = all_52_4
% 113.01/16.93 (108) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.01/16.93 (109) all_58_14 = all_52_11
% 113.01/16.93 (110) all_54_1 = all_52_4
% 113.01/16.93 (111) all_56_13 = all_8_2
% 113.01/16.93 (112) ~ (all_52_1 = all_8_2)
% 113.01/16.93 (113) ~ (all_8_2 = e2)
% 113.01/16.93 (114) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.01/16.93 (115) ~ (all_6_2 = e2)
% 113.01/16.93 (116) ~ (all_52_7 = all_52_11)
% 113.01/16.93 (117) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.01/16.93 (118) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.01/16.93 (119) all_56_7 = all_52_6
% 113.01/16.93 (120) ~ (all_52_9 = all_6_2)
% 113.01/16.93 (121) ~ (all_52_4 = all_52_6)
% 113.01/16.93 (122) ~ (all_52_1 = all_52_2)
% 113.01/16.93 (123) ~ (all_52_4 = all_52_12)
% 113.01/16.93 (124) ~ (all_52_1 = all_52_3)
% 113.01/16.93 (125) all_56_1 = all_52_8
% 113.01/16.93 (126) op(e0, all_4_2) = all_4_1
% 113.01/16.93 (127) all_58_8 = all_6_2
% 113.01/16.93 (128) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.01/16.93 (129) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.01/16.93 (130) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.01/16.93 (131) all_56_4 = all_52_9
% 113.01/16.93 (132) all_58_9 = all_52_12
% 113.01/16.93 (133) all_56_5 = all_52_13
% 113.01/16.93 (134) op(e2, e1) = all_52_9
% 113.01/16.93 (135) ~ (all_52_3 = all_4_2)
% 113.01/16.93 (136) ~ (all_52_6 = all_6_2)
% 113.01/16.93 (137) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.01/16.93 (138) all_56_6 = all_52_2
% 113.01/16.93 (139) ~ (all_52_13 = all_4_2)
% 113.01/16.93 (140) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.01/16.93 (141) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.01/16.93 (142) all_58_12 = all_52_3
% 113.01/16.93 (143) ~ (all_52_2 = all_52_14)
% 113.01/16.93 (144) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.01/16.93 (145) ~ (all_52_8 = all_52_9)
% 113.01/16.93 (146) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.01/16.93 (147) ~ (all_52_12 = all_4_2)
% 113.01/16.93 (148) ~ (all_52_3 = all_10_2)
% 113.01/16.93 (149) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.01/16.93 (150) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.01/16.93 (151) op(e1, e1) = all_6_2
% 113.01/16.93 (152) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.01/16.94 (153) all_56_8 = all_52_14
% 113.01/16.94 (154) op(all_10_1, all_10_2) = e2
% 113.01/16.94 (155) ~ (all_52_4 = all_10_2)
% 113.01/16.94 (156) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.01/16.94 (157) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.01/16.94 (158) all_56_0 = all_52_4
% 113.01/16.94 (159) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.01/16.94 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.01/16.94 (160) all_54_4 = all_52_1
% 113.01/16.94 (161) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.01/16.94 (162) all_54_15 = all_4_2
% 113.01/16.94 (163) op(e2, all_8_2) = e1
% 113.01/16.94 (164) ~ (all_6_2 = e1)
% 113.01/16.94 (165) ~ (all_52_6 = all_52_7)
% 113.01/16.94 (166) ~ (all_52_3 = all_52_11)
% 113.01/16.94 (167) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.01/16.94 (168) all_54_12 = all_52_3
% 113.01/16.94 (169) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.01/16.94 (170) ~ (all_52_3 = all_52_7)
% 113.01/16.94
% 113.01/16.94 Begin of proof
% 113.01/16.94 |
% 113.01/16.94 | BETA: splitting (94) gives:
% 113.01/16.94 |
% 113.01/16.94 | Case 1:
% 113.01/16.94 | |
% 113.01/16.94 | | (171) ~ (all_56_12 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (14), (15),
% 113.01/16.94 | | (16), (17), (20), (22), (23), (24), (26), (29), (30), (31), (32),
% 113.01/16.94 | | (33), (34), (35), (36), (37), (39), (40), (41), (42), (43), (44),
% 113.01/16.94 | | (45), (46), (47), (48), (49), (50), (52), (55), (56), (59), (60),
% 113.01/16.94 | | (61), (62), (63), (64), (66), (68), (69), (70), (71), (72), (73),
% 113.01/16.94 | | (74), (75), (77), (78), (79), (81), (83), (84), (85), (86), (87),
% 113.01/16.94 | | (89), (90), (91), (92), (93), (95), (96), (97), (98), (99),
% 113.01/16.94 | | (100), (101), (102), (104), (105), (106), (109), (111), (112),
% 113.01/16.94 | | (113), (116), (117), (119), (120), (122), (124), (125), (126),
% 113.01/16.94 | | (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 113.01/16.94 | | (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 113.01/16.94 | | (146), (148), (149), (150), (151), (153), (156), (157), (159),
% 113.01/16.94 | | (160), (162), (163), (164), (166), (167), (168), (170), (171) are
% 113.01/16.94 | | inconsistent by sub-proof #66.
% 113.01/16.94 | |
% 113.01/16.94 | Case 2:
% 113.01/16.94 | |
% 113.01/16.94 | | (172) all_56_12 = e2
% 113.01/16.94 | | (173) ~ (all_56_10 = e0)
% 113.01/16.94 | |
% 113.01/16.94 | | COMBINE_EQS: (33), (172) imply:
% 113.01/16.94 | | (174) all_10_2 = e2
% 113.01/16.94 | |
% 113.01/16.94 | | SIMP: (174) implies:
% 113.01/16.94 | | (175) all_10_2 = e2
% 113.01/16.94 | |
% 113.01/16.94 | | COMBINE_EQS: (35), (175) imply:
% 113.01/16.94 | | (176) all_58_0 = e2
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (41), (173) imply:
% 113.01/16.94 | | (177) ~ (all_52_7 = e0)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (97), (175) imply:
% 113.01/16.94 | | (178) ~ (all_52_1 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (2), (175) imply:
% 113.01/16.94 | | (179) ~ (all_52_2 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (155), (175) imply:
% 113.01/16.94 | | (180) ~ (all_52_4 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (1), (175) imply:
% 113.01/16.94 | | (181) ~ (all_52_8 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (29), (175) imply:
% 113.01/16.94 | | (182) ~ (all_52_12 = e2)
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (154), (175) imply:
% 113.01/16.94 | | (183) op(all_10_1, e2) = e2
% 113.01/16.94 | |
% 113.01/16.94 | | REDUCE: (103), (175) imply:
% 113.01/16.94 | | (184) op(e3, e2) = all_10_1
% 113.01/16.94 | |
% 113.01/16.94 | | BETA: splitting (161) gives:
% 113.01/16.94 | |
% 113.01/16.94 | | Case 1:
% 113.01/16.94 | | |
% 113.01/16.94 | | | (185) ~ (all_56_0 = e3)
% 113.01/16.94 | | |
% 113.01/16.94 | | | REDUCE: (158), (185) imply:
% 113.01/16.94 | | | (186) ~ (all_52_4 = e3)
% 113.01/16.94 | | |
% 113.01/16.94 | | | BETA: splitting (82) gives:
% 113.01/16.94 | | |
% 113.01/16.94 | | | Case 1:
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | (187) ~ (all_56_7 = e1)
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | REDUCE: (119), (187) imply:
% 113.01/16.94 | | | | (188) ~ (all_52_6 = e1)
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (13), (14), (17), (18),
% 113.01/16.94 | | | | (19), (20), (21), (23), (25), (27), (28), (31), (32), (37),
% 113.01/16.94 | | | | (38), (39), (40), (44), (45), (46), (47), (50), (51), (53),
% 113.01/16.94 | | | | (54), (55), (56), (57), (58), (59), (62), (63), (64), (65),
% 113.01/16.94 | | | | (67), (68), (71), (73), (74), (75), (76), (77), (79), (80),
% 113.01/16.94 | | | | (83), (84), (85), (88), (89), (92), (95), (96), (98), (99),
% 113.01/16.94 | | | | (100), (102), (104), (107), (108), (109), (110), (111),
% 113.01/16.94 | | | | (112), (113), (114), (115), (116), (117), (118), (121),
% 113.01/16.94 | | | | (122), (123), (124), (126), (127), (131), (132), (133),
% 113.01/16.94 | | | | (134), (135), (136), (137), (138), (139), (142), (143),
% 113.01/16.94 | | | | (146), (147), (152), (153), (157), (158), (159), (160),
% 113.01/16.94 | | | | (161), (162), (163), (164), (165), (168), (169), (172),
% 113.01/16.94 | | | | (176), (177), (178), (179), (180), (181), (182), (183),
% 113.01/16.94 | | | | (184), (186), (188) are inconsistent by sub-proof #57.
% 113.01/16.94 | | | |
% 113.01/16.94 | | | Case 2:
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | (189) ~ (all_56_12 = e2)
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | REDUCE: (172), (189) imply:
% 113.01/16.94 | | | | (190) $false
% 113.01/16.94 | | | |
% 113.01/16.94 | | | | CLOSE: (190) is inconsistent.
% 113.01/16.94 | | | |
% 113.01/16.94 | | | End of split
% 113.01/16.94 | | |
% 113.01/16.94 | | Case 2:
% 113.01/16.94 | | |
% 113.01/16.94 | | | (191) ~ (all_56_12 = e2)
% 113.01/16.94 | | |
% 113.01/16.94 | | | REDUCE: (172), (191) imply:
% 113.01/16.94 | | | (192) $false
% 113.01/16.94 | | |
% 113.01/16.94 | | | CLOSE: (192) is inconsistent.
% 113.01/16.94 | | |
% 113.01/16.94 | | End of split
% 113.01/16.94 | |
% 113.01/16.94 | End of split
% 113.01/16.94 |
% 113.01/16.94 End of proof
% 113.01/16.94
% 113.01/16.94 Sub-proof #49 shows that the following formulas are inconsistent:
% 113.01/16.94 ----------------------------------------------------------------
% 113.01/16.94 (1) ~ (all_52_6 = all_52_14)
% 113.01/16.94 (2) all_54_2 = all_52_8
% 113.01/16.94 (3) all_58_7 = all_52_6
% 113.01/16.94 (4) ~ (all_52_8 = all_52_11)
% 113.01/16.94 (5) ~ (all_52_9 = all_8_2)
% 113.01/16.94 (6) ~ (all_52_1 = e2)
% 113.01/16.94 (7) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 113.01/16.94 (8) ~ (all_4_2 = e0)
% 113.01/16.94 (9) op(e3, e2) = all_52_4
% 113.01/16.94 (10) all_56_14 = all_6_2
% 113.01/16.94 (11) op(e1, all_8_2) = all_8_0
% 113.01/16.94 (12) ~ (all_52_2 = all_52_6)
% 113.01/16.94 (13) op(e0, e2) = all_52_7
% 113.01/16.94 (14) ~ (all_52_7 = all_4_2)
% 113.01/16.94 (15) all_56_11 = all_52_11
% 113.16/16.94 (16) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.16/16.94 (17) ~ (e3 = e1)
% 113.16/16.94 (18) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.16/16.94 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.16/16.94 (20) op(all_10_1, e2) = e2
% 113.16/16.94 (21) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.16/16.94 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.16/16.94 (23) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 113.16/16.94 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.16/16.94 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.16/16.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.16/16.94 (26) all_54_8 = all_52_2
% 113.16/16.94 (27) ~ (all_52_2 = all_6_2)
% 113.16/16.94 (28) ~ (all_52_1 = all_52_9)
% 113.16/16.94 (29) all_54_10 = all_6_2
% 113.16/16.94 (30) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.16/16.94 (31) ~ (all_52_8 = all_6_2)
% 113.16/16.94 (32) all_58_4 = all_52_8
% 113.16/16.94 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.16/16.94 (34) ~ (all_52_4 = all_52_7)
% 113.16/16.94 (35) all_56_2 = all_52_12
% 113.16/16.94 (36) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.16/16.94 (37) all_56_12 = e2
% 113.16/16.94 (38) all_58_3 = all_8_2
% 113.16/16.94 (39) all_58_11 = all_52_14
% 113.16/16.94 (40) ~ (all_52_2 = all_52_3)
% 113.16/16.94 (41) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.16/16.94 (42) ~ (all_52_11 = all_6_2)
% 113.16/16.94 (43) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.16/16.94 (44) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.16/16.94 (45) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.16/16.94 (46) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.16/16.94 (47) ~ (all_52_4 = all_8_2)
% 113.16/16.94 (48) all_58_5 = all_52_9
% 113.16/16.94 (49) all_56_9 = all_52_3
% 113.16/16.94 (50) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.16/16.94 (51) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.16/16.94 (52) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.16/16.94 (53) all_58_15 = all_4_2
% 113.16/16.94 (54) all_58_2 = all_52_1
% 113.16/16.94 (55) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.16/16.94 (56) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.16/16.94 (57) all_58_13 = all_52_7
% 113.16/16.94 (58) ~ (all_52_7 = e0)
% 113.16/16.94 (59) ~ (all_52_14 = all_4_2)
% 113.16/16.94 (60) all_58_6 = all_52_2
% 113.16/16.94 (61) all_54_5 = all_8_2
% 113.16/16.94 (62) all_56_15 = all_4_2
% 113.16/16.94 (63) all_58_0 = e2
% 113.16/16.94 (64) all_58_10 = all_52_13
% 113.16/16.94 (65) ~ (all_52_11 = all_4_2)
% 113.16/16.95 (66) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.16/16.95 (67) ~ (all_52_6 = all_8_2)
% 113.16/16.95 (68) all_58_1 = all_52_4
% 113.16/16.95 (69) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.16/16.95 (70) all_58_14 = all_52_11
% 113.16/16.95 (71) all_56_13 = all_8_2
% 113.16/16.95 (72) ~ (all_52_8 = e2)
% 113.16/16.95 (73) ~ (all_52_1 = all_8_2)
% 113.16/16.95 (74) op(e1, all_6_2) = e3
% 113.16/16.95 (75) ~ (all_8_2 = e2)
% 113.16/16.95 (76) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.16/16.95 (77) ~ (all_6_2 = e2)
% 113.16/16.95 (78) ~ (all_52_7 = all_52_11)
% 113.16/16.95 (79) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.16/16.95 (80) all_56_7 = all_52_6
% 113.16/16.95 (81) op(e3, e2) = all_10_1
% 113.16/16.95 (82) ~ (all_52_1 = all_52_2)
% 113.16/16.95 (83) ~ (all_52_1 = all_52_3)
% 113.16/16.95 (84) op(e0, all_4_2) = all_4_1
% 113.16/16.95 (85) all_58_8 = all_6_2
% 113.16/16.95 (86) all_56_4 = all_52_9
% 113.16/16.95 (87) all_58_9 = all_52_12
% 113.16/16.95 (88) all_56_5 = all_52_13
% 113.16/16.95 (89) op(e2, e1) = all_52_9
% 113.16/16.95 (90) ~ (all_52_3 = all_4_2)
% 113.16/16.95 (91) ~ (all_52_6 = all_6_2)
% 113.16/16.95 (92) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.16/16.95 (93) all_56_6 = all_52_2
% 113.16/16.95 (94) ~ (all_52_13 = all_4_2)
% 113.16/16.95 (95) all_58_12 = all_52_3
% 113.16/16.95 (96) ~ (all_52_2 = all_52_14)
% 113.16/16.95 (97) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.16/16.95 (98) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.16/16.95 (99) ~ (all_52_12 = all_4_2)
% 113.16/16.95 (100) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.16/16.95 (101) all_56_8 = all_52_14
% 113.16/16.95 (102) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.16/16.95 (103) all_56_0 = all_52_4
% 113.16/16.95 (104) ~ (all_8_0 = e3)
% 113.16/16.95 (105) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 113.16/16.95 (106) ~ (e3 = e2)
% 113.16/16.95 (107) ~ (all_52_2 = e2)
% 113.16/16.95 (108) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.16/16.95 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.16/16.95 (109) all_54_4 = all_52_1
% 113.16/16.95 (110) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.16/16.95 (111) all_54_15 = all_4_2
% 113.16/16.95 (112) op(e2, all_8_2) = e1
% 113.16/16.95 (113) ~ (all_6_2 = e1)
% 113.16/16.95 (114) ~ (all_52_6 = all_52_7)
% 113.16/16.95 (115) all_54_12 = all_52_3
% 113.16/16.95 (116) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.16/16.95 (117) ~ (all_52_4 = e2)
% 113.16/16.95 (118) ~ (all_52_3 = all_52_7)
% 113.16/16.95
% 113.16/16.95 Begin of proof
% 113.16/16.95 |
% 113.16/16.95 | BETA: splitting (51) gives:
% 113.16/16.95 |
% 113.16/16.95 | Case 1:
% 113.16/16.95 | |
% 113.16/16.95 | | (119) ~ (all_56_7 = e1)
% 113.16/16.95 | |
% 113.16/16.95 | | REDUCE: (80), (119) imply:
% 113.16/16.95 | | (120) ~ (all_52_6 = e1)
% 113.16/16.95 | |
% 113.16/16.95 | | BETA: splitting (110) gives:
% 113.16/16.95 | |
% 113.16/16.95 | | Case 1:
% 113.16/16.95 | | |
% 113.16/16.95 | | | (121) ~ (all_56_0 = e3)
% 113.16/16.95 | | |
% 113.16/16.95 | | | REDUCE: (103), (121) imply:
% 113.16/16.95 | | | (122) ~ (all_52_4 = e3)
% 113.16/16.95 | | |
% 113.16/16.95 | | | GROUND_INST: instantiating (25) with all_52_4, all_10_1, e2, e3,
% 113.16/16.95 | | | simplifying with (9), (81) gives:
% 113.16/16.95 | | | (123) all_52_4 = all_10_1
% 113.16/16.95 | | |
% 113.16/16.95 | | | COMBINE_EQS: (68), (123) imply:
% 113.16/16.95 | | | (124) all_58_1 = all_10_1
% 113.16/16.95 | | |
% 113.16/16.95 | | | REDUCE: (34), (123) imply:
% 113.16/16.95 | | | (125) ~ (all_52_7 = all_10_1)
% 113.16/16.95 | | |
% 113.16/16.95 | | | SIMP: (125) implies:
% 113.16/16.95 | | | (126) ~ (all_52_7 = all_10_1)
% 113.16/16.95 | | |
% 113.16/16.95 | | | REDUCE: (47), (123) imply:
% 113.16/16.95 | | | (127) ~ (all_10_1 = all_8_2)
% 113.16/16.95 | | |
% 113.16/16.95 | | | REDUCE: (122), (123) imply:
% 113.16/16.95 | | | (128) ~ (all_10_1 = e3)
% 113.16/16.95 | | |
% 113.16/16.95 | | | REDUCE: (117), (123) imply:
% 113.19/16.95 | | | (129) ~ (all_10_1 = e2)
% 113.19/16.95 | | |
% 113.19/16.95 | | | BETA: splitting (56) gives:
% 113.19/16.95 | | |
% 113.19/16.95 | | | Case 1:
% 113.19/16.95 | | | |
% 113.19/16.95 | | | | (130) ~ (all_56_13 = e3)
% 113.19/16.95 | | | |
% 113.19/16.95 | | | | REDUCE: (71), (130) imply:
% 113.19/16.95 | | | | (131) ~ (all_8_2 = e3)
% 113.19/16.95 | | | |
% 113.19/16.95 | | | | BETA: splitting (7) gives:
% 113.19/16.95 | | | |
% 113.19/16.95 | | | | Case 1:
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | (132) ~ (all_56_6 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | REDUCE: (93), (132) imply:
% 113.19/16.95 | | | | | (133) ~ (all_52_2 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | BETA: splitting (79) gives:
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | Case 1:
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | (134) all_58_6 = e1
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | REF_CLOSE: (60), (133), (134) are inconsistent by sub-proof #452.
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | Case 2:
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | (135) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | REF_CLOSE: (3), (5), (19), (23), (25), (39), (61), (71), (75), (85),
% 113.19/16.95 | | | | | | (89), (101), (112), (113), (120), (131), (135) are
% 113.19/16.95 | | | | | | inconsistent by sub-proof #53.
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | End of split
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | Case 2:
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | (136) all_56_6 = e1
% 113.19/16.95 | | | | | (137) ~ (all_56_15 = e3)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | COMBINE_EQS: (93), (136) imply:
% 113.19/16.95 | | | | | (138) all_52_2 = e1
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | SIMP: (138) implies:
% 113.19/16.95 | | | | | (139) all_52_2 = e1
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | REDUCE: (62), (137) imply:
% 113.19/16.95 | | | | | (140) ~ (all_4_2 = e3)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | REDUCE: (40), (139) imply:
% 113.19/16.95 | | | | | (141) ~ (all_52_3 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | SIMP: (141) implies:
% 113.19/16.95 | | | | | (142) ~ (all_52_3 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | REDUCE: (12), (139) imply:
% 113.19/16.95 | | | | | (143) ~ (all_52_6 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | REDUCE: (27), (139) imply:
% 113.19/16.95 | | | | | (144) ~ (all_6_2 = e1)
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | BETA: splitting (36) gives:
% 113.19/16.95 | | | | |
% 113.19/16.95 | | | | | Case 1:
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | (145) ~ (all_56_6 = e1)
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | REDUCE: (136), (145) imply:
% 113.19/16.95 | | | | | | (146) $false
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | CLOSE: (146) is inconsistent.
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | Case 2:
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | (147) ~ (all_56_14 = e3)
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | REDUCE: (10), (147) imply:
% 113.19/16.95 | | | | | | (148) ~ (all_6_2 = e3)
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | BETA: splitting (24) gives:
% 113.19/16.95 | | | | | |
% 113.19/16.95 | | | | | | Case 1:
% 113.19/16.95 | | | | | | |
% 113.19/16.95 | | | | | | | (149) all_54_10 = e3
% 113.19/16.95 | | | | | | |
% 113.19/16.95 | | | | | | | COMBINE_EQS: (29), (149) imply:
% 113.19/16.95 | | | | | | | (150) all_6_2 = e3
% 113.19/16.95 | | | | | | |
% 113.19/16.95 | | | | | | | REDUCE: (148), (150) imply:
% 113.19/16.95 | | | | | | | (151) $false
% 113.19/16.95 | | | | | | |
% 113.19/16.95 | | | | | | | CLOSE: (151) is inconsistent.
% 113.19/16.95 | | | | | | |
% 113.19/16.95 | | | | | | Case 2:
% 113.19/16.95 | | | | | | |
% 113.19/16.96 | | | | | | | (152) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/16.96 | | | | | | |
% 113.19/16.96 | | | | | | | BETA: splitting (152) gives:
% 113.19/16.96 | | | | | | |
% 113.19/16.96 | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | (153) all_54_10 = e2
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | COMBINE_EQS: (29), (153) imply:
% 113.19/16.96 | | | | | | | | (154) all_6_2 = e2
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | REDUCE: (77), (154) imply:
% 113.19/16.96 | | | | | | | | (155) $false
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | CLOSE: (155) is inconsistent.
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | (156) ~ (all_54_10 = e2)
% 113.19/16.96 | | | | | | | | (157) all_54_10 = e1 | all_54_10 = e0
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | BETA: splitting (157) gives:
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | (158) all_54_10 = e1
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | COMBINE_EQS: (29), (158) imply:
% 113.19/16.96 | | | | | | | | | (159) all_6_2 = e1
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | REDUCE: (113), (159) imply:
% 113.19/16.96 | | | | | | | | | (160) $false
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | CLOSE: (160) is inconsistent.
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | (161) all_54_10 = e0
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | COMBINE_EQS: (29), (161) imply:
% 113.19/16.96 | | | | | | | | | (162) all_6_2 = e0
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | REDUCE: (31), (162) imply:
% 113.19/16.96 | | | | | | | | | (163) ~ (all_52_8 = e0)
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | REDUCE: (42), (162) imply:
% 113.19/16.96 | | | | | | | | | (164) ~ (all_52_11 = e0)
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | REDUCE: (74), (162) imply:
% 113.19/16.96 | | | | | | | | | (165) op(e1, e0) = e3
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | BETA: splitting (108) gives:
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | (166) all_58_15 = e0
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | COMBINE_EQS: (53), (166) imply:
% 113.19/16.96 | | | | | | | | | | (167) all_4_2 = e0
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | REDUCE: (8), (167) imply:
% 113.19/16.96 | | | | | | | | | | (168) $false
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | CLOSE: (168) is inconsistent.
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | (169) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.19/16.96 | | | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | ALPHA: (169) implies:
% 113.19/16.96 | | | | | | | | | | (170) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | BETA: splitting (102) gives:
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | (171) all_58_2 = e2
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | REF_CLOSE: (6), (54), (171) are inconsistent by sub-proof
% 113.19/16.96 | | | | | | | | | | | #335.
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | (172) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | BETA: splitting (170) gives:
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | (173) all_58_12 = e0
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | COMBINE_EQS: (95), (173) imply:
% 113.19/16.96 | | | | | | | | | | | | (174) all_52_3 = e0
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | SIMP: (174) implies:
% 113.19/16.96 | | | | | | | | | | | | (175) all_52_3 = e0
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | REDUCE: (118), (175) imply:
% 113.19/16.96 | | | | | | | | | | | | (176) ~ (all_52_7 = e0)
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | REDUCE: (90), (175) imply:
% 113.19/16.96 | | | | | | | | | | | | (177) ~ (all_4_2 = e0)
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | REDUCE: (142), (175) imply:
% 113.19/16.96 | | | | | | | | | | | | (178) ~ (e1 = e0)
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | SIMP: (178) implies:
% 113.19/16.96 | | | | | | | | | | | | (179) ~ (e1 = e0)
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | BETA: splitting (172) gives:
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | (180) all_58_3 = e2
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | COMBINE_EQS: (38), (180) imply:
% 113.19/16.96 | | | | | | | | | | | | | (181) all_8_2 = e2
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | REDUCE: (75), (181) imply:
% 113.19/16.96 | | | | | | | | | | | | | (182) $false
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | (183) all_58_5 = e2 | all_58_10 = e2
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | BETA: splitting (183) gives:
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | (184) all_58_5 = e2
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | COMBINE_EQS: (48), (184) imply:
% 113.19/16.96 | | | | | | | | | | | | | | (185) all_52_9 = e2
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | SIMP: (185) implies:
% 113.19/16.96 | | | | | | | | | | | | | | (186) all_52_9 = e2
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | COMBINE_EQS: (86), (186) imply:
% 113.19/16.96 | | | | | | | | | | | | | | (187) all_56_4 = e2
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | REDUCE: (5), (186) imply:
% 113.19/16.96 | | | | | | | | | | | | | | (188) ~ (all_8_2 = e2)
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | (189) ~ (all_56_4 = e2)
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | REDUCE: (187), (189) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | (190) $false
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | (191) ~ (all_56_13 = e1)
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | REDUCE: (71), (191) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | (192) ~ (all_8_2 = e1)
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | (193) ~ (all_56_4 = e2)
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | REDUCE: (187), (193) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | (194) $false
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | (195) ~ (all_56_15 = e1)
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | REDUCE: (62), (195) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | (196) ~ (all_4_2 = e1)
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | (197) all_58_0 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (106), (197) are inconsistent by sub-proof
% 113.19/16.96 | | | | | | | | | | | | | | | | | #154.
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | (198) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | (199) all_54_5 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (131), (199) are inconsistent by sub-proof
% 113.19/16.96 | | | | | | | | | | | | | | | | | | #339.
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | (200) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | (201) all_54_15 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (140), (201) are inconsistent by sub-proof
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | #312.
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | (202) ~ (all_54_15 = e3)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | (203) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | (204) all_58_1 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (204) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | (205) all_10_1 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (205) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | (206) $false
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | (207) all_58_4 = e3 | all_58_9 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (208) all_58_4 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (208) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (209) all_52_8 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (209) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (210) ~ (all_52_11 = e3)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (211) ~ (all_52_11 = e3)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (209) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (212) ~ (e3 = e0)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (213) all_54_15 = e2
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (213) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (214) all_4_2 = e2
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (215) all_4_2 = e2
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (215) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (216) all_58_15 = e2
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (215) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (217) ~ (all_52_7 = e2)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (215) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (218) ~ (e3 = e2)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (215) imply:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (219) ~ (e2 = e0)
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (10), (11), (15), (16), (17), (18),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (21), (24), (25), (29), (38), (41), (43), (45),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (48), (49), (53), (54), (57), (58), (64), (67),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (70), (71), (75), (76), (86), (88), (91), (95),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (102), (104), (105), (106), (108), (113), (120),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (157), (165), (173), (179), (211), (212), (216),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (217), (219) are inconsistent by sub-proof #52.
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | (220) all_54_15 = e1 | all_54_15 = e0
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (111), (196), (220) are inconsistent by
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | | sub-proof #418.
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (221) all_58_9 = e3
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (61), (69), (71), (75), (87), (192), (200),
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | | (221) are inconsistent by sub-proof #248.
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | (222) all_58_10 = e2
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (45), (64), (77), (88), (113), (152),
% 113.19/16.96 | | | | | | | | | | | | | | (222) are inconsistent by sub-proof #51.
% 113.19/16.96 | | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | Case 2:
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | (223) all_58_13 = e0 | all_58_14 = e0
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | | REF_CLOSE: (57), (58), (70), (164), (223) are inconsistent by
% 113.19/16.96 | | | | | | | | | | | | sub-proof #428.
% 113.19/16.96 | | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | | |
% 113.19/16.96 | | | | | | | | | End of split
% 113.19/16.96 | | | | | | | | |
% 113.19/16.96 | | | | | | | | End of split
% 113.19/16.96 | | | | | | | |
% 113.19/16.96 | | | | | | | End of split
% 113.19/16.96 | | | | | | |
% 113.19/16.96 | | | | | | End of split
% 113.19/16.96 | | | | | |
% 113.19/16.96 | | | | | End of split
% 113.19/16.96 | | | | |
% 113.19/16.96 | | | | End of split
% 113.19/16.96 | | | |
% 113.19/16.96 | | | Case 2:
% 113.19/16.96 | | | |
% 113.19/16.96 | | | | (224) all_56_13 = e3
% 113.19/16.96 | | | | (225) ~ (all_56_9 = e0)
% 113.19/16.96 | | | |
% 113.19/16.96 | | | | COMBINE_EQS: (71), (224) imply:
% 113.19/16.96 | | | | (226) all_8_2 = e3
% 113.19/16.97 | | | |
% 113.19/16.97 | | | | SIMP: (226) implies:
% 113.19/16.97 | | | | (227) all_8_2 = e3
% 113.19/16.97 | | | |
% 113.19/16.97 | | | | COMBINE_EQS: (38), (227) imply:
% 113.19/16.97 | | | | (228) all_58_3 = e3
% 113.19/16.97 | | | |
% 113.19/16.97 | | | | REDUCE: (49), (225) imply:
% 113.19/16.97 | | | | (229) ~ (all_52_3 = e0)
% 113.19/16.97 | | | |
% 113.19/16.97 | | | | REDUCE: (73), (227) imply:
% 113.19/16.97 | | | | (230) ~ (all_52_1 = e3)
% 113.19/16.97 | | | |
% 113.19/16.97 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (13), (15), (16),
% 113.19/16.97 | | | | (18), (19), (20), (21), (22), (24), (25), (26), (27), (29),
% 113.19/16.97 | | | | (30), (31), (32), (33), (35), (38), (39), (40), (41), (42),
% 113.19/16.97 | | | | (43), (44), (45), (46), (48), (49), (50), (52), (53), (54),
% 113.19/16.97 | | | | (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 113.19/16.97 | | | | (65), (66), (69), (70), (71), (72), (75), (76), (77), (78),
% 113.19/16.97 | | | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 113.19/16.97 | | | | (92), (93), (94), (95), (96), (98), (99), (100), (102),
% 113.19/16.97 | | | | (107), (108), (109), (111), (112), (113), (114), (115),
% 113.19/16.97 | | | | (116), (120), (124), (126), (128), (129), (224), (228),
% 113.19/16.97 | | | | (229), (230) are inconsistent by sub-proof #50.
% 113.19/16.97 | | | |
% 113.19/16.97 | | | End of split
% 113.19/16.97 | | |
% 113.19/16.97 | | Case 2:
% 113.19/16.97 | | |
% 113.19/16.97 | | | (231) ~ (all_56_12 = e2)
% 113.19/16.97 | | |
% 113.19/16.97 | | | REDUCE: (37), (231) imply:
% 113.19/16.97 | | | (232) $false
% 113.19/16.97 | | |
% 113.19/16.97 | | | CLOSE: (232) is inconsistent.
% 113.19/16.97 | | |
% 113.19/16.97 | | End of split
% 113.19/16.97 | |
% 113.19/16.97 | Case 2:
% 113.19/16.97 | |
% 113.19/16.97 | | (233) ~ (all_56_12 = e2)
% 113.19/16.97 | |
% 113.19/16.97 | | REDUCE: (37), (233) imply:
% 113.19/16.97 | | (234) $false
% 113.19/16.97 | |
% 113.19/16.97 | | CLOSE: (234) is inconsistent.
% 113.19/16.97 | |
% 113.19/16.97 | End of split
% 113.19/16.97 |
% 113.19/16.97 End of proof
% 113.19/16.97
% 113.19/16.97 Sub-proof #50 shows that the following formulas are inconsistent:
% 113.19/16.97 ----------------------------------------------------------------
% 113.19/16.97 (1) ~ (all_52_3 = e0)
% 113.19/16.97 (2) all_56_13 = e3
% 113.19/16.97 (3) ~ (all_52_6 = all_52_14)
% 113.19/16.97 (4) all_54_2 = all_52_8
% 113.19/16.97 (5) all_58_7 = all_52_6
% 113.19/16.97 (6) ~ (all_52_8 = all_52_11)
% 113.19/16.97 (7) ~ (all_52_9 = all_8_2)
% 113.19/16.97 (8) ~ (all_52_1 = e2)
% 113.19/16.97 (9) ~ (all_4_2 = e0)
% 113.19/16.97 (10) all_56_14 = all_6_2
% 113.19/16.97 (11) op(e0, e2) = all_52_7
% 113.19/16.97 (12) all_56_11 = all_52_11
% 113.19/16.97 (13) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.19/16.97 (14) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.19/16.97 (15) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.19/16.97 (16) op(all_10_1, e2) = e2
% 113.19/16.97 (17) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.19/16.97 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.19/16.97 (19) ~ (all_52_1 = e3)
% 113.19/16.97 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/16.97 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.19/16.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.19/16.97 (22) all_54_8 = all_52_2
% 113.19/16.97 (23) ~ (all_52_2 = all_6_2)
% 113.19/16.97 (24) all_54_10 = all_6_2
% 113.19/16.97 (25) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.19/16.97 (26) ~ (all_52_8 = all_6_2)
% 113.19/16.97 (27) all_58_4 = all_52_8
% 113.19/16.97 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.19/16.97 (29) all_56_2 = all_52_12
% 113.19/16.97 (30) all_58_3 = all_8_2
% 113.19/16.97 (31) all_58_11 = all_52_14
% 113.19/16.97 (32) ~ (all_52_2 = all_52_3)
% 113.19/16.97 (33) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.19/16.97 (34) ~ (all_52_11 = all_6_2)
% 113.19/16.97 (35) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.19/16.97 (36) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.19/16.97 (37) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.19/16.97 (38) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.19/16.97 (39) all_58_5 = all_52_9
% 113.19/16.97 (40) ~ (all_52_7 = all_10_1)
% 113.19/16.97 (41) all_56_9 = all_52_3
% 113.19/16.97 (42) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.19/16.97 (43) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.19/16.97 (44) all_58_15 = all_4_2
% 113.19/16.97 (45) all_58_2 = all_52_1
% 113.19/16.97 (46) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.19/16.97 (47) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.19/16.97 (48) all_58_13 = all_52_7
% 113.19/16.97 (49) ~ (all_52_7 = e0)
% 113.19/16.97 (50) ~ (all_52_14 = all_4_2)
% 113.19/16.97 (51) all_58_6 = all_52_2
% 113.19/16.97 (52) all_58_3 = e3
% 113.19/16.97 (53) all_54_5 = all_8_2
% 113.19/16.97 (54) all_56_15 = all_4_2
% 113.19/16.97 (55) all_58_0 = e2
% 113.19/16.97 (56) all_58_10 = all_52_13
% 113.19/16.97 (57) ~ (all_52_11 = all_4_2)
% 113.19/16.97 (58) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.19/16.97 (59) ~ (all_10_1 = e2)
% 113.19/16.97 (60) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.19/16.97 (61) all_58_14 = all_52_11
% 113.19/16.97 (62) all_56_13 = all_8_2
% 113.19/16.97 (63) ~ (all_52_8 = e2)
% 113.19/16.97 (64) ~ (all_8_2 = e2)
% 113.19/16.97 (65) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.19/16.97 (66) ~ (all_6_2 = e2)
% 113.19/16.97 (67) ~ (all_52_7 = all_52_11)
% 113.19/16.97 (68) ~ (all_52_1 = all_52_2)
% 113.19/16.97 (69) ~ (all_52_1 = all_52_3)
% 113.19/16.97 (70) op(e0, all_4_2) = all_4_1
% 113.19/16.97 (71) all_58_8 = all_6_2
% 113.19/16.97 (72) all_56_4 = all_52_9
% 113.19/16.97 (73) all_58_9 = all_52_12
% 113.19/16.97 (74) all_56_5 = all_52_13
% 113.19/16.97 (75) ~ (all_10_1 = e3)
% 113.19/16.97 (76) op(e2, e1) = all_52_9
% 113.19/16.97 (77) ~ (all_52_3 = all_4_2)
% 113.19/16.97 (78) ~ (all_52_6 = all_6_2)
% 113.19/16.97 (79) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.19/16.97 (80) all_56_6 = all_52_2
% 113.19/16.97 (81) ~ (all_52_13 = all_4_2)
% 113.19/16.97 (82) all_58_12 = all_52_3
% 113.19/16.97 (83) ~ (all_52_2 = all_52_14)
% 113.19/16.97 (84) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.19/16.97 (85) ~ (all_52_12 = all_4_2)
% 113.19/16.97 (86) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.19/16.97 (87) ~ (all_52_6 = e1)
% 113.19/16.97 (88) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.19/16.98 (89) ~ (all_52_2 = e2)
% 113.19/16.98 (90) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.19/16.98 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.19/16.98 (91) all_58_1 = all_10_1
% 113.19/16.98 (92) all_54_4 = all_52_1
% 113.19/16.98 (93) all_54_15 = all_4_2
% 113.19/16.98 (94) op(e2, all_8_2) = e1
% 113.19/16.98 (95) ~ (all_6_2 = e1)
% 113.19/16.98 (96) ~ (all_52_6 = all_52_7)
% 113.19/16.98 (97) all_54_12 = all_52_3
% 113.19/16.98 (98) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.19/16.98
% 113.19/16.98 Begin of proof
% 113.19/16.98 |
% 113.19/16.98 | BETA: splitting (90) gives:
% 113.19/16.98 |
% 113.19/16.98 | Case 1:
% 113.19/16.98 | |
% 113.19/16.98 | | (99) all_58_15 = e0
% 113.19/16.98 | |
% 113.19/16.98 | | COMBINE_EQS: (44), (99) imply:
% 113.19/16.98 | | (100) all_4_2 = e0
% 113.19/16.98 | |
% 113.19/16.98 | | REDUCE: (9), (100) imply:
% 113.19/16.98 | | (101) $false
% 113.19/16.98 | |
% 113.19/16.98 | | CLOSE: (101) is inconsistent.
% 113.19/16.98 | |
% 113.19/16.98 | Case 2:
% 113.19/16.98 | |
% 113.19/16.98 | | (102) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 113.19/16.98 | | | all_58_13 = e0 | all_58_14 = e0)
% 113.19/16.98 | |
% 113.19/16.98 | | ALPHA: (102) implies:
% 113.19/16.98 | | (103) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.19/16.98 | | (104) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 113.19/16.98 | |
% 113.19/16.98 | | BETA: splitting (103) gives:
% 113.19/16.98 | |
% 113.19/16.98 | | Case 1:
% 113.19/16.98 | | |
% 113.19/16.98 | | | (105) all_58_12 = e0
% 113.19/16.98 | | |
% 113.19/16.98 | | | REF_CLOSE: (1), (82), (105) are inconsistent by sub-proof #362.
% 113.19/16.98 | | |
% 113.19/16.98 | | Case 2:
% 113.19/16.98 | | |
% 113.19/16.98 | | | (106) all_58_13 = e0 | all_58_14 = e0
% 113.19/16.98 | | |
% 113.19/16.98 | | | BETA: splitting (106) gives:
% 113.19/16.98 | | |
% 113.19/16.98 | | | Case 1:
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | (107) all_58_13 = e0
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | REF_CLOSE: (48), (49), (107) are inconsistent by sub-proof #430.
% 113.19/16.98 | | | |
% 113.19/16.98 | | | Case 2:
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | (108) all_58_14 = e0
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | COMBINE_EQS: (61), (108) imply:
% 113.19/16.98 | | | | (109) all_52_11 = e0
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | SIMP: (109) implies:
% 113.19/16.98 | | | | (110) all_52_11 = e0
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | COMBINE_EQS: (12), (110) imply:
% 113.19/16.98 | | | | (111) all_56_11 = e0
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | REDUCE: (6), (110) imply:
% 113.19/16.98 | | | | (112) ~ (all_52_8 = e0)
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | REDUCE: (34), (110) imply:
% 113.19/16.98 | | | | (113) ~ (all_6_2 = e0)
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | SIMP: (113) implies:
% 113.19/16.98 | | | | (114) ~ (all_6_2 = e0)
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | REDUCE: (57), (110) imply:
% 113.19/16.98 | | | | (115) ~ (all_4_2 = e0)
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | BETA: splitting (43) gives:
% 113.19/16.98 | | | |
% 113.19/16.98 | | | | Case 1:
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | (116) ~ (all_56_6 = e1)
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | REDUCE: (80), (116) imply:
% 113.19/16.98 | | | | | (117) ~ (all_52_2 = e1)
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 113.19/16.98 | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 113.19/16.98 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 113.19/16.98 | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (44), (45),
% 113.19/16.98 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 113.19/16.98 | | | | | (56), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 113.19/16.98 | | | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 113.19/16.98 | | | | | (78), (79), (81), (82), (83), (84), (85), (86), (87), (88),
% 113.19/16.98 | | | | | (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 113.19/16.98 | | | | | (104), (108), (111), (112), (114), (117) are inconsistent
% 113.19/16.98 | | | | | by sub-proof #58.
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | Case 2:
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | (118) ~ (all_56_13 = e3)
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | REDUCE: (2), (118) imply:
% 113.19/16.98 | | | | | (119) $false
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | | CLOSE: (119) is inconsistent.
% 113.19/16.98 | | | | |
% 113.19/16.98 | | | | End of split
% 113.19/16.98 | | | |
% 113.19/16.98 | | | End of split
% 113.19/16.98 | | |
% 113.19/16.98 | | End of split
% 113.19/16.98 | |
% 113.19/16.98 | End of split
% 113.19/16.98 |
% 113.19/16.98 End of proof
% 113.19/16.98
% 113.19/16.98 Sub-proof #51 shows that the following formulas are inconsistent:
% 113.19/16.98 ----------------------------------------------------------------
% 113.19/16.98 (1) all_58_10 = e2
% 113.19/16.98 (2) all_56_14 = all_6_2
% 113.19/16.98 (3) all_54_10 = all_6_2
% 113.19/16.98 (4) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.19/16.98 (5) all_58_10 = all_52_13
% 113.19/16.98 (6) ~ (all_6_2 = e2)
% 113.19/16.98 (7) all_56_5 = all_52_13
% 113.19/16.98 (8) ~ (all_6_2 = e1)
% 113.19/16.98 (9) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/16.98
% 113.19/16.98 Begin of proof
% 113.19/16.98 |
% 113.19/16.98 | COMBINE_EQS: (1), (5) imply:
% 113.19/16.98 | (10) all_52_13 = e2
% 113.19/16.98 |
% 113.19/16.98 | COMBINE_EQS: (7), (10) imply:
% 113.19/16.98 | (11) all_56_5 = e2
% 113.19/16.98 |
% 113.19/16.98 | REF_CLOSE: (2), (3), (4), (6), (8), (9), (11) are inconsistent by sub-proof
% 113.19/16.98 | #434.
% 113.19/16.98 |
% 113.19/16.98 End of proof
% 113.19/16.98
% 113.19/16.98 Sub-proof #52 shows that the following formulas are inconsistent:
% 113.19/16.98 ----------------------------------------------------------------
% 113.19/16.98 (1) all_58_7 = all_52_6
% 113.19/16.98 (2) ~ (all_52_1 = e2)
% 113.19/16.98 (3) ~ (all_4_2 = e0)
% 113.19/16.98 (4) all_56_14 = all_6_2
% 113.19/16.98 (5) op(e1, all_8_2) = all_8_0
% 113.19/16.98 (6) all_56_11 = all_52_11
% 113.19/16.98 (7) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.19/16.98 (8) all_58_12 = e0
% 113.19/16.98 (9) ~ (e3 = e1)
% 113.19/16.98 (10) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.19/16.98 (11) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.19/16.98 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/16.98 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.19/16.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.19/16.98 (14) all_54_10 = all_6_2
% 113.19/16.98 (15) all_58_3 = all_8_2
% 113.19/16.98 (16) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.19/16.98 (17) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.19/16.98 (18) all_54_10 = e1 | all_54_10 = e0
% 113.19/16.98 (19) ~ (e3 = e0)
% 113.19/16.98 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.19/16.98 (21) all_58_5 = all_52_9
% 113.19/16.98 (22) all_56_9 = all_52_3
% 113.19/16.98 (23) all_58_15 = all_4_2
% 113.19/16.98 (24) all_58_2 = all_52_1
% 113.19/16.98 (25) all_58_13 = all_52_7
% 113.19/16.98 (26) ~ (all_52_7 = e0)
% 113.19/16.98 (27) all_58_10 = all_52_13
% 113.19/16.98 (28) ~ (all_52_7 = e2)
% 113.19/16.98 (29) ~ (all_52_6 = all_8_2)
% 113.19/16.98 (30) all_58_14 = all_52_11
% 113.19/16.98 (31) all_56_13 = all_8_2
% 113.19/16.98 (32) ~ (all_8_2 = e2)
% 113.19/16.98 (33) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.19/16.98 (34) all_58_15 = e2
% 113.19/16.98 (35) all_56_4 = all_52_9
% 113.19/16.98 (36) all_56_5 = all_52_13
% 113.19/16.98 (37) ~ (all_52_6 = all_6_2)
% 113.19/16.98 (38) ~ (e2 = e0)
% 113.19/16.98 (39) all_58_12 = all_52_3
% 113.19/16.98 (40) op(e1, e0) = e3
% 113.19/16.98 (41) ~ (all_52_6 = e1)
% 113.19/16.98 (42) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.19/16.98 (43) ~ (all_8_0 = e3)
% 113.19/16.98 (44) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 113.19/16.98 (45) ~ (e3 = e2)
% 113.19/16.98 (46) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.19/16.98 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.19/16.98 (47) ~ (all_52_11 = e3)
% 113.19/16.98 (48) ~ (all_6_2 = e1)
% 113.19/16.98 (49) ~ (e1 = e0)
% 113.19/16.98
% 113.19/16.98 Begin of proof
% 113.19/16.98 |
% 113.19/16.99 | BETA: splitting (7) gives:
% 113.19/16.99 |
% 113.19/16.99 | Case 1:
% 113.19/16.99 | |
% 113.19/16.99 | | (50) all_58_12 = e3
% 113.19/16.99 | |
% 113.19/16.99 | | COMBINE_EQS: (8), (50) imply:
% 113.19/16.99 | | (51) e3 = e0
% 113.19/16.99 | |
% 113.19/16.99 | | REDUCE: (19), (51) imply:
% 113.19/16.99 | | (52) $false
% 113.19/16.99 | |
% 113.19/16.99 | | CLOSE: (52) is inconsistent.
% 113.19/16.99 | |
% 113.19/16.99 | Case 2:
% 113.19/16.99 | |
% 113.19/16.99 | | (53) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.19/16.99 | |
% 113.19/16.99 | | BETA: splitting (53) gives:
% 113.19/16.99 | |
% 113.19/16.99 | | Case 1:
% 113.19/16.99 | | |
% 113.19/16.99 | | | (54) all_58_13 = e3
% 113.19/16.99 | | |
% 113.19/16.99 | | | COMBINE_EQS: (25), (54) imply:
% 113.19/16.99 | | | (55) all_52_7 = e3
% 113.19/16.99 | | |
% 113.19/16.99 | | | SIMP: (55) implies:
% 113.19/16.99 | | | (56) all_52_7 = e3
% 113.19/16.99 | | |
% 113.19/16.99 | | | BETA: splitting (33) gives:
% 113.19/16.99 | | |
% 113.19/16.99 | | | Case 1:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (57) all_58_1 = e0
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (12), (14), (15),
% 113.19/16.99 | | | | (16), (17), (20), (21), (22), (23), (24), (25), (26), (27),
% 113.19/16.99 | | | | (29), (30), (31), (32), (35), (36), (37), (38), (39), (41),
% 113.19/16.99 | | | | (42), (44), (45), (46), (48), (49), (54), (57) are
% 113.19/16.99 | | | | inconsistent by sub-proof #153.
% 113.19/16.99 | | | |
% 113.19/16.99 | | | Case 2:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (58) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | BETA: splitting (58) gives:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | Case 1:
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | (59) all_58_3 = e0
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | COMBINE_EQS: (15), (59) imply:
% 113.19/16.99 | | | | | (60) all_8_2 = e0
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | REDUCE: (5), (60) imply:
% 113.19/16.99 | | | | | (61) op(e1, e0) = all_8_0
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | GROUND_INST: instantiating (13) with e3, all_8_0, e0, e1, simplifying
% 113.19/16.99 | | | | | with (40), (61) gives:
% 113.19/16.99 | | | | | (62) all_8_0 = e3
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | REDUCE: (43), (62) imply:
% 113.19/16.99 | | | | | (63) $false
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | CLOSE: (63) is inconsistent.
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | Case 2:
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | (64) all_58_7 = e0 | all_58_13 = e0
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | BETA: splitting (64) gives:
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | | Case 1:
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | (65) all_58_7 = e0
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | COMBINE_EQS: (1), (65) imply:
% 113.19/16.99 | | | | | | (66) all_52_6 = e0
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | REDUCE: (37), (66) imply:
% 113.19/16.99 | | | | | | (67) ~ (all_6_2 = e0)
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | SIMP: (67) implies:
% 113.19/16.99 | | | | | | (68) ~ (all_6_2 = e0)
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | REF_CLOSE: (14), (18), (48), (68) are inconsistent by sub-proof
% 113.19/16.99 | | | | | | #436.
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | Case 2:
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | (69) all_58_13 = e0
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | COMBINE_EQS: (25), (69) imply:
% 113.19/16.99 | | | | | | (70) all_52_7 = e0
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | REDUCE: (26), (70) imply:
% 113.19/16.99 | | | | | | (71) $false
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | | CLOSE: (71) is inconsistent.
% 113.19/16.99 | | | | | |
% 113.19/16.99 | | | | | End of split
% 113.19/16.99 | | | | |
% 113.19/16.99 | | | | End of split
% 113.19/16.99 | | | |
% 113.19/16.99 | | | End of split
% 113.19/16.99 | | |
% 113.19/16.99 | | Case 2:
% 113.19/16.99 | | |
% 113.19/16.99 | | | (72) all_58_14 = e3 | all_58_15 = e3
% 113.19/16.99 | | |
% 113.19/16.99 | | | BETA: splitting (72) gives:
% 113.19/16.99 | | |
% 113.19/16.99 | | | Case 1:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (73) all_58_14 = e3
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REF_CLOSE: (30), (47), (73) are inconsistent by sub-proof #218.
% 113.19/16.99 | | | |
% 113.19/16.99 | | | Case 2:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (74) all_58_15 = e3
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REF_CLOSE: (34), (45), (74) are inconsistent by sub-proof #246.
% 113.19/16.99 | | | |
% 113.19/16.99 | | | End of split
% 113.19/16.99 | | |
% 113.19/16.99 | | End of split
% 113.19/16.99 | |
% 113.19/16.99 | End of split
% 113.19/16.99 |
% 113.19/16.99 End of proof
% 113.19/16.99
% 113.19/16.99 Sub-proof #53 shows that the following formulas are inconsistent:
% 113.19/16.99 ----------------------------------------------------------------
% 113.19/16.99 (1) all_58_7 = all_52_6
% 113.19/16.99 (2) ~ (all_52_9 = all_8_2)
% 113.19/16.99 (3) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.19/16.99 (4) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 113.19/16.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.19/16.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.19/16.99 (6) all_58_11 = all_52_14
% 113.19/16.99 (7) ~ (all_8_2 = e3)
% 113.19/16.99 (8) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.19/16.99 (9) all_54_5 = all_8_2
% 113.19/16.99 (10) all_56_13 = all_8_2
% 113.19/16.99 (11) ~ (all_8_2 = e2)
% 113.19/16.99 (12) all_58_8 = all_6_2
% 113.19/16.99 (13) op(e2, e1) = all_52_9
% 113.19/16.99 (14) all_56_8 = all_52_14
% 113.19/16.99 (15) ~ (all_52_6 = e1)
% 113.19/16.99 (16) op(e2, all_8_2) = e1
% 113.19/16.99 (17) ~ (all_6_2 = e1)
% 113.19/16.99
% 113.19/16.99 Begin of proof
% 113.19/16.99 |
% 113.19/16.99 | BETA: splitting (8) gives:
% 113.19/16.99 |
% 113.19/16.99 | Case 1:
% 113.19/16.99 | |
% 113.19/16.99 | | (18) all_58_7 = e1
% 113.19/16.99 | |
% 113.19/16.99 | | COMBINE_EQS: (1), (18) imply:
% 113.19/16.99 | | (19) all_52_6 = e1
% 113.19/16.99 | |
% 113.19/16.99 | | REDUCE: (15), (19) imply:
% 113.19/16.99 | | (20) $false
% 113.19/16.99 | |
% 113.19/16.99 | | CLOSE: (20) is inconsistent.
% 113.19/16.99 | |
% 113.19/16.99 | Case 2:
% 113.19/16.99 | |
% 113.19/16.99 | | (21) all_58_8 = e1 | all_58_11 = e1
% 113.19/16.99 | |
% 113.19/16.99 | | BETA: splitting (21) gives:
% 113.19/16.99 | |
% 113.19/16.99 | | Case 1:
% 113.19/16.99 | | |
% 113.19/16.99 | | | (22) all_58_8 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | COMBINE_EQS: (12), (22) imply:
% 113.19/16.99 | | | (23) all_6_2 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | REDUCE: (17), (23) imply:
% 113.19/16.99 | | | (24) $false
% 113.19/16.99 | | |
% 113.19/16.99 | | | CLOSE: (24) is inconsistent.
% 113.19/16.99 | | |
% 113.19/16.99 | | Case 2:
% 113.19/16.99 | | |
% 113.19/16.99 | | | (25) all_58_11 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | COMBINE_EQS: (6), (25) imply:
% 113.19/16.99 | | | (26) all_52_14 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | SIMP: (26) implies:
% 113.19/16.99 | | | (27) all_52_14 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | COMBINE_EQS: (14), (27) imply:
% 113.19/16.99 | | | (28) all_56_8 = e1
% 113.19/16.99 | | |
% 113.19/16.99 | | | BETA: splitting (4) gives:
% 113.19/16.99 | | |
% 113.19/16.99 | | | Case 1:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (29) ~ (all_56_8 = e1)
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REDUCE: (28), (29) imply:
% 113.19/16.99 | | | | (30) $false
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | CLOSE: (30) is inconsistent.
% 113.19/16.99 | | | |
% 113.19/16.99 | | | Case 2:
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | (31) ~ (all_56_13 = e0)
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REDUCE: (10), (31) imply:
% 113.19/16.99 | | | | (32) ~ (all_8_2 = e0)
% 113.19/16.99 | | | |
% 113.19/16.99 | | | | REF_CLOSE: (2), (3), (5), (7), (9), (11), (13), (16), (32) are
% 113.19/16.99 | | | | inconsistent by sub-proof #79.
% 113.19/16.99 | | | |
% 113.19/16.99 | | | End of split
% 113.19/16.99 | | |
% 113.19/16.99 | | End of split
% 113.19/16.99 | |
% 113.19/16.99 | End of split
% 113.19/16.99 |
% 113.19/16.99 End of proof
% 113.19/16.99
% 113.19/16.99 Sub-proof #54 shows that the following formulas are inconsistent:
% 113.19/16.99 ----------------------------------------------------------------
% 113.19/16.99 (1) ~ (all_52_8 = all_10_2)
% 113.19/16.99 (2) all_58_7 = all_52_6
% 113.19/16.99 (3) ~ (all_52_9 = all_8_2)
% 113.19/16.99 (4) ~ (all_4_2 = e0)
% 113.19/16.99 (5) all_56_14 = all_6_2
% 113.19/16.99 (6) all_56_3 = all_52_1
% 113.19/16.99 (7) all_54_0 = all_10_2
% 113.19/16.99 (8) all_56_11 = all_52_11
% 113.19/16.99 (9) ~ (all_6_1 = e3)
% 113.19/16.99 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.19/16.99 (11) all_56_12 = all_10_2
% 113.19/16.99 (12) all_58_0 = all_10_2
% 113.19/16.99 (13) all_54_11 = all_52_14
% 113.19/16.99 (14) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.19/16.99 (15) ~ (all_52_14 = all_6_2)
% 113.19/16.99 (16) all_56_10 = all_52_7
% 113.19/16.99 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/16.99 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.19/16.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.19/16.99 (19) ~ (all_52_1 = all_52_9)
% 113.19/16.99 (20) all_54_10 = all_6_2
% 113.19/16.99 (21) all_58_4 = all_52_8
% 113.19/16.99 (22) all_56_2 = all_52_12
% 113.19/16.99 (23) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.19/16.99 (24) all_58_3 = all_8_2
% 113.19/16.99 (25) all_58_11 = all_52_14
% 113.19/16.99 (26) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.19/16.99 (27) op(e2, e3) = all_52_1
% 113.19/16.99 (28) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.19/16.99 (29) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.19/16.99 (30) all_56_15 = e1
% 113.19/16.99 (31) op(e1, e0) = all_52_14
% 113.19/16.99 (32) all_58_5 = all_52_9
% 113.19/16.99 (33) all_56_9 = all_52_3
% 113.19/16.99 (34) op(e1, all_6_2) = all_6_1
% 113.19/16.99 (35) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.19/16.99 (36) all_58_15 = all_4_2
% 113.19/16.99 (37) all_58_2 = all_52_1
% 113.19/16.99 (38) ~ (all_52_1 = all_52_13)
% 113.19/16.99 (39) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.19/16.99 (40) ~ (all_10_2 = e3)
% 113.19/16.99 (41) all_58_13 = all_52_7
% 113.19/17.00 (42) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.19/17.00 (43) ~ (all_52_14 = all_4_2)
% 113.19/17.00 (44) all_58_6 = all_52_2
% 113.19/17.00 (45) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.19/17.00 (46) ~ (all_52_1 = all_10_2)
% 113.19/17.00 (47) all_54_5 = all_8_2
% 113.19/17.00 (48) all_56_15 = all_4_2
% 113.19/17.00 (49) all_58_10 = all_52_13
% 113.19/17.00 (50) ~ (all_52_13 = all_8_2)
% 113.19/17.00 (51) ~ (all_52_11 = all_4_2)
% 113.19/17.00 (52) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.19/17.00 (53) all_58_1 = all_52_4
% 113.19/17.00 (54) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.19/17.00 (55) all_58_14 = all_52_11
% 113.19/17.00 (56) all_56_13 = all_8_2
% 113.19/17.00 (57) ~ (all_56_11 = e0)
% 113.19/17.00 (58) ~ (all_52_1 = all_8_2)
% 113.19/17.00 (59) ~ (all_8_2 = e2)
% 113.19/17.00 (60) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.19/17.00 (61) all_56_7 = all_52_6
% 113.19/17.00 (62) all_56_1 = all_52_8
% 113.19/17.00 (63) all_58_8 = all_6_2
% 113.19/17.00 (64) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.19/17.00 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.19/17.00 (66) all_56_4 = all_52_9
% 113.19/17.00 (67) all_58_9 = all_52_12
% 113.19/17.00 (68) all_56_5 = all_52_13
% 113.19/17.00 (69) op(e2, e1) = all_52_9
% 113.19/17.00 (70) all_56_6 = all_52_2
% 113.19/17.00 (71) all_58_12 = all_52_3
% 113.19/17.00 (72) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.19/17.00 (73) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.19/17.00 (74) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.19/17.00 (75) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.19/17.00 (76) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.19/17.00 (77) all_56_0 = all_52_4
% 113.19/17.00 (78) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.19/17.00 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.19/17.00 (79) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 113.19/17.00 (80) all_54_4 = all_52_1
% 113.19/17.00 (81) op(e2, all_8_2) = e1
% 113.19/17.00 (82) ~ (all_6_2 = e1)
% 113.19/17.00 (83) ~ (all_6_1 = e2)
% 113.19/17.00
% 113.19/17.00 Begin of proof
% 113.19/17.00 |
% 113.19/17.00 | COMBINE_EQS: (30), (48) imply:
% 113.19/17.00 | (84) all_4_2 = e1
% 113.19/17.00 |
% 113.19/17.00 | SIMP: (84) implies:
% 113.19/17.00 | (85) all_4_2 = e1
% 113.19/17.00 |
% 113.19/17.00 | COMBINE_EQS: (36), (85) imply:
% 113.19/17.00 | (86) all_58_15 = e1
% 113.19/17.00 |
% 113.19/17.00 | REDUCE: (8), (57) imply:
% 113.19/17.00 | (87) ~ (all_52_11 = e0)
% 113.19/17.00 |
% 113.19/17.00 | REDUCE: (51), (85) imply:
% 113.19/17.00 | (88) ~ (all_52_11 = e1)
% 113.19/17.00 |
% 113.19/17.00 | REDUCE: (43), (85) imply:
% 113.19/17.00 | (89) ~ (all_52_14 = e1)
% 113.19/17.00 |
% 113.19/17.00 | REDUCE: (4), (85) imply:
% 113.19/17.00 | (90) ~ (e1 = e0)
% 113.19/17.00 |
% 113.19/17.00 | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 113.19/17.00 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 113.19/17.00 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 113.19/17.00 | (38), (39), (40), (41), (42), (44), (45), (46), (47), (49), (50),
% 113.19/17.00 | (52), (53), (54), (55), (56), (58), (59), (60), (61), (62), (63),
% 113.19/17.00 | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 113.19/17.00 | (75), (76), (77), (78), (79), (80), (81), (82), (83), (86), (87),
% 113.19/17.00 | (88), (89), (90) are inconsistent by sub-proof #70.
% 113.19/17.00 |
% 113.19/17.00 End of proof
% 113.19/17.00
% 113.19/17.00 Sub-proof #55 shows that the following formulas are inconsistent:
% 113.19/17.00 ----------------------------------------------------------------
% 113.19/17.00 (1) ~ (all_52_8 = all_10_2)
% 113.19/17.00 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.19/17.00 (3) ~ (all_52_2 = all_10_2)
% 113.19/17.00 (4) ~ (all_52_6 = all_52_14)
% 113.19/17.00 (5) all_54_2 = all_52_8
% 113.19/17.00 (6) all_58_7 = all_52_6
% 113.19/17.00 (7) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.19/17.00 (8) ~ (all_52_8 = all_52_11)
% 113.19/17.00 (9) ~ (all_52_9 = all_8_2)
% 113.19/17.00 (10) ~ (all_4_2 = e0)
% 113.19/17.00 (11) op(e3, e2) = all_52_4
% 113.19/17.00 (12) all_56_14 = all_6_2
% 113.19/17.00 (13) all_56_3 = all_52_1
% 113.19/17.00 (14) all_54_0 = all_10_2
% 113.19/17.00 (15) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.19/17.00 (16) all_54_3 = all_52_12
% 113.19/17.00 (17) ~ (all_52_2 = all_52_6)
% 113.19/17.00 (18) ~ (all_52_12 = all_52_14)
% 113.19/17.00 (19) op(e0, e2) = all_52_7
% 113.19/17.00 (20) all_56_11 = all_52_11
% 113.19/17.00 (21) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.19/17.00 (22) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.19/17.00 (23) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.19/17.00 (24) ~ (all_6_1 = e3)
% 113.19/17.00 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.19/17.00 (26) ~ (all_52_4 = all_52_8)
% 113.19/17.00 (27) ~ (all_52_12 = all_10_2)
% 113.19/17.00 (28) ~ (e3 = e1)
% 113.19/17.00 (29) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.19/17.00 (30) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.19/17.00 (31) all_56_12 = all_10_2
% 113.19/17.00 (32) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.19/17.00 (33) all_58_0 = all_10_2
% 113.19/17.00 (34) all_54_11 = all_52_14
% 113.19/17.00 (35) all_54_13 = all_52_7
% 113.19/17.00 (36) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.19/17.00 (37) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.19/17.00 (38) ~ (all_52_14 = all_6_2)
% 113.19/17.00 (39) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.19/17.00 (40) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.19/17.00 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.19/17.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.19/17.00 (42) all_54_8 = all_52_2
% 113.19/17.00 (43) ~ (all_52_2 = all_6_2)
% 113.19/17.00 (44) ~ (all_52_1 = all_52_9)
% 113.19/17.00 (45) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.19/17.00 (46) all_54_10 = all_6_2
% 113.19/17.00 (47) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.19/17.00 (48) ~ (all_52_8 = all_6_2)
% 113.19/17.00 (49) all_58_4 = all_52_8
% 113.19/17.00 (50) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.19/17.00 (51) ~ (all_52_4 = all_52_7)
% 113.19/17.00 (52) all_56_2 = all_52_12
% 113.19/17.00 (53) all_58_3 = all_8_2
% 113.19/17.00 (54) all_58_11 = all_52_14
% 113.19/17.00 (55) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.19/17.00 (56) ~ (all_52_2 = all_52_3)
% 113.19/17.00 (57) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.19/17.00 (58) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.19/17.00 (59) op(e2, e3) = all_52_1
% 113.19/17.00 (60) ~ (all_10_2 = e1)
% 113.19/17.00 (61) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.19/17.01 (62) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.19/17.01 (63) ~ (all_52_7 = all_8_2)
% 113.19/17.01 (64) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.19/17.01 (65) ~ (all_52_4 = all_8_2)
% 113.19/17.01 (66) op(e1, e0) = all_52_14
% 113.19/17.01 (67) all_58_5 = all_52_9
% 113.19/17.01 (68) all_56_9 = all_52_3
% 113.19/17.01 (69) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.19/17.01 (70) op(e1, all_6_2) = all_6_1
% 113.19/17.01 (71) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.19/17.01 (72) all_58_15 = all_4_2
% 113.19/17.01 (73) all_58_2 = all_52_1
% 113.19/17.01 (74) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.19/17.01 (75) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.19/17.01 (76) ~ (all_10_2 = e3)
% 113.19/17.01 (77) all_58_13 = all_52_7
% 113.19/17.01 (78) ~ (all_52_7 = e0)
% 113.19/17.01 (79) ~ (all_52_14 = all_4_2)
% 113.19/17.01 (80) all_58_6 = all_52_2
% 113.19/17.01 (81) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.19/17.01 (82) ~ (all_52_1 = all_10_2)
% 113.19/17.01 (83) all_54_5 = all_8_2
% 113.19/17.01 (84) ~ (all_52_13 = e2)
% 113.19/17.01 (85) ~ (all_52_11 = e2)
% 113.19/17.01 (86) all_56_15 = all_4_2
% 113.19/17.01 (87) all_58_10 = all_52_13
% 113.19/17.01 (88) ~ (all_52_13 = all_8_2)
% 113.19/17.01 (89) ~ (all_52_11 = all_4_2)
% 113.19/17.01 (90) op(e3, all_10_2) = all_10_1
% 113.19/17.01 (91) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.19/17.01 (92) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 113.19/17.01 (93) all_58_1 = all_52_4
% 113.19/17.01 (94) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.19/17.01 (95) ~ (all_52_9 = all_52_11)
% 113.19/17.01 (96) all_58_14 = all_52_11
% 113.19/17.01 (97) all_54_1 = all_52_4
% 113.19/17.01 (98) ~ (all_52_12 = e2)
% 113.19/17.01 (99) all_56_13 = all_8_2
% 113.19/17.01 (100) ~ (all_52_1 = all_8_2)
% 113.19/17.01 (101) ~ (all_8_2 = e2)
% 113.19/17.01 (102) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.19/17.01 (103) ~ (all_52_7 = all_52_11)
% 113.19/17.01 (104) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.19/17.01 (105) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.19/17.01 (106) all_56_7 = all_52_6
% 113.19/17.01 (107) ~ (all_52_9 = all_6_2)
% 113.19/17.01 (108) ~ (all_52_4 = all_52_6)
% 113.19/17.01 (109) ~ (all_52_1 = all_52_2)
% 113.19/17.01 (110) ~ (all_52_4 = all_52_12)
% 113.19/17.01 (111) ~ (all_52_1 = all_52_3)
% 113.32/17.01 (112) all_56_1 = all_52_8
% 113.32/17.01 (113) op(e0, all_4_2) = all_4_1
% 113.32/17.01 (114) all_58_8 = all_6_2
% 113.32/17.01 (115) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.32/17.01 (116) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.32/17.01 (117) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.32/17.01 (118) all_56_4 = all_52_9
% 113.32/17.01 (119) all_58_9 = all_52_12
% 113.32/17.01 (120) all_56_5 = all_52_13
% 113.32/17.01 (121) op(e2, e1) = all_52_9
% 113.32/17.01 (122) ~ (all_52_3 = all_4_2)
% 113.32/17.01 (123) ~ (all_52_6 = all_6_2)
% 113.32/17.01 (124) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.32/17.01 (125) all_56_6 = all_52_2
% 113.32/17.01 (126) ~ (all_52_13 = all_4_2)
% 113.32/17.01 (127) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.32/17.01 (128) all_58_12 = all_52_3
% 113.32/17.01 (129) ~ (all_52_2 = all_52_14)
% 113.32/17.01 (130) ~ (all_52_8 = all_52_9)
% 113.32/17.01 (131) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.32/17.01 (132) op(e2, e0) = all_52_13
% 113.32/17.01 (133) ~ (all_52_12 = all_4_2)
% 113.32/17.01 (134) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.32/17.01 (135) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.32/17.01 (136) all_56_15 = e2
% 113.32/17.01 (137) all_56_8 = all_52_14
% 113.32/17.01 (138) op(all_10_1, all_10_2) = e2
% 113.32/17.01 (139) ~ (all_52_4 = all_10_2)
% 113.32/17.01 (140) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.32/17.01 (141) all_56_0 = all_52_4
% 113.32/17.01 (142) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.32/17.01 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.32/17.01 (143) all_54_4 = all_52_1
% 113.32/17.01 (144) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.32/17.01 (145) all_54_15 = all_4_2
% 113.32/17.01 (146) op(e2, all_8_2) = e1
% 113.32/17.01 (147) ~ (all_6_2 = e1)
% 113.32/17.01 (148) ~ (all_6_1 = e2)
% 113.32/17.01 (149) ~ (all_52_6 = all_52_7)
% 113.32/17.01 (150) all_54_12 = all_52_3
% 113.32/17.01 (151) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.32/17.01 (152) ~ (e1 = e0)
% 113.32/17.01
% 113.32/17.01 Begin of proof
% 113.32/17.01 |
% 113.32/17.01 | BETA: splitting (32) gives:
% 113.32/17.01 |
% 113.32/17.01 | Case 1:
% 113.32/17.01 | |
% 113.32/17.01 | | (153) ~ (all_56_7 = e1)
% 113.32/17.01 | |
% 113.32/17.01 | | REDUCE: (106), (153) imply:
% 113.32/17.01 | | (154) ~ (all_52_6 = e1)
% 113.32/17.02 | |
% 113.32/17.02 | | BETA: splitting (92) gives:
% 113.32/17.02 | |
% 113.32/17.02 | | Case 1:
% 113.32/17.02 | | |
% 113.32/17.02 | | | (155) ~ (all_56_0 = e3)
% 113.32/17.02 | | |
% 113.32/17.02 | | | REDUCE: (141), (155) imply:
% 113.32/17.02 | | | (156) ~ (all_52_4 = e3)
% 113.32/17.02 | | |
% 113.32/17.02 | | | BETA: splitting (94) gives:
% 113.32/17.02 | | |
% 113.32/17.02 | | | Case 1:
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | (157) ~ (all_56_2 = e3)
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | REDUCE: (52), (157) imply:
% 113.32/17.02 | | | | (158) ~ (all_52_12 = e3)
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | REF_CLOSE: (1), (9), (10), (12), (13), (20), (22), (23), (24), (26),
% 113.32/17.02 | | | | (28), (30), (33), (34), (38), (39), (40), (41), (44), (45),
% 113.32/17.02 | | | | (46), (48), (49), (50), (52), (53), (55), (58), (59), (66),
% 113.32/17.02 | | | | (67), (68), (70), (72), (73), (75), (76), (77), (78), (81),
% 113.32/17.02 | | | | (83), (84), (85), (86), (87), (88), (93), (94), (95), (96),
% 113.32/17.02 | | | | (99), (100), (101), (107), (112), (116), (117), (119), (120),
% 113.32/17.02 | | | | (121), (126), (127), (128), (130), (132), (134), (135),
% 113.32/17.02 | | | | (137), (140), (142), (145), (146), (147), (148), (152),
% 113.32/17.02 | | | | (156), (158) are inconsistent by sub-proof #78.
% 113.32/17.02 | | | |
% 113.32/17.02 | | | Case 2:
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | (159) all_56_2 = e3
% 113.32/17.02 | | | | (160) ~ (all_56_13 = e0)
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | COMBINE_EQS: (52), (159) imply:
% 113.32/17.02 | | | | (161) all_52_12 = e3
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | REDUCE: (99), (160) imply:
% 113.32/17.02 | | | | (162) ~ (all_8_2 = e0)
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | REDUCE: (27), (161) imply:
% 113.32/17.02 | | | | (163) ~ (all_10_2 = e3)
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | BETA: splitting (2) gives:
% 113.32/17.02 | | | |
% 113.32/17.02 | | | | Case 1:
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | (164) ~ (all_56_2 = e3)
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | REDUCE: (159), (164) imply:
% 113.32/17.02 | | | | | (165) $false
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | CLOSE: (165) is inconsistent.
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | Case 2:
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | (166) ~ (all_56_12 = e0)
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | REDUCE: (31), (166) imply:
% 113.32/17.02 | | | | | (167) ~ (all_10_2 = e0)
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 113.32/17.02 | | | | | (15), (16), (17), (18), (19), (20), (21), (23), (25), (29),
% 113.32/17.02 | | | | | (30), (31), (33), (35), (36), (37), (38), (39), (41), (42),
% 113.32/17.02 | | | | | (43), (44), (46), (47), (48), (49), (50), (51), (52), (53),
% 113.32/17.02 | | | | | (54), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 113.32/17.02 | | | | | (65), (67), (68), (69), (71), (72), (73), (74), (75), (76),
% 113.32/17.02 | | | | | (77), (78), (79), (80), (82), (83), (84), (86), (87), (89),
% 113.32/17.02 | | | | | (90), (91), (93), (94), (96), (97), (98), (99), (100),
% 113.32/17.02 | | | | | (101), (102), (103), (104), (105), (107), (108), (109),
% 113.32/17.02 | | | | | (110), (111), (113), (114), (115), (118), (119), (120),
% 113.32/17.02 | | | | | (121), (122), (123), (124), (125), (126), (128), (129),
% 113.32/17.02 | | | | | (130), (131), (133), (135), (137), (138), (139), (140),
% 113.32/17.02 | | | | | (141), (142), (143), (144), (145), (146), (147), (149),
% 113.32/17.02 | | | | | (150), (151), (154), (156), (162), (167) are inconsistent
% 113.32/17.02 | | | | | by sub-proof #56.
% 113.32/17.02 | | | | |
% 113.32/17.02 | | | | End of split
% 113.32/17.02 | | | |
% 113.32/17.02 | | | End of split
% 113.32/17.02 | | |
% 113.32/17.02 | | Case 2:
% 113.32/17.02 | | |
% 113.32/17.02 | | | (168) ~ (all_56_15 = e2)
% 113.32/17.02 | | |
% 113.32/17.02 | | | REDUCE: (136), (168) imply:
% 113.32/17.02 | | | (169) $false
% 113.32/17.02 | | |
% 113.32/17.02 | | | CLOSE: (169) is inconsistent.
% 113.32/17.02 | | |
% 113.32/17.02 | | End of split
% 113.32/17.02 | |
% 113.32/17.02 | Case 2:
% 113.32/17.02 | |
% 113.32/17.02 | | (170) ~ (all_56_15 = e2)
% 113.32/17.02 | |
% 113.32/17.02 | | REDUCE: (136), (170) imply:
% 113.32/17.02 | | (171) $false
% 113.32/17.02 | |
% 113.32/17.02 | | CLOSE: (171) is inconsistent.
% 113.32/17.02 | |
% 113.32/17.02 | End of split
% 113.32/17.02 |
% 113.32/17.02 End of proof
% 113.32/17.02
% 113.32/17.02 Sub-proof #56 shows that the following formulas are inconsistent:
% 113.32/17.02 ----------------------------------------------------------------
% 113.32/17.02 (1) ~ (all_52_2 = all_10_2)
% 113.32/17.02 (2) ~ (all_52_6 = all_52_14)
% 113.32/17.02 (3) all_54_2 = all_52_8
% 113.32/17.02 (4) all_58_7 = all_52_6
% 113.32/17.02 (5) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.32/17.02 (6) ~ (all_52_8 = all_52_11)
% 113.32/17.02 (7) ~ (all_52_9 = all_8_2)
% 113.32/17.02 (8) ~ (all_4_2 = e0)
% 113.32/17.02 (9) op(e3, e2) = all_52_4
% 113.32/17.02 (10) all_56_14 = all_6_2
% 113.32/17.02 (11) all_54_0 = all_10_2
% 113.32/17.02 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.32/17.02 (13) all_54_3 = all_52_12
% 113.32/17.02 (14) ~ (all_52_2 = all_52_6)
% 113.32/17.02 (15) ~ (all_52_12 = all_52_14)
% 113.32/17.02 (16) op(e0, e2) = all_52_7
% 113.32/17.02 (17) all_56_11 = all_52_11
% 113.32/17.02 (18) ~ (all_52_4 = e3)
% 113.32/17.02 (19) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.32/17.02 (20) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.32/17.02 (21) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.32/17.02 (22) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.32/17.02 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.32/17.02 (24) all_56_12 = all_10_2
% 113.32/17.02 (25) all_58_0 = all_10_2
% 113.32/17.02 (26) all_54_13 = all_52_7
% 113.32/17.02 (27) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.32/17.02 (28) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.32/17.02 (29) ~ (all_52_14 = all_6_2)
% 113.32/17.02 (30) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.32/17.02 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.32/17.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.32/17.02 (32) all_54_8 = all_52_2
% 113.32/17.02 (33) ~ (all_52_2 = all_6_2)
% 113.32/17.02 (34) ~ (all_52_1 = all_52_9)
% 113.32/17.02 (35) all_54_10 = all_6_2
% 113.32/17.02 (36) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.32/17.02 (37) ~ (all_52_8 = all_6_2)
% 113.32/17.02 (38) all_58_4 = all_52_8
% 113.32/17.02 (39) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.32/17.02 (40) ~ (all_52_4 = all_52_7)
% 113.32/17.02 (41) all_56_2 = all_52_12
% 113.32/17.02 (42) all_58_3 = all_8_2
% 113.32/17.02 (43) all_58_11 = all_52_14
% 113.32/17.02 (44) ~ (all_52_2 = all_52_3)
% 113.32/17.02 (45) ~ (all_8_2 = e0)
% 113.32/17.02 (46) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.32/17.02 (47) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.32/17.02 (48) op(e2, e3) = all_52_1
% 113.32/17.02 (49) ~ (all_10_2 = e1)
% 113.32/17.02 (50) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.32/17.02 (51) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.32/17.02 (52) ~ (all_52_7 = all_8_2)
% 113.32/17.02 (53) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.32/17.02 (54) ~ (all_52_4 = all_8_2)
% 113.32/17.02 (55) all_58_5 = all_52_9
% 113.32/17.02 (56) all_56_9 = all_52_3
% 113.32/17.02 (57) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.32/17.02 (58) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.32/17.02 (59) all_58_15 = all_4_2
% 113.32/17.02 (60) all_58_2 = all_52_1
% 113.32/17.02 (61) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.32/17.02 (62) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.32/17.02 (63) ~ (all_10_2 = e3)
% 113.32/17.02 (64) all_58_13 = all_52_7
% 113.32/17.02 (65) ~ (all_52_7 = e0)
% 113.32/17.02 (66) ~ (all_52_14 = all_4_2)
% 113.32/17.02 (67) all_58_6 = all_52_2
% 113.32/17.02 (68) ~ (all_52_1 = all_10_2)
% 113.32/17.02 (69) all_54_5 = all_8_2
% 113.32/17.02 (70) ~ (all_52_13 = e2)
% 113.32/17.02 (71) all_56_15 = all_4_2
% 113.32/17.02 (72) all_58_10 = all_52_13
% 113.32/17.02 (73) ~ (all_52_11 = all_4_2)
% 113.32/17.02 (74) op(e3, all_10_2) = all_10_1
% 113.32/17.02 (75) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.32/17.02 (76) all_58_1 = all_52_4
% 113.32/17.02 (77) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.32/17.02 (78) all_58_14 = all_52_11
% 113.32/17.02 (79) all_54_1 = all_52_4
% 113.32/17.02 (80) ~ (all_52_12 = e2)
% 113.32/17.02 (81) all_56_13 = all_8_2
% 113.32/17.03 (82) ~ (all_52_1 = all_8_2)
% 113.32/17.03 (83) ~ (all_8_2 = e2)
% 113.32/17.03 (84) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.32/17.03 (85) ~ (all_52_7 = all_52_11)
% 113.32/17.03 (86) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.32/17.03 (87) ~ (all_10_2 = e0)
% 113.32/17.03 (88) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.32/17.03 (89) ~ (all_52_9 = all_6_2)
% 113.32/17.03 (90) ~ (all_52_4 = all_52_6)
% 113.32/17.03 (91) ~ (all_52_1 = all_52_2)
% 113.32/17.03 (92) ~ (all_52_4 = all_52_12)
% 113.32/17.03 (93) ~ (all_52_1 = all_52_3)
% 113.32/17.03 (94) op(e0, all_4_2) = all_4_1
% 113.32/17.03 (95) all_58_8 = all_6_2
% 113.32/17.03 (96) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.32/17.03 (97) all_56_4 = all_52_9
% 113.32/17.03 (98) all_58_9 = all_52_12
% 113.32/17.03 (99) all_56_5 = all_52_13
% 113.32/17.03 (100) op(e2, e1) = all_52_9
% 113.32/17.03 (101) ~ (all_52_3 = all_4_2)
% 113.32/17.03 (102) ~ (all_52_6 = all_6_2)
% 113.32/17.03 (103) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.32/17.03 (104) all_56_6 = all_52_2
% 113.32/17.03 (105) ~ (all_52_13 = all_4_2)
% 113.32/17.03 (106) all_58_12 = all_52_3
% 113.32/17.03 (107) ~ (all_52_2 = all_52_14)
% 113.32/17.03 (108) ~ (all_52_8 = all_52_9)
% 113.32/17.03 (109) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.32/17.03 (110) ~ (all_52_12 = all_4_2)
% 113.32/17.03 (111) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.32/17.03 (112) all_56_8 = all_52_14
% 113.32/17.03 (113) op(all_10_1, all_10_2) = e2
% 113.32/17.03 (114) ~ (all_52_4 = all_10_2)
% 113.32/17.03 (115) ~ (all_52_6 = e1)
% 113.32/17.03 (116) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.32/17.03 (117) all_56_0 = all_52_4
% 113.32/17.03 (118) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.32/17.03 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.32/17.03 (119) all_54_4 = all_52_1
% 113.32/17.03 (120) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.32/17.03 (121) all_54_15 = all_4_2
% 113.32/17.03 (122) op(e2, all_8_2) = e1
% 113.32/17.03 (123) ~ (all_6_2 = e1)
% 113.32/17.03 (124) ~ (all_52_6 = all_52_7)
% 113.32/17.03 (125) all_54_12 = all_52_3
% 113.32/17.03 (126) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.32/17.03
% 113.32/17.03 Begin of proof
% 113.32/17.03 |
% 113.32/17.03 | BETA: splitting (96) gives:
% 113.32/17.03 |
% 113.32/17.03 | Case 1:
% 113.32/17.03 | |
% 113.32/17.03 | | (127) all_54_0 = e3
% 113.32/17.03 | |
% 113.32/17.03 | | REF_CLOSE: (11), (63), (127) are inconsistent by sub-proof #451.
% 113.32/17.03 | |
% 113.32/17.03 | Case 2:
% 113.32/17.03 | |
% 113.32/17.03 | | (128) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.32/17.03 | |
% 113.32/17.03 | | BETA: splitting (128) gives:
% 113.32/17.03 | |
% 113.32/17.03 | | Case 1:
% 113.32/17.03 | | |
% 113.32/17.03 | | | (129) all_54_0 = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | COMBINE_EQS: (11), (129) imply:
% 113.32/17.03 | | | (130) all_10_2 = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | SIMP: (130) implies:
% 113.32/17.03 | | | (131) all_10_2 = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | COMBINE_EQS: (24), (131) imply:
% 113.32/17.03 | | | (132) all_56_12 = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | COMBINE_EQS: (25), (131) imply:
% 113.32/17.03 | | | (133) all_58_0 = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (68), (131) imply:
% 113.32/17.03 | | | (134) ~ (all_52_1 = e2)
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (1), (131) imply:
% 113.32/17.03 | | | (135) ~ (all_52_2 = e2)
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (114), (131) imply:
% 113.32/17.03 | | | (136) ~ (all_52_4 = e2)
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (49), (131) imply:
% 113.32/17.03 | | | (137) ~ (e2 = e1)
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (113), (131) imply:
% 113.32/17.03 | | | (138) op(all_10_1, e2) = e2
% 113.32/17.03 | | |
% 113.32/17.03 | | | REDUCE: (74), (131) imply:
% 113.32/17.03 | | | (139) op(e3, e2) = all_10_1
% 113.32/17.03 | | |
% 113.32/17.03 | | | BETA: splitting (116) gives:
% 113.32/17.03 | | |
% 113.32/17.03 | | | Case 1:
% 113.32/17.03 | | | |
% 113.32/17.03 | | | | (140) all_58_2 = e2
% 113.32/17.03 | | | |
% 113.32/17.03 | | | | REF_CLOSE: (60), (134), (140) are inconsistent by sub-proof #335.
% 113.32/17.03 | | | |
% 113.32/17.03 | | | Case 2:
% 113.32/17.03 | | | |
% 113.32/17.03 | | | | (141) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.32/17.03 | | | |
% 113.32/17.03 | | | | BETA: splitting (141) gives:
% 113.32/17.03 | | | |
% 113.32/17.03 | | | | Case 1:
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | (142) all_58_3 = e2
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | COMBINE_EQS: (42), (142) imply:
% 113.32/17.03 | | | | | (143) all_8_2 = e2
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | REDUCE: (83), (143) imply:
% 113.32/17.03 | | | | | (144) $false
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | CLOSE: (144) is inconsistent.
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | Case 2:
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | (145) all_58_5 = e2 | all_58_10 = e2
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | BETA: splitting (145) gives:
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | | Case 1:
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | (146) all_58_5 = e2
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | COMBINE_EQS: (55), (146) imply:
% 113.32/17.03 | | | | | | (147) all_52_9 = e2
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | SIMP: (147) implies:
% 113.32/17.03 | | | | | | (148) all_52_9 = e2
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | REDUCE: (108), (148) imply:
% 113.32/17.03 | | | | | | (149) ~ (all_52_8 = e2)
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | REDUCE: (7), (148) imply:
% 113.32/17.03 | | | | | | (150) ~ (all_8_2 = e2)
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | REDUCE: (89), (148) imply:
% 113.32/17.03 | | | | | | (151) ~ (all_6_2 = e2)
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | SIMP: (151) implies:
% 113.32/17.03 | | | | | | (152) ~ (all_6_2 = e2)
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 113.32/17.03 | | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 113.32/17.03 | | | | | | (23), (26), (27), (28), (29), (30), (31), (32), (33),
% 113.32/17.03 | | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 113.32/17.03 | | | | | | (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 113.32/17.03 | | | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 113.32/17.03 | | | | | | (64), (65), (66), (67), (69), (71), (72), (73), (75),
% 113.32/17.03 | | | | | | (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 113.32/17.03 | | | | | | (85), (86), (88), (90), (91), (92), (93), (94), (95),
% 113.32/17.03 | | | | | | (97), (98), (99), (100), (101), (102), (103), (104),
% 113.32/17.03 | | | | | | (105), (106), (107), (109), (110), (111), (112), (115),
% 113.32/17.03 | | | | | | (116), (117), (118), (119), (120), (121), (122), (123),
% 113.32/17.03 | | | | | | (124), (125), (126), (132), (133), (134), (135), (136),
% 113.32/17.03 | | | | | | (137), (138), (139), (149), (152) are inconsistent by
% 113.32/17.03 | | | | | | sub-proof #57.
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | Case 2:
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | (153) all_58_10 = e2
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | COMBINE_EQS: (72), (153) imply:
% 113.32/17.03 | | | | | | (154) all_52_13 = e2
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | REDUCE: (70), (154) imply:
% 113.32/17.03 | | | | | | (155) $false
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | | CLOSE: (155) is inconsistent.
% 113.32/17.03 | | | | | |
% 113.32/17.03 | | | | | End of split
% 113.32/17.03 | | | | |
% 113.32/17.03 | | | | End of split
% 113.32/17.03 | | | |
% 113.32/17.03 | | | End of split
% 113.32/17.03 | | |
% 113.32/17.03 | | Case 2:
% 113.32/17.03 | | |
% 113.32/17.03 | | | (156) all_54_0 = e1 | all_54_0 = e0
% 113.32/17.03 | | |
% 113.32/17.04 | | | REF_CLOSE: (11), (49), (87), (156) are inconsistent by sub-proof #423.
% 113.32/17.04 | | |
% 113.32/17.04 | | End of split
% 113.32/17.04 | |
% 113.32/17.04 | End of split
% 113.32/17.04 |
% 113.32/17.04 End of proof
% 113.32/17.04
% 113.32/17.04 Sub-proof #57 shows that the following formulas are inconsistent:
% 113.32/17.04 ----------------------------------------------------------------
% 113.32/17.04 (1) ~ (all_52_6 = all_52_14)
% 113.32/17.04 (2) all_54_2 = all_52_8
% 113.32/17.04 (3) all_58_7 = all_52_6
% 113.32/17.04 (4) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.32/17.04 (5) ~ (all_52_8 = all_52_11)
% 113.32/17.04 (6) ~ (all_52_9 = all_8_2)
% 113.32/17.04 (7) ~ (all_52_1 = e2)
% 113.32/17.04 (8) ~ (all_4_2 = e0)
% 113.32/17.04 (9) op(e3, e2) = all_52_4
% 113.32/17.04 (10) all_56_14 = all_6_2
% 113.32/17.04 (11) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.32/17.04 (12) all_54_3 = all_52_12
% 113.32/17.04 (13) ~ (all_52_2 = all_52_6)
% 113.32/17.04 (14) ~ (all_52_12 = all_52_14)
% 113.32/17.04 (15) op(e0, e2) = all_52_7
% 113.32/17.04 (16) all_56_11 = all_52_11
% 113.32/17.04 (17) ~ (all_52_4 = e3)
% 113.32/17.04 (18) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.32/17.04 (19) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.32/17.04 (20) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.32/17.04 (21) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.32/17.04 (22) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.32/17.04 (23) op(all_10_1, e2) = e2
% 113.32/17.04 (24) all_54_13 = all_52_7
% 113.32/17.04 (25) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.32/17.04 (26) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.32/17.04 (27) ~ (all_52_14 = all_6_2)
% 113.32/17.04 (28) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.32/17.04 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.32/17.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.32/17.04 (30) all_54_8 = all_52_2
% 113.32/17.04 (31) ~ (all_52_2 = all_6_2)
% 113.32/17.04 (32) all_54_10 = all_6_2
% 113.32/17.04 (33) ~ (e2 = e1)
% 113.32/17.04 (34) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.32/17.04 (35) ~ (all_52_8 = all_6_2)
% 113.32/17.04 (36) all_58_4 = all_52_8
% 113.32/17.04 (37) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.32/17.04 (38) ~ (all_52_4 = all_52_7)
% 113.32/17.04 (39) all_56_2 = all_52_12
% 113.32/17.04 (40) all_56_12 = e2
% 113.32/17.04 (41) all_58_3 = all_8_2
% 113.32/17.04 (42) all_58_11 = all_52_14
% 113.32/17.04 (43) ~ (all_52_2 = all_52_3)
% 113.32/17.04 (44) ~ (all_8_2 = e0)
% 113.32/17.04 (45) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.32/17.04 (46) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.32/17.04 (47) op(e2, e3) = all_52_1
% 113.32/17.04 (48) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.32/17.04 (49) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.32/17.04 (50) ~ (all_52_7 = all_8_2)
% 113.32/17.04 (51) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.32/17.04 (52) ~ (all_52_4 = all_8_2)
% 113.32/17.04 (53) all_58_5 = all_52_9
% 113.32/17.04 (54) all_56_9 = all_52_3
% 113.32/17.04 (55) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.32/17.04 (56) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.32/17.04 (57) all_58_15 = all_4_2
% 113.32/17.04 (58) all_58_2 = all_52_1
% 113.32/17.04 (59) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.32/17.04 (60) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.32/17.04 (61) all_58_13 = all_52_7
% 113.32/17.04 (62) ~ (all_52_7 = e0)
% 113.32/17.04 (63) ~ (all_52_14 = all_4_2)
% 113.32/17.04 (64) all_58_6 = all_52_2
% 113.32/17.04 (65) all_54_5 = all_8_2
% 113.32/17.04 (66) all_56_15 = all_4_2
% 113.32/17.04 (67) all_58_0 = e2
% 113.32/17.04 (68) all_58_10 = all_52_13
% 113.32/17.04 (69) ~ (all_52_11 = all_4_2)
% 113.32/17.04 (70) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.32/17.04 (71) all_58_1 = all_52_4
% 113.32/17.04 (72) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.32/17.04 (73) all_58_14 = all_52_11
% 113.32/17.04 (74) all_54_1 = all_52_4
% 113.32/17.04 (75) ~ (all_52_12 = e2)
% 113.32/17.04 (76) all_56_13 = all_8_2
% 113.32/17.04 (77) ~ (all_52_8 = e2)
% 113.32/17.04 (78) ~ (all_52_1 = all_8_2)
% 113.32/17.04 (79) ~ (all_8_2 = e2)
% 113.32/17.04 (80) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.32/17.04 (81) ~ (all_6_2 = e2)
% 113.32/17.04 (82) ~ (all_52_7 = all_52_11)
% 113.32/17.04 (83) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.32/17.04 (84) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.32/17.04 (85) ~ (all_52_4 = all_52_6)
% 113.32/17.04 (86) op(e3, e2) = all_10_1
% 113.32/17.04 (87) ~ (all_52_1 = all_52_2)
% 113.32/17.04 (88) ~ (all_52_4 = all_52_12)
% 113.32/17.04 (89) ~ (all_52_1 = all_52_3)
% 113.32/17.04 (90) op(e0, all_4_2) = all_4_1
% 113.32/17.04 (91) all_58_8 = all_6_2
% 113.32/17.04 (92) all_56_4 = all_52_9
% 113.32/17.04 (93) all_58_9 = all_52_12
% 113.32/17.04 (94) all_56_5 = all_52_13
% 113.32/17.04 (95) op(e2, e1) = all_52_9
% 113.32/17.04 (96) ~ (all_52_3 = all_4_2)
% 113.32/17.04 (97) ~ (all_52_6 = all_6_2)
% 113.32/17.04 (98) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.32/17.04 (99) all_56_6 = all_52_2
% 113.32/17.04 (100) ~ (all_52_13 = all_4_2)
% 113.32/17.04 (101) all_58_12 = all_52_3
% 113.32/17.04 (102) ~ (all_52_2 = all_52_14)
% 113.32/17.04 (103) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.32/17.04 (104) ~ (all_52_12 = all_4_2)
% 113.32/17.04 (105) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.32/17.04 (106) all_56_8 = all_52_14
% 113.32/17.04 (107) ~ (all_52_6 = e1)
% 113.32/17.04 (108) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.32/17.04 (109) all_56_0 = all_52_4
% 113.32/17.04 (110) ~ (all_52_2 = e2)
% 113.32/17.04 (111) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.32/17.04 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.32/17.04 (112) all_54_4 = all_52_1
% 113.32/17.04 (113) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.32/17.05 (114) all_54_15 = all_4_2
% 113.32/17.05 (115) op(e2, all_8_2) = e1
% 113.32/17.05 (116) ~ (all_6_2 = e1)
% 113.32/17.05 (117) ~ (all_52_6 = all_52_7)
% 113.32/17.05 (118) all_54_12 = all_52_3
% 113.32/17.05 (119) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.32/17.05 (120) ~ (all_52_4 = e2)
% 113.32/17.05
% 113.32/17.05 Begin of proof
% 113.32/17.05 |
% 113.32/17.05 | GROUND_INST: instantiating (29) with all_52_4, all_10_1, e2, e3, simplifying
% 113.32/17.05 | with (9), (86) gives:
% 113.32/17.05 | (121) all_52_4 = all_10_1
% 113.32/17.05 |
% 113.32/17.05 | COMBINE_EQS: (71), (121) imply:
% 113.32/17.05 | (122) all_58_1 = all_10_1
% 113.32/17.05 |
% 113.32/17.05 | REDUCE: (38), (121) imply:
% 113.32/17.05 | (123) ~ (all_52_7 = all_10_1)
% 113.32/17.05 |
% 113.32/17.05 | SIMP: (123) implies:
% 113.32/17.05 | (124) ~ (all_52_7 = all_10_1)
% 113.32/17.05 |
% 113.32/17.05 | REDUCE: (88), (121) imply:
% 113.32/17.05 | (125) ~ (all_52_12 = all_10_1)
% 113.32/17.05 |
% 113.32/17.05 | SIMP: (125) implies:
% 113.32/17.05 | (126) ~ (all_52_12 = all_10_1)
% 113.32/17.05 |
% 113.32/17.05 | REDUCE: (17), (121) imply:
% 113.32/17.05 | (127) ~ (all_10_1 = e3)
% 113.32/17.05 |
% 113.32/17.05 | REDUCE: (120), (121) imply:
% 113.32/17.05 | (128) ~ (all_10_1 = e2)
% 113.32/17.05 |
% 113.32/17.05 | BETA: splitting (19) gives:
% 113.32/17.05 |
% 113.32/17.05 | Case 1:
% 113.32/17.05 | |
% 113.32/17.05 | | (129) ~ (all_56_8 = e1)
% 113.32/17.05 | |
% 113.32/17.05 | | REDUCE: (106), (129) imply:
% 113.32/17.05 | | (130) ~ (all_52_14 = e1)
% 113.32/17.05 | |
% 113.32/17.05 | | BETA: splitting (83) gives:
% 113.32/17.05 | |
% 113.32/17.05 | | Case 1:
% 113.32/17.05 | | |
% 113.32/17.05 | | | (131) all_58_6 = e1
% 113.32/17.05 | | |
% 113.32/17.05 | | | COMBINE_EQS: (64), (131) imply:
% 113.32/17.05 | | | (132) all_52_2 = e1
% 113.32/17.05 | | |
% 113.32/17.05 | | | SIMP: (132) implies:
% 113.32/17.05 | | | (133) all_52_2 = e1
% 113.32/17.05 | | |
% 113.32/17.05 | | | COMBINE_EQS: (99), (133) imply:
% 113.32/17.05 | | | (134) all_56_6 = e1
% 113.32/17.05 | | |
% 113.32/17.05 | | | BETA: splitting (56) gives:
% 113.32/17.05 | | |
% 113.32/17.05 | | | Case 1:
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | (135) ~ (all_56_6 = e1)
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | REDUCE: (134), (135) imply:
% 113.32/17.05 | | | | (136) $false
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | CLOSE: (136) is inconsistent.
% 113.32/17.05 | | | |
% 113.32/17.05 | | | Case 2:
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | (137) ~ (all_56_13 = e3)
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | REDUCE: (76), (137) imply:
% 113.32/17.05 | | | | (138) ~ (all_8_2 = e3)
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | REF_CLOSE: (6), (22), (29), (44), (65), (79), (95), (115), (138) are
% 113.32/17.05 | | | | inconsistent by sub-proof #79.
% 113.32/17.05 | | | |
% 113.32/17.05 | | | End of split
% 113.32/17.05 | | |
% 113.32/17.05 | | Case 2:
% 113.32/17.05 | | |
% 113.32/17.05 | | | (139) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.32/17.05 | | |
% 113.32/17.05 | | | REF_CLOSE: (3), (42), (91), (107), (116), (130), (139) are inconsistent by
% 113.32/17.05 | | | sub-proof #354.
% 113.32/17.05 | | |
% 113.32/17.05 | | End of split
% 113.32/17.05 | |
% 113.32/17.05 | Case 2:
% 113.32/17.05 | |
% 113.32/17.05 | | (140) all_56_8 = e1
% 113.32/17.05 | | (141) ~ (all_56_14 = e0)
% 113.32/17.05 | |
% 113.32/17.05 | | COMBINE_EQS: (106), (140) imply:
% 113.32/17.05 | | (142) all_52_14 = e1
% 113.32/17.05 | |
% 113.32/17.05 | | SIMP: (142) implies:
% 113.32/17.05 | | (143) all_52_14 = e1
% 113.32/17.05 | |
% 113.32/17.05 | | REDUCE: (10), (141) imply:
% 113.32/17.05 | | (144) ~ (all_6_2 = e0)
% 113.32/17.05 | |
% 113.32/17.05 | | REDUCE: (102), (143) imply:
% 113.32/17.05 | | (145) ~ (all_52_2 = e1)
% 113.32/17.05 | |
% 113.32/17.05 | | REDUCE: (14), (143) imply:
% 113.32/17.05 | | (146) ~ (all_52_12 = e1)
% 113.32/17.05 | |
% 113.32/17.05 | | REDUCE: (27), (143) imply:
% 113.32/17.05 | | (147) ~ (all_6_2 = e1)
% 113.32/17.05 | |
% 113.32/17.05 | | BETA: splitting (80) gives:
% 113.32/17.05 | |
% 113.32/17.05 | | Case 1:
% 113.32/17.05 | | |
% 113.32/17.05 | | | (148) all_58_1 = e0
% 113.32/17.05 | | |
% 113.32/17.05 | | | COMBINE_EQS: (122), (148) imply:
% 113.32/17.05 | | | (149) all_10_1 = e0
% 113.32/17.05 | | |
% 113.32/17.05 | | | REDUCE: (126), (149) imply:
% 113.32/17.05 | | | (150) ~ (all_52_12 = e0)
% 113.32/17.05 | | |
% 113.32/17.05 | | | BETA: splitting (20) gives:
% 113.32/17.05 | | |
% 113.32/17.05 | | | Case 1:
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | (151) all_54_3 = e3
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | COMBINE_EQS: (12), (151) imply:
% 113.32/17.05 | | | | (152) all_52_12 = e3
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | SIMP: (152) implies:
% 113.32/17.05 | | | | (153) all_52_12 = e3
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | COMBINE_EQS: (39), (153) imply:
% 113.32/17.05 | | | | (154) all_56_2 = e3
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | BETA: splitting (111) gives:
% 113.32/17.05 | | | |
% 113.32/17.05 | | | | Case 1:
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | (155) all_58_15 = e0
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | COMBINE_EQS: (57), (155) imply:
% 113.32/17.05 | | | | | (156) all_4_2 = e0
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | REDUCE: (8), (156) imply:
% 113.32/17.05 | | | | | (157) $false
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | CLOSE: (157) is inconsistent.
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | Case 2:
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | (158) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.32/17.05 | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | ALPHA: (158) implies:
% 113.32/17.05 | | | | | (159) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.32/17.05 | | | | | (160) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | BETA: splitting (159) gives:
% 113.32/17.05 | | | | |
% 113.32/17.05 | | | | | Case 1:
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | (161) all_58_12 = e0
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | COMBINE_EQS: (101), (161) imply:
% 113.32/17.05 | | | | | | (162) all_52_3 = e0
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | SIMP: (162) implies:
% 113.32/17.05 | | | | | | (163) all_52_3 = e0
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | COMBINE_EQS: (54), (163) imply:
% 113.32/17.05 | | | | | | (164) all_56_9 = e0
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | REF_CLOSE: (6), (22), (29), (60), (65), (72), (76), (79), (95),
% 113.32/17.05 | | | | | | (115), (154), (164) are inconsistent by sub-proof #72.
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | Case 2:
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | (165) all_58_13 = e0 | all_58_14 = e0
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | BETA: splitting (165) gives:
% 113.32/17.05 | | | | | |
% 113.32/17.05 | | | | | | Case 1:
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | (166) all_58_13 = e0
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | REF_CLOSE: (61), (62), (166) are inconsistent by sub-proof #430.
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | Case 2:
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | (167) all_58_14 = e0
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | COMBINE_EQS: (73), (167) imply:
% 113.32/17.05 | | | | | | | (168) all_52_11 = e0
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | SIMP: (168) implies:
% 113.32/17.05 | | | | | | | (169) all_52_11 = e0
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | COMBINE_EQS: (16), (169) imply:
% 113.32/17.05 | | | | | | | (170) all_56_11 = e0
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | REDUCE: (5), (169) imply:
% 113.32/17.05 | | | | | | | (171) ~ (all_52_8 = e0)
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | REDUCE: (69), (169) imply:
% 113.32/17.05 | | | | | | | (172) ~ (all_4_2 = e0)
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | BETA: splitting (46) gives:
% 113.32/17.05 | | | | | | |
% 113.32/17.05 | | | | | | | Case 1:
% 113.32/17.05 | | | | | | | |
% 113.46/17.06 | | | | | | | | (173) ~ (all_56_13 = e1)
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | | REDUCE: (76), (173) imply:
% 113.46/17.06 | | | | | | | | (174) ~ (all_8_2 = e1)
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | | BETA: splitting (22) gives:
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | | Case 1:
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | (175) all_54_5 = e3
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | COMBINE_EQS: (65), (175) imply:
% 113.46/17.06 | | | | | | | | | (176) all_8_2 = e3
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | SIMP: (176) implies:
% 113.46/17.06 | | | | | | | | | (177) all_8_2 = e3
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | COMBINE_EQS: (76), (177) imply:
% 113.46/17.06 | | | | | | | | | (178) all_56_13 = e3
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | COMBINE_EQS: (41), (177) imply:
% 113.46/17.06 | | | | | | | | | (179) all_58_3 = e3
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | REDUCE: (78), (177) imply:
% 113.46/17.06 | | | | | | | | | (180) ~ (all_52_1 = e3)
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (15), (16),
% 113.46/17.06 | | | | | | | | | (18), (21), (22), (23), (25), (26), (28), (29),
% 113.46/17.06 | | | | | | | | | (30), (31), (32), (34), (35), (36), (37), (39),
% 113.46/17.06 | | | | | | | | | (41), (42), (43), (45), (46), (48), (49), (51),
% 113.46/17.06 | | | | | | | | | (53), (54), (55), (57), (58), (59), (60), (61),
% 113.46/17.06 | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (70),
% 113.46/17.06 | | | | | | | | | (72), (73), (76), (77), (79), (80), (81), (87),
% 113.46/17.06 | | | | | | | | | (89), (90), (91), (92), (93), (94), (95), (96),
% 113.46/17.06 | | | | | | | | | (97), (98), (100), (101), (102), (103), (104),
% 113.46/17.06 | | | | | | | | | (105), (107), (108), (110), (111), (112), (114),
% 113.46/17.06 | | | | | | | | | (115), (116), (117), (118), (119), (122), (124),
% 113.46/17.06 | | | | | | | | | (127), (128), (144), (145), (160), (167), (170),
% 113.46/17.06 | | | | | | | | | (171), (178), (179), (180) are inconsistent by
% 113.46/17.06 | | | | | | | | | sub-proof #58.
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | Case 2:
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | (181) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | | REF_CLOSE: (65), (72), (76), (79), (154), (174), (181) are
% 113.46/17.06 | | | | | | | | | inconsistent by sub-proof #286.
% 113.46/17.06 | | | | | | | | |
% 113.46/17.06 | | | | | | | | End of split
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | Case 2:
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | | (182) all_56_13 = e1
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | | REF_CLOSE: (7), (8), (10), (16), (21), (28), (32), (33), (41),
% 113.46/17.06 | | | | | | | | (45), (46), (49), (53), (54), (57), (58), (61), (62),
% 113.46/17.06 | | | | | | | | (68), (73), (76), (81), (92), (94), (101), (108),
% 113.46/17.06 | | | | | | | | (111), (116), (182) are inconsistent by sub-proof
% 113.46/17.06 | | | | | | | | #146.
% 113.46/17.06 | | | | | | | |
% 113.46/17.06 | | | | | | | End of split
% 113.46/17.06 | | | | | | |
% 113.46/17.06 | | | | | | End of split
% 113.46/17.06 | | | | | |
% 113.46/17.06 | | | | | End of split
% 113.46/17.06 | | | | |
% 113.46/17.06 | | | | End of split
% 113.46/17.06 | | | |
% 113.46/17.06 | | | Case 2:
% 113.46/17.06 | | | |
% 113.46/17.06 | | | | (183) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.46/17.06 | | | |
% 113.46/17.06 | | | | REF_CLOSE: (12), (75), (146), (150), (183) are inconsistent by sub-proof
% 113.46/17.06 | | | | #283.
% 113.46/17.06 | | | |
% 113.46/17.06 | | | End of split
% 113.46/17.06 | | |
% 113.46/17.06 | | Case 2:
% 113.46/17.06 | | |
% 113.46/17.06 | | | (184) ~ (all_58_1 = e0)
% 113.46/17.06 | | |
% 113.46/17.06 | | | REDUCE: (122), (184) imply:
% 113.46/17.06 | | | (185) ~ (all_10_1 = e0)
% 113.46/17.06 | | |
% 113.46/17.06 | | | REF_CLOSE: (3), (4), (9), (11), (13), (22), (24), (29), (38), (40), (41),
% 113.46/17.06 | | | (44), (47), (50), (52), (54), (58), (60), (61), (62), (64),
% 113.46/17.06 | | | (65), (67), (71), (74), (76), (79), (80), (84), (85), (86),
% 113.46/17.06 | | | (101), (109), (113), (115), (117), (120), (185) are
% 113.46/17.06 | | | inconsistent by sub-proof #84.
% 113.46/17.06 | | |
% 113.46/17.06 | | End of split
% 113.46/17.06 | |
% 113.46/17.06 | End of split
% 113.46/17.06 |
% 113.46/17.06 End of proof
% 113.46/17.06
% 113.46/17.06 Sub-proof #58 shows that the following formulas are inconsistent:
% 113.46/17.06 ----------------------------------------------------------------
% 113.46/17.06 (1) all_56_13 = e3
% 113.46/17.06 (2) ~ (all_52_6 = all_52_14)
% 113.46/17.06 (3) all_54_2 = all_52_8
% 113.46/17.06 (4) all_58_7 = all_52_6
% 113.46/17.06 (5) ~ (all_52_9 = all_8_2)
% 113.46/17.06 (6) ~ (all_52_1 = e2)
% 113.46/17.06 (7) ~ (all_4_2 = e0)
% 113.46/17.06 (8) all_56_14 = all_6_2
% 113.46/17.06 (9) op(e0, e2) = all_52_7
% 113.46/17.06 (10) all_56_11 = all_52_11
% 113.46/17.06 (11) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 113.46/17.06 (12) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.46/17.06 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.06 (14) op(all_10_1, e2) = e2
% 113.46/17.06 (15) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.46/17.06 (16) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.06 (17) ~ (all_52_1 = e3)
% 113.46/17.06 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.06 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.06 (20) all_54_8 = all_52_2
% 113.46/17.06 (21) ~ (all_52_2 = all_6_2)
% 113.46/17.06 (22) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 113.46/17.06 (23) all_54_10 = all_6_2
% 113.46/17.06 (24) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.46/17.06 (25) ~ (all_52_8 = all_6_2)
% 113.46/17.06 (26) all_58_4 = all_52_8
% 113.46/17.06 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.46/17.06 (28) all_56_2 = all_52_12
% 113.46/17.06 (29) all_58_3 = all_8_2
% 113.46/17.06 (30) all_58_11 = all_52_14
% 113.46/17.06 (31) ~ (all_52_2 = all_52_3)
% 113.46/17.06 (32) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.46/17.06 (33) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.46/17.06 (34) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.46/17.06 (35) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.46/17.06 (36) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.46/17.06 (37) all_58_5 = all_52_9
% 113.46/17.06 (38) ~ (all_52_7 = all_10_1)
% 113.46/17.06 (39) all_56_9 = all_52_3
% 113.46/17.06 (40) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.46/17.06 (41) all_58_15 = all_4_2
% 113.46/17.06 (42) all_58_2 = all_52_1
% 113.46/17.06 (43) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.46/17.06 (44) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.46/17.06 (45) all_58_13 = all_52_7
% 113.46/17.06 (46) ~ (all_52_7 = e0)
% 113.46/17.06 (47) ~ (all_52_14 = all_4_2)
% 113.46/17.06 (48) all_58_6 = all_52_2
% 113.46/17.06 (49) all_58_3 = e3
% 113.46/17.06 (50) ~ (all_52_2 = e1)
% 113.46/17.06 (51) all_54_5 = all_8_2
% 113.46/17.06 (52) all_56_15 = all_4_2
% 113.46/17.06 (53) all_58_0 = e2
% 113.46/17.06 (54) all_58_10 = all_52_13
% 113.46/17.06 (55) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.46/17.06 (56) all_58_14 = e0
% 113.46/17.06 (57) ~ (all_10_1 = e2)
% 113.46/17.06 (58) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.46/17.06 (59) all_58_14 = all_52_11
% 113.46/17.06 (60) all_56_13 = all_8_2
% 113.46/17.06 (61) ~ (all_52_8 = e2)
% 113.46/17.06 (62) all_56_11 = e0
% 113.46/17.06 (63) ~ (all_8_2 = e2)
% 113.46/17.06 (64) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.46/17.06 (65) ~ (all_6_2 = e2)
% 113.46/17.06 (66) ~ (all_52_1 = all_52_2)
% 113.46/17.06 (67) ~ (all_52_1 = all_52_3)
% 113.46/17.06 (68) op(e0, all_4_2) = all_4_1
% 113.46/17.06 (69) all_58_8 = all_6_2
% 113.46/17.06 (70) ~ (all_6_2 = e0)
% 113.46/17.06 (71) all_56_4 = all_52_9
% 113.46/17.06 (72) all_58_9 = all_52_12
% 113.46/17.06 (73) all_56_5 = all_52_13
% 113.46/17.07 (74) ~ (all_10_1 = e3)
% 113.46/17.07 (75) op(e2, e1) = all_52_9
% 113.46/17.07 (76) ~ (all_52_3 = all_4_2)
% 113.46/17.07 (77) ~ (all_52_6 = all_6_2)
% 113.46/17.07 (78) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.46/17.07 (79) ~ (all_52_13 = all_4_2)
% 113.46/17.07 (80) all_58_12 = all_52_3
% 113.46/17.07 (81) ~ (all_52_2 = all_52_14)
% 113.46/17.07 (82) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.46/17.07 (83) ~ (all_52_12 = all_4_2)
% 113.46/17.07 (84) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.46/17.07 (85) ~ (all_52_6 = e1)
% 113.46/17.07 (86) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.46/17.07 (87) ~ (all_52_8 = e0)
% 113.46/17.07 (88) ~ (all_52_2 = e2)
% 113.46/17.07 (89) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.46/17.07 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.46/17.07 (90) all_58_1 = all_10_1
% 113.46/17.07 (91) all_54_4 = all_52_1
% 113.46/17.07 (92) all_54_15 = all_4_2
% 113.46/17.07 (93) op(e2, all_8_2) = e1
% 113.46/17.07 (94) ~ (all_6_2 = e1)
% 113.46/17.07 (95) ~ (all_52_6 = all_52_7)
% 113.46/17.07 (96) all_54_12 = all_52_3
% 113.46/17.07 (97) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.46/17.07
% 113.46/17.07 Begin of proof
% 113.46/17.07 |
% 113.46/17.07 | BETA: splitting (18) gives:
% 113.46/17.07 |
% 113.46/17.07 | Case 1:
% 113.46/17.07 | |
% 113.46/17.07 | | (98) all_54_10 = e3
% 113.46/17.07 | |
% 113.46/17.07 | | COMBINE_EQS: (23), (98) imply:
% 113.46/17.07 | | (99) all_6_2 = e3
% 113.46/17.07 | |
% 113.46/17.07 | | SIMP: (99) implies:
% 113.46/17.07 | | (100) all_6_2 = e3
% 113.46/17.07 | |
% 113.46/17.07 | | COMBINE_EQS: (69), (100) imply:
% 113.46/17.07 | | (101) all_58_8 = e3
% 113.46/17.07 | |
% 113.46/17.07 | | REDUCE: (21), (100) imply:
% 113.46/17.07 | | (102) ~ (all_52_2 = e3)
% 113.46/17.07 | |
% 113.46/17.07 | | REDUCE: (77), (100) imply:
% 113.46/17.07 | | (103) ~ (all_52_6 = e3)
% 113.46/17.07 | |
% 113.46/17.07 | | REDUCE: (25), (100) imply:
% 113.46/17.07 | | (104) ~ (all_52_8 = e3)
% 113.46/17.07 | |
% 113.46/17.07 | | REDUCE: (65), (100) imply:
% 113.46/17.07 | | (105) ~ (e3 = e2)
% 113.46/17.07 | |
% 113.46/17.07 | | BETA: splitting (40) gives:
% 113.46/17.07 | |
% 113.46/17.07 | | Case 1:
% 113.46/17.07 | | |
% 113.46/17.07 | | | (106) ~ (all_56_15 = e1)
% 113.46/17.07 | | |
% 113.46/17.07 | | | REDUCE: (52), (106) imply:
% 113.46/17.07 | | | (107) ~ (all_4_2 = e1)
% 113.46/17.07 | | |
% 113.46/17.07 | | | BETA: splitting (84) gives:
% 113.46/17.07 | | |
% 113.46/17.07 | | | Case 1:
% 113.46/17.07 | | | |
% 113.46/17.07 | | | | (108) all_58_0 = e3
% 113.46/17.07 | | | |
% 113.46/17.07 | | | | REF_CLOSE: (53), (105), (108) are inconsistent by sub-proof #154.
% 113.46/17.07 | | | |
% 113.46/17.07 | | | Case 2:
% 113.46/17.07 | | | |
% 113.46/17.07 | | | | (109) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.46/17.07 | | | |
% 113.46/17.07 | | | | BETA: splitting (78) gives:
% 113.46/17.07 | | | |
% 113.46/17.07 | | | | Case 1:
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | | (110) all_54_2 = e3
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | | REF_CLOSE: (3), (104), (110) are inconsistent by sub-proof #179.
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | Case 2:
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | | (111) ~ (all_54_2 = e3)
% 113.46/17.07 | | | | | (112) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | | BETA: splitting (112) gives:
% 113.46/17.07 | | | | |
% 113.46/17.07 | | | | | Case 1:
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | | (113) all_54_2 = e2
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | | REF_CLOSE: (3), (61), (113) are inconsistent by sub-proof #212.
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | Case 2:
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | | (114) all_54_2 = e1 | all_54_2 = e0
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | | BETA: splitting (36) gives:
% 113.46/17.07 | | | | | |
% 113.46/17.07 | | | | | | Case 1:
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | | (115) all_54_8 = e3
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | | REF_CLOSE: (20), (102), (115) are inconsistent by sub-proof #399.
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | Case 2:
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | | (116) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | | BETA: splitting (116) gives:
% 113.46/17.07 | | | | | | |
% 113.46/17.07 | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | | (117) all_54_8 = e2
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | | REF_CLOSE: (20), (88), (117) are inconsistent by sub-proof #382.
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | | (118) ~ (all_54_8 = e2)
% 113.46/17.07 | | | | | | | | (119) all_54_8 = e1 | all_54_8 = e0
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | | BETA: splitting (109) gives:
% 113.46/17.07 | | | | | | | |
% 113.46/17.07 | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | (120) all_58_1 = e3
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | COMBINE_EQS: (90), (120) imply:
% 113.46/17.07 | | | | | | | | | (121) all_10_1 = e3
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | REDUCE: (74), (121) imply:
% 113.46/17.07 | | | | | | | | | (122) $false
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | CLOSE: (122) is inconsistent.
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | (123) all_58_4 = e3 | all_58_9 = e3
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | BETA: splitting (123) gives:
% 113.46/17.07 | | | | | | | | |
% 113.46/17.07 | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | (124) all_58_4 = e3
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | COMBINE_EQS: (26), (124) imply:
% 113.46/17.07 | | | | | | | | | | (125) all_52_8 = e3
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | REDUCE: (104), (125) imply:
% 113.46/17.07 | | | | | | | | | | (126) $false
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | CLOSE: (126) is inconsistent.
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | (127) all_58_9 = e3
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | COMBINE_EQS: (72), (127) imply:
% 113.46/17.07 | | | | | | | | | | (128) all_52_12 = e3
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | COMBINE_EQS: (28), (128) imply:
% 113.46/17.07 | | | | | | | | | | (129) all_56_2 = e3
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | REDUCE: (83), (128) imply:
% 113.46/17.07 | | | | | | | | | | (130) ~ (all_4_2 = e3)
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | SIMP: (130) implies:
% 113.46/17.07 | | | | | | | | | | (131) ~ (all_4_2 = e3)
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | BETA: splitting (27) gives:
% 113.46/17.07 | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | (132) all_54_15 = e3
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | COMBINE_EQS: (92), (132) imply:
% 113.46/17.07 | | | | | | | | | | | (133) all_4_2 = e3
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | REDUCE: (131), (133) imply:
% 113.46/17.07 | | | | | | | | | | | (134) $false
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | (135) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | BETA: splitting (135) gives:
% 113.46/17.07 | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | (136) all_54_15 = e2
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | COMBINE_EQS: (92), (136) imply:
% 113.46/17.07 | | | | | | | | | | | | (137) all_4_2 = e2
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | COMBINE_EQS: (41), (137) imply:
% 113.46/17.07 | | | | | | | | | | | | (138) all_58_15 = e2
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | REDUCE: (76), (137) imply:
% 113.46/17.07 | | | | | | | | | | | | (139) ~ (all_52_3 = e2)
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | REDUCE: (79), (137) imply:
% 113.46/17.07 | | | | | | | | | | | | (140) ~ (all_52_13 = e2)
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | REDUCE: (47), (137) imply:
% 113.46/17.07 | | | | | | | | | | | | (141) ~ (all_52_14 = e2)
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | REDUCE: (68), (137) imply:
% 113.46/17.07 | | | | | | | | | | | | (142) op(e0, e2) = all_4_1
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | BETA: splitting (15) gives:
% 113.46/17.07 | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | (143) all_58_1 = e2
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | COMBINE_EQS: (90), (143) imply:
% 113.46/17.07 | | | | | | | | | | | | | (144) all_10_1 = e2
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | REDUCE: (57), (144) imply:
% 113.46/17.07 | | | | | | | | | | | | | (145) $false
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | (146) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | BETA: splitting (119) gives:
% 113.46/17.07 | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | (147) all_54_8 = e1
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | REF_CLOSE: (20), (50), (147) are inconsistent by sub-proof
% 113.46/17.07 | | | | | | | | | | | | | | #397.
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | (148) all_54_8 = e0
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | COMBINE_EQS: (20), (148) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (149) all_52_2 = e0
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | SIMP: (149) implies:
% 113.46/17.07 | | | | | | | | | | | | | | (150) all_52_2 = e0
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | COMBINE_EQS: (48), (150) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (151) all_58_6 = e0
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | REDUCE: (66), (150) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (152) ~ (all_52_1 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | REDUCE: (31), (150) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (153) ~ (all_52_3 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | SIMP: (153) implies:
% 113.46/17.07 | | | | | | | | | | | | | | (154) ~ (all_52_3 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | REDUCE: (81), (150) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (155) ~ (all_52_14 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | SIMP: (155) implies:
% 113.46/17.07 | | | | | | | | | | | | | | (156) ~ (all_52_14 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | REDUCE: (88), (150) imply:
% 113.46/17.07 | | | | | | | | | | | | | | (157) ~ (e2 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | SIMP: (157) implies:
% 113.46/17.07 | | | | | | | | | | | | | | (158) ~ (e2 = e0)
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 113.46/17.07 | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | (159) all_54_2 = e1
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | COMBINE_EQS: (3), (159) imply:
% 113.46/17.07 | | | | | | | | | | | | | | | (160) all_52_8 = e1
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | SIMP: (160) implies:
% 113.46/17.07 | | | | | | | | | | | | | | | (161) all_52_8 = e1
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | COMBINE_EQS: (26), (161) imply:
% 113.46/17.07 | | | | | | | | | | | | | | | (162) all_58_4 = e1
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | REDUCE: (87), (161) imply:
% 113.46/17.07 | | | | | | | | | | | | | | | (163) ~ (e1 = e0)
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 113.46/17.07 | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | Case 1:
% 113.46/17.07 | | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | | (164) all_54_4 = e3
% 113.46/17.07 | | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (91), (164) are inconsistent by sub-proof
% 113.46/17.07 | | | | | | | | | | | | | | | | #329.
% 113.46/17.07 | | | | | | | | | | | | | | | |
% 113.46/17.07 | | | | | | | | | | | | | | | Case 2:
% 113.46/17.07 | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | (165) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | (166) all_58_12 = e3
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (166) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | (167) all_52_3 = e3
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 113.46/17.08 | | | | | | | | | | | | | | | | | (168) all_52_3 = e3
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (168) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | (169) all_56_9 = e3
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | (170) all_58_6 = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (170) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | (171) e2 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | REDUCE: (158), (171) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | (172) $false
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | (173) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (174) all_58_7 = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (174) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (175) all_52_6 = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | REDUCE: (95), (175) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (176) ~ (all_52_7 = e2)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (177) ~ (all_52_7 = e2)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | REDUCE: (2), (175) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (178) ~ (all_52_14 = e2)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | REDUCE: (103), (175) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (179) ~ (e3 = e2)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | REDUCE: (85), (175) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | (180) ~ (e2 = e1)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (181) all_58_12 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (181) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (182) e3 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (8), (10), (12), (18), (23), (32),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (33), (35), (37), (39), (41), (42), (45), (46),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (49), (54), (59), (65), (71), (73), (80), (86),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (89), (94), (180), (182) are inconsistent by
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | (183) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (184) all_58_13 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (184) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (185) all_52_7 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (186) all_52_7 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (186) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (187) ~ (all_10_1 = e1)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (188) ~ (all_10_1 = e1)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (186) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (189) ~ (e2 = e1)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (186) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (190) op(e0, e2) = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | (191) all_58_9 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (19), (44), (51), (58), (60), (63),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | (75), (93), (127), (129), (169), (191) are
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #59.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | (192) all_58_10 = e0 | all_58_11 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_10 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (193) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | (194) all_52_13 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (195) all_58_9 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (195) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (8), (10), (12), (18), (23), (32),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (33), (35), (37), (39), (41), (42), (45), (46),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (49), (54), (59), (65), (71), (73), (80), (86),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (89), (94), (180), (196) are inconsistent by
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_0 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (198) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | (199) e2 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (199) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_7 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (45), (63), (146), (158), (177), (200) are
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_58_1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (202) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_10_1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (203) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) ~ (e1 = e0)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (203) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) op(e0, e2) = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_10 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (206) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) e1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (208) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) $false
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_11 = e1 | all_58_15 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_11 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (211) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_52_14 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e2, all_4_1, e2, e0,
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (142), (205) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_4_1 = e2
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e1, all_4_1, e2, e0,
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (142), (190) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_4_1 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (214) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) e2 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (215) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_7 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (105), (141), (173), (180), (216) are
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_15 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (217) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) e2 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (218) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_7 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (105), (141), (173), (180), (219) are
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_58_1 = e0)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (220) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_10_1 = e0)
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (222) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_10_1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (221), (223) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_58_4 = e0 | all_58_9 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_4 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (226) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) e1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (227) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) $false
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_58_9 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (19), (44), (51), (58), (60), (63),
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (75), (93), (127), (129), (169), (229) are
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #59.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_11 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (230) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | (231) all_52_14 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (231) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | (232) $false
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | (233) all_58_14 = e1 | all_58_15 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | (234) all_58_14 = e1
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (234) imply:
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | (235) e1 = e0
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.08 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (235) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | (236) $false
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | (237) all_58_15 = e1
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (237) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | (238) e2 = e1
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (238) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | (239) all_58_7 = e1
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (105), (141), (173), (180), (239) are
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275.
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | (240) all_58_8 = e2 | all_58_11 = e2
% 113.46/17.09 | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (105), (141), (240) are inconsistent
% 113.46/17.09 | | | | | | | | | | | | | | | | | | | by sub-proof #345.
% 113.46/17.09 | | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | (241) ~ (all_58_12 = e3)
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | REDUCE: (80), (241) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | (242) ~ (all_52_3 = e3)
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | Case 1:
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (243) all_58_2 = e1
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (243) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (244) all_52_1 = e1
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | REDUCE: (67), (244) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (245) ~ (all_52_3 = e1)
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | SIMP: (245) implies:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (246) ~ (all_52_3 = e1)
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (96), (139), (154), (242), (246) are
% 113.46/17.09 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #405.
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (247) ~ (all_58_2 = e1)
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | REDUCE: (42), (247) imply:
% 113.46/17.09 | | | | | | | | | | | | | | | | | | (248) ~ (all_52_1 = e1)
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (91), (152), (165), (248) are inconsistent by
% 113.46/17.09 | | | | | | | | | | | | | | | | | | sub-proof #62.
% 113.46/17.09 | | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | (249) all_54_2 = e0
% 113.46/17.09 | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | | REF_CLOSE: (3), (87), (249) are inconsistent by sub-proof
% 113.46/17.09 | | | | | | | | | | | | | | | #211.
% 113.46/17.09 | | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | Case 2:
% 113.46/17.09 | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | (250) all_54_15 = e1 | all_54_15 = e0
% 113.46/17.09 | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | | REF_CLOSE: (7), (92), (107), (250) are inconsistent by
% 113.46/17.09 | | | | | | | | | | | | sub-proof #418.
% 113.46/17.09 | | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | | |
% 113.46/17.09 | | | | | | | | | End of split
% 113.46/17.09 | | | | | | | | |
% 113.46/17.09 | | | | | | | | End of split
% 113.46/17.09 | | | | | | | |
% 113.46/17.09 | | | | | | | End of split
% 113.46/17.09 | | | | | | |
% 113.46/17.09 | | | | | | End of split
% 113.46/17.09 | | | | | |
% 113.46/17.09 | | | | | End of split
% 113.46/17.09 | | | | |
% 113.46/17.09 | | | | End of split
% 113.46/17.09 | | | |
% 113.46/17.09 | | | End of split
% 113.46/17.09 | | |
% 113.46/17.09 | | Case 2:
% 113.46/17.09 | | |
% 113.46/17.09 | | | (251) ~ (all_56_11 = e0)
% 113.46/17.09 | | |
% 113.46/17.09 | | | REDUCE: (62), (251) imply:
% 113.46/17.09 | | | (252) $false
% 113.46/17.09 | | |
% 113.46/17.09 | | | CLOSE: (252) is inconsistent.
% 113.46/17.09 | | |
% 113.46/17.09 | | End of split
% 113.46/17.09 | |
% 113.46/17.09 | Case 2:
% 113.46/17.09 | |
% 113.46/17.09 | | (253) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.09 | |
% 113.46/17.09 | | REF_CLOSE: (23), (65), (70), (94), (253) are inconsistent by sub-proof #435.
% 113.46/17.09 | |
% 113.46/17.09 | End of split
% 113.46/17.09 |
% 113.46/17.09 End of proof
% 113.46/17.09
% 113.46/17.09 Sub-proof #59 shows that the following formulas are inconsistent:
% 113.46/17.09 ----------------------------------------------------------------
% 113.46/17.09 (1) ~ (all_52_9 = all_8_2)
% 113.46/17.09 (2) all_58_9 = e3
% 113.46/17.09 (3) all_56_9 = e3
% 113.46/17.09 (4) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.09 (6) all_58_9 = e0
% 113.46/17.09 (7) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.46/17.09 (8) all_54_5 = all_8_2
% 113.46/17.09 (9) all_56_2 = e3
% 113.46/17.09 (10) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.46/17.09 (11) all_56_13 = all_8_2
% 113.46/17.09 (12) ~ (all_8_2 = e2)
% 113.46/17.09 (13) op(e2, e1) = all_52_9
% 113.46/17.09 (14) op(e2, all_8_2) = e1
% 113.46/17.09
% 113.46/17.09 Begin of proof
% 113.46/17.09 |
% 113.46/17.09 | COMBINE_EQS: (2), (6) imply:
% 113.46/17.09 | (15) e3 = e0
% 113.46/17.09 |
% 113.46/17.09 | COMBINE_EQS: (3), (15) imply:
% 113.46/17.09 | (16) all_56_9 = e0
% 113.46/17.09 |
% 113.46/17.09 | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14), (16)
% 113.46/17.09 | are inconsistent by sub-proof #72.
% 113.46/17.09 |
% 113.46/17.09 End of proof
% 113.46/17.09
% 113.46/17.09 Sub-proof #60 shows that the following formulas are inconsistent:
% 113.46/17.09 ----------------------------------------------------------------
% 113.46/17.09 (1) all_56_13 = e3
% 113.46/17.09 (2) ~ (all_52_1 = e2)
% 113.46/17.09 (3) ~ (all_4_2 = e0)
% 113.46/17.09 (4) all_56_14 = all_6_2
% 113.46/17.09 (5) all_56_11 = all_52_11
% 113.46/17.09 (6) e3 = e1
% 113.46/17.09 (7) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.46/17.09 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.09 (9) all_54_10 = all_6_2
% 113.46/17.09 (10) ~ (e2 = e1)
% 113.46/17.09 (11) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.46/17.09 (12) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.46/17.09 (13) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.46/17.09 (14) all_58_5 = all_52_9
% 113.46/17.09 (15) all_56_9 = all_52_3
% 113.46/17.09 (16) all_58_15 = all_4_2
% 113.46/17.09 (17) all_58_2 = all_52_1
% 113.46/17.09 (18) all_58_13 = all_52_7
% 113.46/17.09 (19) ~ (all_52_7 = e0)
% 113.46/17.09 (20) all_58_3 = e3
% 113.46/17.09 (21) all_58_10 = all_52_13
% 113.46/17.09 (22) all_58_14 = all_52_11
% 113.46/17.09 (23) ~ (all_6_2 = e2)
% 113.46/17.09 (24) all_56_4 = all_52_9
% 113.46/17.09 (25) all_56_5 = all_52_13
% 113.46/17.09 (26) all_58_12 = all_52_3
% 113.46/17.09 (27) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.46/17.09 (28) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.46/17.09 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.46/17.09 (29) ~ (all_6_2 = e1)
% 113.46/17.09
% 113.46/17.09 Begin of proof
% 113.46/17.09 |
% 113.46/17.09 | COMBINE_EQS: (1), (6) imply:
% 113.46/17.09 | (30) all_56_13 = e1
% 113.46/17.09 |
% 113.46/17.09 | COMBINE_EQS: (6), (20) imply:
% 113.46/17.09 | (31) all_58_3 = e1
% 113.46/17.09 |
% 113.46/17.09 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 113.46/17.09 | (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 113.46/17.09 | (27), (28), (29), (30), (31) are inconsistent by sub-proof #427.
% 113.46/17.09 |
% 113.46/17.09 End of proof
% 113.46/17.09
% 113.46/17.09 Sub-proof #61 shows that the following formulas are inconsistent:
% 113.46/17.09 ----------------------------------------------------------------
% 113.46/17.09 (1) all_58_7 = all_52_6
% 113.46/17.09 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.46/17.09 (3) ~ (all_52_9 = all_8_2)
% 113.46/17.09 (4) ~ (all_52_13 = all_52_14)
% 113.46/17.09 (5) all_54_0 = all_10_2
% 113.46/17.09 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.09 (7) all_56_12 = all_10_2
% 113.46/17.09 (8) all_58_0 = all_10_2
% 113.46/17.10 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.10 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.10 (11) ~ (all_10_2 = all_4_1)
% 113.46/17.10 (12) all_58_3 = all_8_2
% 113.46/17.10 (13) all_58_11 = all_52_14
% 113.46/17.10 (14) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.46/17.10 (15) all_54_7 = all_52_13
% 113.46/17.10 (16) op(e2, e3) = all_52_1
% 113.46/17.10 (17) ~ (all_10_2 = e1)
% 113.46/17.10 (18) all_58_5 = all_52_9
% 113.46/17.10 (19) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.46/17.10 (20) all_58_2 = all_52_1
% 113.46/17.10 (21) ~ (all_10_2 = e3)
% 113.46/17.10 (22) ~ (all_4_1 = e0)
% 113.46/17.10 (23) all_58_6 = all_52_2
% 113.46/17.10 (24) ~ (all_52_2 = e1)
% 113.46/17.10 (25) ~ (all_52_1 = all_10_2)
% 113.46/17.10 (26) all_54_5 = all_8_2
% 113.46/17.10 (27) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.46/17.10 (28) all_58_10 = all_52_13
% 113.46/17.10 (29) ~ (all_52_13 = all_8_2)
% 113.46/17.10 (30) ~ (all_8_2 = e1)
% 113.46/17.10 (31) all_56_13 = all_8_2
% 113.46/17.10 (32) ~ (all_52_1 = all_8_2)
% 113.46/17.10 (33) ~ (all_8_2 = e2)
% 113.46/17.10 (34) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.46/17.10 (35) all_58_8 = all_6_2
% 113.46/17.10 (36) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.46/17.10 (37) all_56_5 = all_52_13
% 113.46/17.10 (38) all_54_12 = all_4_1
% 113.46/17.10 (39) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.46/17.10 (40) op(e2, e0) = all_52_13
% 113.46/17.10 (41) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.46/17.10 (42) ~ (all_52_1 = all_4_1)
% 113.46/17.10 (43) all_56_8 = all_52_14
% 113.46/17.10 (44) ~ (all_52_6 = e1)
% 113.46/17.10 (45) ~ (all_4_1 = e3)
% 113.46/17.10 (46) all_54_4 = all_52_1
% 113.46/17.10 (47) op(e2, all_8_2) = e1
% 113.46/17.10 (48) ~ (all_6_2 = e1)
% 113.46/17.10
% 113.46/17.10 Begin of proof
% 113.46/17.10 |
% 113.46/17.10 | BETA: splitting (34) gives:
% 113.46/17.10 |
% 113.46/17.10 | Case 1:
% 113.46/17.10 | |
% 113.46/17.10 | | (49) all_58_6 = e1
% 113.46/17.10 | |
% 113.46/17.10 | | REF_CLOSE: (23), (24), (49) are inconsistent by sub-proof #452.
% 113.46/17.10 | |
% 113.46/17.10 | Case 2:
% 113.46/17.10 | |
% 113.46/17.10 | | (50) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.46/17.10 | |
% 113.46/17.10 | | BETA: splitting (50) gives:
% 113.46/17.10 | |
% 113.46/17.10 | | Case 1:
% 113.46/17.10 | | |
% 113.46/17.10 | | | (51) all_58_7 = e1
% 113.46/17.10 | | |
% 113.46/17.10 | | | COMBINE_EQS: (1), (51) imply:
% 113.46/17.10 | | | (52) all_52_6 = e1
% 113.46/17.10 | | |
% 113.46/17.10 | | | REDUCE: (44), (52) imply:
% 113.46/17.10 | | | (53) $false
% 113.46/17.10 | | |
% 113.46/17.10 | | | CLOSE: (53) is inconsistent.
% 113.46/17.10 | | |
% 113.46/17.10 | | Case 2:
% 113.46/17.10 | | |
% 113.46/17.10 | | | (54) all_58_8 = e1 | all_58_11 = e1
% 113.46/17.10 | | |
% 113.46/17.10 | | | BETA: splitting (54) gives:
% 113.46/17.10 | | |
% 113.46/17.10 | | | Case 1:
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | (55) all_58_8 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | COMBINE_EQS: (35), (55) imply:
% 113.46/17.10 | | | | (56) all_6_2 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | REDUCE: (48), (56) imply:
% 113.46/17.10 | | | | (57) $false
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | CLOSE: (57) is inconsistent.
% 113.46/17.10 | | | |
% 113.46/17.10 | | | Case 2:
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | (58) all_58_11 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | COMBINE_EQS: (13), (58) imply:
% 113.46/17.10 | | | | (59) all_52_14 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | SIMP: (59) implies:
% 113.46/17.10 | | | | (60) all_52_14 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | COMBINE_EQS: (43), (60) imply:
% 113.46/17.10 | | | | (61) all_56_8 = e1
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | REDUCE: (4), (60) imply:
% 113.46/17.10 | | | | (62) ~ (all_52_13 = e1)
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | BETA: splitting (6) gives:
% 113.46/17.10 | | | |
% 113.46/17.10 | | | | Case 1:
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | (63) all_54_5 = e3
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | COMBINE_EQS: (26), (63) imply:
% 113.46/17.10 | | | | | (64) all_8_2 = e3
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | SIMP: (64) implies:
% 113.46/17.10 | | | | | (65) all_8_2 = e3
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | REDUCE: (32), (65) imply:
% 113.46/17.10 | | | | | (66) ~ (all_52_1 = e3)
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | REDUCE: (47), (65) imply:
% 113.46/17.10 | | | | | (67) op(e2, e3) = e1
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | BETA: splitting (19) gives:
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | Case 1:
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | (68) ~ (all_56_8 = e1)
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | REDUCE: (61), (68) imply:
% 113.46/17.10 | | | | | | (69) $false
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | CLOSE: (69) is inconsistent.
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | Case 2:
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | (70) ~ (all_56_12 = e0)
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | REDUCE: (7), (70) imply:
% 113.46/17.10 | | | | | | (71) ~ (all_10_2 = e0)
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | BETA: splitting (36) gives:
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | | Case 1:
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | | (72) all_54_0 = e3
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | | REF_CLOSE: (5), (21), (72) are inconsistent by sub-proof #451.
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | Case 2:
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | | (73) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | | BETA: splitting (73) gives:
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | (74) all_54_0 = e2
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | COMBINE_EQS: (5), (74) imply:
% 113.46/17.10 | | | | | | | | (75) all_10_2 = e2
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | SIMP: (75) implies:
% 113.46/17.10 | | | | | | | | (76) all_10_2 = e2
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | COMBINE_EQS: (8), (76) imply:
% 113.46/17.10 | | | | | | | | (77) all_58_0 = e2
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | REDUCE: (25), (76) imply:
% 113.46/17.10 | | | | | | | | (78) ~ (all_52_1 = e2)
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | REDUCE: (11), (76) imply:
% 113.46/17.10 | | | | | | | | (79) ~ (all_4_1 = e2)
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | SIMP: (79) implies:
% 113.46/17.10 | | | | | | | | (80) ~ (all_4_1 = e2)
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | REDUCE: (71), (76) imply:
% 113.46/17.10 | | | | | | | | (81) ~ (e2 = e0)
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | BETA: splitting (39) gives:
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | | (82) all_54_12 = e3
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | | REF_CLOSE: (38), (45), (82) are inconsistent by sub-proof
% 113.46/17.10 | | | | | | | | | #239.
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | | (83) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | | BETA: splitting (83) gives:
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | (84) all_54_12 = e2
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | REF_CLOSE: (38), (80), (84) are inconsistent by sub-proof
% 113.46/17.10 | | | | | | | | | | #238.
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | (85) all_54_12 = e1 | all_54_12 = e0
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | BETA: splitting (85) gives:
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | (86) all_54_12 = e1
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | COMBINE_EQS: (38), (86) imply:
% 113.46/17.10 | | | | | | | | | | | (87) all_4_1 = e1
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | SIMP: (87) implies:
% 113.46/17.10 | | | | | | | | | | | (88) all_4_1 = e1
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | REDUCE: (42), (88) imply:
% 113.46/17.10 | | | | | | | | | | | (89) ~ (all_52_1 = e1)
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | BETA: splitting (9) gives:
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | (90) all_54_4 = e3
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | REF_CLOSE: (46), (66), (90) are inconsistent by sub-proof
% 113.46/17.10 | | | | | | | | | | | | #329.
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | (91) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | BETA: splitting (2) gives:
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | (92) all_58_0 = e0
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | COMBINE_EQS: (77), (92) imply:
% 113.46/17.10 | | | | | | | | | | | | | (93) e2 = e0
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | REDUCE: (81), (93) imply:
% 113.46/17.10 | | | | | | | | | | | | | (94) $false
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | CLOSE: (94) is inconsistent.
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | (95) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | BETA: splitting (95) gives:
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | Case 1:
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | | (96) all_58_2 = e0
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (20), (67), (89), (96) are
% 113.46/17.10 | | | | | | | | | | | | | | inconsistent by sub-proof #128.
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | | (97) ~ (all_58_2 = e0)
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | | REDUCE: (20), (97) imply:
% 113.46/17.10 | | | | | | | | | | | | | | (98) ~ (all_52_1 = e0)
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | | REF_CLOSE: (46), (78), (89), (91), (98) are inconsistent by
% 113.46/17.10 | | | | | | | | | | | | | | sub-proof #62.
% 113.46/17.10 | | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | | End of split
% 113.46/17.10 | | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | | End of split
% 113.46/17.10 | | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | End of split
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | (99) all_54_12 = e0
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | | REF_CLOSE: (22), (38), (99) are inconsistent by sub-proof
% 113.46/17.10 | | | | | | | | | | | #237.
% 113.46/17.10 | | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | | End of split
% 113.46/17.10 | | | | | | | | | |
% 113.46/17.10 | | | | | | | | | End of split
% 113.46/17.10 | | | | | | | | |
% 113.46/17.10 | | | | | | | | End of split
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | Case 2:
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | (100) all_54_0 = e1 | all_54_0 = e0
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | | REF_CLOSE: (5), (17), (71), (100) are inconsistent by sub-proof
% 113.46/17.10 | | | | | | | | #423.
% 113.46/17.10 | | | | | | | |
% 113.46/17.10 | | | | | | | End of split
% 113.46/17.10 | | | | | | |
% 113.46/17.10 | | | | | | End of split
% 113.46/17.10 | | | | | |
% 113.46/17.10 | | | | | End of split
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | Case 2:
% 113.46/17.10 | | | | |
% 113.46/17.10 | | | | | (101) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.11 | | | | |
% 113.46/17.11 | | | | | REF_CLOSE: (3), (6), (10), (12), (14), (15), (16), (18), (20), (26),
% 113.46/17.11 | | | | | (27), (28), (29), (30), (31), (33), (37), (40), (41), (47),
% 113.46/17.11 | | | | | (62), (101) are inconsistent by sub-proof #129.
% 113.46/17.11 | | | | |
% 113.46/17.11 | | | | End of split
% 113.46/17.11 | | | |
% 113.46/17.11 | | | End of split
% 113.46/17.11 | | |
% 113.46/17.11 | | End of split
% 113.46/17.11 | |
% 113.46/17.11 | End of split
% 113.46/17.11 |
% 113.46/17.11 End of proof
% 113.46/17.11
% 113.46/17.11 Sub-proof #62 shows that the following formulas are inconsistent:
% 113.46/17.11 ----------------------------------------------------------------
% 113.46/17.11 (1) ~ (all_52_1 = e2)
% 113.46/17.11 (2) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.11 (3) ~ (all_52_1 = e0)
% 113.46/17.11 (4) ~ (all_52_1 = e1)
% 113.46/17.11 (5) all_54_4 = all_52_1
% 113.46/17.11
% 113.46/17.11 Begin of proof
% 113.46/17.11 |
% 113.46/17.11 | BETA: splitting (2) gives:
% 113.46/17.11 |
% 113.46/17.11 | Case 1:
% 113.46/17.11 | |
% 113.46/17.11 | | (6) all_54_4 = e2
% 113.46/17.11 | |
% 113.46/17.11 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #328.
% 113.46/17.11 | |
% 113.46/17.11 | Case 2:
% 113.46/17.11 | |
% 113.46/17.11 | | (7) all_54_4 = e1 | all_54_4 = e0
% 113.46/17.11 | |
% 113.46/17.11 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #147.
% 113.46/17.11 | |
% 113.46/17.11 | End of split
% 113.46/17.11 |
% 113.46/17.11 End of proof
% 113.46/17.11
% 113.46/17.11 Sub-proof #63 shows that the following formulas are inconsistent:
% 113.46/17.11 ----------------------------------------------------------------
% 113.46/17.11 (1) ~ (all_52_8 = all_10_2)
% 113.46/17.11 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.46/17.11 (3) ~ (all_52_2 = all_10_2)
% 113.46/17.11 (4) all_58_7 = all_52_6
% 113.46/17.11 (5) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.46/17.11 (6) ~ (all_52_9 = all_8_2)
% 113.46/17.11 (7) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 113.46/17.11 (8) ~ (all_4_2 = e0)
% 113.46/17.11 (9) op(e3, e2) = all_52_4
% 113.46/17.11 (10) all_56_14 = all_6_2
% 113.46/17.11 (11) all_56_3 = all_52_1
% 113.46/17.11 (12) all_54_0 = all_10_2
% 113.46/17.11 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.46/17.11 (14) ~ (all_52_2 = all_52_6)
% 113.46/17.11 (15) all_56_11 = all_52_11
% 113.46/17.11 (16) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.46/17.11 (17) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.46/17.11 (18) ~ (all_52_12 = all_10_2)
% 113.46/17.11 (19) ~ (e3 = e1)
% 113.46/17.11 (20) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.46/17.11 (21) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.11 (22) all_56_12 = all_10_2
% 113.46/17.11 (23) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.46/17.11 (24) all_58_0 = all_10_2
% 113.46/17.11 (25) all_54_13 = all_52_7
% 113.46/17.11 (26) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.11 (27) ~ (all_52_14 = all_6_2)
% 113.46/17.11 (28) all_56_10 = all_52_7
% 113.46/17.11 (29) all_54_14 = all_52_11
% 113.46/17.11 (30) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.11 (31) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.46/17.11 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.11 (33) ~ (all_52_1 = all_52_9)
% 113.46/17.11 (34) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.46/17.11 (35) all_54_10 = all_6_2
% 113.46/17.11 (36) all_58_4 = all_52_8
% 113.46/17.11 (37) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.46/17.11 (38) ~ (all_52_4 = all_52_7)
% 113.46/17.11 (39) all_56_2 = all_52_12
% 113.46/17.11 (40) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.46/17.11 (41) all_58_3 = all_8_2
% 113.46/17.11 (42) all_54_6 = all_52_9
% 113.46/17.11 (43) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.46/17.11 (44) all_58_11 = all_52_14
% 113.46/17.11 (45) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.46/17.11 (46) ~ (all_52_2 = all_52_3)
% 113.46/17.11 (47) ~ (all_8_2 = e0)
% 113.46/17.11 (48) all_54_7 = all_52_13
% 113.46/17.11 (49) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.46/17.11 (50) ~ (all_52_11 = all_6_2)
% 113.46/17.11 (51) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.46/17.11 (52) op(e2, e3) = all_52_1
% 113.46/17.11 (53) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.46/17.11 (54) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.46/17.11 (55) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.46/17.11 (56) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.46/17.11 (57) ~ (all_52_7 = all_8_2)
% 113.46/17.11 (58) ~ (all_52_4 = all_8_2)
% 113.46/17.11 (59) all_58_5 = all_52_9
% 113.46/17.11 (60) op(all_4_1, all_4_2) = e1
% 113.46/17.11 (61) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.46/17.11 (62) all_56_9 = all_52_3
% 113.46/17.11 (63) op(e1, all_6_2) = all_6_1
% 113.46/17.11 (64) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.46/17.11 (65) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.46/17.11 (66) all_58_15 = all_4_2
% 113.46/17.11 (67) all_58_2 = all_52_1
% 113.46/17.11 (68) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.46/17.11 (69) op(e0, e3) = all_52_3
% 113.46/17.11 (70) ~ (all_10_2 = e3)
% 113.46/17.11 (71) all_58_13 = all_52_7
% 113.46/17.11 (72) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.46/17.11 (73) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.46/17.11 (74) ~ (all_52_14 = all_4_2)
% 113.46/17.11 (75) all_58_6 = all_52_2
% 113.46/17.11 (76) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.46/17.11 (77) ~ (all_52_1 = all_10_2)
% 113.46/17.11 (78) all_54_5 = all_8_2
% 113.46/17.11 (79) all_56_15 = all_4_2
% 113.46/17.11 (80) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.46/17.11 (81) all_58_10 = all_52_13
% 113.46/17.11 (82) ~ (all_52_13 = all_8_2)
% 113.46/17.11 (83) ~ (all_52_11 = all_4_2)
% 113.46/17.11 (84) op(e3, all_10_2) = all_10_1
% 113.46/17.11 (85) ~ (all_52_6 = all_8_2)
% 113.46/17.11 (86) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.46/17.11 (87) all_58_1 = all_52_4
% 113.46/17.11 (88) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.46/17.11 (89) ~ (all_52_9 = all_52_11)
% 113.46/17.11 (90) all_58_14 = all_52_11
% 113.46/17.11 (91) all_54_1 = all_52_4
% 113.46/17.11 (92) all_56_13 = all_8_2
% 113.46/17.11 (93) ~ (all_52_1 = all_8_2)
% 113.46/17.11 (94) ~ (all_8_2 = e2)
% 113.46/17.11 (95) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.46/17.11 (96) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 113.46/17.11 (97) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.46/17.11 (98) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.46/17.11 (99) all_56_7 = all_52_6
% 113.46/17.11 (100) ~ (all_52_9 = all_6_2)
% 113.46/17.11 (101) ~ (all_52_4 = all_52_6)
% 113.46/17.11 (102) ~ (all_52_1 = all_52_2)
% 113.46/17.11 (103) all_26_2 = all_4_2
% 113.46/17.11 (104) ~ (all_52_1 = all_52_3)
% 113.46/17.11 (105) all_56_1 = all_52_8
% 113.46/17.12 (106) op(e0, all_4_2) = all_4_1
% 113.46/17.12 (107) all_58_8 = all_6_2
% 113.46/17.12 (108) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.46/17.12 (109) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.46/17.12 (110) all_56_4 = all_52_9
% 113.46/17.12 (111) all_58_9 = all_52_12
% 113.46/17.12 (112) all_56_5 = all_52_13
% 113.46/17.12 (113) op(e2, e1) = all_52_9
% 113.46/17.12 (114) ~ (all_52_3 = all_4_2)
% 113.46/17.12 (115) ~ (all_52_6 = all_6_2)
% 113.46/17.12 (116) all_56_6 = all_52_2
% 113.46/17.12 (117) ~ (all_52_13 = all_4_2)
% 113.46/17.12 (118) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.46/17.12 (119) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.46/17.12 (120) all_58_12 = all_52_3
% 113.46/17.12 (121) ~ (all_52_8 = all_52_9)
% 113.46/17.12 (122) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.46/17.12 (123) op(e2, e0) = all_52_13
% 113.46/17.12 (124) ~ (all_52_3 = all_10_2)
% 113.46/17.12 (125) all_24_1 = all_10_1
% 113.46/17.12 (126) op(e1, e3) = all_52_2
% 113.46/17.12 (127) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.46/17.12 (128) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.46/17.12 (129) all_24_2 = all_10_2
% 113.46/17.12 (130) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.46/17.12 (131) op(e1, e1) = all_6_2
% 113.46/17.12 (132) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.46/17.12 (133) all_56_8 = all_52_14
% 113.46/17.12 (134) all_26_1 = all_4_1
% 113.46/17.12 (135) ~ (all_52_4 = all_10_2)
% 113.46/17.12 (136) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.46/17.12 (137) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.46/17.12 (138) all_56_0 = all_52_4
% 113.46/17.12 (139) ~ (e3 = e2)
% 113.46/17.12 (140) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.46/17.12 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.46/17.12 (141) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 113.46/17.12 (142) all_54_4 = all_52_1
% 113.46/17.12 (143) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.46/17.12 (144) all_54_15 = all_4_2
% 113.46/17.12 (145) op(e2, all_8_2) = e1
% 113.46/17.12 (146) ~ (all_6_2 = e1)
% 113.46/17.12 (147) ~ (all_52_6 = all_52_7)
% 113.46/17.12 (148) ~ (all_52_3 = all_52_11)
% 113.46/17.12 (149) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.46/17.12 (150) all_54_12 = all_52_3
% 113.46/17.12 (151) ~ (e1 = e0)
% 113.46/17.12 (152) ~ (all_52_3 = all_52_7)
% 113.46/17.12
% 113.46/17.12 Begin of proof
% 113.46/17.12 |
% 113.46/17.12 | BETA: splitting (72) gives:
% 113.46/17.12 |
% 113.46/17.12 | Case 1:
% 113.46/17.12 | |
% 113.46/17.12 | | (153) ~ (all_56_14 = e2)
% 113.46/17.12 | |
% 113.46/17.12 | | REDUCE: (10), (153) imply:
% 113.46/17.12 | | (154) ~ (all_6_2 = e2)
% 113.46/17.12 | |
% 113.46/17.12 | | BETA: splitting (73) gives:
% 113.46/17.12 | |
% 113.46/17.12 | | Case 1:
% 113.46/17.12 | | |
% 113.46/17.12 | | | (155) ~ (all_56_12 = e2)
% 113.46/17.12 | | |
% 113.46/17.12 | | | REDUCE: (22), (155) imply:
% 113.46/17.12 | | | (156) ~ (all_10_2 = e2)
% 113.46/17.12 | | |
% 113.46/17.12 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (15),
% 113.46/17.12 | | | (17), (18), (20), (21), (22), (23), (24), (26), (27), (28),
% 113.46/17.12 | | | (29), (30), (32), (33), (34), (35), (36), (37), (39), (40),
% 113.46/17.12 | | | (41), (42), (43), (44), (45), (46), (48), (49), (50), (52),
% 113.46/17.12 | | | (53), (54), (55), (56), (57), (58), (59), (60), (62), (63),
% 113.46/17.12 | | | (64), (65), (66), (67), (69), (70), (71), (74), (75), (76),
% 113.46/17.12 | | | (77), (78), (79), (80), (81), (82), (83), (85), (86), (87),
% 113.46/17.12 | | | (88), (89), (90), (92), (93), (94), (96), (97), (99), (100),
% 113.46/17.12 | | | (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 113.46/17.12 | | | (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 113.46/17.12 | | | (120), (122), (123), (124), (126), (127), (128), (130), (131),
% 113.46/17.12 | | | (132), (133), (134), (136), (137), (139), (140), (142), (144),
% 113.46/17.12 | | | (145), (146), (148), (149), (150), (152), (154), (156) are
% 113.46/17.12 | | | inconsistent by sub-proof #91.
% 113.46/17.12 | | |
% 113.46/17.12 | | Case 2:
% 113.46/17.12 | | |
% 113.46/17.12 | | | (157) all_56_12 = e2
% 113.46/17.12 | | |
% 113.46/17.12 | | | COMBINE_EQS: (22), (157) imply:
% 113.46/17.12 | | | (158) all_10_2 = e2
% 113.46/17.12 | | |
% 113.46/17.12 | | | REF_CLOSE: (4), (5), (9), (13), (14), (21), (22), (24), (25), (28), (32),
% 113.46/17.12 | | | (38), (41), (47), (52), (57), (58), (61), (62), (67), (68),
% 113.46/17.12 | | | (71), (73), (75), (78), (84), (87), (91), (92), (94), (95),
% 113.46/17.12 | | | (98), (101), (120), (125), (129), (135), (138), (143), (145),
% 113.46/17.12 | | | (147), (158) are inconsistent by sub-proof #82.
% 113.46/17.12 | | |
% 113.46/17.12 | | End of split
% 113.46/17.12 | |
% 113.46/17.12 | Case 2:
% 113.46/17.12 | |
% 113.46/17.12 | | (159) all_56_14 = e2
% 113.46/17.12 | | (160) ~ (all_56_10 = e0)
% 113.46/17.12 | |
% 113.46/17.12 | | REF_CLOSE: (6), (8), (10), (11), (15), (16), (19), (21), (24), (28), (31),
% 113.46/17.12 | | (32), (34), (36), (37), (39), (41), (45), (50), (51), (52), (59),
% 113.46/17.12 | | (62), (66), (67), (68), (70), (71), (76), (78), (79), (81), (82),
% 113.46/17.12 | | (87), (88), (89), (90), (92), (93), (94), (100), (105), (109),
% 113.46/17.12 | | (111), (112), (113), (117), (119), (120), (121), (123), (128),
% 113.46/17.12 | | (132), (137), (138), (140), (141), (144), (145), (151), (159),
% 113.46/17.12 | | (160) are inconsistent by sub-proof #104.
% 113.46/17.12 | |
% 113.46/17.12 | End of split
% 113.46/17.12 |
% 113.46/17.12 End of proof
% 113.46/17.12
% 113.46/17.12 Sub-proof #64 shows that the following formulas are inconsistent:
% 113.46/17.12 ----------------------------------------------------------------
% 113.46/17.12 (1) ~ (all_52_8 = all_10_2)
% 113.46/17.12 (2) all_58_7 = all_52_6
% 113.46/17.12 (3) ~ (all_52_9 = all_8_2)
% 113.46/17.12 (4) all_28_1 = all_6_1
% 113.46/17.12 (5) all_56_14 = all_6_2
% 113.46/17.12 (6) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 113.46/17.12 (7) all_56_3 = all_52_1
% 113.46/17.12 (8) all_54_0 = all_10_2
% 113.46/17.12 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.12 (10) all_56_12 = all_10_2
% 113.46/17.12 (11) all_58_0 = all_10_2
% 113.46/17.12 (12) all_54_11 = all_52_14
% 113.46/17.12 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.12 (14) ~ (all_52_14 = all_6_2)
% 113.46/17.12 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.12 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.12 (17) ~ (all_52_1 = all_52_9)
% 113.46/17.12 (18) all_54_10 = all_6_2
% 113.46/17.12 (19) all_58_4 = all_52_8
% 113.46/17.12 (20) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.46/17.12 (21) all_58_3 = all_8_2
% 113.46/17.12 (22) all_58_11 = all_52_14
% 113.46/17.12 (23) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.46/17.12 (24) op(e2, e3) = all_52_1
% 113.46/17.12 (25) all_28_2 = all_6_2
% 113.46/17.12 (26) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.46/17.12 (27) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.46/17.12 (28) all_56_15 = e1
% 113.46/17.12 (29) op(e1, e0) = all_52_14
% 113.46/17.12 (30) all_58_5 = all_52_9
% 113.46/17.12 (31) op(e1, all_6_2) = all_6_1
% 113.46/17.12 (32) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.46/17.12 (33) all_58_2 = all_52_1
% 113.46/17.12 (34) ~ (all_52_1 = all_52_13)
% 113.46/17.12 (35) ~ (all_10_2 = e3)
% 113.46/17.12 (36) ~ (all_52_14 = all_4_2)
% 113.46/17.12 (37) all_58_6 = all_52_2
% 113.46/17.12 (38) ~ (all_52_1 = all_10_2)
% 113.46/17.12 (39) all_54_5 = all_8_2
% 113.46/17.12 (40) all_56_15 = all_4_2
% 113.46/17.12 (41) all_58_10 = all_52_13
% 113.46/17.12 (42) ~ (all_52_13 = all_8_2)
% 113.46/17.13 (43) ~ (all_52_11 = all_4_2)
% 113.46/17.13 (44) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.46/17.13 (45) all_58_14 = all_52_11
% 113.46/17.13 (46) all_56_13 = all_8_2
% 113.46/17.13 (47) ~ (all_52_1 = all_8_2)
% 113.46/17.13 (48) ~ (all_8_2 = e2)
% 113.46/17.13 (49) ~ (all_6_2 = e2)
% 113.46/17.13 (50) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.46/17.13 (51) all_56_7 = all_52_6
% 113.46/17.13 (52) all_58_8 = all_6_2
% 113.46/17.13 (53) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.46/17.13 (54) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.46/17.13 (55) all_56_4 = all_52_9
% 113.46/17.13 (56) all_56_5 = all_52_13
% 113.46/17.13 (57) all_56_6 = all_52_2
% 113.46/17.13 (58) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.46/17.13 (59) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.46/17.13 (60) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.46/17.13 (61) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.46/17.13 (62) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.46/17.13 (63) all_54_4 = all_52_1
% 113.46/17.13 (64) op(e2, all_8_2) = e1
% 113.46/17.13 (65) ~ (all_6_2 = e1)
% 113.46/17.13 (66) ~ (all_6_1 = e2)
% 113.46/17.13
% 113.46/17.13 Begin of proof
% 113.46/17.13 |
% 113.46/17.13 | COMBINE_EQS: (28), (40) imply:
% 113.46/17.13 | (67) all_4_2 = e1
% 113.46/17.13 |
% 113.46/17.13 | SIMP: (67) implies:
% 113.46/17.13 | (68) all_4_2 = e1
% 113.46/17.13 |
% 113.46/17.13 | REDUCE: (43), (68) imply:
% 113.46/17.13 | (69) ~ (all_52_11 = e1)
% 113.46/17.13 |
% 113.46/17.13 | REDUCE: (36), (68) imply:
% 113.46/17.13 | (70) ~ (all_52_14 = e1)
% 113.46/17.13 |
% 113.46/17.13 | BETA: splitting (58) gives:
% 113.46/17.13 |
% 113.46/17.13 | Case 1:
% 113.46/17.13 | |
% 113.46/17.13 | | (71) ~ (all_56_4 = e2)
% 113.46/17.13 | |
% 113.46/17.13 | | REDUCE: (55), (71) imply:
% 113.46/17.13 | | (72) ~ (all_52_9 = e2)
% 113.46/17.13 | |
% 113.46/17.13 | | BETA: splitting (60) gives:
% 113.46/17.13 | |
% 113.46/17.13 | | Case 1:
% 113.46/17.13 | | |
% 113.46/17.13 | | | (73) ~ (all_56_5 = e2)
% 113.46/17.13 | | |
% 113.46/17.13 | | | REDUCE: (56), (73) imply:
% 113.46/17.13 | | | (74) ~ (all_52_13 = e2)
% 113.46/17.13 | | |
% 113.46/17.13 | | | BETA: splitting (62) gives:
% 113.46/17.13 | | |
% 113.46/17.13 | | | Case 1:
% 113.46/17.13 | | | |
% 113.46/17.13 | | | | (75) all_58_2 = e2
% 113.46/17.13 | | | |
% 113.46/17.13 | | | | REF_CLOSE: (4), (5), (6), (7), (11), (12), (14), (15), (16), (18), (25),
% 113.46/17.13 | | | | (29), (31), (33), (35), (44), (49), (54), (61), (65), (66),
% 113.46/17.13 | | | | (70), (75) are inconsistent by sub-proof #276.
% 113.46/17.13 | | | |
% 113.46/17.13 | | | Case 2:
% 113.46/17.13 | | | |
% 113.46/17.13 | | | | (76) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.46/17.13 | | | |
% 113.46/17.13 | | | | REF_CLOSE: (21), (30), (41), (48), (72), (74), (76) are inconsistent by
% 113.46/17.13 | | | | sub-proof #401.
% 113.46/17.13 | | | |
% 113.46/17.13 | | | End of split
% 113.46/17.13 | | |
% 113.46/17.13 | | Case 2:
% 113.46/17.13 | | |
% 113.46/17.13 | | | (77) all_56_5 = e2
% 113.46/17.13 | | | (78) ~ (all_56_12 = e0)
% 113.46/17.13 | | |
% 113.46/17.13 | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (13), (15), (16), (17),
% 113.46/17.13 | | | (18), (19), (20), (22), (23), (24), (26), (27), (30), (32),
% 113.46/17.13 | | | (33), (34), (35), (37), (38), (39), (42), (45), (46), (47),
% 113.46/17.13 | | | (49), (50), (51), (52), (53), (56), (57), (59), (63), (64),
% 113.46/17.13 | | | (65), (69), (70), (77), (78) are inconsistent by sub-proof #89.
% 113.46/17.13 | | |
% 113.46/17.13 | | End of split
% 113.46/17.13 | |
% 113.46/17.13 | Case 2:
% 113.46/17.13 | |
% 113.46/17.13 | | (79) ~ (all_56_15 = e1)
% 113.46/17.13 | |
% 113.46/17.13 | | REDUCE: (28), (79) imply:
% 113.46/17.13 | | (80) $false
% 113.46/17.13 | |
% 113.46/17.13 | | CLOSE: (80) is inconsistent.
% 113.46/17.13 | |
% 113.46/17.13 | End of split
% 113.46/17.13 |
% 113.46/17.13 End of proof
% 113.46/17.13
% 113.46/17.13 Sub-proof #65 shows that the following formulas are inconsistent:
% 113.46/17.13 ----------------------------------------------------------------
% 113.46/17.13 (1) ~ (all_52_8 = all_10_2)
% 113.46/17.13 (2) all_28_1 = all_6_1
% 113.46/17.13 (3) all_56_14 = all_6_2
% 113.46/17.13 (4) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 113.46/17.13 (5) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.46/17.13 (6) all_58_0 = all_10_2
% 113.46/17.13 (7) all_54_11 = all_52_14
% 113.46/17.13 (8) ~ (all_52_14 = all_6_2)
% 113.46/17.13 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.13 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.13 (11) all_54_5 = e3
% 113.46/17.13 (12) all_54_10 = all_6_2
% 113.46/17.13 (13) ~ (all_52_8 = all_6_2)
% 113.46/17.13 (14) all_58_4 = all_52_8
% 113.46/17.13 (15) all_28_2 = all_6_2
% 113.46/17.13 (16) ~ (all_52_4 = all_8_2)
% 113.46/17.13 (17) op(e1, e0) = all_52_14
% 113.46/17.13 (18) op(e1, all_6_2) = all_6_1
% 113.46/17.13 (19) ~ (all_10_2 = e3)
% 113.46/17.13 (20) all_54_5 = all_8_2
% 113.46/17.13 (21) ~ (all_52_12 = e3)
% 113.46/17.13 (22) all_58_1 = all_52_4
% 113.46/17.13 (23) ~ (all_6_2 = e2)
% 113.46/17.13 (24) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.46/17.13 (25) all_58_9 = all_52_12
% 113.46/17.13 (26) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.46/17.13 (27) all_56_8 = all_52_14
% 113.46/17.13 (28) ~ (all_6_2 = e1)
% 113.46/17.13 (29) ~ (all_6_1 = e2)
% 113.46/17.13
% 113.46/17.13 Begin of proof
% 113.46/17.13 |
% 113.46/17.13 | COMBINE_EQS: (11), (20) imply:
% 113.46/17.13 | (30) all_8_2 = e3
% 113.46/17.13 |
% 113.46/17.13 | SIMP: (30) implies:
% 113.46/17.13 | (31) all_8_2 = e3
% 113.46/17.13 |
% 113.46/17.13 | REDUCE: (16), (31) imply:
% 113.46/17.13 | (32) ~ (all_52_4 = e3)
% 113.46/17.13 |
% 113.46/17.13 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 113.46/17.13 | (14), (15), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 113.46/17.13 | (27), (28), (29), (32) are inconsistent by sub-proof #251.
% 113.46/17.13 |
% 113.46/17.13 End of proof
% 113.46/17.13
% 113.46/17.13 Sub-proof #66 shows that the following formulas are inconsistent:
% 113.46/17.13 ----------------------------------------------------------------
% 113.46/17.13 (1) ~ (all_52_8 = all_10_2)
% 113.46/17.13 (2) ~ (all_52_2 = all_10_2)
% 113.46/17.13 (3) all_54_2 = all_52_8
% 113.46/17.13 (4) all_58_7 = all_52_6
% 113.46/17.13 (5) ~ (all_52_8 = all_52_11)
% 113.46/17.13 (6) ~ (all_52_9 = all_8_2)
% 113.46/17.13 (7) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 113.46/17.13 (8) ~ (all_52_13 = all_52_14)
% 113.46/17.13 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 113.46/17.13 (10) ~ (all_4_2 = e0)
% 113.46/17.13 (11) all_56_14 = all_6_2
% 113.46/17.13 (12) all_56_3 = all_52_1
% 113.46/17.13 (13) all_54_0 = all_10_2
% 113.46/17.13 (14) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.46/17.13 (15) ~ (all_52_12 = all_52_14)
% 113.46/17.13 (16) ~ (all_52_7 = all_4_2)
% 113.46/17.13 (17) all_56_11 = all_52_11
% 113.46/17.13 (18) ~ (all_4_0 = e1)
% 113.46/17.13 (19) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.46/17.13 (20) ~ (all_52_12 = all_10_2)
% 113.46/17.13 (21) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 113.46/17.13 (22) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.46/17.13 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.46/17.13 (24) all_56_12 = all_10_2
% 113.46/17.13 (25) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.46/17.13 (26) all_58_0 = all_10_2
% 113.46/17.13 (27) all_54_11 = all_52_14
% 113.46/17.13 (28) all_54_13 = all_52_7
% 113.46/17.13 (29) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.46/17.14 (30) ~ (all_52_14 = all_6_2)
% 113.46/17.14 (31) all_56_10 = all_52_7
% 113.46/17.14 (32) all_54_14 = all_52_11
% 113.46/17.14 (33) op(all_4_1, all_4_2) = all_4_0
% 113.46/17.14 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.46/17.14 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.46/17.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.46/17.14 (36) all_54_8 = all_52_2
% 113.46/17.14 (37) ~ (all_52_2 = all_6_2)
% 113.46/17.14 (38) ~ (all_52_1 = all_52_9)
% 113.46/17.14 (39) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.46/17.14 (40) all_54_10 = all_6_2
% 113.46/17.14 (41) op(e1, all_8_2) = e3
% 113.46/17.14 (42) all_58_4 = all_52_8
% 113.46/17.14 (43) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.46/17.14 (44) ~ (all_56_12 = e2)
% 113.46/17.14 (45) all_58_3 = all_8_2
% 113.46/17.14 (46) all_54_6 = all_52_9
% 113.46/17.14 (47) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 113.46/17.14 (48) all_58_11 = all_52_14
% 113.46/17.14 (49) ~ (all_52_2 = all_52_3)
% 113.46/17.14 (50) ~ (all_8_2 = e0)
% 113.46/17.14 (51) ~ (all_52_11 = all_6_2)
% 113.46/17.14 (52) op(e2, e3) = all_52_1
% 113.46/17.14 (53) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.46/17.14 (54) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.46/17.14 (55) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.46/17.14 (56) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.46/17.14 (57) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.46/17.14 (58) ~ (all_52_7 = all_8_2)
% 113.46/17.14 (59) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.46/17.14 (60) all_58_5 = all_52_9
% 113.46/17.14 (61) ~ (all_52_9 = all_52_13)
% 113.46/17.14 (62) all_56_9 = all_52_3
% 113.46/17.14 (63) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.46/17.14 (64) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.46/17.14 (65) all_58_15 = all_4_2
% 113.46/17.14 (66) all_58_2 = all_52_1
% 113.46/17.14 (67) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.46/17.14 (68) ~ (all_52_1 = all_52_13)
% 113.46/17.14 (69) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.46/17.14 (70) op(e0, e3) = all_52_3
% 113.46/17.14 (71) ~ (all_10_2 = e3)
% 113.46/17.14 (72) all_58_13 = all_52_7
% 113.46/17.14 (73) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.46/17.14 (74) ~ (all_52_14 = all_4_2)
% 113.46/17.14 (75) all_58_6 = all_52_2
% 113.46/17.14 (76) ~ (all_52_1 = all_10_2)
% 113.46/17.14 (77) all_54_5 = all_8_2
% 113.46/17.14 (78) all_56_15 = all_4_2
% 113.46/17.14 (79) all_58_10 = all_52_13
% 113.46/17.14 (80) ~ (all_52_13 = all_8_2)
% 113.46/17.14 (81) ~ (all_52_11 = all_4_2)
% 113.46/17.14 (82) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.46/17.14 (83) ~ (all_52_6 = all_8_2)
% 113.46/17.14 (84) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.46/17.14 (85) all_58_14 = all_52_11
% 113.46/17.14 (86) all_56_13 = all_8_2
% 113.46/17.14 (87) ~ (all_52_1 = all_8_2)
% 113.46/17.14 (88) ~ (all_8_2 = e2)
% 113.46/17.14 (89) ~ (all_52_7 = all_52_11)
% 113.46/17.14 (90) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.46/17.14 (91) all_56_7 = all_52_6
% 113.46/17.14 (92) ~ (all_52_9 = all_6_2)
% 113.46/17.14 (93) ~ (all_52_1 = all_52_2)
% 113.46/17.14 (94) ~ (all_52_1 = all_52_3)
% 113.46/17.14 (95) all_56_1 = all_52_8
% 113.46/17.14 (96) op(e0, all_4_2) = all_4_1
% 113.46/17.14 (97) all_58_8 = all_6_2
% 113.46/17.14 (98) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.46/17.14 (99) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.46/17.14 (100) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.46/17.14 (101) all_56_4 = all_52_9
% 113.46/17.14 (102) all_58_9 = all_52_12
% 113.46/17.14 (103) all_56_5 = all_52_13
% 113.46/17.14 (104) op(e2, e1) = all_52_9
% 113.46/17.14 (105) ~ (all_52_3 = all_4_2)
% 113.46/17.14 (106) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.46/17.14 (107) all_56_6 = all_52_2
% 113.46/17.14 (108) ~ (all_52_13 = all_4_2)
% 113.46/17.14 (109) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.46/17.14 (110) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.71/17.14 (111) all_58_12 = all_52_3
% 113.71/17.14 (112) ~ (all_52_2 = all_52_14)
% 113.71/17.14 (113) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.71/17.14 (114) ~ (all_52_8 = all_52_9)
% 113.71/17.14 (115) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.71/17.14 (116) ~ (all_52_3 = all_10_2)
% 113.71/17.14 (117) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.71/17.14 (118) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.71/17.14 (119) op(e1, e1) = all_6_2
% 113.71/17.14 (120) all_56_8 = all_52_14
% 113.71/17.14 (121) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.71/17.14 (122) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.71/17.14 (123) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.71/17.14 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.71/17.14 (124) all_54_4 = all_52_1
% 113.71/17.14 (125) all_54_15 = all_4_2
% 113.71/17.14 (126) op(e2, all_8_2) = e1
% 113.71/17.14 (127) ~ (all_6_2 = e1)
% 113.71/17.14 (128) ~ (all_52_3 = all_52_11)
% 113.71/17.14 (129) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.71/17.14 (130) all_54_12 = all_52_3
% 113.71/17.14 (131) ~ (all_52_3 = all_52_7)
% 113.71/17.14
% 113.71/17.14 Begin of proof
% 113.71/17.14 |
% 113.71/17.15 | REDUCE: (24), (44) imply:
% 113.71/17.15 | (132) ~ (all_10_2 = e2)
% 113.71/17.15 |
% 113.71/17.15 | BETA: splitting (99) gives:
% 113.71/17.15 |
% 113.71/17.15 | Case 1:
% 113.71/17.15 | |
% 113.71/17.15 | | (133) ~ (all_56_15 = e3)
% 113.71/17.15 | |
% 113.71/17.15 | | REDUCE: (78), (133) imply:
% 113.71/17.15 | | (134) ~ (all_4_2 = e3)
% 113.71/17.15 | |
% 113.71/17.15 | | BETA: splitting (118) gives:
% 113.71/17.15 | |
% 113.71/17.15 | | Case 1:
% 113.71/17.15 | | |
% 113.71/17.15 | | | (135) ~ (all_56_5 = e2)
% 113.71/17.15 | | |
% 113.71/17.15 | | | REDUCE: (103), (135) imply:
% 113.71/17.15 | | | (136) ~ (all_52_13 = e2)
% 113.71/17.15 | | |
% 113.71/17.15 | | | BETA: splitting (69) gives:
% 113.71/17.15 | | |
% 113.71/17.15 | | | Case 1:
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | (137) ~ (all_56_13 = e3)
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | REDUCE: (86), (137) imply:
% 113.71/17.15 | | | | (138) ~ (all_8_2 = e3)
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | BETA: splitting (23) gives:
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | Case 1:
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | (139) all_54_5 = e3
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | REF_CLOSE: (77), (138), (139) are inconsistent by sub-proof #339.
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | Case 2:
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | (140) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | BETA: splitting (140) gives:
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | Case 1:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | (141) all_54_5 = e2
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | REF_CLOSE: (77), (88), (141) are inconsistent by sub-proof #338.
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | Case 2:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | (142) ~ (all_54_5 = e2)
% 113.71/17.15 | | | | | | (143) all_54_5 = e1 | all_54_5 = e0
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | BETA: splitting (143) gives:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | Case 1:
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | (144) all_54_5 = e1
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | COMBINE_EQS: (77), (144) imply:
% 113.71/17.15 | | | | | | | (145) all_8_2 = e1
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | SIMP: (145) implies:
% 113.71/17.15 | | | | | | | (146) all_8_2 = e1
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | COMBINE_EQS: (86), (146) imply:
% 113.71/17.15 | | | | | | | (147) all_56_13 = e1
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | REDUCE: (41), (146) imply:
% 113.71/17.15 | | | | | | | (148) op(e1, e1) = e3
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | REF_CLOSE: (11), (12), (22), (35), (45), (60), (66), (79), (84),
% 113.71/17.15 | | | | | | | (88), (101), (119), (122), (136), (147), (148) are
% 113.71/17.15 | | | | | | | inconsistent by sub-proof #103.
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | Case 2:
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | (149) all_54_5 = e0
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | REF_CLOSE: (50), (77), (149) are inconsistent by sub-proof #311.
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | End of split
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | End of split
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | End of split
% 113.71/17.15 | | | |
% 113.71/17.15 | | | Case 2:
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | (150) all_56_13 = e3
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | COMBINE_EQS: (86), (150) imply:
% 113.71/17.15 | | | | (151) all_8_2 = e3
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | SIMP: (151) implies:
% 113.71/17.15 | | | | (152) all_8_2 = e3
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | COMBINE_EQS: (45), (152) imply:
% 113.71/17.15 | | | | (153) all_58_3 = e3
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | REDUCE: (87), (152) imply:
% 113.71/17.15 | | | | (154) ~ (all_52_1 = e3)
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | REDUCE: (88), (152) imply:
% 113.71/17.15 | | | | (155) ~ (e3 = e2)
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | BETA: splitting (19) gives:
% 113.71/17.15 | | | |
% 113.71/17.15 | | | | Case 1:
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | (156) ~ (all_56_3 = e2)
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | REDUCE: (12), (156) imply:
% 113.71/17.15 | | | | | (157) ~ (all_52_1 = e2)
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | BETA: splitting (122) gives:
% 113.71/17.15 | | | | |
% 113.71/17.15 | | | | | Case 1:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | (158) all_58_2 = e2
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | COMBINE_EQS: (66), (158) imply:
% 113.71/17.15 | | | | | | (159) all_52_1 = e2
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | REDUCE: (157), (159) imply:
% 113.71/17.15 | | | | | | (160) $false
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | CLOSE: (160) is inconsistent.
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | Case 2:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | (161) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | BETA: splitting (161) gives:
% 113.71/17.15 | | | | | |
% 113.71/17.15 | | | | | | Case 1:
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | (162) all_58_3 = e2
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | COMBINE_EQS: (153), (162) imply:
% 113.71/17.15 | | | | | | | (163) e3 = e2
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | REDUCE: (155), (163) imply:
% 113.71/17.15 | | | | | | | (164) $false
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | CLOSE: (164) is inconsistent.
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | Case 2:
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | (165) all_58_5 = e2 | all_58_10 = e2
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | BETA: splitting (165) gives:
% 113.71/17.15 | | | | | | |
% 113.71/17.15 | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | (166) all_58_5 = e2
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | COMBINE_EQS: (60), (166) imply:
% 113.71/17.15 | | | | | | | | (167) all_52_9 = e2
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | COMBINE_EQS: (101), (167) imply:
% 113.71/17.15 | | | | | | | | (168) all_56_4 = e2
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | REDUCE: (61), (167) imply:
% 113.71/17.15 | | | | | | | | (169) ~ (all_52_13 = e2)
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | BETA: splitting (67) gives:
% 113.71/17.15 | | | | | | | |
% 113.71/17.15 | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | (170) ~ (all_56_4 = e2)
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | REDUCE: (168), (170) imply:
% 113.71/17.15 | | | | | | | | | (171) $false
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | CLOSE: (171) is inconsistent.
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | (172) ~ (all_56_12 = e1)
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | REDUCE: (24), (172) imply:
% 113.71/17.15 | | | | | | | | | (173) ~ (all_10_2 = e1)
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | BETA: splitting (98) gives:
% 113.71/17.15 | | | | | | | | |
% 113.71/17.15 | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | (174) all_54_0 = e3
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | REF_CLOSE: (13), (71), (174) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | #451.
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | (175) ~ (all_54_0 = e3)
% 113.71/17.15 | | | | | | | | | | (176) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | BETA: splitting (176) gives:
% 113.71/17.15 | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | (177) all_54_0 = e2
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | REF_CLOSE: (13), (132), (177) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | | #450.
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | (178) ~ (all_54_0 = e2)
% 113.71/17.15 | | | | | | | | | | | (179) all_54_0 = e1 | all_54_0 = e0
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | BETA: splitting (179) gives:
% 113.71/17.15 | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | (180) all_54_0 = e1
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | REF_CLOSE: (13), (173), (180) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | | | #449.
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | (181) all_54_0 = e0
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | COMBINE_EQS: (13), (181) imply:
% 113.71/17.15 | | | | | | | | | | | | (182) all_10_2 = e0
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | SIMP: (182) implies:
% 113.71/17.15 | | | | | | | | | | | | (183) all_10_2 = e0
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | REDUCE: (76), (183) imply:
% 113.71/17.15 | | | | | | | | | | | | (184) ~ (all_52_1 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | REDUCE: (2), (183) imply:
% 113.71/17.15 | | | | | | | | | | | | (185) ~ (all_52_2 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | REDUCE: (71), (183) imply:
% 113.71/17.15 | | | | | | | | | | | | (186) ~ (e3 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | SIMP: (186) implies:
% 113.71/17.15 | | | | | | | | | | | | (187) ~ (e3 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | REDUCE: (132), (183) imply:
% 113.71/17.15 | | | | | | | | | | | | (188) ~ (e2 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | SIMP: (188) implies:
% 113.71/17.15 | | | | | | | | | | | | (189) ~ (e2 = e0)
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | BETA: splitting (113) gives:
% 113.71/17.15 | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | (190) ~ (all_56_4 = e2)
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | REDUCE: (168), (190) imply:
% 113.71/17.15 | | | | | | | | | | | | | (191) $false
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | (192) ~ (all_56_15 = e1)
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | REDUCE: (78), (192) imply:
% 113.71/17.15 | | | | | | | | | | | | | (193) ~ (all_4_2 = e1)
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | BETA: splitting (117) gives:
% 113.71/17.15 | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | (194) all_58_2 = e0
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | COMBINE_EQS: (66), (194) imply:
% 113.71/17.15 | | | | | | | | | | | | | | (195) all_52_1 = e0
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | REDUCE: (184), (195) imply:
% 113.71/17.15 | | | | | | | | | | | | | | (196) $false
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | (197) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 113.71/17.15 | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | (198) all_54_4 = e3
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | REF_CLOSE: (124), (154), (198) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | | | | | | #329.
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | (199) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 113.71/17.15 | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | (200) all_54_15 = e3
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | REF_CLOSE: (125), (134), (200) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | | | | | | | #312.
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | (201) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 113.71/17.15 | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | (202) ~ (all_56_8 = e1)
% 113.71/17.15 | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | REDUCE: (120), (202) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | (203) ~ (all_52_14 = e1)
% 113.71/17.15 | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 113.71/17.15 | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | (204) all_58_3 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (204) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | (205) e3 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | REDUCE: (187), (205) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | (206) $false
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | (207) all_58_5 = e0 | all_58_10 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 113.71/17.15 | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (208) all_58_5 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (208) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (209) e2 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | REDUCE: (189), (209) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (210) $false
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (211) all_58_10 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (211) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (212) all_52_13 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | REDUCE: (8), (212) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (213) ~ (all_52_14 = e0)
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | SIMP: (213) implies:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (214) ~ (all_52_14 = e0)
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | REDUCE: (108), (212) imply:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | (215) ~ (all_4_2 = e0)
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | (216) all_54_4 = e2
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (157), (216) are inconsistent by sub-proof
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | #328.
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | (217) all_54_4 = e1 | all_54_4 = e0
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.15 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (218) all_54_4 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (218) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (219) all_52_1 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (220) all_52_1 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (220) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (221) ~ (all_52_2 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (221) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_52_2 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (220) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (223) ~ (all_52_3 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (224) ~ (all_52_3 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | (225) all_54_15 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (225) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | (226) all_4_2 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (226) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | (227) all_56_15 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (226) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_52_14 = e2)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_56_7 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (91), (229) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_52_6 = e1)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (231) all_54_11 = e3
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (231) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (232) all_52_14 = e3
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (232) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (233) ~ (all_52_2 = e3)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (232) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_52_12 = e3)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (232) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_6_2 = e3)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_6_2 = e3)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_54_8 = e3
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (233), (237) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | #399.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_54_8 = e3)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_54_10 = e3
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (236), (240) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | #352.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_54_8 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (242) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_52_2 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (243) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_52_2 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (244) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_56_6 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (244) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_58_6 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (244) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) ~ (all_6_2 = e2)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (247) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_6_2 = e2)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (244) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (e3 = e2)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_54_10 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (248), (250) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_54_10 = e1 | all_54_10 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_54_10 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (127), (252) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_54_10 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (253) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_6_2 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_6_2 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (255) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_52_11 = e0)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_6 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (257) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e2 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (258) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_56_6 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (20), (22), (23), (24), (35), (45),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (48), (55), (56), (58), (60), (63), (64),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (66), (71), (72), (77), (79), (85), (86),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (94), (98), (101), (102), (104), (105),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (110), (111), (115), (116), (120), (122),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (126), (130), (131), (132), (136), (155),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173), (214), (224), (234), (256), (259) are
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #135.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (48), (97), (127), (203), (230), (260) are
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_54_8 = e1 | all_54_8 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (185), (222), (261) are inconsistent by
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #396.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_54_11 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (263) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_52_14 = e2
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (228), (264) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (265) $false
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_54_11 = e1 | all_54_11 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (27), (63), (120), (132), (173),
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | (176), (214), (266) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | | #383.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | (267) ~ (all_56_15 = e2)
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (227), (267) imply:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | (268) $false
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | (269) all_54_15 = e1 | all_54_15 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (125), (193), (269) are inconsistent by
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | | sub-proof #418.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | (270) all_54_4 = e0
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (184), (270) are inconsistent by sub-proof
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | | #323.
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | (271) all_56_8 = e1
% 113.71/17.16 | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (63), (132), (173), (176), (271) are
% 113.71/17.16 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #385.
% 113.71/17.16 | | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | | |
% 113.71/17.16 | | | | | | | | | End of split
% 113.71/17.16 | | | | | | | | |
% 113.71/17.16 | | | | | | | | End of split
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | Case 2:
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | | (272) all_58_10 = e2
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | | COMBINE_EQS: (79), (272) imply:
% 113.71/17.16 | | | | | | | | (273) all_52_13 = e2
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | | REDUCE: (136), (273) imply:
% 113.71/17.16 | | | | | | | | (274) $false
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | | CLOSE: (274) is inconsistent.
% 113.71/17.16 | | | | | | | |
% 113.71/17.16 | | | | | | | End of split
% 113.71/17.16 | | | | | | |
% 113.71/17.16 | | | | | | End of split
% 113.71/17.16 | | | | | |
% 113.71/17.16 | | | | | End of split
% 113.71/17.16 | | | | |
% 113.71/17.16 | | | | Case 2:
% 113.71/17.16 | | | | |
% 113.71/17.16 | | | | | (275) ~ (all_56_13 = e3)
% 113.71/17.16 | | | | |
% 113.71/17.16 | | | | | REDUCE: (150), (275) imply:
% 113.71/17.16 | | | | | (276) $false
% 113.71/17.16 | | | | |
% 113.71/17.16 | | | | | CLOSE: (276) is inconsistent.
% 113.71/17.16 | | | | |
% 113.71/17.16 | | | | End of split
% 113.71/17.16 | | | |
% 113.71/17.16 | | | End of split
% 113.71/17.16 | | |
% 113.71/17.16 | | Case 2:
% 113.71/17.16 | | |
% 113.71/17.16 | | | (277) all_56_5 = e2
% 113.71/17.16 | | | (278) ~ (all_56_12 = e0)
% 113.71/17.16 | | |
% 113.71/17.16 | | | COMBINE_EQS: (103), (277) imply:
% 113.71/17.16 | | | (279) all_52_13 = e2
% 113.71/17.16 | | |
% 113.71/17.16 | | | REDUCE: (24), (278) imply:
% 113.71/17.16 | | | (280) ~ (all_10_2 = e0)
% 113.71/17.16 | | |
% 113.71/17.16 | | | REDUCE: (68), (279) imply:
% 113.71/17.16 | | | (281) ~ (all_52_1 = e2)
% 113.71/17.16 | | |
% 113.71/17.16 | | | REDUCE: (80), (279) imply:
% 113.71/17.16 | | | (282) ~ (all_8_2 = e2)
% 113.71/17.16 | | |
% 113.71/17.16 | | | REDUCE: (108), (279) imply:
% 113.71/17.16 | | | (283) ~ (all_4_2 = e2)
% 113.71/17.16 | | |
% 113.71/17.16 | | | SIMP: (283) implies:
% 113.71/17.16 | | | (284) ~ (all_4_2 = e2)
% 113.71/17.16 | | |
% 113.71/17.16 | | | REF_CLOSE: (1), (6), (10), (13), (23), (29), (35), (38), (42), (43), (50),
% 113.71/17.16 | | | (52), (53), (60), (66), (71), (76), (77), (81), (85), (87),
% 113.71/17.16 | | | (88), (97), (98), (117), (124), (125), (126), (127), (132),
% 113.71/17.16 | | | (134), (280), (281), (284) are inconsistent by sub-proof #122.
% 113.71/17.16 | | |
% 113.71/17.16 | | End of split
% 113.71/17.16 | |
% 113.71/17.16 | Case 2:
% 113.71/17.16 | |
% 113.71/17.16 | | (285) all_56_15 = e3
% 113.71/17.16 | | (286) ~ (all_56_9 = e0)
% 113.71/17.16 | |
% 113.71/17.16 | | COMBINE_EQS: (78), (285) imply:
% 113.71/17.16 | | (287) all_4_2 = e3
% 113.71/17.16 | |
% 113.71/17.16 | | SIMP: (287) implies:
% 113.71/17.16 | | (288) all_4_2 = e3
% 113.71/17.16 | |
% 113.71/17.16 | | REDUCE: (62), (286) imply:
% 113.71/17.16 | | (289) ~ (all_52_3 = e0)
% 113.71/17.16 | |
% 113.71/17.16 | | REDUCE: (105), (288) imply:
% 113.71/17.16 | | (290) ~ (all_52_3 = e3)
% 113.71/17.16 | |
% 113.71/17.16 | | REDUCE: (16), (288) imply:
% 113.71/17.16 | | (291) ~ (all_52_7 = e3)
% 113.71/17.16 | |
% 113.71/17.16 | | REDUCE: (81), (288) imply:
% 113.71/17.17 | | (292) ~ (all_52_11 = e3)
% 113.71/17.17 | |
% 113.71/17.17 | | REDUCE: (33), (288) imply:
% 113.71/17.17 | | (293) op(all_4_1, e3) = all_4_0
% 113.71/17.17 | |
% 113.71/17.17 | | REDUCE: (96), (288) imply:
% 113.71/17.17 | | (294) op(e0, e3) = all_4_1
% 113.71/17.17 | |
% 113.71/17.17 | | BETA: splitting (39) gives:
% 113.71/17.17 | |
% 113.71/17.17 | | Case 1:
% 113.71/17.17 | | |
% 113.71/17.17 | | | (295) ~ (all_56_3 = e2)
% 113.71/17.17 | | |
% 113.71/17.17 | | | REDUCE: (12), (295) imply:
% 113.71/17.17 | | | (296) ~ (all_52_1 = e2)
% 113.71/17.17 | | |
% 113.71/17.17 | | | BETA: splitting (7) gives:
% 113.71/17.17 | | |
% 113.71/17.17 | | | Case 1:
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | (297) ~ (all_56_6 = e1)
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | REDUCE: (107), (297) imply:
% 113.71/17.17 | | | | (298) ~ (all_52_2 = e1)
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (11), (13), (14), (17), (18),
% 113.71/17.17 | | | | (21), (23), (24), (26), (28), (29), (31), (32), (34), (35),
% 113.71/17.17 | | | | (36), (37), (38), (40), (42), (45), (47), (48), (49), (50),
% 113.71/17.17 | | | | (51), (52), (54), (57), (58), (59), (60), (63), (66), (67),
% 113.71/17.17 | | | | (68), (70), (71), (73), (75), (76), (77), (79), (80), (82),
% 113.71/17.17 | | | | (83), (87), (88), (89), (90), (92), (93), (94), (95), (97),
% 113.71/17.17 | | | | (98), (101), (103), (104), (106), (110), (111), (114), (115),
% 113.71/17.17 | | | | (116), (117), (120), (121), (122), (124), (126), (127),
% 113.71/17.17 | | | | (128), (129), (130), (131), (132), (289), (290), (291),
% 113.71/17.17 | | | | (292), (293), (294), (296), (298) are inconsistent by
% 113.71/17.17 | | | | sub-proof #114.
% 113.71/17.17 | | | |
% 113.71/17.17 | | | Case 2:
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | (299) ~ (all_56_15 = e3)
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | REDUCE: (285), (299) imply:
% 113.71/17.17 | | | | (300) $false
% 113.71/17.17 | | | |
% 113.71/17.17 | | | | CLOSE: (300) is inconsistent.
% 113.71/17.17 | | | |
% 113.71/17.17 | | | End of split
% 113.71/17.17 | | |
% 113.71/17.17 | | Case 2:
% 113.71/17.17 | | |
% 113.71/17.17 | | | (301) ~ (all_56_15 = e3)
% 113.71/17.17 | | |
% 113.71/17.17 | | | REDUCE: (285), (301) imply:
% 113.71/17.17 | | | (302) $false
% 113.71/17.17 | | |
% 113.71/17.17 | | | CLOSE: (302) is inconsistent.
% 113.71/17.17 | | |
% 113.71/17.17 | | End of split
% 113.71/17.17 | |
% 113.71/17.17 | End of split
% 113.71/17.17 |
% 113.71/17.17 End of proof
% 113.71/17.17
% 113.71/17.17 Sub-proof #67 shows that the following formulas are inconsistent:
% 113.71/17.17 ----------------------------------------------------------------
% 113.71/17.17 (1) ~ (all_52_9 = all_8_2)
% 113.71/17.17 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.71/17.17 (3) all_58_0 = all_10_2
% 113.71/17.17 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.71/17.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.71/17.17 (5) all_58_4 = all_52_8
% 113.71/17.17 (6) all_56_2 = all_52_12
% 113.71/17.17 (7) all_56_12 = e2
% 113.71/17.17 (8) all_58_15 = e1
% 113.71/17.17 (9) all_56_9 = all_52_3
% 113.71/17.17 (10) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.71/17.17 (11) ~ (all_10_2 = e3)
% 113.71/17.17 (12) all_58_13 = all_52_7
% 113.71/17.17 (13) ~ (all_52_7 = e0)
% 113.71/17.17 (14) all_54_5 = all_8_2
% 113.71/17.17 (15) all_58_1 = all_52_4
% 113.71/17.17 (16) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.71/17.17 (17) all_58_14 = all_52_11
% 113.71/17.17 (18) all_56_13 = all_8_2
% 113.71/17.17 (19) ~ (all_52_8 = e3)
% 113.71/17.17 (20) ~ (all_8_2 = e2)
% 113.71/17.17 (21) all_58_9 = all_52_12
% 113.71/17.17 (22) op(e2, e1) = all_52_9
% 113.71/17.17 (23) all_58_12 = all_52_3
% 113.71/17.17 (24) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.71/17.17 (25) all_56_0 = all_52_4
% 113.71/17.17 (26) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.71/17.17 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.71/17.17 (27) ~ (all_52_11 = e0)
% 113.71/17.17 (28) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.71/17.17 (29) op(e2, all_8_2) = e1
% 113.71/17.17 (30) ~ (e1 = e0)
% 113.71/17.17
% 113.71/17.17 Begin of proof
% 113.71/17.17 |
% 113.71/17.17 | BETA: splitting (28) gives:
% 113.71/17.17 |
% 113.71/17.17 | Case 1:
% 113.71/17.17 | |
% 113.71/17.17 | | (31) ~ (all_56_0 = e3)
% 113.71/17.17 | |
% 113.71/17.17 | | REDUCE: (25), (31) imply:
% 113.71/17.17 | | (32) ~ (all_52_4 = e3)
% 113.71/17.17 | |
% 113.71/17.17 | | BETA: splitting (26) gives:
% 113.71/17.17 | |
% 113.71/17.17 | | Case 1:
% 113.71/17.17 | | |
% 113.71/17.17 | | | (33) all_58_15 = e0
% 113.71/17.17 | | |
% 113.71/17.17 | | | COMBINE_EQS: (8), (33) imply:
% 113.71/17.17 | | | (34) e1 = e0
% 113.71/17.17 | | |
% 113.71/17.17 | | | REDUCE: (30), (34) imply:
% 113.71/17.17 | | | (35) $false
% 113.71/17.17 | | |
% 113.71/17.17 | | | CLOSE: (35) is inconsistent.
% 113.71/17.17 | | |
% 113.71/17.17 | | Case 2:
% 113.71/17.17 | | |
% 113.71/17.17 | | | (36) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 113.71/17.17 | | | e0 | all_58_13 = e0 | all_58_14 = e0)
% 113.71/17.17 | | |
% 113.71/17.17 | | | ALPHA: (36) implies:
% 113.71/17.17 | | | (37) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.71/17.17 | | |
% 113.71/17.17 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13),
% 113.71/17.17 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 113.71/17.17 | | | (24), (27), (29), (32), (37) are inconsistent by sub-proof #71.
% 113.71/17.17 | | |
% 113.71/17.17 | | End of split
% 113.71/17.17 | |
% 113.71/17.17 | Case 2:
% 113.71/17.17 | |
% 113.71/17.17 | | (38) ~ (all_56_12 = e2)
% 113.71/17.17 | |
% 113.71/17.17 | | REDUCE: (7), (38) imply:
% 113.71/17.17 | | (39) $false
% 113.71/17.17 | |
% 113.71/17.17 | | CLOSE: (39) is inconsistent.
% 113.71/17.17 | |
% 113.71/17.17 | End of split
% 113.71/17.17 |
% 113.71/17.17 End of proof
% 113.71/17.17
% 113.71/17.17 Sub-proof #68 shows that the following formulas are inconsistent:
% 113.71/17.17 ----------------------------------------------------------------
% 113.71/17.17 (1) ~ (all_52_8 = all_10_2)
% 113.71/17.17 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.71/17.17 (3) ~ (all_52_2 = all_10_2)
% 113.71/17.17 (4) all_54_2 = all_52_8
% 113.71/17.17 (5) all_58_7 = all_52_6
% 113.71/17.17 (6) ~ (all_52_8 = all_52_11)
% 113.71/17.17 (7) ~ (all_52_9 = all_8_2)
% 113.71/17.17 (8) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 113.71/17.17 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 113.71/17.17 (10) ~ (all_4_2 = e0)
% 113.71/17.17 (11) all_56_14 = all_6_2
% 113.71/17.17 (12) all_56_3 = all_52_1
% 113.71/17.17 (13) all_54_0 = all_10_2
% 113.71/17.17 (14) op(e1, all_8_2) = all_8_0
% 113.71/17.17 (15) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.71/17.17 (16) ~ (all_52_2 = all_52_6)
% 113.71/17.17 (17) ~ (all_52_7 = all_4_2)
% 113.71/17.17 (18) all_56_11 = all_52_11
% 113.71/17.17 (19) ~ (all_4_0 = e1)
% 113.71/17.17 (20) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.71/17.17 (21) ~ (all_52_4 = all_52_8)
% 113.71/17.17 (22) ~ (all_52_12 = all_10_2)
% 113.71/17.17 (23) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 113.71/17.17 (24) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.71/17.17 (25) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.71/17.17 (26) all_56_12 = all_10_2
% 113.71/17.17 (27) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.71/17.17 (28) all_58_0 = all_10_2
% 113.71/17.17 (29) all_54_13 = all_52_7
% 113.71/17.17 (30) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.71/17.17 (31) ~ (all_52_14 = all_6_2)
% 113.71/17.17 (32) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 113.71/17.17 (33) all_56_10 = all_52_7
% 113.71/17.17 (34) all_54_14 = all_52_11
% 113.71/17.17 (35) op(all_4_1, all_4_2) = all_4_0
% 113.71/17.17 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.71/17.17 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.71/17.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.71/17.17 (38) all_54_8 = all_52_2
% 113.71/17.18 (39) ~ (all_52_2 = all_6_2)
% 113.71/17.18 (40) ~ (all_52_1 = all_52_9)
% 113.71/17.18 (41) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.71/17.18 (42) all_54_10 = all_6_2
% 113.71/17.18 (43) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 113.71/17.18 (44) all_58_4 = all_52_8
% 113.71/17.18 (45) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.71/17.18 (46) ~ (all_52_4 = all_52_7)
% 113.71/17.18 (47) all_56_2 = all_52_12
% 113.71/17.18 (48) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.71/17.18 (49) ~ (all_56_12 = e2)
% 113.71/17.18 (50) all_58_3 = all_8_2
% 113.71/17.18 (51) all_54_6 = all_52_9
% 113.71/17.18 (52) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.71/17.18 (53) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 113.71/17.18 (54) all_58_11 = all_52_14
% 113.71/17.18 (55) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.71/17.18 (56) ~ (all_52_2 = all_52_3)
% 113.71/17.18 (57) all_54_7 = all_52_13
% 113.71/17.18 (58) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.71/17.18 (59) ~ (all_52_11 = all_6_2)
% 113.71/17.18 (60) op(e2, e3) = all_52_1
% 113.71/17.18 (61) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.71/17.18 (62) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.71/17.18 (63) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.71/17.18 (64) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.71/17.18 (65) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.71/17.18 (66) ~ (all_52_7 = all_8_2)
% 113.71/17.18 (67) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.71/17.18 (68) ~ (all_52_4 = all_8_2)
% 113.71/17.18 (69) op(e1, e0) = all_52_14
% 113.71/17.18 (70) all_58_5 = all_52_9
% 113.71/17.18 (71) all_56_9 = all_52_3
% 113.71/17.18 (72) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.71/17.18 (73) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.71/17.18 (74) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.71/17.18 (75) all_58_15 = all_4_2
% 113.71/17.18 (76) all_58_2 = all_52_1
% 113.71/17.18 (77) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.71/17.18 (78) ~ (all_52_1 = all_52_13)
% 113.71/17.18 (79) op(e0, e3) = all_52_3
% 113.71/17.18 (80) ~ (all_10_2 = e3)
% 113.71/17.18 (81) ~ (all_52_12 = all_52_13)
% 113.71/17.18 (82) all_58_13 = all_52_7
% 113.71/17.18 (83) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.71/17.18 (84) ~ (all_52_14 = all_4_2)
% 113.71/17.18 (85) all_58_6 = all_52_2
% 113.71/17.18 (86) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.71/17.18 (87) ~ (all_52_1 = all_10_2)
% 113.71/17.18 (88) all_54_5 = all_8_2
% 113.71/17.18 (89) all_56_15 = all_4_2
% 113.71/17.18 (90) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.71/17.18 (91) all_58_10 = all_52_13
% 113.71/17.18 (92) ~ (all_52_13 = all_8_2)
% 113.71/17.18 (93) ~ (all_52_11 = all_4_2)
% 113.71/17.18 (94) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.71/17.18 (95) ~ (all_52_6 = all_8_2)
% 113.71/17.18 (96) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.71/17.18 (97) all_58_1 = all_52_4
% 113.71/17.18 (98) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.71/17.18 (99) all_58_14 = all_52_11
% 113.71/17.18 (100) all_56_13 = all_8_2
% 113.71/17.18 (101) ~ (all_52_1 = all_8_2)
% 113.71/17.18 (102) op(e1, all_6_2) = e3
% 113.71/17.18 (103) ~ (all_8_2 = e2)
% 113.71/17.18 (104) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 113.71/17.18 (105) ~ (all_6_2 = e2)
% 113.71/17.18 (106) ~ (all_52_7 = all_52_11)
% 113.71/17.18 (107) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.71/17.18 (108) all_56_7 = all_52_6
% 113.71/17.18 (109) ~ (all_52_9 = all_6_2)
% 113.71/17.18 (110) ~ (all_52_4 = all_52_6)
% 113.71/17.18 (111) ~ (all_52_1 = all_52_2)
% 113.71/17.18 (112) ~ (all_52_1 = all_52_3)
% 113.71/17.18 (113) all_56_1 = all_52_8
% 113.71/17.18 (114) op(e0, all_4_2) = all_4_1
% 113.71/17.18 (115) all_58_8 = all_6_2
% 113.71/17.18 (116) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.71/17.18 (117) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.71/17.18 (118) all_56_4 = all_52_9
% 113.71/17.18 (119) all_58_9 = all_52_12
% 113.71/17.18 (120) all_56_5 = all_52_13
% 113.71/17.18 (121) op(e2, e1) = all_52_9
% 113.71/17.18 (122) ~ (all_52_3 = all_4_2)
% 113.71/17.18 (123) ~ (all_52_6 = all_6_2)
% 113.71/17.18 (124) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.71/17.18 (125) all_56_6 = all_52_2
% 113.71/17.18 (126) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.71/17.18 (127) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.71/17.18 (128) all_58_12 = all_52_3
% 113.71/17.18 (129) ~ (all_52_2 = all_52_14)
% 113.71/17.18 (130) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.71/17.18 (131) ~ (all_52_8 = all_52_9)
% 113.71/17.18 (132) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.71/17.18 (133) op(e2, e0) = all_52_13
% 113.71/17.18 (134) ~ (all_52_12 = all_4_2)
% 113.71/17.18 (135) ~ (all_52_3 = all_10_2)
% 113.71/17.18 (136) op(e1, e3) = all_52_2
% 113.71/17.18 (137) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.71/17.18 (138) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.71/17.18 (139) op(e1, e1) = all_6_2
% 113.71/17.18 (140) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.71/17.18 (141) all_56_8 = all_52_14
% 113.88/17.18 (142) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.88/17.18 (143) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.18 (144) ~ (e3 = e2)
% 113.88/17.19 (145) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.19 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.19 (146) all_54_4 = all_52_1
% 113.88/17.19 (147) all_54_15 = all_4_2
% 113.88/17.19 (148) op(e2, all_8_2) = e1
% 113.88/17.19 (149) ~ (all_6_2 = e1)
% 113.88/17.19 (150) ~ (all_52_6 = all_52_7)
% 113.88/17.19 (151) ~ (all_52_3 = all_52_11)
% 113.88/17.19 (152) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.88/17.19 (153) all_54_12 = all_52_3
% 113.88/17.19 (154) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.88/17.19 (155) ~ (all_52_3 = all_52_7)
% 113.88/17.19
% 113.88/17.19 Begin of proof
% 113.88/17.19 |
% 113.88/17.19 | REDUCE: (26), (49) imply:
% 113.88/17.19 | (156) ~ (all_10_2 = e2)
% 113.88/17.19 |
% 113.88/17.19 | BETA: splitting (117) gives:
% 113.88/17.19 |
% 113.88/17.19 | Case 1:
% 113.88/17.19 | |
% 113.88/17.19 | | (157) ~ (all_56_15 = e3)
% 113.88/17.19 | |
% 113.88/17.19 | | REDUCE: (89), (157) imply:
% 113.88/17.19 | | (158) ~ (all_4_2 = e3)
% 113.88/17.19 | |
% 113.88/17.19 | | BETA: splitting (27) gives:
% 113.88/17.19 | |
% 113.88/17.19 | | Case 1:
% 113.88/17.19 | | |
% 113.88/17.19 | | | (159) ~ (all_56_7 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (108), (159) imply:
% 113.88/17.19 | | | (160) ~ (all_52_6 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REF_CLOSE: (3), (5), (10), (11), (13), (18), (20), (22), (24), (25), (26),
% 113.88/17.19 | | | (31), (33), (36), (37), (42), (45), (47), (48), (50), (51),
% 113.88/17.19 | | | (52), (54), (56), (58), (59), (63), (64), (65), (66), (70),
% 113.88/17.19 | | | (71), (73), (74), (75), (76), (80), (82), (84), (85), (88),
% 113.88/17.19 | | | (89), (91), (99), (100), (103), (105), (107), (112), (115),
% 113.88/17.19 | | | (116), (118), (119), (120), (121), (122), (125), (126), (127),
% 113.88/17.19 | | | (128), (132), (135), (137), (141), (142), (143), (144), (145),
% 113.88/17.19 | | | (147), (148), (149), (153), (155), (156), (158), (160) are
% 113.88/17.19 | | | inconsistent by sub-proof #134.
% 113.88/17.19 | | |
% 113.88/17.19 | | Case 2:
% 113.88/17.19 | | |
% 113.88/17.19 | | | (161) all_56_7 = e1
% 113.88/17.19 | | | (162) ~ (all_56_15 = e2)
% 113.88/17.19 | | |
% 113.88/17.19 | | | COMBINE_EQS: (108), (161) imply:
% 113.88/17.19 | | | (163) all_52_6 = e1
% 113.88/17.19 | | |
% 113.88/17.19 | | | SIMP: (163) implies:
% 113.88/17.19 | | | (164) all_52_6 = e1
% 113.88/17.19 | | |
% 113.88/17.19 | | | COMBINE_EQS: (5), (164) imply:
% 113.88/17.19 | | | (165) all_58_7 = e1
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (89), (162) imply:
% 113.88/17.19 | | | (166) ~ (all_4_2 = e2)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (16), (164) imply:
% 113.88/17.19 | | | (167) ~ (all_52_2 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (110), (164) imply:
% 113.88/17.19 | | | (168) ~ (all_52_4 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (95), (164) imply:
% 113.88/17.19 | | | (169) ~ (all_8_2 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | SIMP: (169) implies:
% 113.88/17.19 | | | (170) ~ (all_8_2 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | REDUCE: (123), (164) imply:
% 113.88/17.19 | | | (171) ~ (all_6_2 = e1)
% 113.88/17.19 | | |
% 113.88/17.19 | | | BETA: splitting (45) gives:
% 113.88/17.19 | | |
% 113.88/17.19 | | | Case 1:
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | (172) all_54_15 = e3
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | COMBINE_EQS: (147), (172) imply:
% 113.88/17.19 | | | | (173) all_4_2 = e3
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | REDUCE: (158), (173) imply:
% 113.88/17.19 | | | | (174) $false
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | CLOSE: (174) is inconsistent.
% 113.88/17.19 | | | |
% 113.88/17.19 | | | Case 2:
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | (175) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | BETA: splitting (175) gives:
% 113.88/17.19 | | | |
% 113.88/17.19 | | | | Case 1:
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | (176) all_54_15 = e2
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | COMBINE_EQS: (147), (176) imply:
% 113.88/17.19 | | | | | (177) all_4_2 = e2
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | REDUCE: (166), (177) imply:
% 113.88/17.19 | | | | | (178) $false
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | CLOSE: (178) is inconsistent.
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | Case 2:
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | (179) ~ (all_54_15 = e2)
% 113.88/17.19 | | | | | (180) all_54_15 = e1 | all_54_15 = e0
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | BETA: splitting (180) gives:
% 113.88/17.19 | | | | |
% 113.88/17.19 | | | | | Case 1:
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | (181) all_54_15 = e1
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | COMBINE_EQS: (147), (181) imply:
% 113.88/17.19 | | | | | | (182) all_4_2 = e1
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | COMBINE_EQS: (89), (182) imply:
% 113.88/17.19 | | | | | | (183) all_56_15 = e1
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | COMBINE_EQS: (75), (182) imply:
% 113.88/17.19 | | | | | | (184) all_58_15 = e1
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | REDUCE: (17), (182) imply:
% 113.88/17.19 | | | | | | (185) ~ (all_52_7 = e1)
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | REDUCE: (166), (182) imply:
% 113.88/17.19 | | | | | | (186) ~ (e2 = e1)
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | SIMP: (186) implies:
% 113.88/17.19 | | | | | | (187) ~ (e2 = e1)
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | BETA: splitting (72) gives:
% 113.88/17.19 | | | | | |
% 113.88/17.19 | | | | | | Case 1:
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | (188) ~ (all_56_15 = e1)
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | REDUCE: (183), (188) imply:
% 113.88/17.19 | | | | | | | (189) $false
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | CLOSE: (189) is inconsistent.
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | Case 2:
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | (190) ~ (all_56_11 = e0)
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | REDUCE: (18), (190) imply:
% 113.88/17.19 | | | | | | | (191) ~ (all_52_11 = e0)
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | BETA: splitting (86) gives:
% 113.88/17.19 | | | | | | |
% 113.88/17.19 | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | |
% 113.88/17.19 | | | | | | | | (192) ~ (all_56_1 = e3)
% 113.88/17.19 | | | | | | | |
% 113.88/17.19 | | | | | | | | REDUCE: (113), (192) imply:
% 113.88/17.19 | | | | | | | | (193) ~ (all_52_8 = e3)
% 113.88/17.19 | | | | | | | |
% 113.88/17.19 | | | | | | | | BETA: splitting (130) gives:
% 113.88/17.19 | | | | | | | |
% 113.88/17.19 | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | |
% 113.88/17.19 | | | | | | | | | (194) ~ (all_56_4 = e2)
% 113.88/17.19 | | | | | | | | |
% 113.88/17.19 | | | | | | | | | REDUCE: (118), (194) imply:
% 113.88/17.19 | | | | | | | | | (195) ~ (all_52_9 = e2)
% 113.88/17.19 | | | | | | | | |
% 113.88/17.19 | | | | | | | | | BETA: splitting (98) gives:
% 113.88/17.19 | | | | | | | | |
% 113.88/17.19 | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | (196) ~ (all_56_2 = e3)
% 113.88/17.19 | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | REDUCE: (47), (196) imply:
% 113.88/17.19 | | | | | | | | | | (197) ~ (all_52_12 = e3)
% 113.88/17.19 | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | BETA: splitting (140) gives:
% 113.88/17.19 | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | (198) all_58_0 = e3
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | COMBINE_EQS: (28), (198) imply:
% 113.88/17.19 | | | | | | | | | | | (199) all_10_2 = e3
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | REDUCE: (80), (199) imply:
% 113.88/17.19 | | | | | | | | | | | (200) $false
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | Case 2:
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | (201) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | BETA: splitting (201) gives:
% 113.88/17.19 | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | (202) all_58_1 = e3
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | COMBINE_EQS: (97), (202) imply:
% 113.88/17.19 | | | | | | | | | | | | (203) all_52_4 = e3
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | REDUCE: (46), (203) imply:
% 113.88/17.19 | | | | | | | | | | | | (204) ~ (all_52_7 = e3)
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | SIMP: (204) implies:
% 113.88/17.19 | | | | | | | | | | | | (205) ~ (all_52_7 = e3)
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | REDUCE: (68), (203) imply:
% 113.88/17.19 | | | | | | | | | | | | (206) ~ (all_8_2 = e3)
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | SIMP: (206) implies:
% 113.88/17.19 | | | | | | | | | | | | (207) ~ (all_8_2 = e3)
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | REDUCE: (168), (203) imply:
% 113.88/17.19 | | | | | | | | | | | | (208) ~ (e3 = e1)
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | BETA: splitting (25) gives:
% 113.88/17.19 | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | (209) all_54_5 = e3
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | REF_CLOSE: (88), (207), (209) are inconsistent by sub-proof
% 113.88/17.19 | | | | | | | | | | | | | #339.
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | Case 2:
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | (210) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | BETA: splitting (210) gives:
% 113.88/17.19 | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | (211) all_54_5 = e2
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | REF_CLOSE: (88), (103), (211) are inconsistent by sub-proof
% 113.88/17.19 | | | | | | | | | | | | | | #338.
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | Case 2:
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | (212) ~ (all_54_5 = e2)
% 113.88/17.19 | | | | | | | | | | | | | | (213) all_54_5 = e1 | all_54_5 = e0
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 113.88/17.19 | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | (214) all_54_5 = e1
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | REF_CLOSE: (88), (170), (214) are inconsistent by sub-proof
% 113.88/17.19 | | | | | | | | | | | | | | | #337.
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | Case 2:
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | (215) all_54_5 = e0
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | COMBINE_EQS: (88), (215) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (216) all_8_2 = e0
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | SIMP: (216) implies:
% 113.88/17.19 | | | | | | | | | | | | | | | (217) all_8_2 = e0
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | COMBINE_EQS: (100), (217) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (218) all_56_13 = e0
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | REDUCE: (66), (217) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (219) ~ (all_52_7 = e0)
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | REDUCE: (170), (217) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (220) ~ (e1 = e0)
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | SIMP: (220) implies:
% 113.88/17.19 | | | | | | | | | | | | | | | (221) ~ (e1 = e0)
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | REDUCE: (148), (217) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (222) op(e2, e0) = e1
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | REDUCE: (14), (217) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | (223) op(e1, e0) = all_8_0
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 113.88/17.19 | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | (224) all_58_15 = e0
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (224) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | | (225) e1 = e0
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | REDUCE: (221), (225) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | | (226) $false
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | Case 2:
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | (227) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 113.88/17.19 | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 113.88/17.19 | | | | | | | | | | | | | | | | e0)
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 113.88/17.19 | | | | | | | | | | | | | | | | (228) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 113.88/17.19 | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | | (229) ~ (all_56_5 = e2)
% 113.88/17.19 | | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | | REDUCE: (120), (229) imply:
% 113.88/17.19 | | | | | | | | | | | | | | | | | (230) ~ (all_52_13 = e2)
% 113.88/17.19 | | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 113.88/17.19 | | | | | | | | | | | | | | | | |
% 113.88/17.19 | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.19 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | (231) all_54_13 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (205), (231) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | #336.
% 113.88/17.20 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | (232) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (233) all_58_2 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (233) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (234) all_52_1 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (235) all_52_1 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (235) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (236) all_56_3 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | REDUCE: (111), (235) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (237) ~ (all_52_2 = e2)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | SIMP: (237) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | (238) ~ (all_52_2 = e2)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | (239) ~ (all_56_3 = e2)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (239) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | (240) $false
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | (241) ~ (all_56_14 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (241) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | (242) ~ (all_6_2 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (243) all_54_7 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (243) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (244) all_52_13 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (245) all_52_13 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (245) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (246) all_58_10 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (245) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (247) op(e2, e0) = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (248) all_58_12 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (248) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (249) all_52_3 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (250) all_52_3 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (250) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_52_2 = e0)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (252) all_54_8 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (252) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (253) all_52_2 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (253) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (254) all_52_2 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (254) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_6 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (254) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_52_14 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_52_14 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (254) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (258) ~ (all_6_2 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (259) all_58_6 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (259) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (260) e3 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (260) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (261) e3 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (261) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_58_10 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (64), (119), (144), (184), (197), (208),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (257), (262) are inconsistent by sub-proof #201.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_54_10 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (242), (264) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | #352.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_7 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (187), (266) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | #346.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_8 = e2 | all_58_11 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_58_8 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (268) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_6_2 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (269) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) $false
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_11 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (271) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_52_14 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (272) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_6_2 = e2)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (272) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) op(e1, e0) = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_54_10 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (105), (275) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_54_10 = e1 | all_54_10 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_54_10 = e1
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (149), (277) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_54_10 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (278) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_6_2 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_6_2 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (280) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) op(e1, e0) = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with e3, all_8_0, e0, e1,
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (281) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_8_0 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with e2, all_8_0, e0, e1,
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (274) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_8_0 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with e1, e3, e0, e2,
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (222), (247) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) e3 = e1
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) e3 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (285) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) e3 = e2
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (286) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) e2 = e1
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (284) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_1 = e1
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (29), (41), (44), (45), (66), (86),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (103), (113), (119), (147), (170),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (197), (201), (208), (210), (232), (236),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) are inconsistent by sub-proof #307.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (289) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (167), (238), (251), (289) are inconsistent
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #381.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (290) all_58_13 = e0 | all_58_14 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (99), (191), (219), (290) are inconsistent
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #428.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_54_7 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (291) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | (292) ~ (all_52_13 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (293) all_54_10 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (293) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (294) all_6_2 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (242), (294) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (295) $false
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | (296) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_9 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (42), (47), (52), (105), (119), (149),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (296), (297) are inconsistent by sub-proof #149.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_58_9 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (300) all_58_10 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (300) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (301) all_52_13 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (302) all_52_13 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (302) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (303) $false
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_11 = e3 | all_58_15 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_11 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (305) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_52_14 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (306) implies:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_52_14 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (307) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_2 = e3)
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (39), (42), (67), (105), (149), (167),
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (238), (296), (308) are inconsistent by sub-proof
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | #296.
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_15 = e3
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (309) imply:
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | | (310) e3 = e1
% 113.88/17.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (310) implies:
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | (311) e3 = e1
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (311) imply:
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_58_1 = e1
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (29), (41), (44), (45), (66), (86),
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | (88), (89), (103), (113), (119), (147), (170),
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | (185), (197), (201), (208), (210), (232), (236),
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | | (312) are inconsistent by sub-proof #307.
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | (313) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.21 | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (70), (91), (103), (195), (230), (313) are
% 113.88/17.21 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401.
% 113.88/17.21 | | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | (314) ~ (all_56_13 = e0)
% 113.88/17.21 | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | REDUCE: (218), (314) imply:
% 113.88/17.21 | | | | | | | | | | | | | | | | | (315) $false
% 113.88/17.21 | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent.
% 113.88/17.21 | | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | (316) all_58_4 = e3 | all_58_9 = e3
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | REF_CLOSE: (44), (119), (193), (197), (316) are inconsistent
% 113.88/17.21 | | | | | | | | | | | | by sub-proof #184.
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | (317) all_56_2 = e3
% 113.88/17.21 | | | | | | | | | | (318) ~ (all_56_13 = e0)
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | COMBINE_EQS: (47), (317) imply:
% 113.88/17.21 | | | | | | | | | | (319) all_52_12 = e3
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | REDUCE: (100), (318) imply:
% 113.88/17.21 | | | | | | | | | | (320) ~ (all_8_2 = e0)
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | REDUCE: (22), (319) imply:
% 113.88/17.21 | | | | | | | | | | (321) ~ (all_10_2 = e3)
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | BETA: splitting (52) gives:
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | Case 1:
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | (322) ~ (all_56_2 = e3)
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | REDUCE: (317), (322) imply:
% 113.88/17.21 | | | | | | | | | | | (323) $false
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | CLOSE: (323) is inconsistent.
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | (324) ~ (all_56_14 = e0)
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | REDUCE: (11), (324) imply:
% 113.88/17.21 | | | | | | | | | | | (325) ~ (all_6_2 = e0)
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | BETA: splitting (36) gives:
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | Case 1:
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | (326) all_54_10 = e3
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | COMBINE_EQS: (42), (326) imply:
% 113.88/17.21 | | | | | | | | | | | | (327) all_6_2 = e3
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | REDUCE: (139), (327) imply:
% 113.88/17.21 | | | | | | | | | | | | (328) op(e1, e1) = e3
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | BETA: splitting (96) gives:
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | Case 1:
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | (329) ~ (all_56_3 = e2)
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | REDUCE: (12), (329) imply:
% 113.88/17.21 | | | | | | | | | | | | | (330) ~ (all_52_1 = e2)
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | BETA: splitting (2) gives:
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | Case 1:
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | (331) ~ (all_56_2 = e3)
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | REDUCE: (317), (331) imply:
% 113.88/17.21 | | | | | | | | | | | | | | (332) $false
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | (333) ~ (all_56_12 = e0)
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | REDUCE: (26), (333) imply:
% 113.88/17.21 | | | | | | | | | | | | | | (334) ~ (all_10_2 = e0)
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (10), (13), (25), (30), (37), (40),
% 113.88/17.21 | | | | | | | | | | | | | | (44), (60), (61), (70), (76), (80), (87), (88),
% 113.88/17.21 | | | | | | | | | | | | | | (93), (99), (101), (103), (115), (116), (138),
% 113.88/17.21 | | | | | | | | | | | | | | (146), (147), (148), (149), (156), (166), (175),
% 113.88/17.21 | | | | | | | | | | | | | | (320), (330), (334) are inconsistent by sub-proof
% 113.88/17.21 | | | | | | | | | | | | | | #123.
% 113.88/17.21 | | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | (335) all_56_3 = e2
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | | REF_CLOSE: (11), (37), (96), (139), (328), (335) are
% 113.88/17.21 | | | | | | | | | | | | | inconsistent by sub-proof #121.
% 113.88/17.21 | | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | (336) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | | REF_CLOSE: (42), (105), (149), (325), (336) are inconsistent
% 113.88/17.21 | | | | | | | | | | | | by sub-proof #435.
% 113.88/17.21 | | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | | |
% 113.88/17.21 | | | | | | | | | End of split
% 113.88/17.21 | | | | | | | | |
% 113.88/17.21 | | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | | |
% 113.88/17.21 | | | | | | | | | (337) ~ (all_56_15 = e1)
% 113.88/17.21 | | | | | | | | |
% 113.88/17.21 | | | | | | | | | REDUCE: (183), (337) imply:
% 113.88/17.21 | | | | | | | | | (338) $false
% 113.88/17.21 | | | | | | | | |
% 113.88/17.21 | | | | | | | | | CLOSE: (338) is inconsistent.
% 113.88/17.21 | | | | | | | | |
% 113.88/17.21 | | | | | | | | End of split
% 113.88/17.21 | | | | | | | |
% 113.88/17.21 | | | | | | | Case 2:
% 113.88/17.21 | | | | | | | |
% 113.88/17.21 | | | | | | | | (339) ~ (all_56_15 = e1)
% 113.88/17.21 | | | | | | | |
% 113.88/17.21 | | | | | | | | REDUCE: (183), (339) imply:
% 113.88/17.21 | | | | | | | | (340) $false
% 113.88/17.21 | | | | | | | |
% 113.88/17.21 | | | | | | | | CLOSE: (340) is inconsistent.
% 113.88/17.21 | | | | | | | |
% 113.88/17.21 | | | | | | | End of split
% 113.88/17.21 | | | | | | |
% 113.88/17.21 | | | | | | End of split
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | Case 2:
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | | (341) all_54_15 = e0
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | | COMBINE_EQS: (147), (341) imply:
% 113.88/17.21 | | | | | | (342) all_4_2 = e0
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | | REDUCE: (10), (342) imply:
% 113.88/17.21 | | | | | | (343) $false
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | | CLOSE: (343) is inconsistent.
% 113.88/17.21 | | | | | |
% 113.88/17.21 | | | | | End of split
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | End of split
% 113.88/17.21 | | | |
% 113.88/17.21 | | | End of split
% 113.88/17.21 | | |
% 113.88/17.21 | | End of split
% 113.88/17.21 | |
% 113.88/17.21 | Case 2:
% 113.88/17.21 | |
% 113.88/17.21 | | (344) all_56_15 = e3
% 113.88/17.21 | | (345) ~ (all_56_9 = e0)
% 113.88/17.21 | |
% 113.88/17.21 | | COMBINE_EQS: (89), (344) imply:
% 113.88/17.21 | | (346) all_4_2 = e3
% 113.88/17.21 | |
% 113.88/17.21 | | SIMP: (346) implies:
% 113.88/17.21 | | (347) all_4_2 = e3
% 113.88/17.21 | |
% 113.88/17.21 | | COMBINE_EQS: (75), (347) imply:
% 113.88/17.21 | | (348) all_58_15 = e3
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (71), (345) imply:
% 113.88/17.21 | | (349) ~ (all_52_3 = e0)
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (122), (347) imply:
% 113.88/17.21 | | (350) ~ (all_52_3 = e3)
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (17), (347) imply:
% 113.88/17.21 | | (351) ~ (all_52_7 = e3)
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (93), (347) imply:
% 113.88/17.21 | | (352) ~ (all_52_11 = e3)
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (134), (347) imply:
% 113.88/17.21 | | (353) ~ (all_52_12 = e3)
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (35), (347) imply:
% 113.88/17.21 | | (354) op(all_4_1, e3) = all_4_0
% 113.88/17.21 | |
% 113.88/17.21 | | REDUCE: (114), (347) imply:
% 113.88/17.21 | | (355) op(e0, e3) = all_4_1
% 113.88/17.21 | |
% 113.88/17.21 | | BETA: splitting (41) gives:
% 113.88/17.21 | |
% 113.88/17.21 | | Case 1:
% 113.88/17.21 | | |
% 113.88/17.21 | | | (356) ~ (all_56_3 = e2)
% 113.88/17.21 | | |
% 113.88/17.21 | | | REDUCE: (12), (356) imply:
% 113.88/17.21 | | | (357) ~ (all_52_1 = e2)
% 113.88/17.21 | | |
% 113.88/17.21 | | | BETA: splitting (8) gives:
% 113.88/17.21 | | |
% 113.88/17.21 | | | Case 1:
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | (358) ~ (all_56_6 = e1)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | REDUCE: (125), (358) imply:
% 113.88/17.21 | | | | (359) ~ (all_52_2 = e1)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | GROUND_INST: instantiating (37) with all_52_3, all_4_1, e3, e0,
% 113.88/17.21 | | | | simplifying with (79), (355) gives:
% 113.88/17.21 | | | | (360) all_52_3 = all_4_1
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | COMBINE_EQS: (128), (360) imply:
% 113.88/17.21 | | | | (361) all_58_12 = all_4_1
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | REDUCE: (155), (360) imply:
% 113.88/17.21 | | | | (362) ~ (all_52_7 = all_4_1)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | SIMP: (362) implies:
% 113.88/17.21 | | | | (363) ~ (all_52_7 = all_4_1)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | REDUCE: (350), (360) imply:
% 113.88/17.21 | | | | (364) ~ (all_4_1 = e3)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | REDUCE: (349), (360) imply:
% 113.88/17.21 | | | | (365) ~ (all_4_1 = e0)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | BETA: splitting (32) gives:
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | Case 1:
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | | (366) ~ (all_56_8 = e1)
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | | REDUCE: (141), (366) imply:
% 113.88/17.21 | | | | | (367) ~ (all_52_14 = e1)
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | | REF_CLOSE: (1), (5), (9), (13), (15), (19), (21), (23), (25), (26),
% 113.88/17.21 | | | | | (28), (29), (30), (36), (37), (39), (42), (43), (44), (46),
% 113.88/17.21 | | | | | (50), (54), (59), (60), (62), (63), (66), (68), (76), (80),
% 113.88/17.21 | | | | | (82), (85), (87), (88), (95), (97), (99), (101), (102),
% 113.88/17.21 | | | | | (103), (104), (105), (106), (107), (113), (115), (116),
% 113.88/17.21 | | | | | (119), (123), (136), (140), (145), (146), (149), (150),
% 113.88/17.21 | | | | | (156), (348), (351), (353), (354), (357), (359), (361),
% 113.88/17.21 | | | | | (363), (364), (365), (367) are inconsistent by sub-proof
% 113.88/17.21 | | | | | #320.
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | Case 2:
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | | (368) all_56_8 = e1
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (13), (15), (18), (19),
% 113.88/17.21 | | | | | (23), (25), (26), (28), (29), (30), (32), (33), (34), (36),
% 113.88/17.21 | | | | | (37), (38), (39), (40), (42), (44), (50), (53), (54), (56),
% 113.88/17.21 | | | | | (59), (60), (62), (65), (66), (67), (70), (73), (76), (77),
% 113.88/17.21 | | | | | (78), (79), (80), (83), (85), (87), (88), (91), (92), (94),
% 113.88/17.21 | | | | | (95), (100), (101), (103), (106), (107), (109), (111),
% 113.88/17.21 | | | | | (112), (113), (115), (116), (118), (120), (121), (124),
% 113.88/17.21 | | | | | (127), (128), (131), (132), (135), (138), (141), (142),
% 113.88/17.21 | | | | | (143), (146), (148), (149), (151), (152), (153), (155),
% 113.88/17.21 | | | | | (156), (349), (350), (351), (352), (354), (355), (357),
% 113.88/17.21 | | | | | (359), (368) are inconsistent by sub-proof #100.
% 113.88/17.21 | | | | |
% 113.88/17.21 | | | | End of split
% 113.88/17.21 | | | |
% 113.88/17.21 | | | Case 2:
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | (369) ~ (all_56_15 = e3)
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | REDUCE: (344), (369) imply:
% 113.88/17.21 | | | | (370) $false
% 113.88/17.21 | | | |
% 113.88/17.21 | | | | CLOSE: (370) is inconsistent.
% 113.88/17.21 | | | |
% 113.88/17.21 | | | End of split
% 113.88/17.21 | | |
% 113.88/17.22 | | Case 2:
% 113.88/17.22 | | |
% 113.88/17.22 | | | (371) ~ (all_56_15 = e3)
% 113.88/17.22 | | |
% 113.88/17.22 | | | REDUCE: (344), (371) imply:
% 113.88/17.22 | | | (372) $false
% 113.88/17.22 | | |
% 113.88/17.22 | | | CLOSE: (372) is inconsistent.
% 113.88/17.22 | | |
% 113.88/17.22 | | End of split
% 113.88/17.22 | |
% 113.88/17.22 | End of split
% 113.88/17.22 |
% 113.88/17.22 End of proof
% 113.88/17.22
% 113.88/17.22 Sub-proof #69 shows that the following formulas are inconsistent:
% 113.88/17.22 ----------------------------------------------------------------
% 113.88/17.22 (1) ~ (all_52_8 = all_10_2)
% 113.88/17.22 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.88/17.22 (3) all_58_7 = all_52_6
% 113.88/17.22 (4) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.22 (5) op(e3, e2) = all_52_4
% 113.88/17.22 (6) all_54_0 = all_10_2
% 113.88/17.22 (7) op(e1, all_8_2) = all_8_0
% 113.88/17.22 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.22 (9) ~ (all_52_2 = all_52_6)
% 113.88/17.22 (10) ~ (all_52_12 = all_10_2)
% 113.88/17.22 (11) ~ (e3 = e1)
% 113.88/17.22 (12) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.22 (13) all_56_12 = all_10_2
% 113.88/17.22 (14) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.88/17.22 (15) all_58_0 = all_10_2
% 113.88/17.22 (16) all_54_11 = all_52_14
% 113.88/17.22 (17) all_54_13 = all_52_7
% 113.88/17.22 (18) ~ (all_52_14 = all_6_2)
% 113.88/17.22 (19) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 113.88/17.22 (20) all_56_10 = all_52_7
% 113.88/17.22 (21) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.22 (22) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.88/17.22 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.22 (24) ~ (all_52_2 = all_6_2)
% 113.88/17.22 (25) all_54_10 = all_6_2
% 113.88/17.22 (26) ~ (all_52_8 = all_6_2)
% 113.88/17.22 (27) all_58_4 = all_52_8
% 113.88/17.22 (28) ~ (all_52_4 = all_52_7)
% 113.88/17.22 (29) all_56_2 = all_52_12
% 113.88/17.22 (30) all_58_3 = all_8_2
% 113.88/17.22 (31) all_54_6 = all_52_9
% 113.88/17.22 (32) all_58_11 = all_52_14
% 113.88/17.22 (33) op(e2, e3) = all_52_1
% 113.88/17.22 (34) ~ (all_10_2 = e1)
% 113.88/17.22 (35) ~ (all_52_7 = all_8_2)
% 113.88/17.22 (36) ~ (all_52_4 = all_8_2)
% 113.88/17.22 (37) op(e1, e0) = all_52_14
% 113.88/17.22 (38) all_58_5 = all_52_9
% 113.88/17.22 (39) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.22 (40) all_56_9 = all_52_3
% 113.88/17.22 (41) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.88/17.22 (42) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.88/17.22 (43) all_58_2 = all_52_1
% 113.88/17.22 (44) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.22 (45) ~ (all_10_2 = e3)
% 113.88/17.22 (46) all_58_13 = all_52_7
% 113.88/17.22 (47) ~ (all_52_7 = e0)
% 113.88/17.22 (48) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.88/17.22 (49) all_58_6 = all_52_2
% 113.88/17.22 (50) all_54_5 = all_8_2
% 113.88/17.22 (51) ~ (all_52_13 = e2)
% 113.88/17.22 (52) all_58_10 = all_52_13
% 113.88/17.22 (53) ~ (all_52_13 = all_8_2)
% 113.88/17.22 (54) op(e3, all_10_2) = all_10_1
% 113.88/17.22 (55) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 113.88/17.22 (56) all_58_1 = all_52_4
% 113.88/17.22 (57) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.22 (58) all_54_1 = all_52_4
% 113.88/17.22 (59) all_56_13 = all_8_2
% 113.88/17.22 (60) ~ (all_52_1 = all_8_2)
% 113.88/17.22 (61) ~ (all_8_2 = e2)
% 113.88/17.22 (62) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.22 (63) ~ (all_52_14 = e2)
% 113.88/17.22 (64) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.22 (65) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.22 (66) all_56_7 = all_52_6
% 113.88/17.22 (67) ~ (all_52_9 = all_6_2)
% 113.88/17.22 (68) ~ (all_52_4 = all_52_6)
% 113.88/17.22 (69) all_56_1 = all_52_8
% 113.88/17.22 (70) all_58_8 = all_6_2
% 113.88/17.22 (71) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.22 (72) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.88/17.22 (73) all_58_9 = all_52_12
% 113.88/17.22 (74) all_56_6 = all_52_2
% 113.88/17.22 (75) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.88/17.22 (76) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.88/17.22 (77) all_58_12 = all_52_3
% 113.88/17.22 (78) ~ (all_52_2 = all_52_14)
% 113.88/17.22 (79) ~ (all_52_8 = all_52_9)
% 113.88/17.22 (80) op(e2, e0) = all_52_13
% 113.88/17.22 (81) all_24_1 = all_10_1
% 113.88/17.22 (82) all_24_2 = all_10_2
% 113.88/17.22 (83) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.22 (84) all_56_15 = e2
% 113.88/17.22 (85) all_56_8 = all_52_14
% 113.88/17.22 (86) ~ (all_52_4 = all_10_2)
% 113.88/17.22 (87) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.22 (88) all_56_0 = all_52_4
% 113.88/17.22 (89) ~ (all_8_0 = e3)
% 113.88/17.22 (90) ~ (e3 = e2)
% 113.88/17.22 (91) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.22 (92) op(e2, all_8_2) = e1
% 113.88/17.22 (93) ~ (all_6_2 = e1)
% 113.88/17.22 (94) ~ (all_52_6 = all_52_7)
% 113.88/17.22
% 113.88/17.22 Begin of proof
% 113.88/17.22 |
% 113.88/17.22 | BETA: splitting (55) gives:
% 113.88/17.22 |
% 113.88/17.22 | Case 1:
% 113.88/17.22 | |
% 113.88/17.22 | | (95) ~ (all_56_0 = e3)
% 113.88/17.22 | |
% 113.88/17.22 | | REDUCE: (88), (95) imply:
% 113.88/17.22 | | (96) ~ (all_52_4 = e3)
% 113.88/17.22 | |
% 113.88/17.22 | | BETA: splitting (14) gives:
% 113.88/17.22 | |
% 113.88/17.22 | | Case 1:
% 113.88/17.22 | | |
% 113.88/17.22 | | | (97) ~ (all_56_7 = e1)
% 113.88/17.22 | | |
% 113.88/17.22 | | | REDUCE: (66), (97) imply:
% 113.88/17.22 | | | (98) ~ (all_52_6 = e1)
% 113.88/17.22 | | |
% 113.88/17.22 | | | BETA: splitting (2) gives:
% 113.88/17.22 | | |
% 113.88/17.22 | | | Case 1:
% 113.88/17.22 | | | |
% 113.88/17.22 | | | | (99) ~ (all_56_2 = e3)
% 113.88/17.22 | | | |
% 113.88/17.22 | | | | REDUCE: (29), (99) imply:
% 113.88/17.22 | | | | (100) ~ (all_52_12 = e3)
% 113.88/17.22 | | | |
% 113.88/17.22 | | | | BETA: splitting (83) gives:
% 113.88/17.22 | | | |
% 113.88/17.22 | | | | Case 1:
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | (101) all_58_0 = e3
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | COMBINE_EQS: (15), (101) imply:
% 113.88/17.22 | | | | | (102) all_10_2 = e3
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | REDUCE: (45), (102) imply:
% 113.88/17.22 | | | | | (103) $false
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | CLOSE: (103) is inconsistent.
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | Case 2:
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | (104) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | BETA: splitting (104) gives:
% 113.88/17.22 | | | | |
% 113.88/17.22 | | | | | Case 1:
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | (105) all_58_1 = e3
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | COMBINE_EQS: (56), (105) imply:
% 113.88/17.22 | | | | | | (106) all_52_4 = e3
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | REDUCE: (96), (106) imply:
% 113.88/17.22 | | | | | | (107) $false
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | CLOSE: (107) is inconsistent.
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | Case 2:
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | (108) all_58_4 = e3 | all_58_9 = e3
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | BETA: splitting (108) gives:
% 113.88/17.22 | | | | | |
% 113.88/17.22 | | | | | | Case 1:
% 113.88/17.22 | | | | | | |
% 113.88/17.22 | | | | | | | (109) all_58_4 = e3
% 113.88/17.22 | | | | | | |
% 113.88/17.22 | | | | | | | COMBINE_EQS: (27), (109) imply:
% 113.88/17.23 | | | | | | | (110) all_52_8 = e3
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | COMBINE_EQS: (69), (110) imply:
% 113.88/17.23 | | | | | | | (111) all_56_1 = e3
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | REDUCE: (79), (110) imply:
% 113.88/17.23 | | | | | | | (112) ~ (all_52_9 = e3)
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | SIMP: (112) implies:
% 113.88/17.23 | | | | | | | (113) ~ (all_52_9 = e3)
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | REDUCE: (1), (110) imply:
% 113.88/17.23 | | | | | | | (114) ~ (all_10_2 = e3)
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | REDUCE: (26), (110) imply:
% 113.88/17.23 | | | | | | | (115) ~ (all_6_2 = e3)
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | SIMP: (115) implies:
% 113.88/17.23 | | | | | | | (116) ~ (all_6_2 = e3)
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | BETA: splitting (22) gives:
% 113.88/17.23 | | | | | | |
% 113.88/17.23 | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | (117) ~ (all_56_1 = e3)
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | REDUCE: (111), (117) imply:
% 113.88/17.23 | | | | | | | | (118) $false
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | CLOSE: (118) is inconsistent.
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | (119) ~ (all_56_13 = e1)
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | REDUCE: (59), (119) imply:
% 113.88/17.23 | | | | | | | | (120) ~ (all_8_2 = e1)
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | BETA: splitting (42) gives:
% 113.88/17.23 | | | | | | | |
% 113.88/17.23 | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | (121) ~ (all_56_6 = e1)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | REDUCE: (74), (121) imply:
% 113.88/17.23 | | | | | | | | | (122) ~ (all_52_2 = e1)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | BETA: splitting (64) gives:
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | (123) all_58_6 = e1
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | REF_CLOSE: (49), (122), (123) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | #452.
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | (124) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | BETA: splitting (124) gives:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | (125) all_58_7 = e1
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | COMBINE_EQS: (3), (125) imply:
% 113.88/17.23 | | | | | | | | | | | (126) all_52_6 = e1
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | REDUCE: (98), (126) imply:
% 113.88/17.23 | | | | | | | | | | | (127) $false
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | (128) all_58_8 = e1 | all_58_11 = e1
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | BETA: splitting (128) gives:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | (129) all_58_8 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | COMBINE_EQS: (70), (129) imply:
% 113.88/17.23 | | | | | | | | | | | | (130) all_6_2 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REDUCE: (93), (130) imply:
% 113.88/17.23 | | | | | | | | | | | | (131) $false
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | (132) all_58_11 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | COMBINE_EQS: (32), (132) imply:
% 113.88/17.23 | | | | | | | | | | | | (133) all_52_14 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | SIMP: (133) implies:
% 113.88/17.23 | | | | | | | | | | | | (134) all_52_14 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | COMBINE_EQS: (85), (134) imply:
% 113.88/17.23 | | | | | | | | | | | | (135) all_56_8 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | BETA: splitting (41) gives:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | (136) ~ (all_56_8 = e1)
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | REDUCE: (135), (136) imply:
% 113.88/17.23 | | | | | | | | | | | | | (137) $false
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | (138) ~ (all_56_12 = e0)
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | REDUCE: (13), (138) imply:
% 113.88/17.23 | | | | | | | | | | | | | (139) ~ (all_10_2 = e0)
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | BETA: splitting (19) gives:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | (140) ~ (all_56_8 = e1)
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | REDUCE: (135), (140) imply:
% 113.88/17.23 | | | | | | | | | | | | | | (141) $false
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | (142) ~ (all_56_13 = e0)
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | REDUCE: (59), (142) imply:
% 113.88/17.23 | | | | | | | | | | | | | | (143) ~ (all_8_2 = e0)
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (13), (15),
% 113.88/17.23 | | | | | | | | | | | | | | (17), (20), (23), (28), (30), (33), (34), (35),
% 113.88/17.23 | | | | | | | | | | | | | | (36), (39), (40), (43), (44), (45), (46), (48),
% 113.88/17.23 | | | | | | | | | | | | | | (49), (50), (54), (56), (58), (59), (61), (62),
% 113.88/17.23 | | | | | | | | | | | | | | (65), (68), (71), (77), (81), (82), (86), (88),
% 113.88/17.23 | | | | | | | | | | | | | | (91), (92), (94), (139), (143) are inconsistent by
% 113.88/17.23 | | | | | | | | | | | | | | sub-proof #80.
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | End of split
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | End of split
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | End of split
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | End of split
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | End of split
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | (144) all_56_6 = e1
% 113.88/17.23 | | | | | | | | | (145) ~ (all_56_13 = e3)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | COMBINE_EQS: (74), (144) imply:
% 113.88/17.23 | | | | | | | | | (146) all_52_2 = e1
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | REDUCE: (59), (145) imply:
% 113.88/17.23 | | | | | | | | | (147) ~ (all_8_2 = e3)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | REDUCE: (78), (146) imply:
% 113.88/17.23 | | | | | | | | | (148) ~ (all_52_14 = e1)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | SIMP: (148) implies:
% 113.88/17.23 | | | | | | | | | (149) ~ (all_52_14 = e1)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | REDUCE: (24), (146) imply:
% 113.88/17.23 | | | | | | | | | (150) ~ (all_6_2 = e1)
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | BETA: splitting (12) gives:
% 113.88/17.23 | | | | | | | | |
% 113.88/17.23 | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | (151) all_54_5 = e3
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | REF_CLOSE: (50), (147), (151) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | #339.
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | (152) ~ (all_54_5 = e3)
% 113.88/17.23 | | | | | | | | | | (153) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | BETA: splitting (153) gives:
% 113.88/17.23 | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | (154) all_54_5 = e2
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | REF_CLOSE: (50), (61), (154) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | #338.
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | (155) ~ (all_54_5 = e2)
% 113.88/17.23 | | | | | | | | | | | (156) all_54_5 = e1 | all_54_5 = e0
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | BETA: splitting (156) gives:
% 113.88/17.23 | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | (157) all_54_5 = e1
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REF_CLOSE: (50), (120), (157) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | | #337.
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | (158) all_54_5 = e0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | COMBINE_EQS: (50), (158) imply:
% 113.88/17.23 | | | | | | | | | | | | (159) all_8_2 = e0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | SIMP: (159) implies:
% 113.88/17.23 | | | | | | | | | | | | (160) all_8_2 = e0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REDUCE: (7), (160) imply:
% 113.88/17.23 | | | | | | | | | | | | (161) op(e1, e0) = all_8_0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_52_14, all_8_0, e0,
% 113.88/17.23 | | | | | | | | | | | | e1, simplifying with (37), (161) gives:
% 113.88/17.23 | | | | | | | | | | | | (162) all_52_14 = all_8_0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | COMBINE_EQS: (16), (162) imply:
% 113.88/17.23 | | | | | | | | | | | | (163) all_54_11 = all_8_0
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REDUCE: (18), (162) imply:
% 113.88/17.23 | | | | | | | | | | | | (164) ~ (all_8_0 = all_6_2)
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REDUCE: (63), (162) imply:
% 113.88/17.23 | | | | | | | | | | | | (165) ~ (all_8_0 = e2)
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | REDUCE: (149), (162) imply:
% 113.88/17.23 | | | | | | | | | | | | (166) ~ (all_8_0 = e1)
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | BETA: splitting (75) gives:
% 113.88/17.23 | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | (167) all_54_6 = e3
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | REF_CLOSE: (31), (113), (167) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | | | #268.
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | (168) ~ (all_54_6 = e3)
% 113.88/17.23 | | | | | | | | | | | | | (169) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | BETA: splitting (169) gives:
% 113.88/17.23 | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | (170) all_54_6 = e2
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | COMBINE_EQS: (31), (170) imply:
% 113.88/17.23 | | | | | | | | | | | | | | (171) all_52_9 = e2
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | SIMP: (171) implies:
% 113.88/17.23 | | | | | | | | | | | | | | (172) all_52_9 = e2
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | REDUCE: (67), (172) imply:
% 113.88/17.23 | | | | | | | | | | | | | | (173) ~ (all_6_2 = e2)
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | SIMP: (173) implies:
% 113.88/17.23 | | | | | | | | | | | | | | (174) ~ (all_6_2 = e2)
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 113.88/17.23 | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | (175) all_54_11 = e3
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | COMBINE_EQS: (163), (175) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | (176) all_8_0 = e3
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | SIMP: (176) implies:
% 113.88/17.23 | | | | | | | | | | | | | | | (177) all_8_0 = e3
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | REDUCE: (89), (177) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | (178) $false
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | CLOSE: (178) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | (179) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 113.88/17.23 | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | (180) all_54_10 = e3
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | REF_CLOSE: (25), (116), (180) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | | | | | | #352.
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | (181) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 113.88/17.23 | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | (182) all_54_10 = e2
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (174), (182) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | | | | | | | #438.
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | (183) all_54_10 = e1 | all_54_10 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 113.88/17.23 | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | (184) all_54_10 = e1
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (93), (184) are inconsistent by sub-proof
% 113.88/17.23 | | | | | | | | | | | | | | | | | | #437.
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | (185) all_54_10 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (185) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | (186) all_6_2 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | SIMP: (186) implies:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | (187) all_6_2 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | REDUCE: (164), (187) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | (188) ~ (all_8_0 = e0)
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 113.88/17.23 | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | (189) all_54_11 = e2
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (189) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | (190) all_8_0 = e2
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | (191) all_8_0 = e2
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | REDUCE: (165), (191) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | (192) $false
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | CLOSE: (192) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | (193) all_54_11 = e1 | all_54_11 = e0
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | (194) all_54_11 = e1
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (194) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | (195) all_8_0 = e1
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | SIMP: (195) implies:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | (196) all_8_0 = e1
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (196) imply:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | (197) $false
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.23 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | (198) all_54_11 = e0
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (198) imply:
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | (199) all_8_0 = e0
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | SIMP: (199) implies:
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | (200) all_8_0 = e0
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (200) imply:
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | (201) $false
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent.
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | Case 2:
% 113.88/17.24 | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | (202) ~ (all_54_6 = e2)
% 113.88/17.24 | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | REDUCE: (31), (202) imply:
% 113.88/17.24 | | | | | | | | | | | | | | (203) ~ (all_52_9 = e2)
% 113.88/17.24 | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (22), (23), (30), (38), (43), (50),
% 113.88/17.24 | | | | | | | | | | | | | | (51), (52), (53), (59), (60), (61), (76), (80),
% 113.88/17.24 | | | | | | | | | | | | | | (87), (90), (92), (111), (113), (147), (203) are
% 113.88/17.24 | | | | | | | | | | | | | | inconsistent by sub-proof #111.
% 113.88/17.24 | | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | | |
% 113.88/17.24 | | | | | | | | | End of split
% 113.88/17.24 | | | | | | | | |
% 113.88/17.24 | | | | | | | | End of split
% 113.88/17.24 | | | | | | | |
% 113.88/17.24 | | | | | | | End of split
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | Case 2:
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | | (204) all_58_9 = e3
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | | COMBINE_EQS: (73), (204) imply:
% 113.88/17.24 | | | | | | | (205) all_52_12 = e3
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | | REDUCE: (100), (205) imply:
% 113.88/17.24 | | | | | | | (206) $false
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | | CLOSE: (206) is inconsistent.
% 113.88/17.24 | | | | | | |
% 113.88/17.24 | | | | | | End of split
% 113.88/17.24 | | | | | |
% 113.88/17.24 | | | | | End of split
% 113.88/17.24 | | | | |
% 113.88/17.24 | | | | End of split
% 113.88/17.24 | | | |
% 113.88/17.24 | | | Case 2:
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | (207) all_56_2 = e3
% 113.88/17.24 | | | | (208) ~ (all_56_12 = e0)
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (12), (13), (15), (17),
% 113.88/17.24 | | | | (23), (28), (29), (30), (33), (34), (35), (36), (39), (40),
% 113.88/17.24 | | | | (43), (44), (46), (47), (49), (50), (54), (56), (57), (58),
% 113.88/17.24 | | | | (59), (61), (62), (65), (68), (71), (77), (81), (82), (86),
% 113.88/17.24 | | | | (88), (91), (92), (94), (207), (208) are inconsistent by
% 113.88/17.24 | | | | sub-proof #76.
% 113.88/17.24 | | | |
% 113.88/17.24 | | | End of split
% 113.88/17.24 | | |
% 113.88/17.24 | | Case 2:
% 113.88/17.24 | | |
% 113.88/17.24 | | | (209) ~ (all_56_15 = e2)
% 113.88/17.24 | | |
% 113.88/17.24 | | | REDUCE: (84), (209) imply:
% 113.88/17.24 | | | (210) $false
% 113.88/17.24 | | |
% 113.88/17.24 | | | CLOSE: (210) is inconsistent.
% 113.88/17.24 | | |
% 113.88/17.24 | | End of split
% 113.88/17.24 | |
% 113.88/17.24 | Case 2:
% 113.88/17.24 | |
% 113.88/17.24 | | (211) ~ (all_56_15 = e2)
% 113.88/17.24 | |
% 113.88/17.24 | | REDUCE: (84), (211) imply:
% 113.88/17.24 | | (212) $false
% 113.88/17.24 | |
% 113.88/17.24 | | CLOSE: (212) is inconsistent.
% 113.88/17.24 | |
% 113.88/17.24 | End of split
% 113.88/17.24 |
% 113.88/17.24 End of proof
% 113.88/17.24
% 113.88/17.24 Sub-proof #70 shows that the following formulas are inconsistent:
% 113.88/17.24 ----------------------------------------------------------------
% 113.88/17.24 (1) ~ (all_52_8 = all_10_2)
% 113.88/17.24 (2) all_58_7 = all_52_6
% 113.88/17.24 (3) ~ (all_52_9 = all_8_2)
% 113.88/17.24 (4) all_56_14 = all_6_2
% 113.88/17.24 (5) all_56_3 = all_52_1
% 113.88/17.24 (6) all_54_0 = all_10_2
% 113.88/17.24 (7) ~ (all_6_1 = e3)
% 113.88/17.24 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.24 (9) all_56_12 = all_10_2
% 113.88/17.24 (10) all_58_0 = all_10_2
% 113.88/17.24 (11) all_54_11 = all_52_14
% 113.88/17.24 (12) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.88/17.24 (13) ~ (all_52_14 = all_6_2)
% 113.88/17.24 (14) all_56_10 = all_52_7
% 113.88/17.24 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.24 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.24 (17) ~ (all_52_1 = all_52_9)
% 113.88/17.24 (18) all_54_10 = all_6_2
% 113.88/17.24 (19) ~ (all_52_14 = e1)
% 113.88/17.24 (20) all_58_4 = all_52_8
% 113.88/17.24 (21) all_56_2 = all_52_12
% 113.88/17.24 (22) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.88/17.24 (23) all_58_3 = all_8_2
% 113.88/17.24 (24) all_58_11 = all_52_14
% 113.88/17.24 (25) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.88/17.24 (26) all_58_15 = e1
% 113.88/17.24 (27) op(e2, e3) = all_52_1
% 113.88/17.24 (28) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.88/17.24 (29) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.88/17.24 (30) all_56_15 = e1
% 113.88/17.24 (31) op(e1, e0) = all_52_14
% 113.88/17.24 (32) all_58_5 = all_52_9
% 113.88/17.24 (33) all_56_9 = all_52_3
% 113.88/17.24 (34) op(e1, all_6_2) = all_6_1
% 113.88/17.24 (35) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.88/17.24 (36) all_58_2 = all_52_1
% 113.88/17.24 (37) ~ (all_52_1 = all_52_13)
% 113.88/17.24 (38) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.24 (39) ~ (all_10_2 = e3)
% 113.88/17.24 (40) all_58_13 = all_52_7
% 113.88/17.24 (41) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.88/17.24 (42) all_58_6 = all_52_2
% 113.88/17.24 (43) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.88/17.24 (44) ~ (all_52_1 = all_10_2)
% 113.88/17.24 (45) all_54_5 = all_8_2
% 113.88/17.24 (46) all_58_10 = all_52_13
% 113.88/17.24 (47) ~ (all_52_13 = all_8_2)
% 113.88/17.24 (48) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.88/17.24 (49) all_58_1 = all_52_4
% 113.88/17.24 (50) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.24 (51) all_58_14 = all_52_11
% 113.88/17.24 (52) all_56_13 = all_8_2
% 113.88/17.24 (53) ~ (all_52_1 = all_8_2)
% 113.88/17.24 (54) ~ (all_8_2 = e2)
% 113.88/17.24 (55) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.24 (56) all_56_7 = all_52_6
% 113.88/17.24 (57) all_56_1 = all_52_8
% 113.88/17.24 (58) all_58_8 = all_6_2
% 113.88/17.24 (59) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.24 (60) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.88/17.24 (61) all_56_4 = all_52_9
% 113.88/17.24 (62) all_58_9 = all_52_12
% 113.88/17.24 (63) all_56_5 = all_52_13
% 113.88/17.24 (64) op(e2, e1) = all_52_9
% 113.88/17.24 (65) all_56_6 = all_52_2
% 113.88/17.24 (66) all_58_12 = all_52_3
% 113.88/17.24 (67) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.88/17.24 (68) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.88/17.24 (69) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.88/17.24 (70) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.24 (71) ~ (all_52_11 = e1)
% 113.88/17.24 (72) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.24 (73) all_56_0 = all_52_4
% 113.88/17.24 (74) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.24 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.24 (75) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 113.88/17.24 (76) ~ (all_52_11 = e0)
% 113.88/17.24 (77) all_54_4 = all_52_1
% 113.88/17.24 (78) op(e2, all_8_2) = e1
% 113.88/17.24 (79) ~ (all_6_2 = e1)
% 113.88/17.24 (80) ~ (all_6_1 = e2)
% 113.88/17.24 (81) ~ (e1 = e0)
% 113.88/17.24
% 113.88/17.24 Begin of proof
% 113.88/17.24 |
% 113.88/17.24 | BETA: splitting (43) gives:
% 113.88/17.24 |
% 113.88/17.24 | Case 1:
% 113.88/17.24 | |
% 113.88/17.24 | | (82) ~ (all_56_1 = e3)
% 113.88/17.24 | |
% 113.88/17.24 | | REDUCE: (57), (82) imply:
% 113.88/17.24 | | (83) ~ (all_52_8 = e3)
% 113.88/17.24 | |
% 113.88/17.24 | | BETA: splitting (67) gives:
% 113.88/17.24 | |
% 113.88/17.24 | | Case 1:
% 113.88/17.24 | | |
% 113.88/17.24 | | | (84) ~ (all_56_4 = e2)
% 113.88/17.24 | | |
% 113.88/17.24 | | | REDUCE: (61), (84) imply:
% 113.88/17.24 | | | (85) ~ (all_52_9 = e2)
% 113.88/17.24 | | |
% 113.88/17.24 | | | BETA: splitting (41) gives:
% 113.88/17.24 | | |
% 113.88/17.24 | | | Case 1:
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | (86) ~ (all_56_14 = e2)
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | REDUCE: (4), (86) imply:
% 113.88/17.24 | | | | (87) ~ (all_6_2 = e2)
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | BETA: splitting (69) gives:
% 113.88/17.24 | | | |
% 113.88/17.24 | | | | Case 1:
% 113.88/17.24 | | | | |
% 113.88/17.24 | | | | | (88) ~ (all_56_5 = e2)
% 113.88/17.24 | | | | |
% 113.88/17.24 | | | | | REDUCE: (63), (88) imply:
% 113.88/17.24 | | | | | (89) ~ (all_52_13 = e2)
% 113.88/17.24 | | | | |
% 113.88/17.25 | | | | | REF_CLOSE: (4), (5), (7), (10), (11), (13), (15), (16), (18), (19),
% 113.88/17.25 | | | | | (23), (31), (32), (34), (36), (39), (46), (48), (54), (60),
% 113.88/17.25 | | | | | (70), (72), (79), (80), (85), (87), (89) are inconsistent
% 113.88/17.25 | | | | | by sub-proof #400.
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | Case 2:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | (90) all_56_5 = e2
% 113.88/17.25 | | | | | (91) ~ (all_56_12 = e0)
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | COMBINE_EQS: (63), (90) imply:
% 113.88/17.25 | | | | | (92) all_52_13 = e2
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REDUCE: (9), (91) imply:
% 113.88/17.25 | | | | | (93) ~ (all_10_2 = e0)
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REDUCE: (37), (92) imply:
% 113.88/17.25 | | | | | (94) ~ (all_52_1 = e2)
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REDUCE: (47), (92) imply:
% 113.88/17.25 | | | | | (95) ~ (all_8_2 = e2)
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (12), (15), (16), (17),
% 113.88/17.25 | | | | | (18), (19), (20), (22), (24), (25), (27), (28), (29), (32),
% 113.88/17.25 | | | | | (35), (36), (39), (42), (44), (45), (51), (52), (53), (54),
% 113.88/17.25 | | | | | (55), (56), (58), (59), (65), (68), (71), (77), (78), (79),
% 113.88/17.25 | | | | | (87), (90), (93), (94) are inconsistent by sub-proof #90.
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | End of split
% 113.88/17.25 | | | |
% 113.88/17.25 | | | Case 2:
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | (96) all_56_14 = e2
% 113.88/17.25 | | | | (97) ~ (all_56_10 = e0)
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | REDUCE: (14), (97) imply:
% 113.88/17.25 | | | | (98) ~ (all_52_7 = e0)
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | BETA: splitting (74) gives:
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | Case 1:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | (99) all_58_15 = e0
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | COMBINE_EQS: (26), (99) imply:
% 113.88/17.25 | | | | | (100) e1 = e0
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REDUCE: (81), (100) imply:
% 113.88/17.25 | | | | | (101) $false
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | CLOSE: (101) is inconsistent.
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | Case 2:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | (102) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.25 | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | ALPHA: (102) implies:
% 113.88/17.25 | | | | | (103) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | BETA: splitting (75) gives:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | Case 1:
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | (104) ~ (all_56_0 = e3)
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | REDUCE: (73), (104) imply:
% 113.88/17.25 | | | | | | (105) ~ (all_52_4 = e3)
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | REF_CLOSE: (3), (8), (10), (16), (20), (21), (33), (38), (39), (40),
% 113.88/17.25 | | | | | | (45), (49), (50), (51), (52), (54), (62), (64), (66),
% 113.88/17.25 | | | | | | (70), (76), (78), (83), (98), (103), (105) are
% 113.88/17.25 | | | | | | inconsistent by sub-proof #71.
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | Case 2:
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | (106) ~ (all_56_14 = e2)
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | REDUCE: (96), (106) imply:
% 113.88/17.25 | | | | | | (107) $false
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | | CLOSE: (107) is inconsistent.
% 113.88/17.25 | | | | | |
% 113.88/17.25 | | | | | End of split
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | End of split
% 113.88/17.25 | | | |
% 113.88/17.25 | | | End of split
% 113.88/17.25 | | |
% 113.88/17.25 | | Case 2:
% 113.88/17.25 | | |
% 113.88/17.25 | | | (108) ~ (all_56_15 = e1)
% 113.88/17.25 | | |
% 113.88/17.25 | | | REDUCE: (30), (108) imply:
% 113.88/17.25 | | | (109) $false
% 113.88/17.25 | | |
% 113.88/17.25 | | | CLOSE: (109) is inconsistent.
% 113.88/17.25 | | |
% 113.88/17.25 | | End of split
% 113.88/17.25 | |
% 113.88/17.25 | Case 2:
% 113.88/17.25 | |
% 113.88/17.25 | | (110) ~ (all_56_15 = e1)
% 113.88/17.25 | |
% 113.88/17.25 | | REDUCE: (30), (110) imply:
% 113.88/17.25 | | (111) $false
% 113.88/17.25 | |
% 113.88/17.25 | | CLOSE: (111) is inconsistent.
% 113.88/17.25 | |
% 113.88/17.25 | End of split
% 113.88/17.25 |
% 113.88/17.25 End of proof
% 113.88/17.25
% 113.88/17.25 Sub-proof #71 shows that the following formulas are inconsistent:
% 113.88/17.25 ----------------------------------------------------------------
% 113.88/17.25 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.25 (2) ~ (all_52_4 = e3)
% 113.88/17.25 (3) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.25 (4) all_58_0 = all_10_2
% 113.88/17.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.25 (6) all_58_4 = all_52_8
% 113.88/17.25 (7) all_56_2 = all_52_12
% 113.88/17.25 (8) all_56_9 = all_52_3
% 113.88/17.25 (9) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.25 (10) ~ (all_10_2 = e3)
% 113.88/17.25 (11) all_58_13 = all_52_7
% 113.88/17.25 (12) ~ (all_52_7 = e0)
% 113.88/17.25 (13) all_54_5 = all_8_2
% 113.88/17.25 (14) all_58_1 = all_52_4
% 113.88/17.25 (15) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.25 (16) all_58_14 = all_52_11
% 113.88/17.25 (17) all_56_13 = all_8_2
% 113.88/17.25 (18) ~ (all_52_8 = e3)
% 113.88/17.25 (19) ~ (all_8_2 = e2)
% 113.88/17.25 (20) all_58_9 = all_52_12
% 113.88/17.25 (21) op(e2, e1) = all_52_9
% 113.88/17.25 (22) all_58_12 = all_52_3
% 113.88/17.25 (23) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.88/17.25 (24) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.25 (25) ~ (all_52_11 = e0)
% 113.88/17.25 (26) op(e2, all_8_2) = e1
% 113.88/17.25
% 113.88/17.25 Begin of proof
% 113.88/17.25 |
% 113.88/17.25 | BETA: splitting (24) gives:
% 113.88/17.25 |
% 113.88/17.25 | Case 1:
% 113.88/17.25 | |
% 113.88/17.25 | | (27) all_58_0 = e3
% 113.88/17.25 | |
% 113.88/17.25 | | COMBINE_EQS: (4), (27) imply:
% 113.88/17.25 | | (28) all_10_2 = e3
% 113.88/17.25 | |
% 113.88/17.25 | | REDUCE: (10), (28) imply:
% 113.88/17.25 | | (29) $false
% 113.88/17.25 | |
% 113.88/17.25 | | CLOSE: (29) is inconsistent.
% 113.88/17.25 | |
% 113.88/17.25 | Case 2:
% 113.88/17.25 | |
% 113.88/17.25 | | (30) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.25 | |
% 113.88/17.25 | | BETA: splitting (30) gives:
% 113.88/17.25 | |
% 113.88/17.25 | | Case 1:
% 113.88/17.25 | | |
% 113.88/17.25 | | | (31) all_58_1 = e3
% 113.88/17.25 | | |
% 113.88/17.25 | | | COMBINE_EQS: (14), (31) imply:
% 113.88/17.25 | | | (32) all_52_4 = e3
% 113.88/17.25 | | |
% 113.88/17.25 | | | REDUCE: (2), (32) imply:
% 113.88/17.25 | | | (33) $false
% 113.88/17.25 | | |
% 113.88/17.25 | | | CLOSE: (33) is inconsistent.
% 113.88/17.25 | | |
% 113.88/17.25 | | Case 2:
% 113.88/17.25 | | |
% 113.88/17.25 | | | (34) all_58_4 = e3 | all_58_9 = e3
% 113.88/17.25 | | |
% 113.88/17.25 | | | BETA: splitting (23) gives:
% 113.88/17.25 | | |
% 113.88/17.25 | | | Case 1:
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | (35) all_58_12 = e0
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | COMBINE_EQS: (22), (35) imply:
% 113.88/17.25 | | | | (36) all_52_3 = e0
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | SIMP: (36) implies:
% 113.88/17.25 | | | | (37) all_52_3 = e0
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | COMBINE_EQS: (8), (37) imply:
% 113.88/17.25 | | | | (38) all_56_9 = e0
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | BETA: splitting (34) gives:
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | Case 1:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | (39) all_58_4 = e3
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | COMBINE_EQS: (6), (39) imply:
% 113.88/17.25 | | | | | (40) all_52_8 = e3
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REDUCE: (18), (40) imply:
% 113.88/17.25 | | | | | (41) $false
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | CLOSE: (41) is inconsistent.
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | Case 2:
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | (42) all_58_9 = e3
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | COMBINE_EQS: (20), (42) imply:
% 113.88/17.25 | | | | | (43) all_52_12 = e3
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | COMBINE_EQS: (7), (43) imply:
% 113.88/17.25 | | | | | (44) all_56_2 = e3
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | | REF_CLOSE: (1), (3), (5), (9), (13), (15), (17), (19), (21), (26),
% 113.88/17.25 | | | | | (38), (44) are inconsistent by sub-proof #72.
% 113.88/17.25 | | | | |
% 113.88/17.25 | | | | End of split
% 113.88/17.25 | | | |
% 113.88/17.25 | | | Case 2:
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | (45) all_58_13 = e0 | all_58_14 = e0
% 113.88/17.25 | | | |
% 113.88/17.25 | | | | REF_CLOSE: (11), (12), (16), (25), (45) are inconsistent by sub-proof
% 113.88/17.25 | | | | #428.
% 113.88/17.25 | | | |
% 113.88/17.25 | | | End of split
% 113.88/17.25 | | |
% 113.88/17.25 | | End of split
% 113.88/17.25 | |
% 113.88/17.25 | End of split
% 113.88/17.25 |
% 113.88/17.25 End of proof
% 113.88/17.25
% 113.88/17.25 Sub-proof #72 shows that the following formulas are inconsistent:
% 113.88/17.25 ----------------------------------------------------------------
% 113.88/17.25 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.25 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.25 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.25 (4) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.25 (5) all_54_5 = all_8_2
% 113.88/17.25 (6) all_56_2 = e3
% 113.88/17.25 (7) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.25 (8) all_56_13 = all_8_2
% 113.88/17.25 (9) ~ (all_8_2 = e2)
% 113.88/17.25 (10) all_56_9 = e0
% 113.88/17.25 (11) op(e2, e1) = all_52_9
% 113.88/17.25 (12) op(e2, all_8_2) = e1
% 113.88/17.25
% 113.88/17.25 Begin of proof
% 113.88/17.25 |
% 113.88/17.25 | BETA: splitting (7) gives:
% 113.88/17.25 |
% 113.88/17.25 | Case 1:
% 113.88/17.25 | |
% 113.88/17.25 | | (13) ~ (all_56_2 = e3)
% 113.88/17.25 | |
% 113.88/17.25 | | REDUCE: (6), (13) imply:
% 113.88/17.25 | | (14) $false
% 113.88/17.25 | |
% 113.88/17.25 | | CLOSE: (14) is inconsistent.
% 113.88/17.25 | |
% 113.88/17.25 | Case 2:
% 113.88/17.25 | |
% 113.88/17.25 | | (15) ~ (all_56_13 = e0)
% 113.88/17.25 | |
% 113.88/17.25 | | REDUCE: (8), (15) imply:
% 113.88/17.25 | | (16) ~ (all_8_2 = e0)
% 113.88/17.25 | |
% 113.88/17.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (16) are
% 113.88/17.25 | | inconsistent by sub-proof #73.
% 113.88/17.25 | |
% 113.88/17.25 | End of split
% 113.88/17.25 |
% 113.88/17.25 End of proof
% 113.88/17.25
% 113.88/17.25 Sub-proof #73 shows that the following formulas are inconsistent:
% 113.88/17.25 ----------------------------------------------------------------
% 113.88/17.25 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.25 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.26 (4) ~ (all_8_2 = e0)
% 113.88/17.26 (5) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.26 (6) all_54_5 = all_8_2
% 113.88/17.26 (7) all_56_13 = all_8_2
% 113.88/17.26 (8) ~ (all_8_2 = e2)
% 113.88/17.26 (9) all_56_9 = e0
% 113.88/17.26 (10) op(e2, e1) = all_52_9
% 113.88/17.26 (11) op(e2, all_8_2) = e1
% 113.88/17.26
% 113.88/17.26 Begin of proof
% 113.88/17.26 |
% 113.88/17.26 | BETA: splitting (5) gives:
% 113.88/17.26 |
% 113.88/17.26 | Case 1:
% 113.88/17.26 | |
% 113.88/17.26 | | (12) ~ (all_56_13 = e3)
% 113.88/17.26 | |
% 113.88/17.26 | | REDUCE: (7), (12) imply:
% 113.88/17.26 | | (13) ~ (all_8_2 = e3)
% 113.88/17.26 | |
% 113.88/17.26 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (13) are inconsistent
% 113.88/17.26 | | by sub-proof #79.
% 113.88/17.26 | |
% 113.88/17.26 | Case 2:
% 113.88/17.26 | |
% 113.88/17.26 | | (14) ~ (all_56_9 = e0)
% 113.88/17.26 | |
% 113.88/17.26 | | REDUCE: (9), (14) imply:
% 113.88/17.26 | | (15) $false
% 113.88/17.26 | |
% 113.88/17.26 | | CLOSE: (15) is inconsistent.
% 113.88/17.26 | |
% 113.88/17.26 | End of split
% 113.88/17.26 |
% 113.88/17.26 End of proof
% 113.88/17.26
% 113.88/17.26 Sub-proof #74 shows that the following formulas are inconsistent:
% 113.88/17.26 ----------------------------------------------------------------
% 113.88/17.26 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.26 (2) ~ (all_4_2 = e0)
% 113.88/17.26 (3) all_56_3 = all_52_1
% 113.88/17.26 (4) ~ (all_4_2 = e1)
% 113.88/17.26 (5) all_56_11 = all_52_11
% 113.88/17.26 (6) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.88/17.26 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.26 (8) all_58_0 = all_10_2
% 113.88/17.26 (9) all_56_10 = all_52_7
% 113.88/17.26 (10) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.88/17.26 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.26 (12) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.88/17.26 (13) all_58_4 = all_52_8
% 113.88/17.26 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.26 (15) all_56_2 = all_52_12
% 113.88/17.26 (16) all_58_3 = all_8_2
% 113.88/17.26 (17) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.88/17.26 (18) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.88/17.26 (19) op(e2, e3) = all_52_1
% 113.88/17.26 (20) all_10_2 = e1
% 113.88/17.26 (21) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.88/17.26 (22) ~ (all_52_7 = all_8_2)
% 113.88/17.26 (23) ~ (all_52_4 = all_8_2)
% 113.88/17.26 (24) all_58_5 = all_52_9
% 113.88/17.26 (25) all_56_9 = all_52_3
% 113.88/17.26 (26) all_58_15 = all_4_2
% 113.88/17.26 (27) all_58_2 = all_52_1
% 113.88/17.26 (28) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.88/17.26 (29) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.26 (30) ~ (all_10_2 = e3)
% 113.88/17.26 (31) all_58_13 = all_52_7
% 113.88/17.26 (32) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.88/17.26 (33) all_54_5 = all_8_2
% 113.88/17.26 (34) all_56_15 = all_4_2
% 113.88/17.26 (35) all_58_10 = all_52_13
% 113.88/17.26 (36) ~ (all_52_13 = all_8_2)
% 113.88/17.26 (37) all_56_12 = e1
% 113.88/17.26 (38) ~ (all_52_11 = all_4_2)
% 113.88/17.26 (39) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 113.88/17.26 (40) all_58_1 = all_52_4
% 113.88/17.26 (41) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.26 (42) ~ (all_52_9 = all_52_11)
% 113.88/17.26 (43) all_58_14 = all_52_11
% 113.88/17.26 (44) all_56_13 = all_8_2
% 113.88/17.26 (45) ~ (all_56_11 = e0)
% 113.88/17.26 (46) ~ (all_52_1 = all_8_2)
% 113.88/17.26 (47) ~ (all_8_2 = e2)
% 113.88/17.26 (48) all_56_1 = all_52_8
% 113.88/17.26 (49) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.88/17.26 (50) all_56_4 = all_52_9
% 113.88/17.26 (51) all_58_9 = all_52_12
% 113.88/17.26 (52) all_56_5 = all_52_13
% 113.88/17.26 (53) op(e2, e1) = all_52_9
% 113.88/17.26 (54) ~ (all_52_13 = all_4_2)
% 113.88/17.26 (55) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.88/17.26 (56) all_58_12 = all_52_3
% 113.88/17.26 (57) ~ (all_52_8 = all_52_9)
% 113.88/17.26 (58) op(e2, e0) = all_52_13
% 113.88/17.26 (59) ~ (all_52_12 = all_4_2)
% 113.88/17.26 (60) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.88/17.26 (61) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.88/17.26 (62) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.26 (63) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.26 (64) all_56_0 = all_52_4
% 113.88/17.26 (65) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.26 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.26 (66) all_54_15 = all_4_2
% 113.88/17.26 (67) op(e2, all_8_2) = e1
% 113.88/17.26 (68) ~ (e1 = e0)
% 113.88/17.26
% 113.88/17.26 Begin of proof
% 113.88/17.26 |
% 113.88/17.26 | COMBINE_EQS: (8), (20) imply:
% 113.88/17.26 | (69) all_58_0 = e1
% 113.88/17.26 |
% 113.88/17.26 | REDUCE: (5), (45) imply:
% 113.88/17.26 | (70) ~ (all_52_11 = e0)
% 113.88/17.26 |
% 113.88/17.26 | REDUCE: (20), (30) imply:
% 113.88/17.26 | (71) ~ (e3 = e1)
% 113.88/17.26 |
% 113.88/17.26 | SIMP: (71) implies:
% 113.88/17.26 | (72) ~ (e3 = e1)
% 113.88/17.26 |
% 113.88/17.26 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 113.88/17.26 | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 113.88/17.26 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 113.88/17.26 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 113.88/17.26 | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 113.88/17.26 | (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 113.88/17.26 | (70), (72) are inconsistent by sub-proof #75.
% 113.88/17.26 |
% 113.88/17.26 End of proof
% 113.88/17.26
% 113.88/17.26 Sub-proof #75 shows that the following formulas are inconsistent:
% 113.88/17.26 ----------------------------------------------------------------
% 113.88/17.26 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.26 (2) ~ (all_4_2 = e0)
% 113.88/17.26 (3) all_56_3 = all_52_1
% 113.88/17.26 (4) ~ (all_4_2 = e1)
% 113.88/17.26 (5) all_56_11 = all_52_11
% 113.88/17.26 (6) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.88/17.26 (7) ~ (e3 = e1)
% 113.88/17.26 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.26 (9) all_58_0 = all_10_2
% 113.88/17.26 (10) all_56_10 = all_52_7
% 113.88/17.26 (11) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.88/17.26 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.26 (13) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.88/17.26 (14) all_58_4 = all_52_8
% 113.88/17.26 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.26 (16) all_56_2 = all_52_12
% 113.88/17.26 (17) all_58_3 = all_8_2
% 113.88/17.26 (18) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.88/17.26 (19) all_58_0 = e1
% 113.88/17.26 (20) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.88/17.27 (21) op(e2, e3) = all_52_1
% 113.88/17.27 (22) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.88/17.27 (23) ~ (all_52_7 = all_8_2)
% 113.88/17.27 (24) ~ (all_52_4 = all_8_2)
% 113.88/17.27 (25) all_58_5 = all_52_9
% 113.88/17.27 (26) all_56_9 = all_52_3
% 113.88/17.27 (27) all_58_15 = all_4_2
% 113.88/17.27 (28) all_58_2 = all_52_1
% 113.88/17.27 (29) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.88/17.27 (30) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.27 (31) ~ (all_10_2 = e3)
% 113.88/17.27 (32) all_58_13 = all_52_7
% 113.88/17.27 (33) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.88/17.27 (34) all_54_5 = all_8_2
% 113.88/17.27 (35) all_56_15 = all_4_2
% 113.88/17.27 (36) all_58_10 = all_52_13
% 113.88/17.27 (37) ~ (all_52_13 = all_8_2)
% 113.88/17.27 (38) all_56_12 = e1
% 113.88/17.27 (39) ~ (all_52_11 = all_4_2)
% 113.88/17.27 (40) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 113.88/17.27 (41) all_58_1 = all_52_4
% 113.88/17.27 (42) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.27 (43) ~ (all_52_9 = all_52_11)
% 113.88/17.27 (44) all_58_14 = all_52_11
% 113.88/17.27 (45) all_56_13 = all_8_2
% 113.88/17.27 (46) ~ (all_52_1 = all_8_2)
% 113.88/17.27 (47) ~ (all_8_2 = e2)
% 113.88/17.27 (48) all_56_1 = all_52_8
% 113.88/17.27 (49) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.88/17.27 (50) all_56_4 = all_52_9
% 113.88/17.27 (51) all_58_9 = all_52_12
% 113.88/17.27 (52) all_56_5 = all_52_13
% 113.88/17.27 (53) op(e2, e1) = all_52_9
% 113.88/17.27 (54) ~ (all_52_13 = all_4_2)
% 113.88/17.27 (55) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.88/17.27 (56) all_58_12 = all_52_3
% 113.88/17.27 (57) ~ (all_52_8 = all_52_9)
% 113.88/17.27 (58) op(e2, e0) = all_52_13
% 113.88/17.27 (59) ~ (all_52_12 = all_4_2)
% 113.88/17.27 (60) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.88/17.27 (61) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.88/17.27 (62) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.27 (63) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.27 (64) all_56_0 = all_52_4
% 113.88/17.27 (65) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.27 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.27 (66) ~ (all_52_11 = e0)
% 113.88/17.27 (67) all_54_15 = all_4_2
% 113.88/17.27 (68) op(e2, all_8_2) = e1
% 113.88/17.27 (69) ~ (e1 = e0)
% 113.88/17.27
% 113.88/17.27 Begin of proof
% 113.88/17.27 |
% 113.88/17.27 | BETA: splitting (22) gives:
% 113.88/17.27 |
% 113.88/17.27 | Case 1:
% 113.88/17.27 | |
% 113.88/17.27 | | (70) ~ (all_56_1 = e3)
% 113.88/17.27 | |
% 113.88/17.27 | | REDUCE: (48), (70) imply:
% 113.88/17.27 | | (71) ~ (all_52_8 = e3)
% 113.88/17.27 | |
% 113.88/17.27 | | BETA: splitting (29) gives:
% 113.88/17.27 | |
% 113.88/17.27 | | Case 1:
% 113.88/17.27 | | |
% 113.88/17.27 | | | (72) ~ (all_56_4 = e2)
% 113.88/17.27 | | |
% 113.88/17.27 | | | REDUCE: (50), (72) imply:
% 113.88/17.27 | | | (73) ~ (all_52_9 = e2)
% 113.88/17.27 | | |
% 113.88/17.27 | | | BETA: splitting (49) gives:
% 113.88/17.27 | | |
% 113.88/17.27 | | | Case 1:
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | (74) ~ (all_56_15 = e3)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | REDUCE: (35), (74) imply:
% 113.88/17.27 | | | | (75) ~ (all_4_2 = e3)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | BETA: splitting (15) gives:
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | Case 1:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | (76) all_54_15 = e3
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | REF_CLOSE: (67), (75), (76) are inconsistent by sub-proof #312.
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | Case 2:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | (77) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | BETA: splitting (77) gives:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | Case 1:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | (78) all_54_15 = e2
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | COMBINE_EQS: (67), (78) imply:
% 113.88/17.27 | | | | | | (79) all_4_2 = e2
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | SIMP: (79) implies:
% 113.88/17.27 | | | | | | (80) all_4_2 = e2
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | COMBINE_EQS: (35), (80) imply:
% 113.88/17.27 | | | | | | (81) all_56_15 = e2
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | REDUCE: (39), (80) imply:
% 113.88/17.27 | | | | | | (82) ~ (all_52_11 = e2)
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | BETA: splitting (60) gives:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | Case 1:
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | (83) ~ (all_56_15 = e2)
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | REDUCE: (81), (83) imply:
% 113.88/17.27 | | | | | | | (84) $false
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | CLOSE: (84) is inconsistent.
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | Case 2:
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | (85) ~ (all_56_10 = e0)
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | REDUCE: (10), (85) imply:
% 113.88/17.27 | | | | | | | (86) ~ (all_52_7 = e0)
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | BETA: splitting (40) gives:
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | Case 1:
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | (87) ~ (all_56_0 = e3)
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | REDUCE: (64), (87) imply:
% 113.88/17.27 | | | | | | | | (88) ~ (all_52_4 = e3)
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12),
% 113.88/17.27 | | | | | | | | (13), (14), (15), (16), (17), (18), (20), (21), (25),
% 113.88/17.27 | | | | | | | | (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 113.88/17.27 | | | | | | | | (36), (37), (41), (42), (43), (44), (45), (46), (47),
% 113.88/17.27 | | | | | | | | (48), (49), (51), (52), (53), (54), (55), (56), (57),
% 113.88/17.27 | | | | | | | | (58), (61), (62), (63), (65), (67), (68), (69), (73),
% 113.88/17.27 | | | | | | | | (82), (86), (88) are inconsistent by sub-proof #105.
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | Case 2:
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | (89) ~ (all_56_15 = e2)
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | REDUCE: (81), (89) imply:
% 113.88/17.27 | | | | | | | | (90) $false
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | CLOSE: (90) is inconsistent.
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | End of split
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | End of split
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | Case 2:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | (91) all_54_15 = e1 | all_54_15 = e0
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | REF_CLOSE: (2), (4), (67), (91) are inconsistent by sub-proof #418.
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | End of split
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | End of split
% 113.88/17.27 | | | |
% 113.88/17.27 | | | Case 2:
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | (92) all_56_15 = e3
% 113.88/17.27 | | | | (93) ~ (all_56_9 = e0)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | COMBINE_EQS: (35), (92) imply:
% 113.88/17.27 | | | | (94) all_4_2 = e3
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | SIMP: (94) implies:
% 113.88/17.27 | | | | (95) all_4_2 = e3
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | COMBINE_EQS: (27), (95) imply:
% 113.88/17.27 | | | | (96) all_58_15 = e3
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | REDUCE: (26), (93) imply:
% 113.88/17.27 | | | | (97) ~ (all_52_3 = e0)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | REDUCE: (59), (95) imply:
% 113.88/17.27 | | | | (98) ~ (all_52_12 = e3)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | REDUCE: (2), (95) imply:
% 113.88/17.27 | | | | (99) ~ (e3 = e0)
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | BETA: splitting (65) gives:
% 113.88/17.27 | | | |
% 113.88/17.27 | | | | Case 1:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | (100) all_58_15 = e0
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | COMBINE_EQS: (96), (100) imply:
% 113.88/17.27 | | | | | (101) e3 = e0
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | REDUCE: (99), (101) imply:
% 113.88/17.27 | | | | | (102) $false
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | CLOSE: (102) is inconsistent.
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | Case 2:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | (103) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.27 | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | ALPHA: (103) implies:
% 113.88/17.27 | | | | | (104) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | BETA: splitting (104) gives:
% 113.88/17.27 | | | | |
% 113.88/17.27 | | | | | Case 1:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | (105) all_58_12 = e0
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | REF_CLOSE: (56), (97), (105) are inconsistent by sub-proof #362.
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | Case 2:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | (106) all_58_13 = e0 | all_58_14 = e0
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | BETA: splitting (106) gives:
% 113.88/17.27 | | | | | |
% 113.88/17.27 | | | | | | Case 1:
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | (107) all_58_13 = e0
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | COMBINE_EQS: (32), (107) imply:
% 113.88/17.27 | | | | | | | (108) all_52_7 = e0
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | SIMP: (108) implies:
% 113.88/17.27 | | | | | | | (109) all_52_7 = e0
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | REDUCE: (23), (109) imply:
% 113.88/17.27 | | | | | | | (110) ~ (all_8_2 = e0)
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | SIMP: (110) implies:
% 113.88/17.27 | | | | | | | (111) ~ (all_8_2 = e0)
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | BETA: splitting (62) gives:
% 113.88/17.27 | | | | | | |
% 113.88/17.27 | | | | | | | Case 1:
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | (112) all_58_0 = e3
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | REF_CLOSE: (7), (19), (112) are inconsistent by sub-proof #319.
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | Case 2:
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | (113) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | BETA: splitting (113) gives:
% 113.88/17.27 | | | | | | | |
% 113.88/17.27 | | | | | | | | Case 1:
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | (114) all_58_1 = e3
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | COMBINE_EQS: (41), (114) imply:
% 113.88/17.27 | | | | | | | | | (115) all_52_4 = e3
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | REDUCE: (24), (115) imply:
% 113.88/17.27 | | | | | | | | | (116) ~ (all_8_2 = e3)
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | SIMP: (116) implies:
% 113.88/17.27 | | | | | | | | | (117) ~ (all_8_2 = e3)
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | REF_CLOSE: (1), (8), (12), (34), (47), (53), (68), (111),
% 113.88/17.27 | | | | | | | | | (117) are inconsistent by sub-proof #79.
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | Case 2:
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | (118) all_58_4 = e3 | all_58_9 = e3
% 113.88/17.27 | | | | | | | | |
% 113.88/17.27 | | | | | | | | | REF_CLOSE: (14), (51), (71), (98), (118) are inconsistent by
% 113.88/17.28 | | | | | | | | | sub-proof #184.
% 113.88/17.28 | | | | | | | | |
% 113.88/17.28 | | | | | | | | End of split
% 113.88/17.28 | | | | | | | |
% 113.88/17.28 | | | | | | | End of split
% 113.88/17.28 | | | | | | |
% 113.88/17.28 | | | | | | Case 2:
% 113.88/17.28 | | | | | | |
% 113.88/17.28 | | | | | | | (119) all_58_14 = e0
% 113.88/17.28 | | | | | | |
% 113.88/17.28 | | | | | | | REF_CLOSE: (44), (66), (119) are inconsistent by sub-proof #429.
% 113.88/17.28 | | | | | | |
% 113.88/17.28 | | | | | | End of split
% 113.88/17.28 | | | | | |
% 113.88/17.28 | | | | | End of split
% 113.88/17.28 | | | | |
% 113.88/17.28 | | | | End of split
% 113.88/17.28 | | | |
% 113.88/17.28 | | | End of split
% 113.88/17.28 | | |
% 113.88/17.28 | | Case 2:
% 113.88/17.28 | | |
% 113.88/17.28 | | | (120) ~ (all_56_12 = e1)
% 113.88/17.28 | | |
% 113.88/17.28 | | | REDUCE: (38), (120) imply:
% 113.88/17.28 | | | (121) $false
% 113.88/17.28 | | |
% 113.88/17.28 | | | CLOSE: (121) is inconsistent.
% 113.88/17.28 | | |
% 113.88/17.28 | | End of split
% 113.88/17.28 | |
% 113.88/17.28 | Case 2:
% 113.88/17.28 | |
% 113.88/17.28 | | (122) ~ (all_56_12 = e1)
% 113.88/17.28 | |
% 113.88/17.28 | | REDUCE: (38), (122) imply:
% 113.88/17.28 | | (123) $false
% 113.88/17.28 | |
% 113.88/17.28 | | CLOSE: (123) is inconsistent.
% 113.88/17.28 | |
% 113.88/17.28 | End of split
% 113.88/17.28 |
% 113.88/17.28 End of proof
% 113.88/17.28
% 113.88/17.28 Sub-proof #76 shows that the following formulas are inconsistent:
% 113.88/17.28 ----------------------------------------------------------------
% 113.88/17.28 (1) all_58_7 = all_52_6
% 113.88/17.28 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.28 (3) op(e3, e2) = all_52_4
% 113.88/17.28 (4) all_54_0 = all_10_2
% 113.88/17.28 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.28 (6) ~ (all_52_2 = all_52_6)
% 113.88/17.28 (7) ~ (all_52_12 = all_10_2)
% 113.88/17.28 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.28 (9) all_56_12 = all_10_2
% 113.88/17.28 (10) all_58_0 = all_10_2
% 113.88/17.28 (11) all_54_13 = all_52_7
% 113.88/17.28 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.28 (13) ~ (all_52_4 = all_52_7)
% 113.88/17.28 (14) all_56_2 = all_52_12
% 113.88/17.28 (15) all_58_3 = all_8_2
% 113.88/17.28 (16) op(e2, e3) = all_52_1
% 113.88/17.28 (17) ~ (all_10_2 = e1)
% 113.88/17.28 (18) ~ (all_52_7 = all_8_2)
% 113.88/17.28 (19) ~ (all_52_4 = all_8_2)
% 113.88/17.28 (20) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.28 (21) all_56_9 = all_52_3
% 113.88/17.28 (22) all_58_2 = all_52_1
% 113.88/17.28 (23) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.28 (24) ~ (all_56_12 = e0)
% 113.88/17.28 (25) all_58_13 = all_52_7
% 113.88/17.28 (26) ~ (all_52_7 = e0)
% 113.88/17.28 (27) all_58_6 = all_52_2
% 113.88/17.28 (28) all_54_5 = all_8_2
% 113.88/17.28 (29) all_56_2 = e3
% 113.88/17.28 (30) op(e3, all_10_2) = all_10_1
% 113.88/17.28 (31) all_58_1 = all_52_4
% 113.88/17.28 (32) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.28 (33) all_54_1 = all_52_4
% 113.88/17.28 (34) all_56_13 = all_8_2
% 113.88/17.28 (35) ~ (all_8_2 = e2)
% 113.88/17.28 (36) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.28 (37) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.28 (38) ~ (all_52_4 = all_52_6)
% 113.88/17.28 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.28 (40) all_58_12 = all_52_3
% 113.88/17.28 (41) all_24_1 = all_10_1
% 113.88/17.28 (42) all_24_2 = all_10_2
% 113.88/17.28 (43) ~ (all_52_4 = all_10_2)
% 113.88/17.28 (44) all_56_0 = all_52_4
% 113.88/17.28 (45) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.28 (46) op(e2, all_8_2) = e1
% 113.88/17.28 (47) ~ (all_52_6 = all_52_7)
% 113.88/17.28
% 113.88/17.28 Begin of proof
% 113.88/17.28 |
% 113.88/17.28 | COMBINE_EQS: (14), (29) imply:
% 113.88/17.28 | (48) all_52_12 = e3
% 113.88/17.28 |
% 113.88/17.28 | REDUCE: (9), (24) imply:
% 113.88/17.28 | (49) ~ (all_10_2 = e0)
% 113.88/17.28 |
% 113.88/17.28 | REDUCE: (7), (48) imply:
% 113.88/17.28 | (50) ~ (all_10_2 = e3)
% 113.88/17.28 |
% 113.88/17.28 | SIMP: (50) implies:
% 113.88/17.28 | (51) ~ (all_10_2 = e3)
% 113.88/17.28 |
% 113.88/17.28 | BETA: splitting (32) gives:
% 113.88/17.28 |
% 113.88/17.28 | Case 1:
% 113.88/17.28 | |
% 113.88/17.28 | | (52) ~ (all_56_2 = e3)
% 113.88/17.28 | |
% 113.88/17.28 | | REDUCE: (29), (52) imply:
% 113.88/17.28 | | (53) $false
% 113.88/17.28 | |
% 113.88/17.28 | | CLOSE: (53) is inconsistent.
% 113.88/17.28 | |
% 113.88/17.28 | Case 2:
% 113.88/17.28 | |
% 113.88/17.28 | | (54) ~ (all_56_13 = e0)
% 113.88/17.28 | |
% 113.88/17.28 | | REDUCE: (34), (54) imply:
% 113.88/17.28 | | (55) ~ (all_8_2 = e0)
% 113.88/17.28 | |
% 113.88/17.28 | | BETA: splitting (39) gives:
% 113.88/17.28 | |
% 113.88/17.28 | | Case 1:
% 113.88/17.28 | | |
% 113.88/17.28 | | | (56) all_54_0 = e3
% 113.88/17.28 | | |
% 113.88/17.28 | | | REF_CLOSE: (4), (51), (56) are inconsistent by sub-proof #451.
% 113.88/17.28 | | |
% 113.88/17.28 | | Case 2:
% 113.88/17.28 | | |
% 113.88/17.28 | | | (57) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.28 | | |
% 113.88/17.28 | | | BETA: splitting (57) gives:
% 113.88/17.28 | | |
% 113.88/17.28 | | | Case 1:
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | (58) all_54_0 = e2
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | COMBINE_EQS: (4), (58) imply:
% 113.88/17.28 | | | | (59) all_10_2 = e2
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | SIMP: (59) implies:
% 113.88/17.28 | | | | (60) all_10_2 = e2
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13),
% 113.88/17.28 | | | | (15), (16), (18), (19), (20), (21), (22), (23), (25), (26),
% 113.88/17.28 | | | | (27), (28), (30), (31), (33), (34), (35), (36), (37), (38),
% 113.88/17.28 | | | | (40), (41), (42), (43), (44), (45), (46), (47), (55), (60)
% 113.88/17.28 | | | | are inconsistent by sub-proof #77.
% 113.88/17.28 | | | |
% 113.88/17.28 | | | Case 2:
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | (61) all_54_0 = e1 | all_54_0 = e0
% 113.88/17.28 | | | |
% 113.88/17.28 | | | | REF_CLOSE: (4), (17), (49), (61) are inconsistent by sub-proof #423.
% 113.88/17.28 | | | |
% 113.88/17.28 | | | End of split
% 113.88/17.28 | | |
% 113.88/17.28 | | End of split
% 113.88/17.28 | |
% 113.88/17.28 | End of split
% 113.88/17.28 |
% 113.88/17.28 End of proof
% 113.88/17.28
% 113.88/17.28 Sub-proof #77 shows that the following formulas are inconsistent:
% 113.88/17.28 ----------------------------------------------------------------
% 113.88/17.28 (1) all_58_7 = all_52_6
% 113.88/17.28 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.28 (3) op(e3, e2) = all_52_4
% 113.88/17.28 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.28 (5) ~ (all_52_2 = all_52_6)
% 113.88/17.28 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.28 (7) all_56_12 = all_10_2
% 113.88/17.28 (8) all_58_0 = all_10_2
% 113.88/17.28 (9) all_54_13 = all_52_7
% 113.88/17.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.28 (11) all_10_2 = e2
% 113.88/17.28 (12) ~ (all_52_4 = all_52_7)
% 113.88/17.28 (13) all_58_3 = all_8_2
% 113.88/17.28 (14) ~ (all_8_2 = e0)
% 113.88/17.28 (15) op(e2, e3) = all_52_1
% 113.88/17.28 (16) ~ (all_52_7 = all_8_2)
% 113.88/17.28 (17) ~ (all_52_4 = all_8_2)
% 113.88/17.28 (18) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.28 (19) all_56_9 = all_52_3
% 113.88/17.28 (20) all_58_2 = all_52_1
% 113.88/17.28 (21) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.28 (22) all_58_13 = all_52_7
% 113.88/17.28 (23) ~ (all_52_7 = e0)
% 113.88/17.28 (24) all_58_6 = all_52_2
% 113.88/17.28 (25) all_54_5 = all_8_2
% 113.88/17.28 (26) op(e3, all_10_2) = all_10_1
% 113.88/17.28 (27) all_58_1 = all_52_4
% 113.88/17.28 (28) all_54_1 = all_52_4
% 113.88/17.28 (29) all_56_13 = all_8_2
% 113.88/17.28 (30) ~ (all_8_2 = e2)
% 113.88/17.28 (31) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.28 (32) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.28 (33) ~ (all_52_4 = all_52_6)
% 113.88/17.28 (34) all_58_12 = all_52_3
% 113.88/17.28 (35) all_24_1 = all_10_1
% 113.88/17.28 (36) all_24_2 = all_10_2
% 113.88/17.28 (37) ~ (all_52_4 = all_10_2)
% 113.88/17.28 (38) all_56_0 = all_52_4
% 113.88/17.28 (39) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.28 (40) op(e2, all_8_2) = e1
% 113.88/17.28 (41) ~ (all_52_6 = all_52_7)
% 113.88/17.28
% 113.88/17.28 Begin of proof
% 113.88/17.28 |
% 113.88/17.28 | COMBINE_EQS: (11), (36) imply:
% 113.88/17.28 | (42) all_24_2 = e2
% 113.88/17.28 |
% 113.88/17.28 | COMBINE_EQS: (7), (11) imply:
% 113.88/17.28 | (43) all_56_12 = e2
% 113.88/17.28 |
% 113.88/17.28 | COMBINE_EQS: (8), (11) imply:
% 113.88/17.28 | (44) all_58_0 = e2
% 113.88/17.28 |
% 113.88/17.28 | REDUCE: (11), (37) imply:
% 113.88/17.29 | (45) ~ (all_52_4 = e2)
% 113.88/17.29 |
% 113.88/17.29 | REDUCE: (11), (26) imply:
% 113.88/17.29 | (46) op(e3, e2) = all_10_1
% 113.88/17.29 |
% 113.88/17.29 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (13), (14), (15),
% 113.88/17.29 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 113.88/17.29 | (28), (29), (30), (31), (32), (33), (34), (35), (38), (39), (40),
% 113.88/17.29 | (41), (42), (43), (44), (45), (46) are inconsistent by sub-proof
% 113.88/17.29 | #83.
% 113.88/17.29 |
% 113.88/17.29 End of proof
% 113.88/17.29
% 113.88/17.29 Sub-proof #78 shows that the following formulas are inconsistent:
% 113.88/17.29 ----------------------------------------------------------------
% 113.88/17.29 (1) ~ (all_52_8 = all_10_2)
% 113.88/17.29 (2) ~ (all_52_9 = all_8_2)
% 113.88/17.29 (3) ~ (all_4_2 = e0)
% 113.88/17.29 (4) all_56_14 = all_6_2
% 113.88/17.29 (5) all_56_3 = all_52_1
% 113.88/17.29 (6) all_56_11 = all_52_11
% 113.88/17.29 (7) ~ (all_52_4 = e3)
% 113.88/17.29 (8) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.88/17.29 (9) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.88/17.29 (10) ~ (all_6_1 = e3)
% 113.88/17.29 (11) ~ (all_52_4 = all_52_8)
% 113.88/17.29 (12) ~ (e3 = e1)
% 113.88/17.29 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.29 (14) all_58_0 = all_10_2
% 113.88/17.29 (15) all_54_11 = all_52_14
% 113.88/17.29 (16) ~ (all_52_14 = all_6_2)
% 113.88/17.29 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.29 (18) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.88/17.29 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.29 (20) ~ (all_52_1 = all_52_9)
% 113.88/17.29 (21) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.88/17.29 (22) all_54_10 = all_6_2
% 113.88/17.29 (23) ~ (all_52_8 = all_6_2)
% 113.88/17.29 (24) all_58_4 = all_52_8
% 113.88/17.29 (25) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.29 (26) all_56_2 = all_52_12
% 113.88/17.29 (27) all_58_3 = all_8_2
% 113.88/17.29 (28) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.88/17.29 (29) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.88/17.29 (30) op(e2, e3) = all_52_1
% 113.88/17.29 (31) op(e1, e0) = all_52_14
% 113.88/17.29 (32) all_58_5 = all_52_9
% 113.88/17.29 (33) all_56_9 = all_52_3
% 113.88/17.29 (34) op(e1, all_6_2) = all_6_1
% 113.88/17.29 (35) all_58_15 = all_4_2
% 113.88/17.29 (36) all_58_2 = all_52_1
% 113.88/17.29 (37) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.29 (38) ~ (all_10_2 = e3)
% 113.88/17.29 (39) all_58_13 = all_52_7
% 113.88/17.29 (40) ~ (all_52_7 = e0)
% 113.88/17.29 (41) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.88/17.29 (42) all_54_5 = all_8_2
% 113.88/17.29 (43) ~ (all_52_13 = e2)
% 113.88/17.29 (44) ~ (all_52_11 = e2)
% 113.88/17.29 (45) ~ (all_52_12 = e3)
% 113.88/17.29 (46) all_56_15 = all_4_2
% 113.88/17.29 (47) all_58_10 = all_52_13
% 113.88/17.29 (48) ~ (all_52_13 = all_8_2)
% 113.88/17.29 (49) all_58_1 = all_52_4
% 113.88/17.29 (50) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.29 (51) ~ (all_52_9 = all_52_11)
% 113.88/17.29 (52) all_58_14 = all_52_11
% 113.88/17.29 (53) all_56_13 = all_8_2
% 113.88/17.29 (54) ~ (all_52_1 = all_8_2)
% 113.88/17.29 (55) ~ (all_8_2 = e2)
% 113.88/17.29 (56) ~ (all_52_9 = all_6_2)
% 113.88/17.29 (57) all_56_1 = all_52_8
% 113.88/17.29 (58) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.88/17.29 (59) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.88/17.29 (60) all_58_9 = all_52_12
% 113.88/17.29 (61) all_56_5 = all_52_13
% 113.88/17.29 (62) op(e2, e1) = all_52_9
% 113.88/17.29 (63) ~ (all_52_13 = all_4_2)
% 113.88/17.29 (64) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.88/17.29 (65) all_58_12 = all_52_3
% 113.88/17.29 (66) ~ (all_52_8 = all_52_9)
% 113.88/17.29 (67) op(e2, e0) = all_52_13
% 113.88/17.29 (68) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.88/17.29 (69) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.29 (70) all_56_8 = all_52_14
% 113.88/17.29 (71) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.29 (72) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.29 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.29 (73) all_54_15 = all_4_2
% 113.88/17.29 (74) op(e2, all_8_2) = e1
% 113.88/17.29 (75) ~ (all_6_2 = e1)
% 113.88/17.29 (76) ~ (all_6_1 = e2)
% 113.88/17.29 (77) ~ (e1 = e0)
% 113.88/17.29
% 113.88/17.29 Begin of proof
% 113.88/17.29 |
% 113.88/17.29 | BETA: splitting (69) gives:
% 113.88/17.29 |
% 113.88/17.29 | Case 1:
% 113.88/17.29 | |
% 113.88/17.29 | | (78) all_58_0 = e3
% 113.88/17.29 | |
% 113.88/17.29 | | COMBINE_EQS: (14), (78) imply:
% 113.88/17.29 | | (79) all_10_2 = e3
% 113.88/17.29 | |
% 113.88/17.29 | | REDUCE: (38), (79) imply:
% 113.88/17.29 | | (80) $false
% 113.88/17.29 | |
% 113.88/17.29 | | CLOSE: (80) is inconsistent.
% 113.88/17.29 | |
% 113.88/17.29 | Case 2:
% 113.88/17.29 | |
% 113.88/17.29 | | (81) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.29 | |
% 113.88/17.29 | | BETA: splitting (81) gives:
% 113.88/17.29 | |
% 113.88/17.29 | | Case 1:
% 113.88/17.29 | | |
% 113.88/17.29 | | | (82) all_58_1 = e3
% 113.88/17.29 | | |
% 113.88/17.29 | | | COMBINE_EQS: (49), (82) imply:
% 113.88/17.29 | | | (83) all_52_4 = e3
% 113.88/17.29 | | |
% 113.88/17.29 | | | REDUCE: (7), (83) imply:
% 113.88/17.29 | | | (84) $false
% 113.88/17.29 | | |
% 113.88/17.29 | | | CLOSE: (84) is inconsistent.
% 113.88/17.29 | | |
% 113.88/17.29 | | Case 2:
% 113.88/17.29 | | |
% 113.88/17.29 | | | (85) all_58_4 = e3 | all_58_9 = e3
% 113.88/17.29 | | |
% 113.88/17.29 | | | BETA: splitting (85) gives:
% 113.88/17.29 | | |
% 113.88/17.29 | | | Case 1:
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | (86) all_58_4 = e3
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | COMBINE_EQS: (24), (86) imply:
% 113.88/17.29 | | | | (87) all_52_8 = e3
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | REDUCE: (1), (87) imply:
% 113.88/17.29 | | | | (88) ~ (all_10_2 = e3)
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | REDUCE: (23), (87) imply:
% 113.88/17.29 | | | | (89) ~ (all_6_2 = e3)
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | SIMP: (89) implies:
% 113.88/17.29 | | | | (90) ~ (all_6_2 = e3)
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | BETA: splitting (8) gives:
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | Case 1:
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | (91) ~ (all_56_3 = e2)
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | REDUCE: (5), (91) imply:
% 113.88/17.29 | | | | | (92) ~ (all_52_1 = e2)
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | REF_CLOSE: (4), (9), (10), (14), (15), (16), (17), (19), (22), (27),
% 113.88/17.29 | | | | | (31), (32), (34), (36), (38), (43), (47), (55), (56), (59),
% 113.88/17.29 | | | | | (69), (70), (71), (75), (76), (90), (92) are inconsistent
% 113.88/17.29 | | | | | by sub-proof #85.
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | Case 2:
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | (93) all_56_3 = e2
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | COMBINE_EQS: (5), (93) imply:
% 113.88/17.29 | | | | | (94) all_52_1 = e2
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | REDUCE: (20), (94) imply:
% 113.88/17.29 | | | | | (95) ~ (all_52_9 = e2)
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | SIMP: (95) implies:
% 113.88/17.29 | | | | | (96) ~ (all_52_9 = e2)
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | REDUCE: (54), (94) imply:
% 113.88/17.29 | | | | | (97) ~ (all_8_2 = e2)
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (12), (13), (14), (18), (19),
% 113.88/17.29 | | | | | (21), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 113.88/17.29 | | | | | (35), (36), (37), (38), (39), (40), (41), (42), (44), (46),
% 113.88/17.29 | | | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (57),
% 113.88/17.29 | | | | | (58), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 113.88/17.29 | | | | | (69), (71), (72), (73), (74), (77), (96) are inconsistent
% 113.88/17.29 | | | | | by sub-proof #105.
% 113.88/17.29 | | | | |
% 113.88/17.29 | | | | End of split
% 113.88/17.29 | | | |
% 113.88/17.29 | | | Case 2:
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | (98) all_58_9 = e3
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | COMBINE_EQS: (60), (98) imply:
% 113.88/17.29 | | | | (99) all_52_12 = e3
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | REDUCE: (45), (99) imply:
% 113.88/17.29 | | | | (100) $false
% 113.88/17.29 | | | |
% 113.88/17.29 | | | | CLOSE: (100) is inconsistent.
% 113.88/17.29 | | | |
% 113.88/17.29 | | | End of split
% 113.88/17.29 | | |
% 113.88/17.29 | | End of split
% 113.88/17.29 | |
% 113.88/17.29 | End of split
% 113.88/17.29 |
% 113.88/17.29 End of proof
% 113.88/17.29
% 113.88/17.29 Sub-proof #79 shows that the following formulas are inconsistent:
% 113.88/17.29 ----------------------------------------------------------------
% 113.88/17.30 (1) ~ (all_52_9 = all_8_2)
% 113.88/17.30 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.30 (4) ~ (all_8_2 = e0)
% 113.88/17.30 (5) ~ (all_8_2 = e3)
% 113.88/17.30 (6) all_54_5 = all_8_2
% 113.88/17.30 (7) ~ (all_8_2 = e2)
% 113.88/17.30 (8) op(e2, e1) = all_52_9
% 113.88/17.30 (9) op(e2, all_8_2) = e1
% 113.88/17.30
% 113.88/17.30 Begin of proof
% 113.88/17.30 |
% 113.88/17.30 | BETA: splitting (2) gives:
% 113.88/17.30 |
% 113.88/17.30 | Case 1:
% 113.88/17.30 | |
% 113.88/17.30 | | (10) all_54_5 = e3
% 113.88/17.30 | |
% 113.88/17.30 | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #339.
% 113.88/17.30 | |
% 113.88/17.30 | Case 2:
% 113.88/17.30 | |
% 113.88/17.30 | | (11) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.30 | |
% 113.88/17.30 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (11) are inconsistent by
% 113.88/17.30 | | sub-proof #108.
% 113.88/17.30 | |
% 113.88/17.30 | End of split
% 113.88/17.30 |
% 113.88/17.30 End of proof
% 113.88/17.30
% 113.88/17.30 Sub-proof #80 shows that the following formulas are inconsistent:
% 113.88/17.30 ----------------------------------------------------------------
% 113.88/17.30 (1) all_58_7 = all_52_6
% 113.88/17.30 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.30 (3) op(e3, e2) = all_52_4
% 113.88/17.30 (4) all_54_0 = all_10_2
% 113.88/17.30 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.30 (6) ~ (all_52_2 = all_52_6)
% 113.88/17.30 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.30 (8) all_56_12 = all_10_2
% 113.88/17.30 (9) all_58_0 = all_10_2
% 113.88/17.30 (10) all_54_13 = all_52_7
% 113.88/17.30 (11) all_56_10 = all_52_7
% 113.88/17.30 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.30 (13) ~ (all_52_4 = all_52_7)
% 113.88/17.30 (14) all_58_3 = all_8_2
% 113.88/17.30 (15) ~ (all_8_2 = e0)
% 113.88/17.30 (16) op(e2, e3) = all_52_1
% 113.88/17.30 (17) ~ (all_10_2 = e1)
% 113.88/17.30 (18) ~ (all_52_7 = all_8_2)
% 113.88/17.30 (19) ~ (all_52_4 = all_8_2)
% 113.88/17.30 (20) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.30 (21) all_56_9 = all_52_3
% 113.88/17.30 (22) all_58_2 = all_52_1
% 113.88/17.30 (23) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.30 (24) ~ (all_10_2 = e3)
% 113.88/17.30 (25) all_58_13 = all_52_7
% 113.88/17.30 (26) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.88/17.30 (27) all_58_6 = all_52_2
% 113.88/17.30 (28) all_54_5 = all_8_2
% 113.88/17.30 (29) op(e3, all_10_2) = all_10_1
% 113.88/17.30 (30) all_58_1 = all_52_4
% 113.88/17.30 (31) all_54_1 = all_52_4
% 113.88/17.30 (32) all_56_13 = all_8_2
% 113.88/17.30 (33) ~ (all_8_2 = e2)
% 113.88/17.30 (34) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.30 (35) ~ (all_10_2 = e0)
% 113.88/17.30 (36) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.30 (37) ~ (all_52_4 = all_52_6)
% 113.88/17.30 (38) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.30 (39) all_58_12 = all_52_3
% 113.88/17.30 (40) all_24_1 = all_10_1
% 113.88/17.30 (41) all_24_2 = all_10_2
% 113.88/17.30 (42) ~ (all_52_4 = all_10_2)
% 113.88/17.30 (43) all_56_0 = all_52_4
% 113.88/17.30 (44) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.30 (45) op(e2, all_8_2) = e1
% 113.88/17.30 (46) ~ (all_52_6 = all_52_7)
% 113.88/17.30
% 113.88/17.30 Begin of proof
% 113.88/17.30 |
% 113.88/17.30 | BETA: splitting (38) gives:
% 113.88/17.30 |
% 113.88/17.30 | Case 1:
% 113.88/17.30 | |
% 113.88/17.30 | | (47) all_54_0 = e3
% 113.88/17.30 | |
% 113.88/17.30 | | REF_CLOSE: (4), (24), (47) are inconsistent by sub-proof #451.
% 113.88/17.30 | |
% 113.88/17.30 | Case 2:
% 113.88/17.30 | |
% 113.88/17.30 | | (48) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.30 | |
% 113.88/17.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 113.88/17.30 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 113.88/17.30 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 113.88/17.30 | | (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (48)
% 113.88/17.30 | | are inconsistent by sub-proof #81.
% 113.88/17.30 | |
% 113.88/17.30 | End of split
% 113.88/17.30 |
% 113.88/17.30 End of proof
% 113.88/17.30
% 113.88/17.30 Sub-proof #81 shows that the following formulas are inconsistent:
% 113.88/17.30 ----------------------------------------------------------------
% 113.88/17.30 (1) all_58_7 = all_52_6
% 113.88/17.30 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.30 (3) op(e3, e2) = all_52_4
% 113.88/17.30 (4) all_54_0 = all_10_2
% 113.88/17.30 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.30 (6) ~ (all_52_2 = all_52_6)
% 113.88/17.30 (7) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.30 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.30 (9) all_56_12 = all_10_2
% 113.88/17.30 (10) all_58_0 = all_10_2
% 113.88/17.30 (11) all_54_13 = all_52_7
% 113.88/17.30 (12) all_56_10 = all_52_7
% 113.88/17.30 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.30 (14) ~ (all_52_4 = all_52_7)
% 113.88/17.30 (15) all_58_3 = all_8_2
% 113.88/17.30 (16) ~ (all_8_2 = e0)
% 113.88/17.30 (17) op(e2, e3) = all_52_1
% 113.88/17.30 (18) ~ (all_10_2 = e1)
% 113.88/17.30 (19) ~ (all_52_7 = all_8_2)
% 113.88/17.30 (20) ~ (all_52_4 = all_8_2)
% 113.88/17.30 (21) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.30 (22) all_56_9 = all_52_3
% 113.88/17.30 (23) all_58_2 = all_52_1
% 113.88/17.30 (24) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.30 (25) all_58_13 = all_52_7
% 113.88/17.30 (26) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.88/17.30 (27) all_58_6 = all_52_2
% 113.88/17.30 (28) all_54_5 = all_8_2
% 113.88/17.30 (29) op(e3, all_10_2) = all_10_1
% 113.88/17.30 (30) all_58_1 = all_52_4
% 113.88/17.30 (31) all_54_1 = all_52_4
% 113.88/17.30 (32) all_56_13 = all_8_2
% 113.88/17.30 (33) ~ (all_8_2 = e2)
% 113.88/17.30 (34) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.30 (35) ~ (all_10_2 = e0)
% 113.88/17.30 (36) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.30 (37) ~ (all_52_4 = all_52_6)
% 113.88/17.30 (38) all_58_12 = all_52_3
% 113.88/17.30 (39) all_24_1 = all_10_1
% 113.88/17.30 (40) all_24_2 = all_10_2
% 113.88/17.30 (41) ~ (all_52_4 = all_10_2)
% 113.88/17.30 (42) all_56_0 = all_52_4
% 113.88/17.30 (43) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.30 (44) op(e2, all_8_2) = e1
% 113.88/17.30 (45) ~ (all_52_6 = all_52_7)
% 113.88/17.30
% 113.88/17.30 Begin of proof
% 113.88/17.30 |
% 113.88/17.30 | BETA: splitting (7) gives:
% 113.88/17.30 |
% 113.88/17.30 | Case 1:
% 113.88/17.30 | |
% 113.88/17.30 | | (46) all_54_0 = e2
% 113.88/17.30 | |
% 113.88/17.30 | | COMBINE_EQS: (4), (46) imply:
% 113.88/17.30 | | (47) all_10_2 = e2
% 113.88/17.30 | |
% 113.88/17.30 | | SIMP: (47) implies:
% 113.88/17.30 | | (48) all_10_2 = e2
% 113.88/17.30 | |
% 113.88/17.31 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 113.88/17.31 | | (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 113.88/17.31 | | (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), (38),
% 113.88/17.31 | | (39), (40), (41), (42), (43), (44), (45), (48) are inconsistent
% 113.88/17.31 | | by sub-proof #82.
% 113.88/17.31 | |
% 113.88/17.31 | Case 2:
% 113.88/17.31 | |
% 113.88/17.31 | | (49) all_54_0 = e1 | all_54_0 = e0
% 113.88/17.31 | |
% 113.88/17.31 | | REF_CLOSE: (4), (18), (35), (49) are inconsistent by sub-proof #423.
% 113.88/17.31 | |
% 113.88/17.31 | End of split
% 113.88/17.31 |
% 113.88/17.31 End of proof
% 113.88/17.31
% 113.88/17.31 Sub-proof #82 shows that the following formulas are inconsistent:
% 113.88/17.31 ----------------------------------------------------------------
% 113.88/17.31 (1) all_58_7 = all_52_6
% 113.88/17.31 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.31 (3) op(e3, e2) = all_52_4
% 113.88/17.31 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.31 (5) ~ (all_52_2 = all_52_6)
% 113.88/17.31 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.31 (7) all_56_12 = all_10_2
% 113.88/17.31 (8) all_58_0 = all_10_2
% 113.88/17.31 (9) all_54_13 = all_52_7
% 113.88/17.31 (10) all_56_10 = all_52_7
% 113.88/17.31 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.31 (12) all_10_2 = e2
% 113.88/17.31 (13) ~ (all_52_4 = all_52_7)
% 113.88/17.31 (14) all_58_3 = all_8_2
% 113.88/17.31 (15) ~ (all_8_2 = e0)
% 113.88/17.31 (16) op(e2, e3) = all_52_1
% 113.88/17.31 (17) ~ (all_52_7 = all_8_2)
% 113.88/17.31 (18) ~ (all_52_4 = all_8_2)
% 113.88/17.31 (19) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.31 (20) all_56_9 = all_52_3
% 113.88/17.31 (21) all_58_2 = all_52_1
% 113.88/17.31 (22) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.31 (23) all_58_13 = all_52_7
% 113.88/17.31 (24) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.88/17.31 (25) all_58_6 = all_52_2
% 113.88/17.31 (26) all_54_5 = all_8_2
% 113.88/17.31 (27) op(e3, all_10_2) = all_10_1
% 113.88/17.31 (28) all_58_1 = all_52_4
% 113.88/17.31 (29) all_54_1 = all_52_4
% 113.88/17.31 (30) all_56_13 = all_8_2
% 113.88/17.31 (31) ~ (all_8_2 = e2)
% 113.88/17.31 (32) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.31 (33) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.31 (34) ~ (all_52_4 = all_52_6)
% 113.88/17.31 (35) all_58_12 = all_52_3
% 113.88/17.31 (36) all_24_1 = all_10_1
% 113.88/17.31 (37) all_24_2 = all_10_2
% 113.88/17.31 (38) ~ (all_52_4 = all_10_2)
% 113.88/17.31 (39) all_56_0 = all_52_4
% 113.88/17.31 (40) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.31 (41) op(e2, all_8_2) = e1
% 113.88/17.31 (42) ~ (all_52_6 = all_52_7)
% 113.88/17.31
% 113.88/17.31 Begin of proof
% 113.88/17.31 |
% 113.88/17.31 | COMBINE_EQS: (12), (37) imply:
% 113.88/17.31 | (43) all_24_2 = e2
% 113.88/17.31 |
% 113.88/17.31 | COMBINE_EQS: (7), (12) imply:
% 113.88/17.31 | (44) all_56_12 = e2
% 113.88/17.31 |
% 113.88/17.31 | COMBINE_EQS: (8), (12) imply:
% 113.88/17.31 | (45) all_58_0 = e2
% 113.88/17.31 |
% 113.88/17.31 | REDUCE: (12), (38) imply:
% 113.88/17.31 | (46) ~ (all_52_4 = e2)
% 113.88/17.31 |
% 113.88/17.31 | REDUCE: (12), (27) imply:
% 113.88/17.31 | (47) op(e3, e2) = all_10_1
% 113.88/17.31 |
% 113.88/17.31 | BETA: splitting (24) gives:
% 113.88/17.31 |
% 113.88/17.31 | Case 1:
% 113.88/17.31 | |
% 113.88/17.31 | | (48) ~ (all_56_12 = e2)
% 113.88/17.31 | |
% 113.88/17.31 | | REDUCE: (44), (48) imply:
% 113.88/17.31 | | (49) $false
% 113.88/17.31 | |
% 113.88/17.31 | | CLOSE: (49) is inconsistent.
% 113.88/17.31 | |
% 113.88/17.31 | Case 2:
% 113.88/17.31 | |
% 113.88/17.31 | | (50) ~ (all_56_10 = e0)
% 113.88/17.31 | |
% 113.88/17.31 | | REDUCE: (10), (50) imply:
% 113.88/17.31 | | (51) ~ (all_52_7 = e0)
% 113.88/17.31 | |
% 113.88/17.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (13), (14), (15), (16),
% 113.88/17.31 | | (17), (18), (19), (20), (21), (22), (23), (25), (26), (28), (29),
% 113.88/17.31 | | (30), (31), (32), (33), (34), (35), (36), (39), (40), (41), (42),
% 113.88/17.31 | | (43), (44), (45), (46), (47), (51) are inconsistent by sub-proof
% 113.88/17.31 | | #83.
% 113.88/17.31 | |
% 113.88/17.31 | End of split
% 113.88/17.31 |
% 113.88/17.31 End of proof
% 113.88/17.31
% 113.88/17.31 Sub-proof #83 shows that the following formulas are inconsistent:
% 113.88/17.31 ----------------------------------------------------------------
% 113.88/17.31 (1) all_58_7 = all_52_6
% 113.88/17.31 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.31 (3) op(e3, e2) = all_52_4
% 113.88/17.31 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.31 (5) ~ (all_52_2 = all_52_6)
% 113.88/17.31 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.31 (7) all_54_13 = all_52_7
% 113.88/17.31 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.31 (9) ~ (all_52_4 = all_52_7)
% 113.88/17.31 (10) all_56_12 = e2
% 113.88/17.31 (11) all_58_3 = all_8_2
% 113.88/17.31 (12) all_24_2 = e2
% 113.88/17.31 (13) ~ (all_8_2 = e0)
% 113.88/17.31 (14) op(e2, e3) = all_52_1
% 113.88/17.31 (15) ~ (all_52_7 = all_8_2)
% 113.88/17.31 (16) ~ (all_52_4 = all_8_2)
% 113.88/17.31 (17) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 113.88/17.31 (18) all_56_9 = all_52_3
% 113.88/17.31 (19) all_58_2 = all_52_1
% 113.88/17.31 (20) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.31 (21) all_58_13 = all_52_7
% 113.88/17.31 (22) ~ (all_52_7 = e0)
% 113.88/17.31 (23) all_58_6 = all_52_2
% 113.88/17.31 (24) all_54_5 = all_8_2
% 113.88/17.31 (25) all_58_0 = e2
% 113.88/17.31 (26) all_58_1 = all_52_4
% 113.88/17.31 (27) all_54_1 = all_52_4
% 113.88/17.31 (28) all_56_13 = all_8_2
% 113.88/17.31 (29) ~ (all_8_2 = e2)
% 113.88/17.31 (30) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.31 (31) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.31 (32) ~ (all_52_4 = all_52_6)
% 113.88/17.31 (33) op(e3, e2) = all_10_1
% 113.88/17.31 (34) all_58_12 = all_52_3
% 113.88/17.31 (35) all_24_1 = all_10_1
% 113.88/17.31 (36) all_56_0 = all_52_4
% 113.88/17.31 (37) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.31 (38) op(e2, all_8_2) = e1
% 113.88/17.31 (39) ~ (all_52_6 = all_52_7)
% 113.88/17.31 (40) ~ (all_52_4 = e2)
% 113.88/17.31
% 113.88/17.31 Begin of proof
% 113.88/17.31 |
% 113.88/17.31 | BETA: splitting (17) gives:
% 113.88/17.31 |
% 113.88/17.31 | Case 1:
% 113.88/17.31 | |
% 113.88/17.31 | | (41) ~ (all_24_2 = e2)
% 113.88/17.31 | |
% 113.88/17.31 | | REDUCE: (12), (41) imply:
% 113.88/17.31 | | (42) $false
% 113.88/17.31 | |
% 113.88/17.31 | | CLOSE: (42) is inconsistent.
% 113.88/17.31 | |
% 113.88/17.31 | Case 2:
% 113.88/17.31 | |
% 113.88/17.31 | | (43) ~ (all_24_1 = e0)
% 113.88/17.31 | |
% 113.88/17.31 | | REDUCE: (35), (43) imply:
% 113.88/17.31 | | (44) ~ (all_10_1 = e0)
% 113.88/17.31 | |
% 113.88/17.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 113.88/17.31 | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 113.88/17.31 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 113.88/17.31 | | (38), (39), (40), (44) are inconsistent by sub-proof #84.
% 113.88/17.31 | |
% 113.88/17.31 | End of split
% 113.88/17.31 |
% 113.88/17.31 End of proof
% 113.88/17.31
% 113.88/17.31 Sub-proof #84 shows that the following formulas are inconsistent:
% 113.88/17.31 ----------------------------------------------------------------
% 113.88/17.31 (1) all_58_7 = all_52_6
% 113.88/17.31 (2) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.31 (3) op(e3, e2) = all_52_4
% 113.88/17.31 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.31 (5) ~ (all_52_2 = all_52_6)
% 113.88/17.32 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.32 (7) all_54_13 = all_52_7
% 113.88/17.32 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.32 (9) ~ (all_52_4 = all_52_7)
% 113.88/17.32 (10) all_56_12 = e2
% 113.88/17.32 (11) all_58_3 = all_8_2
% 113.88/17.32 (12) ~ (all_8_2 = e0)
% 113.88/17.32 (13) op(e2, e3) = all_52_1
% 113.88/17.32 (14) ~ (all_52_7 = all_8_2)
% 113.88/17.32 (15) ~ (all_52_4 = all_8_2)
% 113.88/17.32 (16) all_56_9 = all_52_3
% 113.88/17.32 (17) all_58_2 = all_52_1
% 113.88/17.32 (18) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.32 (19) all_58_13 = all_52_7
% 113.88/17.32 (20) ~ (all_52_7 = e0)
% 113.88/17.32 (21) all_58_6 = all_52_2
% 113.88/17.32 (22) all_54_5 = all_8_2
% 113.88/17.32 (23) all_58_0 = e2
% 113.88/17.32 (24) all_58_1 = all_52_4
% 113.88/17.32 (25) all_54_1 = all_52_4
% 113.88/17.32 (26) all_56_13 = all_8_2
% 113.88/17.32 (27) ~ (all_8_2 = e2)
% 113.88/17.32 (28) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.32 (29) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.32 (30) ~ (all_52_4 = all_52_6)
% 113.88/17.32 (31) op(e3, e2) = all_10_1
% 113.88/17.32 (32) ~ (all_10_1 = e0)
% 113.88/17.32 (33) all_58_12 = all_52_3
% 113.88/17.32 (34) all_56_0 = all_52_4
% 113.88/17.32 (35) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.32 (36) op(e2, all_8_2) = e1
% 113.88/17.32 (37) ~ (all_52_6 = all_52_7)
% 113.88/17.32 (38) ~ (all_52_4 = e2)
% 113.88/17.32
% 113.88/17.32 Begin of proof
% 113.88/17.32 |
% 113.88/17.32 | BETA: splitting (35) gives:
% 113.88/17.32 |
% 113.88/17.32 | Case 1:
% 113.88/17.32 | |
% 113.88/17.32 | | (39) ~ (all_56_0 = e3)
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (34), (39) imply:
% 113.88/17.32 | | (40) ~ (all_52_4 = e3)
% 113.88/17.32 | |
% 113.88/17.32 | | GROUND_INST: instantiating (8) with all_52_4, all_10_1, e2, e3, simplifying
% 113.88/17.32 | | with (3), (31) gives:
% 113.88/17.32 | | (41) all_52_4 = all_10_1
% 113.88/17.32 | |
% 113.88/17.32 | | COMBINE_EQS: (25), (41) imply:
% 113.88/17.32 | | (42) all_54_1 = all_10_1
% 113.88/17.32 | |
% 113.88/17.32 | | COMBINE_EQS: (24), (41) imply:
% 113.88/17.32 | | (43) all_58_1 = all_10_1
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (30), (41) imply:
% 113.88/17.32 | | (44) ~ (all_52_6 = all_10_1)
% 113.88/17.32 | |
% 113.88/17.32 | | SIMP: (44) implies:
% 113.88/17.32 | | (45) ~ (all_52_6 = all_10_1)
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (9), (41) imply:
% 113.88/17.32 | | (46) ~ (all_52_7 = all_10_1)
% 113.88/17.32 | |
% 113.88/17.32 | | SIMP: (46) implies:
% 113.88/17.32 | | (47) ~ (all_52_7 = all_10_1)
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (15), (41) imply:
% 113.88/17.32 | | (48) ~ (all_10_1 = all_8_2)
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (40), (41) imply:
% 113.88/17.32 | | (49) ~ (all_10_1 = e3)
% 113.88/17.32 | |
% 113.88/17.32 | | REDUCE: (38), (41) imply:
% 113.88/17.32 | | (50) ~ (all_10_1 = e2)
% 113.88/17.32 | |
% 113.88/17.32 | | BETA: splitting (29) gives:
% 113.88/17.32 | |
% 113.88/17.32 | | Case 1:
% 113.88/17.32 | | |
% 113.88/17.32 | | | (51) all_54_1 = e3
% 113.88/17.32 | | |
% 113.88/17.32 | | | REF_CLOSE: (42), (49), (51) are inconsistent by sub-proof #443.
% 113.88/17.32 | | |
% 113.88/17.32 | | Case 2:
% 113.88/17.32 | | |
% 113.88/17.32 | | | (52) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.32 | | |
% 113.88/17.32 | | | BETA: splitting (28) gives:
% 113.88/17.32 | | |
% 113.88/17.32 | | | Case 1:
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | (53) all_58_1 = e0
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | COMBINE_EQS: (43), (53) imply:
% 113.88/17.32 | | | | (54) all_10_1 = e0
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | REDUCE: (32), (54) imply:
% 113.88/17.32 | | | | (55) $false
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | CLOSE: (55) is inconsistent.
% 113.88/17.32 | | | |
% 113.88/17.32 | | | Case 2:
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | (56) ~ (all_58_1 = e0)
% 113.88/17.32 | | | | (57) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | BETA: splitting (52) gives:
% 113.88/17.32 | | | |
% 113.88/17.32 | | | | Case 1:
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | | (58) all_54_1 = e2
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | | REF_CLOSE: (42), (50), (58) are inconsistent by sub-proof #442.
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | Case 2:
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | | (59) all_54_1 = e1 | all_54_1 = e0
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | | BETA: splitting (59) gives:
% 113.88/17.32 | | | | |
% 113.88/17.32 | | | | | Case 1:
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | (60) all_54_1 = e1
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | COMBINE_EQS: (42), (60) imply:
% 113.88/17.32 | | | | | | (61) all_10_1 = e1
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | SIMP: (61) implies:
% 113.88/17.32 | | | | | | (62) all_10_1 = e1
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | REDUCE: (45), (62) imply:
% 113.88/17.32 | | | | | | (63) ~ (all_52_6 = e1)
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | REDUCE: (47), (62) imply:
% 113.88/17.32 | | | | | | (64) ~ (all_52_7 = e1)
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | REDUCE: (48), (62) imply:
% 113.88/17.32 | | | | | | (65) ~ (all_8_2 = e1)
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | SIMP: (65) implies:
% 113.88/17.32 | | | | | | (66) ~ (all_8_2 = e1)
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | BETA: splitting (6) gives:
% 113.88/17.32 | | | | | |
% 113.88/17.32 | | | | | | Case 1:
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | (67) all_54_5 = e3
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | COMBINE_EQS: (22), (67) imply:
% 113.88/17.32 | | | | | | | (68) all_8_2 = e3
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | SIMP: (68) implies:
% 113.88/17.32 | | | | | | | (69) all_8_2 = e3
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | COMBINE_EQS: (26), (69) imply:
% 113.88/17.32 | | | | | | | (70) all_56_13 = e3
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | COMBINE_EQS: (11), (69) imply:
% 113.88/17.32 | | | | | | | (71) all_58_3 = e3
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | REDUCE: (14), (69) imply:
% 113.88/17.32 | | | | | | | (72) ~ (all_52_7 = e3)
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | REDUCE: (12), (69) imply:
% 113.88/17.32 | | | | | | | (73) ~ (e3 = e0)
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | REDUCE: (36), (69) imply:
% 113.88/17.32 | | | | | | | (74) op(e2, e3) = e1
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | BETA: splitting (4) gives:
% 113.88/17.32 | | | | | | |
% 113.88/17.32 | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | | (75) all_54_13 = e3
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | | REF_CLOSE: (7), (72), (75) are inconsistent by sub-proof #336.
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | | (76) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | | BETA: splitting (76) gives:
% 113.88/17.32 | | | | | | | |
% 113.88/17.32 | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | (77) all_54_13 = e2
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | COMBINE_EQS: (7), (77) imply:
% 113.88/17.32 | | | | | | | | | (78) all_52_7 = e2
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | SIMP: (78) implies:
% 113.88/17.32 | | | | | | | | | (79) all_52_7 = e2
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | COMBINE_EQS: (19), (79) imply:
% 113.88/17.32 | | | | | | | | | (80) all_58_13 = e2
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | REDUCE: (37), (79) imply:
% 113.88/17.32 | | | | | | | | | (81) ~ (all_52_6 = e2)
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | REDUCE: (20), (79) imply:
% 113.88/17.32 | | | | | | | | | (82) ~ (e2 = e0)
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | BETA: splitting (18) gives:
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | (83) ~ (all_56_13 = e3)
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | REDUCE: (70), (83) imply:
% 113.88/17.32 | | | | | | | | | | (84) $false
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | CLOSE: (84) is inconsistent.
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | (85) ~ (all_56_9 = e0)
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | REDUCE: (16), (85) imply:
% 113.88/17.32 | | | | | | | | | | (86) ~ (all_52_3 = e0)
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | BETA: splitting (57) gives:
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | (87) all_58_3 = e0
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | COMBINE_EQS: (71), (87) imply:
% 113.88/17.32 | | | | | | | | | | | (88) e3 = e0
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | REDUCE: (73), (88) imply:
% 113.88/17.32 | | | | | | | | | | | (89) $false
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | CLOSE: (89) is inconsistent.
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | (90) all_58_7 = e0 | all_58_13 = e0
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | BETA: splitting (90) gives:
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | (91) all_58_7 = e0
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | COMBINE_EQS: (1), (91) imply:
% 113.88/17.32 | | | | | | | | | | | | (92) all_52_6 = e0
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | REDUCE: (5), (92) imply:
% 113.88/17.32 | | | | | | | | | | | | (93) ~ (all_52_2 = e0)
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | REDUCE: (81), (92) imply:
% 113.88/17.32 | | | | | | | | | | | | (94) ~ (e2 = e0)
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | REDUCE: (63), (92) imply:
% 113.88/17.32 | | | | | | | | | | | | (95) ~ (e1 = e0)
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | SIMP: (95) implies:
% 113.88/17.32 | | | | | | | | | | | | (96) ~ (e1 = e0)
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | BETA: splitting (2) gives:
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | (97) all_58_0 = e0
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | COMBINE_EQS: (23), (97) imply:
% 113.88/17.32 | | | | | | | | | | | | | (98) e2 = e0
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | REDUCE: (82), (98) imply:
% 113.88/17.32 | | | | | | | | | | | | | (99) $false
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | (100) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | BETA: splitting (100) gives:
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | Case 1:
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | | (101) all_58_2 = e0
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | | COMBINE_EQS: (17), (101) imply:
% 113.88/17.32 | | | | | | | | | | | | | | (102) all_52_1 = e0
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (74), (96), (102) are inconsistent by
% 113.88/17.32 | | | | | | | | | | | | | | sub-proof #132.
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | | (103) all_58_6 = e0 | all_58_12 = e0
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (86), (93), (103) are inconsistent by
% 113.88/17.32 | | | | | | | | | | | | | | sub-proof #217.
% 113.88/17.32 | | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | | End of split
% 113.88/17.32 | | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | End of split
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | (104) all_58_13 = e0
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | COMBINE_EQS: (80), (104) imply:
% 113.88/17.32 | | | | | | | | | | | | (105) e2 = e0
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | REDUCE: (82), (105) imply:
% 113.88/17.32 | | | | | | | | | | | | (106) $false
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | | CLOSE: (106) is inconsistent.
% 113.88/17.32 | | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | | End of split
% 113.88/17.32 | | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | | End of split
% 113.88/17.32 | | | | | | | | | |
% 113.88/17.32 | | | | | | | | | End of split
% 113.88/17.32 | | | | | | | | |
% 113.88/17.32 | | | | | | | | Case 2:
% 113.88/17.32 | | | | | | | | |
% 113.88/17.33 | | | | | | | | | (107) all_54_13 = e1 | all_54_13 = e0
% 113.88/17.33 | | | | | | | | |
% 113.88/17.33 | | | | | | | | | REF_CLOSE: (7), (20), (64), (107) are inconsistent by
% 113.88/17.33 | | | | | | | | | sub-proof #333.
% 113.88/17.33 | | | | | | | | |
% 113.88/17.33 | | | | | | | | End of split
% 113.88/17.33 | | | | | | | |
% 113.88/17.33 | | | | | | | End of split
% 113.88/17.33 | | | | | | |
% 113.88/17.33 | | | | | | Case 2:
% 113.88/17.33 | | | | | | |
% 113.88/17.33 | | | | | | | (108) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.33 | | | | | | |
% 113.88/17.33 | | | | | | | REF_CLOSE: (12), (22), (27), (66), (108) are inconsistent by
% 113.88/17.33 | | | | | | | sub-proof #310.
% 113.88/17.33 | | | | | | |
% 113.88/17.33 | | | | | | End of split
% 113.88/17.33 | | | | | |
% 113.88/17.33 | | | | | Case 2:
% 113.88/17.33 | | | | | |
% 113.88/17.33 | | | | | | (109) all_54_1 = e0
% 113.88/17.33 | | | | | |
% 113.88/17.33 | | | | | | REF_CLOSE: (32), (42), (109) are inconsistent by sub-proof #198.
% 113.88/17.33 | | | | | |
% 113.88/17.33 | | | | | End of split
% 113.88/17.33 | | | | |
% 113.88/17.33 | | | | End of split
% 113.88/17.33 | | | |
% 113.88/17.33 | | | End of split
% 113.88/17.33 | | |
% 113.88/17.33 | | End of split
% 113.88/17.33 | |
% 113.88/17.33 | Case 2:
% 113.88/17.33 | |
% 113.88/17.33 | | (110) ~ (all_56_12 = e2)
% 113.88/17.33 | |
% 113.88/17.33 | | REDUCE: (10), (110) imply:
% 113.88/17.33 | | (111) $false
% 113.88/17.33 | |
% 113.88/17.33 | | CLOSE: (111) is inconsistent.
% 113.88/17.33 | |
% 113.88/17.33 | End of split
% 113.88/17.33 |
% 113.88/17.33 End of proof
% 113.88/17.33
% 113.88/17.33 Sub-proof #85 shows that the following formulas are inconsistent:
% 113.88/17.33 ----------------------------------------------------------------
% 113.88/17.33 (1) ~ (all_52_1 = e2)
% 113.88/17.33 (2) all_56_14 = all_6_2
% 113.88/17.33 (3) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.88/17.33 (4) ~ (all_6_1 = e3)
% 113.88/17.33 (5) all_58_0 = all_10_2
% 113.88/17.33 (6) all_54_11 = all_52_14
% 113.88/17.33 (7) ~ (all_52_14 = all_6_2)
% 113.88/17.33 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.33 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.33 (10) all_54_10 = all_6_2
% 113.88/17.33 (11) all_58_3 = all_8_2
% 113.88/17.33 (12) op(e1, e0) = all_52_14
% 113.88/17.33 (13) all_58_5 = all_52_9
% 113.88/17.33 (14) op(e1, all_6_2) = all_6_1
% 113.88/17.33 (15) all_58_2 = all_52_1
% 113.88/17.33 (16) ~ (all_10_2 = e3)
% 113.88/17.33 (17) ~ (all_52_13 = e2)
% 113.88/17.33 (18) all_58_10 = all_52_13
% 113.88/17.33 (19) ~ (all_8_2 = e2)
% 113.88/17.33 (20) ~ (all_52_9 = all_6_2)
% 113.88/17.33 (21) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 113.88/17.33 (22) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.33 (23) all_56_8 = all_52_14
% 113.88/17.33 (24) ~ (all_6_2 = e3)
% 113.88/17.33 (25) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.33 (26) ~ (all_6_2 = e1)
% 113.88/17.33 (27) ~ (all_6_1 = e2)
% 113.88/17.33
% 113.88/17.33 Begin of proof
% 113.88/17.33 |
% 113.88/17.33 | BETA: splitting (25) gives:
% 113.88/17.33 |
% 113.88/17.33 | Case 1:
% 113.88/17.33 | |
% 113.88/17.33 | | (28) all_58_2 = e2
% 113.88/17.33 | |
% 113.88/17.33 | | REF_CLOSE: (1), (15), (28) are inconsistent by sub-proof #335.
% 113.88/17.33 | |
% 113.88/17.33 | Case 2:
% 113.88/17.33 | |
% 113.88/17.33 | | (29) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.33 | |
% 113.88/17.33 | | BETA: splitting (29) gives:
% 113.88/17.33 | |
% 113.88/17.33 | | Case 1:
% 113.88/17.33 | | |
% 113.88/17.33 | | | (30) all_58_3 = e2
% 113.88/17.33 | | |
% 113.88/17.33 | | | COMBINE_EQS: (11), (30) imply:
% 113.88/17.33 | | | (31) all_8_2 = e2
% 113.88/17.33 | | |
% 113.88/17.33 | | | REDUCE: (19), (31) imply:
% 113.88/17.33 | | | (32) $false
% 113.88/17.33 | | |
% 113.88/17.33 | | | CLOSE: (32) is inconsistent.
% 113.88/17.33 | | |
% 113.88/17.33 | | Case 2:
% 113.88/17.33 | | |
% 113.88/17.33 | | | (33) all_58_5 = e2 | all_58_10 = e2
% 113.88/17.33 | | |
% 113.88/17.33 | | | BETA: splitting (33) gives:
% 113.88/17.33 | | |
% 113.88/17.33 | | | Case 1:
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | (34) all_58_5 = e2
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | COMBINE_EQS: (13), (34) imply:
% 113.88/17.33 | | | | (35) all_52_9 = e2
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | SIMP: (35) implies:
% 113.88/17.33 | | | | (36) all_52_9 = e2
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | REDUCE: (20), (36) imply:
% 113.88/17.33 | | | | (37) ~ (all_6_2 = e2)
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | SIMP: (37) implies:
% 113.88/17.33 | | | | (38) ~ (all_6_2 = e2)
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 113.88/17.33 | | | | (16), (21), (22), (23), (24), (26), (27), (38) are
% 113.88/17.33 | | | | inconsistent by sub-proof #413.
% 113.88/17.33 | | | |
% 113.88/17.33 | | | Case 2:
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | (39) all_58_10 = e2
% 113.88/17.33 | | | |
% 113.88/17.33 | | | | REF_CLOSE: (17), (18), (39) are inconsistent by sub-proof #95.
% 113.88/17.33 | | | |
% 113.88/17.33 | | | End of split
% 113.88/17.33 | | |
% 113.88/17.33 | | End of split
% 113.88/17.33 | |
% 113.88/17.33 | End of split
% 113.88/17.33 |
% 113.88/17.33 End of proof
% 113.88/17.33
% 113.88/17.33 Sub-proof #86 shows that the following formulas are inconsistent:
% 113.88/17.33 ----------------------------------------------------------------
% 113.88/17.33 (1) ~ (all_52_8 = all_10_2)
% 113.88/17.33 (2) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 113.88/17.33 (3) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 113.88/17.33 (4) ~ (all_52_2 = all_10_2)
% 113.88/17.33 (5) all_54_2 = all_52_8
% 113.88/17.33 (6) all_58_7 = all_52_6
% 113.88/17.33 (7) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 113.88/17.33 (8) ~ (all_52_8 = all_52_11)
% 113.88/17.33 (9) ~ (all_52_9 = all_8_2)
% 113.88/17.33 (10) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 113.88/17.33 (11) ~ (all_52_13 = all_52_14)
% 113.88/17.33 (12) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 113.88/17.33 (13) ~ (all_4_2 = e0)
% 113.88/17.33 (14) op(e3, e2) = all_52_4
% 113.88/17.33 (15) all_56_14 = all_6_2
% 113.88/17.33 (16) all_56_3 = all_52_1
% 113.88/17.33 (17) all_38_1 = all_10_1
% 113.88/17.33 (18) all_54_0 = all_10_2
% 113.88/17.33 (19) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 113.88/17.33 (20) all_54_3 = all_52_12
% 113.88/17.33 (21) ~ (all_52_2 = all_52_6)
% 113.88/17.33 (22) op(e0, e2) = all_52_7
% 113.88/17.33 (23) ~ (all_52_7 = all_4_2)
% 113.88/17.33 (24) all_56_11 = all_52_11
% 113.88/17.33 (25) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 113.88/17.33 (26) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 113.88/17.33 (27) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 113.88/17.33 (28) ~ (all_52_4 = all_52_8)
% 113.88/17.33 (29) ~ (all_52_12 = all_10_2)
% 113.88/17.33 (30) ~ (e3 = e1)
% 113.88/17.33 (31) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 113.88/17.33 (32) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 113.88/17.33 (33) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.33 (34) all_56_12 = all_10_2
% 113.88/17.33 (35) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 113.88/17.33 (36) all_58_0 = all_10_2
% 113.88/17.33 (37) all_54_13 = all_52_7
% 113.88/17.33 (38) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 113.88/17.33 (39) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 113.88/17.33 (40) ~ (all_52_14 = all_6_2)
% 113.88/17.33 (41) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 113.88/17.33 (42) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 113.88/17.33 (43) all_56_10 = all_52_7
% 113.88/17.33 (44) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 113.88/17.33 (45) all_54_14 = all_52_11
% 113.88/17.33 (46) op(all_4_1, all_4_2) = all_4_0
% 113.88/17.33 (47) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.33 (48) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 113.88/17.33 (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 113.88/17.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 113.88/17.33 (50) all_54_8 = all_52_2
% 113.88/17.33 (51) ~ (all_52_2 = all_6_2)
% 113.88/17.33 (52) all_32_2 = all_10_2
% 113.88/17.33 (53) ~ (all_52_1 = all_52_9)
% 113.88/17.33 (54) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 113.88/17.33 (55) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 113.88/17.33 (56) all_54_10 = all_6_2
% 113.88/17.33 (57) op(e3, e0) = all_52_12
% 113.88/17.34 (58) ~ (all_52_8 = all_6_2)
% 113.88/17.34 (59) all_58_4 = all_52_8
% 113.88/17.34 (60) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.34 (61) ~ (all_52_4 = all_52_7)
% 113.88/17.34 (62) all_56_2 = all_52_12
% 113.88/17.34 (63) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 113.88/17.34 (64) all_58_3 = all_8_2
% 113.88/17.34 (65) all_54_6 = all_52_9
% 113.88/17.34 (66) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 113.88/17.34 (67) ~ (all_10_0 = e2)
% 113.88/17.34 (68) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 113.88/17.34 (69) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 113.88/17.34 (70) all_58_11 = all_52_14
% 113.88/17.34 (71) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 113.88/17.34 (72) all_54_9 = all_52_6
% 113.88/17.34 (73) op(e3, e1) = all_52_8
% 113.88/17.34 (74) ~ (all_52_2 = all_52_3)
% 113.88/17.34 (75) all_54_7 = all_52_13
% 113.88/17.34 (76) op(all_10_1, all_10_2) = all_10_0
% 113.88/17.34 (77) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 113.88/17.34 (78) ~ (all_52_11 = all_6_2)
% 113.88/17.34 (79) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 113.88/17.34 (80) op(e2, e3) = all_52_1
% 113.88/17.34 (81) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 113.88/17.34 (82) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 113.88/17.34 (83) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 113.88/17.34 (84) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 113.88/17.34 (85) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 113.88/17.34 (86) ~ (all_52_7 = all_8_2)
% 113.88/17.34 (87) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.88/17.34 (88) ~ (all_52_4 = all_8_2)
% 113.88/17.34 (89) all_58_5 = all_52_9
% 113.88/17.34 (90) ~ (all_4_0 = e3)
% 113.88/17.34 (91) all_56_9 = all_52_3
% 113.88/17.34 (92) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 113.88/17.34 (93) op(e1, all_6_2) = all_6_1
% 113.88/17.34 (94) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 113.88/17.34 (95) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 113.88/17.34 (96) all_32_0 = all_10_0
% 113.88/17.34 (97) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 113.88/17.34 (98) all_58_15 = all_4_2
% 113.88/17.34 (99) all_58_2 = all_52_1
% 113.88/17.34 (100) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 113.88/17.34 (101) ~ (all_52_1 = all_52_13)
% 113.88/17.34 (102) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 113.88/17.34 (103) op(e0, e3) = all_52_3
% 113.88/17.34 (104) ~ (all_10_2 = e3)
% 113.88/17.34 (105) ~ (all_52_12 = all_52_13)
% 113.88/17.34 (106) all_58_13 = all_52_7
% 113.88/17.34 (107) all_32_1 = all_10_1
% 113.88/17.34 (108) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 113.88/17.34 (109) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 113.88/17.34 (110) ~ (all_52_14 = all_4_2)
% 113.88/17.34 (111) all_58_6 = all_52_2
% 113.88/17.34 (112) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 113.88/17.34 (113) ~ (all_52_1 = all_10_2)
% 113.88/17.34 (114) all_54_5 = all_8_2
% 113.88/17.34 (115) all_56_15 = all_4_2
% 113.88/17.34 (116) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.88/17.34 (117) all_58_10 = all_52_13
% 113.88/17.34 (118) ~ (all_52_13 = all_8_2)
% 113.88/17.34 (119) ~ (all_52_11 = all_4_2)
% 113.88/17.34 (120) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 113.88/17.34 (121) op(e3, all_10_2) = all_10_1
% 113.88/17.34 (122) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 113.88/17.34 (123) ~ (all_52_6 = all_8_2)
% 113.88/17.34 (124) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 113.88/17.34 (125) all_58_1 = all_52_4
% 113.88/17.34 (126) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 113.88/17.34 (127) ~ (all_52_9 = all_52_11)
% 113.88/17.34 (128) all_58_14 = all_52_11
% 113.88/17.34 (129) all_54_1 = all_52_4
% 113.88/17.34 (130) all_56_13 = all_8_2
% 113.88/17.34 (131) op(e0, e1) = all_52_11
% 113.88/17.34 (132) ~ (all_52_1 = all_8_2)
% 113.88/17.34 (133) ~ (all_8_2 = e2)
% 113.88/17.34 (134) ~ (all_52_7 = all_52_11)
% 113.88/17.34 (135) op(e1, e2) = all_52_6
% 113.88/17.34 (136) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 113.88/17.34 (137) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.34 (138) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.34 (139) all_56_7 = all_52_6
% 113.88/17.34 (140) ~ (all_52_9 = all_6_2)
% 113.88/17.34 (141) ~ (all_52_4 = all_52_6)
% 113.88/17.34 (142) ~ (all_52_1 = all_52_2)
% 113.88/17.34 (143) all_26_2 = all_4_2
% 113.88/17.34 (144) ~ (all_52_4 = all_52_12)
% 113.88/17.34 (145) ~ (all_52_1 = all_52_3)
% 113.88/17.34 (146) all_56_1 = all_52_8
% 113.88/17.34 (147) op(e0, all_4_2) = all_4_1
% 113.88/17.34 (148) all_58_8 = all_6_2
% 113.88/17.34 (149) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.34 (150) ~ (all_10_0 = e1)
% 113.88/17.34 (151) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 113.88/17.34 (152) all_56_4 = all_52_9
% 113.88/17.34 (153) all_58_9 = all_52_12
% 113.88/17.34 (154) all_56_5 = all_52_13
% 113.88/17.34 (155) op(e2, e1) = all_52_9
% 113.88/17.34 (156) ~ (all_52_3 = all_4_2)
% 113.88/17.34 (157) ~ (all_52_6 = all_6_2)
% 113.88/17.34 (158) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.88/17.34 (159) all_56_6 = all_52_2
% 113.88/17.34 (160) ~ (all_52_13 = all_4_2)
% 113.88/17.34 (161) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 113.88/17.34 (162) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 113.88/17.34 (163) all_58_12 = all_52_3
% 113.88/17.34 (164) ~ (all_52_2 = all_52_14)
% 113.88/17.34 (165) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 113.88/17.34 (166) ~ (all_52_8 = all_52_9)
% 113.88/17.34 (167) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.88/17.34 (168) op(e2, e0) = all_52_13
% 113.88/17.34 (169) ~ (all_52_12 = all_4_2)
% 113.88/17.34 (170) ~ (all_52_3 = all_10_2)
% 113.88/17.34 (171) op(e1, e3) = all_52_2
% 113.88/17.34 (172) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 113.88/17.34 (173) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 113.88/17.34 (174) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 113.88/17.34 (175) op(e1, e1) = all_6_2
% 113.88/17.34 (176) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 113.88/17.34 (177) ~ (all_52_8 = all_52_12)
% 113.88/17.35 (178) all_56_8 = all_52_14
% 113.88/17.35 (179) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 113.88/17.35 (180) all_26_1 = all_4_1
% 113.88/17.35 (181) ~ (all_52_4 = all_10_2)
% 113.88/17.35 (182) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 113.88/17.35 (183) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 113.88/17.35 (184) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.35 (185) all_56_0 = all_52_4
% 113.88/17.35 (186) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 113.88/17.35 (187) ~ (e3 = e2)
% 113.88/17.35 (188) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 113.88/17.35 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 113.88/17.35 (189) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 113.88/17.35 (190) all_54_4 = all_52_1
% 113.88/17.35 (191) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 113.88/17.35 (192) all_54_15 = all_4_2
% 113.88/17.35 (193) op(e2, all_8_2) = e1
% 113.88/17.35 (194) ~ (all_6_2 = e1)
% 113.88/17.35 (195) ~ (all_52_6 = all_52_7)
% 113.88/17.35 (196) ~ (all_52_3 = all_52_11)
% 113.88/17.35 (197) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.88/17.35 (198) all_54_12 = all_52_3
% 113.88/17.35 (199) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.88/17.35 (200) ~ (e1 = e0)
% 113.88/17.35 (201) ~ (all_52_3 = all_52_7)
% 113.88/17.35 (202) all_26_0 = all_4_0
% 113.88/17.35
% 113.88/17.35 Begin of proof
% 113.88/17.35 |
% 113.88/17.35 | BETA: splitting (179) gives:
% 113.88/17.35 |
% 113.88/17.35 | Case 1:
% 113.88/17.35 | |
% 113.88/17.35 | | (203) ~ (all_26_0 = e1)
% 113.88/17.35 | |
% 113.88/17.35 | | REDUCE: (202), (203) imply:
% 113.88/17.35 | | (204) ~ (all_4_0 = e1)
% 113.88/17.35 | |
% 113.88/17.35 | | BETA: splitting (7) gives:
% 113.88/17.35 | |
% 113.88/17.35 | | Case 1:
% 113.88/17.35 | | |
% 113.88/17.35 | | | (205) ~ (all_32_1 = e1)
% 113.88/17.35 | | |
% 113.88/17.35 | | | REDUCE: (107), (205) imply:
% 113.88/17.35 | | | (206) ~ (all_10_1 = e1)
% 113.88/17.35 | | |
% 113.88/17.35 | | | BETA: splitting (55) gives:
% 113.88/17.35 | | |
% 113.88/17.35 | | | Case 1:
% 113.88/17.35 | | | |
% 113.88/17.35 | | | | (207) ~ (all_38_1 = e2)
% 113.88/17.35 | | | |
% 113.88/17.35 | | | | REDUCE: (17), (207) imply:
% 113.88/17.35 | | | | (208) ~ (all_10_1 = e2)
% 113.88/17.35 | | | |
% 113.88/17.35 | | | | BETA: splitting (108) gives:
% 113.88/17.35 | | | |
% 113.88/17.35 | | | | Case 1:
% 113.88/17.35 | | | | |
% 113.88/17.35 | | | | | (209) ~ (all_56_14 = e2)
% 113.88/17.35 | | | | |
% 113.88/17.35 | | | | | REDUCE: (15), (209) imply:
% 113.88/17.35 | | | | | (210) ~ (all_6_2 = e2)
% 113.88/17.35 | | | | |
% 113.88/17.35 | | | | | BETA: splitting (109) gives:
% 113.88/17.35 | | | | |
% 113.88/17.35 | | | | | Case 1:
% 113.88/17.35 | | | | | |
% 113.88/17.35 | | | | | | (211) ~ (all_56_12 = e2)
% 113.88/17.35 | | | | | |
% 113.88/17.35 | | | | | | REDUCE: (34), (211) imply:
% 113.88/17.35 | | | | | | (212) ~ (all_10_2 = e2)
% 113.88/17.35 | | | | | |
% 113.88/17.35 | | | | | | BETA: splitting (151) gives:
% 113.88/17.35 | | | | | |
% 113.88/17.35 | | | | | | Case 1:
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | (213) ~ (all_56_15 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (115), (213) imply:
% 113.88/17.35 | | | | | | | (214) ~ (all_4_2 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (13), (15), (16), (18), (24),
% 113.88/17.35 | | | | | | | (26), (29), (32), (33), (34), (35), (36), (39), (40),
% 113.88/17.35 | | | | | | | (43), (47), (49), (53), (56), (59), (60), (62), (63),
% 113.88/17.35 | | | | | | | (64), (65), (66), (70), (71), (74), (75), (77), (78),
% 113.88/17.35 | | | | | | | (80), (81), (83), (84), (85), (86), (88), (89), (91),
% 113.88/17.35 | | | | | | | (94), (97), (98), (99), (104), (106), (110), (111),
% 113.88/17.35 | | | | | | | (112), (113), (114), (115), (116), (117), (118), (119),
% 113.88/17.35 | | | | | | | (123), (124), (125), (126), (128), (130), (132), (133),
% 113.88/17.35 | | | | | | | (137), (139), (145), (146), (148), (149), (152), (153),
% 113.88/17.35 | | | | | | | (154), (155), (156), (157), (159), (160), (161), (162),
% 113.88/17.35 | | | | | | | (163), (167), (168), (170), (172), (173), (175), (176),
% 113.88/17.35 | | | | | | | (178), (183), (184), (187), (188), (190), (192), (193),
% 113.88/17.35 | | | | | | | (194), (198), (201), (210), (212), (214) are
% 113.88/17.35 | | | | | | | inconsistent by sub-proof #120.
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | Case 2:
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | (215) all_56_15 = e3
% 113.88/17.35 | | | | | | | (216) ~ (all_56_9 = e0)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | COMBINE_EQS: (115), (215) imply:
% 113.88/17.35 | | | | | | | (217) all_4_2 = e3
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | SIMP: (217) implies:
% 113.88/17.35 | | | | | | | (218) all_4_2 = e3
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (91), (216) imply:
% 113.88/17.35 | | | | | | | (219) ~ (all_52_3 = e0)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (156), (218) imply:
% 113.88/17.35 | | | | | | | (220) ~ (all_52_3 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (23), (218) imply:
% 113.88/17.35 | | | | | | | (221) ~ (all_52_7 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (119), (218) imply:
% 113.88/17.35 | | | | | | | (222) ~ (all_52_11 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (169), (218) imply:
% 113.88/17.35 | | | | | | | (223) ~ (all_52_12 = e3)
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (46), (218) imply:
% 113.88/17.35 | | | | | | | (224) op(all_4_1, e3) = all_4_0
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | REDUCE: (147), (218) imply:
% 113.88/17.35 | | | | | | | (225) op(e0, e3) = all_4_1
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | BETA: splitting (10) gives:
% 113.88/17.35 | | | | | | |
% 113.88/17.35 | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | |
% 113.88/17.35 | | | | | | | | (226) ~ (all_56_6 = e1)
% 113.88/17.35 | | | | | | | |
% 113.88/17.35 | | | | | | | | REDUCE: (159), (226) imply:
% 113.88/17.35 | | | | | | | | (227) ~ (all_52_2 = e1)
% 113.88/17.35 | | | | | | | |
% 113.88/17.35 | | | | | | | | BETA: splitting (54) gives:
% 113.88/17.35 | | | | | | | |
% 113.88/17.35 | | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | (228) ~ (all_56_3 = e2)
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | REDUCE: (16), (228) imply:
% 113.88/17.35 | | | | | | | | | (229) ~ (all_52_1 = e2)
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | GROUND_INST: instantiating (49) with all_52_3, all_4_1, e3, e0,
% 113.88/17.35 | | | | | | | | | simplifying with (103), (225) gives:
% 113.88/17.35 | | | | | | | | | (230) all_52_3 = all_4_1
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | BETA: splitting (184) gives:
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | (231) all_58_2 = e2
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | REF_CLOSE: (99), (229), (231) are inconsistent by sub-proof
% 113.88/17.35 | | | | | | | | | | #335.
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | Case 2:
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | (232) ~ (all_58_2 = e2)
% 113.88/17.35 | | | | | | | | | | (233) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | BETA: splitting (233) gives:
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | (234) all_58_3 = e2
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | COMBINE_EQS: (64), (234) imply:
% 113.88/17.35 | | | | | | | | | | | (235) all_8_2 = e2
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | REDUCE: (133), (235) imply:
% 113.88/17.35 | | | | | | | | | | | (236) $false
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | Case 2:
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | (237) ~ (all_58_3 = e2)
% 113.88/17.35 | | | | | | | | | | | (238) all_58_5 = e2 | all_58_10 = e2
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | BETA: splitting (238) gives:
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | (239) all_58_5 = e2
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | COMBINE_EQS: (89), (239) imply:
% 113.88/17.35 | | | | | | | | | | | | (240) all_52_9 = e2
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | SIMP: (240) implies:
% 113.88/17.35 | | | | | | | | | | | | (241) all_52_9 = e2
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | COMBINE_EQS: (152), (241) imply:
% 113.88/17.35 | | | | | | | | | | | | (242) all_56_4 = e2
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | REDUCE: (9), (241) imply:
% 113.88/17.35 | | | | | | | | | | | | (243) ~ (all_8_2 = e2)
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | BETA: splitting (100) gives:
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | Case 1:
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | (244) ~ (all_56_4 = e2)
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | REDUCE: (242), (244) imply:
% 113.88/17.35 | | | | | | | | | | | | | (245) $false
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | Case 2:
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | (246) ~ (all_56_12 = e1)
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | REDUCE: (34), (246) imply:
% 113.88/17.35 | | | | | | | | | | | | | (247) ~ (all_10_2 = e1)
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | | REF_CLOSE: (6), (10), (13), (14), (15), (18), (20), (22),
% 113.88/17.35 | | | | | | | | | | | | | (24), (27), (29), (32), (34), (38), (40), (47),
% 113.88/17.35 | | | | | | | | | | | | | (49), (56), (57), (61), (64), (67), (70), (76),
% 113.88/17.35 | | | | | | | | | | | | | (77), (79), (85), (89), (91), (94), (95), (98),
% 113.88/17.35 | | | | | | | | | | | | | (99), (104), (106), (111), (113), (117), (121),
% 113.88/17.35 | | | | | | | | | | | | | (125), (128), (129), (130), (133), (137), (138),
% 113.88/17.35 | | | | | | | | | | | | | (139), (148), (149), (150), (152), (154), (157),
% 113.88/17.35 | | | | | | | | | | | | | (159), (163), (178), (181), (184), (185), (186),
% 113.88/17.35 | | | | | | | | | | | | | (188), (191), (194), (206), (208), (215), (223),
% 113.88/17.35 | | | | | | | | | | | | | (247) are inconsistent by sub-proof #421.
% 113.88/17.35 | | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | End of split
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | Case 2:
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | (248) all_58_10 = e2
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 113.88/17.35 | | | | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (43),
% 113.88/17.35 | | | | | | | | | | | | (45), (47), (49), (50), (51), (53), (56), (59),
% 113.88/17.35 | | | | | | | | | | | | (64), (69), (70), (71), (74), (78), (80), (82),
% 113.88/17.35 | | | | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 113.88/17.35 | | | | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 113.88/17.35 | | | | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 113.88/17.35 | | | | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 113.88/17.35 | | | | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 113.88/17.35 | | | | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 113.88/17.35 | | | | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 113.88/17.35 | | | | | | | | | | | | (212), (219), (220), (221), (222), (224), (225),
% 113.88/17.35 | | | | | | | | | | | | (227), (229), (248) are inconsistent by sub-proof
% 113.88/17.35 | | | | | | | | | | | | #112.
% 113.88/17.35 | | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | | End of split
% 113.88/17.35 | | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | | End of split
% 113.88/17.35 | | | | | | | | | |
% 113.88/17.35 | | | | | | | | | End of split
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | Case 2:
% 113.88/17.35 | | | | | | | | |
% 113.88/17.35 | | | | | | | | | (249) ~ (all_56_15 = e3)
% 113.88/17.35 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (215), (249) imply:
% 113.88/17.36 | | | | | | | | | (250) $false
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | CLOSE: (250) is inconsistent.
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | End of split
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | Case 2:
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | (251) ~ (all_56_15 = e3)
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | REDUCE: (215), (251) imply:
% 113.88/17.36 | | | | | | | | (252) $false
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | CLOSE: (252) is inconsistent.
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | End of split
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | End of split
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | Case 2:
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | (253) all_56_12 = e2
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | COMBINE_EQS: (34), (253) imply:
% 113.88/17.36 | | | | | | (254) all_10_2 = e2
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | SIMP: (254) implies:
% 113.88/17.36 | | | | | | (255) all_10_2 = e2
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | REF_CLOSE: (6), (13), (14), (15), (22), (24), (32), (38), (47),
% 113.88/17.36 | | | | | | (49), (56), (61), (64), (67), (76), (77), (79), (85),
% 113.88/17.36 | | | | | | (89), (91), (95), (98), (99), (106), (113), (117), (121),
% 113.88/17.36 | | | | | | (125), (128), (129), (130), (133), (138), (139), (150),
% 113.88/17.36 | | | | | | (152), (154), (157), (163), (181), (184), (185), (186),
% 113.88/17.36 | | | | | | (188), (191), (194), (206), (253), (255) are inconsistent
% 113.88/17.36 | | | | | | by sub-proof #425.
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | End of split
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | Case 2:
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | (256) all_56_14 = e2
% 113.88/17.36 | | | | | (257) ~ (all_56_10 = e0)
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | REF_CLOSE: (9), (13), (15), (16), (24), (25), (30), (33), (36), (43),
% 113.88/17.36 | | | | | (48), (49), (54), (59), (60), (62), (64), (71), (78), (79),
% 113.88/17.36 | | | | | (80), (89), (91), (98), (99), (102), (104), (106), (112),
% 113.88/17.36 | | | | | (114), (115), (117), (118), (125), (126), (127), (128),
% 113.88/17.36 | | | | | (130), (132), (133), (140), (146), (151), (153), (154),
% 113.88/17.36 | | | | | (155), (160), (162), (163), (166), (168), (173), (176),
% 113.88/17.36 | | | | | (184), (185), (188), (189), (192), (193), (200), (256),
% 113.88/17.36 | | | | | (257) are inconsistent by sub-proof #104.
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | End of split
% 113.88/17.36 | | | |
% 113.88/17.36 | | | Case 2:
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | (258) all_38_1 = e2
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | COMBINE_EQS: (17), (258) imply:
% 113.88/17.36 | | | | (259) all_10_1 = e2
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | SIMP: (259) implies:
% 113.88/17.36 | | | | (260) all_10_1 = e2
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | REDUCE: (76), (260) imply:
% 113.88/17.36 | | | | (261) op(e2, all_10_2) = all_10_0
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | REDUCE: (121), (260) imply:
% 113.88/17.36 | | | | (262) op(e3, all_10_2) = e2
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | BETA: splitting (108) gives:
% 113.88/17.36 | | | |
% 113.88/17.36 | | | | Case 1:
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | (263) ~ (all_56_14 = e2)
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | REDUCE: (15), (263) imply:
% 113.88/17.36 | | | | | (264) ~ (all_6_2 = e2)
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | BETA: splitting (109) gives:
% 113.88/17.36 | | | | |
% 113.88/17.36 | | | | | Case 1:
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | (265) ~ (all_56_12 = e2)
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | REDUCE: (34), (265) imply:
% 113.88/17.36 | | | | | | (266) ~ (all_10_2 = e2)
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | BETA: splitting (151) gives:
% 113.88/17.36 | | | | | |
% 113.88/17.36 | | | | | | Case 1:
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | (267) ~ (all_56_15 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (115), (267) imply:
% 113.88/17.36 | | | | | | | (268) ~ (all_4_2 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (13), (15), (16), (18), (24),
% 113.88/17.36 | | | | | | | (26), (29), (32), (33), (34), (35), (36), (39), (40),
% 113.88/17.36 | | | | | | | (43), (47), (49), (53), (56), (59), (60), (62), (63),
% 113.88/17.36 | | | | | | | (64), (65), (66), (70), (71), (74), (75), (77), (78),
% 113.88/17.36 | | | | | | | (80), (81), (83), (84), (85), (86), (88), (89), (91),
% 113.88/17.36 | | | | | | | (94), (97), (98), (99), (104), (106), (110), (111),
% 113.88/17.36 | | | | | | | (112), (113), (114), (115), (116), (117), (118), (119),
% 113.88/17.36 | | | | | | | (123), (124), (125), (126), (128), (130), (132), (133),
% 113.88/17.36 | | | | | | | (137), (139), (145), (146), (148), (149), (152), (153),
% 113.88/17.36 | | | | | | | (154), (155), (156), (157), (159), (160), (161), (162),
% 113.88/17.36 | | | | | | | (163), (167), (168), (170), (172), (173), (175), (176),
% 113.88/17.36 | | | | | | | (178), (183), (184), (187), (188), (190), (192), (193),
% 113.88/17.36 | | | | | | | (194), (198), (201), (264), (266), (268) are
% 113.88/17.36 | | | | | | | inconsistent by sub-proof #120.
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | Case 2:
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | (269) all_56_15 = e3
% 113.88/17.36 | | | | | | | (270) ~ (all_56_9 = e0)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | COMBINE_EQS: (115), (269) imply:
% 113.88/17.36 | | | | | | | (271) all_4_2 = e3
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | SIMP: (271) implies:
% 113.88/17.36 | | | | | | | (272) all_4_2 = e3
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (91), (270) imply:
% 113.88/17.36 | | | | | | | (273) ~ (all_52_3 = e0)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (156), (272) imply:
% 113.88/17.36 | | | | | | | (274) ~ (all_52_3 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (23), (272) imply:
% 113.88/17.36 | | | | | | | (275) ~ (all_52_7 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (119), (272) imply:
% 113.88/17.36 | | | | | | | (276) ~ (all_52_11 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (169), (272) imply:
% 113.88/17.36 | | | | | | | (277) ~ (all_52_12 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (160), (272) imply:
% 113.88/17.36 | | | | | | | (278) ~ (all_52_13 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (110), (272) imply:
% 113.88/17.36 | | | | | | | (279) ~ (all_52_14 = e3)
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (46), (272) imply:
% 113.88/17.36 | | | | | | | (280) op(all_4_1, e3) = all_4_0
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | REDUCE: (147), (272) imply:
% 113.88/17.36 | | | | | | | (281) op(e0, e3) = all_4_1
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | BETA: splitting (54) gives:
% 113.88/17.36 | | | | | | |
% 113.88/17.36 | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | (282) ~ (all_56_3 = e2)
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | REDUCE: (16), (282) imply:
% 113.88/17.36 | | | | | | | | (283) ~ (all_52_1 = e2)
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | BETA: splitting (10) gives:
% 113.88/17.36 | | | | | | | |
% 113.88/17.36 | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | (284) ~ (all_56_6 = e1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (159), (284) imply:
% 113.88/17.36 | | | | | | | | | (285) ~ (all_52_2 = e1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | GROUND_INST: instantiating (49) with all_52_3, all_4_1, e3, e0,
% 113.88/17.36 | | | | | | | | | simplifying with (103), (281) gives:
% 113.88/17.36 | | | | | | | | | (286) all_52_3 = all_4_1
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | COMBINE_EQS: (198), (286) imply:
% 113.88/17.36 | | | | | | | | | (287) all_54_12 = all_4_1
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | COMBINE_EQS: (163), (286) imply:
% 113.88/17.36 | | | | | | | | | (288) all_58_12 = all_4_1
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (145), (286) imply:
% 113.88/17.36 | | | | | | | | | (289) ~ (all_52_1 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (74), (286) imply:
% 113.88/17.36 | | | | | | | | | (290) ~ (all_52_2 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (201), (286) imply:
% 113.88/17.36 | | | | | | | | | (291) ~ (all_52_7 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | SIMP: (291) implies:
% 113.88/17.36 | | | | | | | | | (292) ~ (all_52_7 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (196), (286) imply:
% 113.88/17.36 | | | | | | | | | (293) ~ (all_52_11 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | SIMP: (293) implies:
% 113.88/17.36 | | | | | | | | | (294) ~ (all_52_11 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (170), (286) imply:
% 113.88/17.36 | | | | | | | | | (295) ~ (all_10_2 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | SIMP: (295) implies:
% 113.88/17.36 | | | | | | | | | (296) ~ (all_10_2 = all_4_1)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (274), (286) imply:
% 113.88/17.36 | | | | | | | | | (297) ~ (all_4_1 = e3)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | REDUCE: (273), (286) imply:
% 113.88/17.36 | | | | | | | | | (298) ~ (all_4_1 = e0)
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | BETA: splitting (41) gives:
% 113.88/17.36 | | | | | | | | |
% 113.88/17.36 | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | (299) ~ (all_56_8 = e1)
% 113.88/17.36 | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | REDUCE: (178), (299) imply:
% 113.88/17.36 | | | | | | | | | | (300) ~ (all_52_14 = e1)
% 113.88/17.36 | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | BETA: splitting (137) gives:
% 113.88/17.36 | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | (301) all_58_6 = e1
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | REF_CLOSE: (111), (285), (301) are inconsistent by sub-proof
% 113.88/17.36 | | | | | | | | | | | #452.
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | Case 2:
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | (302) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | BETA: splitting (302) gives:
% 113.88/17.36 | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | (303) all_58_7 = e1
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | COMBINE_EQS: (6), (303) imply:
% 113.88/17.36 | | | | | | | | | | | | (304) all_52_6 = e1
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | REDUCE: (141), (304) imply:
% 113.88/17.36 | | | | | | | | | | | | (305) ~ (all_52_4 = e1)
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | REDUCE: (157), (304) imply:
% 113.88/17.36 | | | | | | | | | | | | (306) ~ (all_6_2 = e1)
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | BETA: splitting (183) gives:
% 113.88/17.36 | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | (307) ~ (all_56_12 = e1)
% 113.88/17.36 | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | REDUCE: (34), (307) imply:
% 113.88/17.36 | | | | | | | | | | | | | (308) ~ (all_10_2 = e1)
% 113.88/17.36 | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 113.88/17.36 | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | (309) all_54_0 = e3
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | REF_CLOSE: (18), (104), (309) are inconsistent by sub-proof
% 113.88/17.36 | | | | | | | | | | | | | | #451.
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | Case 2:
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | (310) ~ (all_54_0 = e3)
% 113.88/17.36 | | | | | | | | | | | | | | (311) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 113.88/17.36 | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | (312) all_54_0 = e2
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | REF_CLOSE: (18), (266), (312) are inconsistent by sub-proof
% 113.88/17.36 | | | | | | | | | | | | | | | #450.
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | Case 2:
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | (313) ~ (all_54_0 = e2)
% 113.88/17.36 | | | | | | | | | | | | | | | (314) all_54_0 = e1 | all_54_0 = e0
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 113.88/17.36 | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | Case 1:
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | (315) all_54_0 = e1
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (308), (315) are inconsistent by sub-proof
% 113.88/17.36 | | | | | | | | | | | | | | | | #449.
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | Case 2:
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | (316) all_54_0 = e0
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (316) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (317) all_10_2 = e0
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | SIMP: (317) implies:
% 113.88/17.36 | | | | | | | | | | | | | | | | (318) all_10_2 = e0
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (319) all_58_0 = e0
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REDUCE: (113), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (320) ~ (all_52_1 = e0)
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REDUCE: (4), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (321) ~ (all_52_2 = e0)
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REDUCE: (181), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (322) ~ (all_52_4 = e0)
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REDUCE: (29), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (323) ~ (all_52_12 = e0)
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.36 | | | | | | | | | | | | | | | | REDUCE: (104), (318) imply:
% 113.88/17.36 | | | | | | | | | | | | | | | | (324) ~ (e3 = e0)
% 113.88/17.36 | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | SIMP: (324) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | (325) ~ (e3 = e0)
% 113.88/17.37 | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | REDUCE: (262), (318) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | (326) op(e3, e0) = e2
% 113.88/17.37 | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | REDUCE: (261), (318) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | (327) op(e2, e0) = all_10_0
% 113.88/17.37 | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | (328) ~ (all_56_5 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (154), (328) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (329) ~ (all_52_13 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (49) with all_52_13, all_10_0, e0,
% 113.88/17.37 | | | | | | | | | | | | | | | | | e2, simplifying with (168), (327) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (330) all_52_13 = all_10_0
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (49) with all_52_12, e2, e0, e3,
% 113.88/17.37 | | | | | | | | | | | | | | | | | simplifying with (57), (326) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (331) all_52_12 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (330) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (332) all_54_7 = all_10_0
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (330) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (333) all_56_5 = all_10_0
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (144), (331) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (334) ~ (all_52_4 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (277), (331) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (335) ~ (e3 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (323), (331) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (336) ~ (e2 = e0)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (118), (330) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (337) ~ (all_10_0 = all_8_2)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | REDUCE: (278), (330) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | (338) ~ (all_10_0 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | (339) all_58_6 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (339) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | (340) all_52_2 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | SIMP: (340) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | (341) all_52_2 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (342) all_54_1 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (342) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (343) all_52_4 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | SIMP: (343) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (344) all_52_4 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | REDUCE: (61), (344) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (345) ~ (all_52_7 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | REDUCE: (88), (344) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (346) ~ (all_8_2 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | SIMP: (346) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (347) ~ (all_8_2 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | (348) all_54_5 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (347), (348) are inconsistent by sub-proof
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | #339.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | (349) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | (350) all_54_5 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (133), (350) are inconsistent by sub-proof
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | #338.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_54_5 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | (352) all_54_5 = e1 | all_54_5 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | (353) all_54_7 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (353) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | (354) all_10_0 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | SIMP: (354) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | (355) all_10_0 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (355) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | (356) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (356) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | (357) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_6 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (358) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | (359) e3 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (359) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | (360) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | (361) all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_7 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (362) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | (363) e3 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (363) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | (364) e3 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (364) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | (365) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | (366) all_58_8 = e3 | all_58_11 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_8 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (367) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (368) all_6_2 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (368) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (369) op(e1, e1) = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_54_5 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (32), (49), (64), (89), (99), (114),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (124), (130), (133), (152), (175), (184),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (329), (369), (370) are inconsistent by sub-proof
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | #102.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_54_5 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (371) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_8_2 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (372) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_8_2 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (373) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ~ (all_10_0 = e0)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (357) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) all_54_7 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (375) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) all_10_0 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (376) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) all_10_0 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (377) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) all_56_5 = e2
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (43),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (49), (50), (51), (53), (56), (59),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (69), (70), (71), (74), (78), (80), (82),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (266), (273), (274), (275), (276), (280), (281),
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (283), (285), (378) are inconsistent by sub-proof
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | #113.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) all_54_7 = e1 | all_54_7 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_54_7 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (380) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_10_0 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (381) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_10_0 = e1
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (382) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) all_54_7 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (384) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_10_0 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (385) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_10_0 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (386) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (387) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_58_11 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (388) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (389) all_52_14 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (389) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | (390) $false
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (391) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (305), (322), (334), (391) are inconsistent
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | by sub-proof #101.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | (392) ~ (all_58_6 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | REDUCE: (111), (392) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | (393) ~ (all_52_2 = e2)
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (394) all_54_4 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (190), (394) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (395) all_52_1 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | SIMP: (395) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (396) all_52_1 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | REDUCE: (142), (396) imply:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (397) ~ (all_52_2 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | SIMP: (397) implies:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | (398) ~ (all_52_2 = e3)
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | (399) all_54_8 = e3
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (398), (399) are inconsistent by sub-proof
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | | #399.
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.37 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | | (400) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (285), (321), (393), (400) are inconsistent
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | | by sub-proof #381.
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | (401) ~ (all_54_4 = e3)
% 113.88/17.38 | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | REDUCE: (190), (401) imply:
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | (402) ~ (all_52_1 = e3)
% 113.88/17.38 | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (31), (39), (49), (80), (99), (187), (190),
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | (204), (280), (283), (288), (297), (319), (320),
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | (325), (336), (402) are inconsistent by sub-proof
% 113.88/17.38 | | | | | | | | | | | | | | | | | | | #322.
% 113.88/17.38 | | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | (403) all_56_5 = e2
% 113.88/17.38 | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (43),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (45), (47), (49), (50), (51), (53), (56), (59),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (64), (69), (70), (71), (74), (78), (80), (82),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (266), (273), (274), (275), (276), (280), (281),
% 113.88/17.38 | | | | | | | | | | | | | | | | | (283), (285), (403) are inconsistent by sub-proof
% 113.88/17.38 | | | | | | | | | | | | | | | | | #113.
% 113.88/17.38 | | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | (404) all_56_12 = e1
% 113.88/17.38 | | | | | | | | | | | | | (405) ~ (all_56_11 = e0)
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | COMBINE_EQS: (34), (404) imply:
% 113.88/17.38 | | | | | | | | | | | | | (406) all_10_2 = e1
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | COMBINE_EQS: (36), (406) imply:
% 113.88/17.38 | | | | | | | | | | | | | (407) all_58_0 = e1
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | REDUCE: (24), (405) imply:
% 113.88/17.38 | | | | | | | | | | | | | (408) ~ (all_52_11 = e0)
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | REDUCE: (113), (406) imply:
% 113.88/17.38 | | | | | | | | | | | | | (409) ~ (all_52_1 = e1)
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | REDUCE: (296), (406) imply:
% 113.88/17.38 | | | | | | | | | | | | | (410) ~ (all_4_1 = e1)
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | SIMP: (410) implies:
% 113.88/17.38 | | | | | | | | | | | | | (411) ~ (all_4_1 = e1)
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (15), (19), (31), (33), (37), (39),
% 113.88/17.38 | | | | | | | | | | | | | (43), (45), (47), (49), (50), (51), (53), (56),
% 113.88/17.38 | | | | | | | | | | | | | (59), (64), (69), (78), (82), (85), (86), (87),
% 113.88/17.38 | | | | | | | | | | | | | (89), (99), (100), (101), (108), (114), (117),
% 113.88/17.38 | | | | | | | | | | | | | (118), (122), (132), (133), (134), (140), (142),
% 113.88/17.38 | | | | | | | | | | | | | (146), (152), (154), (155), (158), (162), (166),
% 113.88/17.38 | | | | | | | | | | | | | (167), (173), (184), (190), (193), (197), (204),
% 113.88/17.38 | | | | | | | | | | | | | (275), (276), (280), (285), (287), (289), (290),
% 113.88/17.38 | | | | | | | | | | | | | (292), (294), (297), (298), (404), (407), (408),
% 113.88/17.38 | | | | | | | | | | | | | (409), (411) are inconsistent by sub-proof #115.
% 113.88/17.38 | | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | (412) all_58_8 = e1 | all_58_11 = e1
% 113.88/17.38 | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | | REF_CLOSE: (70), (148), (194), (300), (412) are inconsistent
% 113.88/17.38 | | | | | | | | | | | | by sub-proof #445.
% 113.88/17.38 | | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | (413) all_56_8 = e1
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 113.88/17.38 | | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (41),
% 113.88/17.38 | | | | | | | | | | (43), (45), (47), (49), (50), (51), (53), (56),
% 113.88/17.38 | | | | | | | | | | (59), (64), (69), (70), (74), (78), (80), (82),
% 113.88/17.38 | | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 113.88/17.38 | | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 113.88/17.38 | | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 113.88/17.38 | | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 113.88/17.38 | | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 113.88/17.38 | | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 113.88/17.38 | | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 113.88/17.38 | | | | | | | | | | (266), (273), (274), (275), (276), (280), (281),
% 113.88/17.38 | | | | | | | | | | (283), (285), (413) are inconsistent by sub-proof
% 113.88/17.38 | | | | | | | | | | #100.
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | End of split
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | (414) ~ (all_56_15 = e3)
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | REDUCE: (269), (414) imply:
% 113.88/17.38 | | | | | | | | | (415) $false
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | CLOSE: (415) is inconsistent.
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | End of split
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | (416) ~ (all_56_15 = e3)
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | REDUCE: (269), (416) imply:
% 113.88/17.38 | | | | | | | | (417) $false
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | CLOSE: (417) is inconsistent.
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | End of split
% 113.88/17.38 | | | | | | |
% 113.88/17.38 | | | | | | End of split
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | Case 2:
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | (418) all_56_12 = e2
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | REF_CLOSE: (14), (34), (49), (181), (262), (418) are inconsistent by
% 113.88/17.38 | | | | | | sub-proof #300.
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | End of split
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | Case 2:
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | (419) all_56_14 = e2
% 113.88/17.38 | | | | | (420) ~ (all_56_10 = e0)
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | REF_CLOSE: (9), (13), (15), (16), (24), (25), (30), (33), (36), (43),
% 113.88/17.38 | | | | | (48), (49), (54), (59), (60), (62), (64), (71), (78), (79),
% 113.88/17.38 | | | | | (80), (89), (91), (98), (99), (102), (104), (106), (112),
% 113.88/17.38 | | | | | (114), (115), (117), (118), (125), (126), (127), (128),
% 113.88/17.38 | | | | | (130), (132), (133), (140), (146), (151), (153), (154),
% 113.88/17.38 | | | | | (155), (160), (162), (163), (166), (168), (173), (176),
% 113.88/17.38 | | | | | (184), (185), (188), (189), (192), (193), (200), (419),
% 113.88/17.38 | | | | | (420) are inconsistent by sub-proof #104.
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | End of split
% 113.88/17.38 | | | |
% 113.88/17.38 | | | End of split
% 113.88/17.38 | | |
% 113.88/17.38 | | Case 2:
% 113.88/17.38 | | |
% 113.88/17.38 | | | (421) all_32_1 = e1
% 113.88/17.38 | | | (422) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 113.88/17.38 | | |
% 113.88/17.38 | | | COMBINE_EQS: (107), (421) imply:
% 113.88/17.38 | | | (423) all_10_1 = e1
% 113.88/17.38 | | |
% 113.88/17.38 | | | REDUCE: (76), (423) imply:
% 113.88/17.38 | | | (424) op(e1, all_10_2) = all_10_0
% 113.88/17.38 | | |
% 113.88/17.38 | | | REDUCE: (121), (423) imply:
% 113.88/17.38 | | | (425) op(e3, all_10_2) = e1
% 113.88/17.38 | | |
% 113.88/17.38 | | | BETA: splitting (108) gives:
% 113.88/17.38 | | |
% 113.88/17.38 | | | Case 1:
% 113.88/17.38 | | | |
% 113.88/17.38 | | | | (426) ~ (all_56_14 = e2)
% 113.88/17.38 | | | |
% 113.88/17.38 | | | | REDUCE: (15), (426) imply:
% 113.88/17.38 | | | | (427) ~ (all_6_2 = e2)
% 113.88/17.38 | | | |
% 113.88/17.38 | | | | BETA: splitting (109) gives:
% 113.88/17.38 | | | |
% 113.88/17.38 | | | | Case 1:
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | (428) ~ (all_56_12 = e2)
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | REDUCE: (34), (428) imply:
% 113.88/17.38 | | | | | (429) ~ (all_10_2 = e2)
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | BETA: splitting (151) gives:
% 113.88/17.38 | | | | |
% 113.88/17.38 | | | | | Case 1:
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | (430) ~ (all_56_15 = e3)
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | REDUCE: (115), (430) imply:
% 113.88/17.38 | | | | | | (431) ~ (all_4_2 = e3)
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | BETA: splitting (35) gives:
% 113.88/17.38 | | | | | |
% 113.88/17.38 | | | | | | Case 1:
% 113.88/17.38 | | | | | | |
% 113.88/17.38 | | | | | | | (432) ~ (all_56_7 = e1)
% 113.88/17.38 | | | | | | |
% 113.88/17.38 | | | | | | | REDUCE: (139), (432) imply:
% 113.88/17.38 | | | | | | | (433) ~ (all_52_6 = e1)
% 113.88/17.38 | | | | | | |
% 113.88/17.38 | | | | | | | BETA: splitting (77) gives:
% 113.88/17.38 | | | | | | |
% 113.88/17.38 | | | | | | | Case 1:
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | (434) ~ (all_56_14 = e3)
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | REDUCE: (15), (434) imply:
% 113.88/17.38 | | | | | | | | (435) ~ (all_6_2 = e3)
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | BETA: splitting (47) gives:
% 113.88/17.38 | | | | | | | |
% 113.88/17.38 | | | | | | | | Case 1:
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | (436) all_54_10 = e3
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | COMBINE_EQS: (56), (436) imply:
% 113.88/17.38 | | | | | | | | | (437) all_6_2 = e3
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | REDUCE: (435), (437) imply:
% 113.88/17.38 | | | | | | | | | (438) $false
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | CLOSE: (438) is inconsistent.
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | (439) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | BETA: splitting (439) gives:
% 113.88/17.38 | | | | | | | | |
% 113.88/17.38 | | | | | | | | | Case 1:
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | (440) all_54_10 = e2
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | COMBINE_EQS: (56), (440) imply:
% 113.88/17.38 | | | | | | | | | | (441) all_6_2 = e2
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | REDUCE: (427), (441) imply:
% 113.88/17.38 | | | | | | | | | | (442) $false
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | CLOSE: (442) is inconsistent.
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | (443) all_54_10 = e1 | all_54_10 = e0
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | BETA: splitting (443) gives:
% 113.88/17.38 | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | Case 1:
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | (444) all_54_10 = e1
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | COMBINE_EQS: (56), (444) imply:
% 113.88/17.38 | | | | | | | | | | | (445) all_6_2 = e1
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | REDUCE: (194), (445) imply:
% 113.88/17.38 | | | | | | | | | | | (446) $false
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | CLOSE: (446) is inconsistent.
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | Case 2:
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.38 | | | | | | | | | | | (447) all_54_10 = e0
% 113.88/17.38 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | COMBINE_EQS: (56), (447) imply:
% 113.88/17.39 | | | | | | | | | | | (448) all_6_2 = e0
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | COMBINE_EQS: (15), (448) imply:
% 113.88/17.39 | | | | | | | | | | | (449) all_56_14 = e0
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | REDUCE: (78), (448) imply:
% 113.88/17.39 | | | | | | | | | | | (450) ~ (all_52_11 = e0)
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | REDUCE: (40), (448) imply:
% 113.88/17.39 | | | | | | | | | | | (451) ~ (all_52_14 = e0)
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | BETA: splitting (66) gives:
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | (452) ~ (all_56_2 = e3)
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | REDUCE: (62), (452) imply:
% 113.88/17.39 | | | | | | | | | | | | (453) ~ (all_52_12 = e3)
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | BETA: splitting (85) gives:
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | (454) ~ (all_56_5 = e2)
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | REDUCE: (154), (454) imply:
% 113.88/17.39 | | | | | | | | | | | | | (455) ~ (all_52_13 = e2)
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | BETA: splitting (137) gives:
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | (456) all_58_6 = e1
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | COMBINE_EQS: (111), (456) imply:
% 113.88/17.39 | | | | | | | | | | | | | | (457) all_52_2 = e1
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | SIMP: (457) implies:
% 113.88/17.39 | | | | | | | | | | | | | | (458) all_52_2 = e1
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | COMBINE_EQS: (159), (458) imply:
% 113.88/17.39 | | | | | | | | | | | | | | (459) all_56_6 = e1
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | REDUCE: (74), (458) imply:
% 113.88/17.39 | | | | | | | | | | | | | | (460) ~ (all_52_3 = e1)
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | SIMP: (460) implies:
% 113.88/17.39 | | | | | | | | | | | | | | (461) ~ (all_52_3 = e1)
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | REDUCE: (4), (458) imply:
% 113.88/17.39 | | | | | | | | | | | | | | (462) ~ (all_10_2 = e1)
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | SIMP: (462) implies:
% 113.88/17.39 | | | | | | | | | | | | | | (463) ~ (all_10_2 = e1)
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | REF_CLOSE: (13), (18), (29), (32), (33), (34), (49), (64),
% 113.88/17.39 | | | | | | | | | | | | | | (65), (70), (83), (84), (86), (89), (94), (97),
% 113.88/17.39 | | | | | | | | | | | | | | (98), (99), (104), (106), (114), (117), (128),
% 113.88/17.39 | | | | | | | | | | | | | | (130), (133), (145), (149), (152), (153), (155),
% 113.88/17.39 | | | | | | | | | | | | | | (156), (161), (162), (163), (167), (170), (178),
% 113.88/17.39 | | | | | | | | | | | | | | (184), (187), (188), (193), (198), (201), (429),
% 113.88/17.39 | | | | | | | | | | | | | | (450), (451), (453), (455), (459), (461), (463)
% 113.88/17.39 | | | | | | | | | | | | | | are inconsistent by sub-proof #135.
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | (464) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (13), (15), (18), (23), (24),
% 113.88/17.39 | | | | | | | | | | | | | | (26), (28), (34), (36), (38), (43), (49), (59),
% 113.88/17.39 | | | | | | | | | | | | | | (60), (64), (69), (70), (73), (74), (82), (94),
% 113.88/17.39 | | | | | | | | | | | | | | (98), (104), (106), (110), (111), (115), (120),
% 113.88/17.39 | | | | | | | | | | | | | | (125), (128), (133), (146), (148), (149), (156),
% 113.88/17.39 | | | | | | | | | | | | | | (158), (163), (170), (172), (178), (183), (188),
% 113.88/17.39 | | | | | | | | | | | | | | (192), (194), (425), (429), (431), (433), (464)
% 113.88/17.39 | | | | | | | | | | | | | | are inconsistent by sub-proof #97.
% 113.88/17.39 | | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | (465) ~ (all_56_14 = e0)
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | REDUCE: (449), (465) imply:
% 113.88/17.39 | | | | | | | | | | | | | (466) $false
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | | CLOSE: (466) is inconsistent.
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | (467) ~ (all_56_14 = e0)
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | REDUCE: (449), (467) imply:
% 113.88/17.39 | | | | | | | | | | | | (468) $false
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | End of split
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | (469) all_56_14 = e3
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | BETA: splitting (63) gives:
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | (470) ~ (all_56_6 = e1)
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | REDUCE: (159), (470) imply:
% 113.88/17.39 | | | | | | | | | (471) ~ (all_52_2 = e1)
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | BETA: splitting (137) gives:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | (472) all_58_6 = e1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REF_CLOSE: (111), (471), (472) are inconsistent by sub-proof
% 113.88/17.39 | | | | | | | | | | #452.
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | (473) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (13), (15), (18), (23), (24),
% 113.88/17.39 | | | | | | | | | | (26), (28), (34), (36), (38), (43), (49), (59),
% 113.88/17.39 | | | | | | | | | | (60), (64), (69), (70), (73), (74), (82), (94),
% 113.88/17.39 | | | | | | | | | | (98), (104), (106), (110), (111), (115), (120),
% 113.88/17.39 | | | | | | | | | | (125), (128), (133), (146), (148), (149), (156),
% 113.88/17.39 | | | | | | | | | | (158), (163), (170), (172), (178), (183), (188),
% 113.88/17.39 | | | | | | | | | | (192), (194), (425), (429), (431), (433), (473)
% 113.88/17.39 | | | | | | | | | | are inconsistent by sub-proof #97.
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | End of split
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | (474) ~ (all_56_14 = e3)
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | REDUCE: (469), (474) imply:
% 113.88/17.39 | | | | | | | | | (475) $false
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | CLOSE: (475) is inconsistent.
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | End of split
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | End of split
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | Case 2:
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | (476) all_56_7 = e1
% 113.88/17.39 | | | | | | | (477) ~ (all_56_15 = e2)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | COMBINE_EQS: (139), (476) imply:
% 113.88/17.39 | | | | | | | (478) all_52_6 = e1
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | SIMP: (478) implies:
% 113.88/17.39 | | | | | | | (479) all_52_6 = e1
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | COMBINE_EQS: (6), (479) imply:
% 113.88/17.39 | | | | | | | (480) all_58_7 = e1
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | REDUCE: (115), (477) imply:
% 113.88/17.39 | | | | | | | (481) ~ (all_4_2 = e2)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | REDUCE: (21), (479) imply:
% 113.88/17.39 | | | | | | | (482) ~ (all_52_2 = e1)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | REDUCE: (123), (479) imply:
% 113.88/17.39 | | | | | | | (483) ~ (all_8_2 = e1)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | SIMP: (483) implies:
% 113.88/17.39 | | | | | | | (484) ~ (all_8_2 = e1)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | REDUCE: (157), (479) imply:
% 113.88/17.39 | | | | | | | (485) ~ (all_6_2 = e1)
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | BETA: splitting (60) gives:
% 113.88/17.39 | | | | | | |
% 113.88/17.39 | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | (486) all_54_15 = e3
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | COMBINE_EQS: (192), (486) imply:
% 113.88/17.39 | | | | | | | | (487) all_4_2 = e3
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | REDUCE: (431), (487) imply:
% 113.88/17.39 | | | | | | | | (488) $false
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | CLOSE: (488) is inconsistent.
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | (489) ~ (all_54_15 = e3)
% 113.88/17.39 | | | | | | | | (490) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | BETA: splitting (490) gives:
% 113.88/17.39 | | | | | | | |
% 113.88/17.39 | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | (491) all_54_15 = e2
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | COMBINE_EQS: (192), (491) imply:
% 113.88/17.39 | | | | | | | | | (492) all_4_2 = e2
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | REDUCE: (481), (492) imply:
% 113.88/17.39 | | | | | | | | | (493) $false
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | CLOSE: (493) is inconsistent.
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | (494) ~ (all_54_15 = e2)
% 113.88/17.39 | | | | | | | | | (495) all_54_15 = e1 | all_54_15 = e0
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | BETA: splitting (495) gives:
% 113.88/17.39 | | | | | | | | |
% 113.88/17.39 | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | (496) all_54_15 = e1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | COMBINE_EQS: (192), (496) imply:
% 113.88/17.39 | | | | | | | | | | (497) all_4_2 = e1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | COMBINE_EQS: (115), (497) imply:
% 113.88/17.39 | | | | | | | | | | (498) all_56_15 = e1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REDUCE: (156), (497) imply:
% 113.88/17.39 | | | | | | | | | | (499) ~ (all_52_3 = e1)
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REDUCE: (119), (497) imply:
% 113.88/17.39 | | | | | | | | | | (500) ~ (all_52_11 = e1)
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REDUCE: (481), (497) imply:
% 113.88/17.39 | | | | | | | | | | (501) ~ (e2 = e1)
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | SIMP: (501) implies:
% 113.88/17.39 | | | | | | | | | | (502) ~ (e2 = e1)
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REDUCE: (46), (497) imply:
% 113.88/17.39 | | | | | | | | | | (503) op(all_4_1, e1) = all_4_0
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | REDUCE: (147), (497) imply:
% 113.88/17.39 | | | | | | | | | | (504) op(e0, e1) = all_4_1
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | BETA: splitting (92) gives:
% 113.88/17.39 | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | (505) ~ (all_56_15 = e1)
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | REDUCE: (498), (505) imply:
% 113.88/17.39 | | | | | | | | | | | (506) $false
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | CLOSE: (506) is inconsistent.
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | Case 2:
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | (507) ~ (all_56_11 = e0)
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | REDUCE: (24), (507) imply:
% 113.88/17.39 | | | | | | | | | | | (508) ~ (all_52_11 = e0)
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | BETA: splitting (112) gives:
% 113.88/17.39 | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | (509) ~ (all_56_1 = e3)
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | REDUCE: (146), (509) imply:
% 113.88/17.39 | | | | | | | | | | | | (510) ~ (all_52_8 = e3)
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | BETA: splitting (165) gives:
% 113.88/17.39 | | | | | | | | | | | |
% 113.88/17.39 | | | | | | | | | | | | Case 1:
% 113.88/17.39 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | (511) ~ (all_56_4 = e2)
% 113.88/17.40 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | REDUCE: (152), (511) imply:
% 113.88/17.40 | | | | | | | | | | | | | (512) ~ (all_52_9 = e2)
% 113.88/17.40 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | GROUND_INST: instantiating (49) with all_52_11, all_4_1, e1,
% 113.88/17.40 | | | | | | | | | | | | | e0, simplifying with (131), (504) gives:
% 113.88/17.40 | | | | | | | | | | | | | (513) all_52_11 = all_4_1
% 113.88/17.40 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | COMBINE_EQS: (45), (513) imply:
% 113.88/17.40 | | | | | | | | | | | | | (514) all_54_14 = all_4_1
% 113.88/17.40 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | BETA: splitting (174) gives:
% 113.88/17.40 | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | (515) ~ (all_56_5 = e2)
% 113.88/17.40 | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | REDUCE: (154), (515) imply:
% 113.88/17.40 | | | | | | | | | | | | | | (516) ~ (all_52_13 = e2)
% 113.88/17.40 | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 113.88/17.40 | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | (517) all_58_2 = e2
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | COMBINE_EQS: (99), (517) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | (518) all_52_1 = e2
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | SIMP: (518) implies:
% 113.88/17.40 | | | | | | | | | | | | | | | (519) all_52_1 = e2
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | COMBINE_EQS: (16), (519) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | (520) all_56_3 = e2
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | REDUCE: (142), (519) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | (521) ~ (all_52_2 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | SIMP: (521) implies:
% 113.88/17.40 | | | | | | | | | | | | | | | (522) ~ (all_52_2 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | REDUCE: (145), (519) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | (523) ~ (all_52_3 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | SIMP: (523) implies:
% 113.88/17.40 | | | | | | | | | | | | | | | (524) ~ (all_52_3 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | REDUCE: (113), (519) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | (525) ~ (all_10_2 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 113.88/17.40 | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | (526) ~ (all_56_3 = e2)
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | REDUCE: (520), (526) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | (527) $false
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | CLOSE: (527) is inconsistent.
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | (528) ~ (all_56_14 = e3)
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | REDUCE: (15), (528) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | (529) ~ (all_6_2 = e3)
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | (530) all_54_10 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (530) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | (531) all_6_2 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | REDUCE: (529), (531) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | (532) $false
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | CLOSE: (532) is inconsistent.
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | (533) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | BETA: splitting (533) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | (534) all_54_10 = e2
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (534) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | (535) all_6_2 = e2
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | REDUCE: (427), (535) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | (536) $false
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | CLOSE: (536) is inconsistent.
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | (537) all_54_10 = e1 | all_54_10 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (538) all_58_6 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (538) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (539) all_52_2 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | SIMP: (539) implies:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (540) all_52_2 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | REDUCE: (74), (540) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (541) ~ (all_52_3 = e3)
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | SIMP: (541) implies:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (542) ~ (all_52_3 = e3)
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | REDUCE: (4), (540) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | (543) ~ (all_10_2 = e3)
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | (544) all_54_12 = e3
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (542), (544) are inconsistent by sub-proof
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | #410.
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | (545) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | (546) all_54_12 = e2
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (524), (546) are inconsistent by sub-proof
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | #409.
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | (547) all_54_12 = e1 | all_54_12 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (547) gives:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | (548) all_54_12 = e1
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (499), (548) are inconsistent by sub-proof
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | #408.
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | (549) all_54_12 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (549) imply:
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | (550) all_52_3 = e0
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.40 | | | | | | | | | | | | | | | | | | | | | | SIMP: (550) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | (551) all_52_3 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (551) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | (552) ~ (all_10_2 = e0)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | SIMP: (552) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | (553) ~ (all_10_2 = e0)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | (554) all_54_0 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (104), (554) are inconsistent by sub-proof
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | #451.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | (555) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | (556) all_58_0 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (556) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | (557) all_10_2 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (557) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | (558) ~ (all_52_8 = e1)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (557) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | (559) op(e3, e1) = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_54_10 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (194), (560) are inconsistent by sub-proof
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_54_10 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (561) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_6_2 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (562) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_6_2 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (563) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (564) ~ (all_52_8 = e0)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_54_2 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (510), (565) are inconsistent by sub-proof
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | #179.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (566) ~ (all_54_2 = e3)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_54_2 = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (568) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_52_8 = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (569) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_52_8 = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (570) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) op(e3, e1) = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_54_14 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (514), (572) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_4_1 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (573) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_4_1 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (503), (574) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) op(e3, e1) = all_4_0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (49) with e2, all_4_0, e1, e3,
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (571), (575) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_4_0 = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (49) with e1, all_4_0, e1, e3,
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (559), (575) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_4_0 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (576), (577) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) e2 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (502), (578) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) $false
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (579) is inconsistent.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (8), (18), (36), (45), (49), (59),
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (73), (158), (425), (429), (500), (508),
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510), (553), (555), (580) are inconsistent by
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_54_2 = e1 | all_54_2 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (558), (564), (581) are inconsistent by
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #210.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | (582) all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (582) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_58_2 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (502), (517), (583) are inconsistent by sub-proof
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | #326.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_58_6 = e1 | all_58_12 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_58_6 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (482), (585) are inconsistent by sub-proof
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_58_12 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (163), (586) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_52_3 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (587) implies:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_52_3 = e1
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (499), (588) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (589) $false
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (589) is inconsistent.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.41 | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | (590) ~ (all_58_6 = e3)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | REDUCE: (111), (590) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | (591) ~ (all_52_2 = e3)
% 113.88/17.41 | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | (592) all_54_8 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (592) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | (593) all_52_2 = e3
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (593) imply:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | (594) $false
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | CLOSE: (594) is inconsistent.
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | (595) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | (596) all_54_8 = e2
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.41 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (596) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | (597) all_52_2 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (522), (597) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | (598) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | CLOSE: (598) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | (599) all_54_8 = e1 | all_54_8 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (599) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (600) all_54_8 = e1
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (600) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (601) all_52_2 = e1
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (482), (601) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (602) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (602) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (603) all_54_8 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (603) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (604) all_52_2 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (604) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (605) ~ (all_6_2 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | SIMP: (605) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (606) ~ (all_6_2 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (194), (537), (606) are inconsistent by
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | sub-proof #436.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | (607) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | REF_CLOSE: (64), (89), (117), (133), (512), (516), (607) are
% 113.88/17.42 | | | | | | | | | | | | | | | inconsistent by sub-proof #401.
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | (608) all_56_5 = e2
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | COMBINE_EQS: (154), (608) imply:
% 113.88/17.42 | | | | | | | | | | | | | | (609) all_52_13 = e2
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | SIMP: (609) implies:
% 113.88/17.42 | | | | | | | | | | | | | | (610) all_52_13 = e2
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | REDUCE: (118), (610) imply:
% 113.88/17.42 | | | | | | | | | | | | | | (611) ~ (all_8_2 = e2)
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 113.88/17.42 | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | (612) ~ (all_56_5 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | REDUCE: (608), (612) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | (613) $false
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | CLOSE: (613) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | (614) ~ (all_56_13 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | REDUCE: (130), (614) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | (615) ~ (all_8_2 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 113.88/17.42 | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | (616) ~ (all_56_7 = e1)
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | REDUCE: (476), (616) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | (617) $false
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | CLOSE: (617) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | (618) all_54_5 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (114), (618) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | (619) all_8_2 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | SIMP: (619) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | (620) all_8_2 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (620) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | (621) all_56_13 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (620) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | (622) all_58_3 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | (623) ~ (all_56_13 = e3)
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | REDUCE: (621), (623) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | (624) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | CLOSE: (624) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | (625) ~ (all_56_9 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | REDUCE: (91), (625) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | (626) ~ (all_52_3 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | (627) ~ (all_56_3 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | REDUCE: (16), (627) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | (628) ~ (all_52_1 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | (629) all_54_15 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (431), (629) are inconsistent by sub-proof
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | #312.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (490) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | (630) all_54_15 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (481), (630) are inconsistent by sub-proof
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | #420.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (496) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (631) all_4_2 = e1
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (497) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | (632) ~ (all_52_13 = e1)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | (633) ~ (all_56_15 = e1)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (498), (633) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | (634) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (634) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_2 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (635) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (636) all_52_1 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (628), (636) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (637) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (637) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (638) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_58_3 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (639) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) e3 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (640) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (641) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_58_5 = e2 | all_58_10 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_58_5 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (643) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_52_9 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (644) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (645) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_58_10 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (610) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) ~ (all_52_14 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (647) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) ~ (all_52_14 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_58_6 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (649) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_52_2 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (650) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_52_2 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (651) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) ~ (all_52_3 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (652) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) ~ (all_52_3 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (651) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) ~ (all_10_2 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) ~ (all_56_5 = e2)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (608), (655) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (656) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) ~ (all_56_12 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (657) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) ~ (all_10_2 = e0)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_54_12 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (198), (659) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_52_3 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (660) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) ~ (all_52_11 = e3)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (661) implies:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) ~ (all_52_11 = e3)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (660) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) ~ (all_10_2 = e3)
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_54_14 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (664) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_52_11 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (662), (665) imply:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) $false
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (666) is inconsistent.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_54_0 = e3
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (104), (668) are inconsistent by sub-proof
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (8), (18), (36), (45), (49), (59),
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (69), (73), (158), (425), (429), (500), (508),
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510), (658), (667), (669) are inconsistent by
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (499), (626), (653), (670) are inconsistent
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #406.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (47), (56), (70), (85), (148), (194), (427),
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (502), (608), (648), (671) are inconsistent
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #273.
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 113.88/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | (672) ~ (all_56_15 = e1)
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (498), (672) imply:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | (673) $false
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (673) is inconsistent.
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | (674) ~ (all_56_15 = e1)
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (498), (674) imply:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | (675) $false
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (675) is inconsistent.
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | (676) all_54_15 = e0
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (192), (676) are inconsistent by sub-proof
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | | #419.
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.42 | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | (677) ~ (all_56_13 = e3)
% 114.69/17.42 | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | REDUCE: (621), (677) imply:
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | (678) $false
% 114.69/17.42 | | | | | | | | | | | | | | | | | | |
% 114.69/17.42 | | | | | | | | | | | | | | | | | | | CLOSE: (678) is inconsistent.
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | (679) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (133), (484), (615), (679) are inconsistent
% 114.69/17.43 | | | | | | | | | | | | | | | | | by sub-proof #310.
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | (680) ~ (all_56_15 = e1)
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | REDUCE: (498), (680) imply:
% 114.69/17.43 | | | | | | | | | | | | | (681) $false
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | CLOSE: (681) is inconsistent.
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | (682) ~ (all_56_15 = e1)
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | REDUCE: (498), (682) imply:
% 114.69/17.43 | | | | | | | | | | | | (683) $false
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | CLOSE: (683) is inconsistent.
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | (684) all_54_15 = e0
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | COMBINE_EQS: (192), (684) imply:
% 114.69/17.43 | | | | | | | | | | (685) all_4_2 = e0
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | REDUCE: (13), (685) imply:
% 114.69/17.43 | | | | | | | | | | (686) $false
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | CLOSE: (686) is inconsistent.
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | |
% 114.69/17.43 | | | | | | | | End of split
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | End of split
% 114.69/17.43 | | | | | | |
% 114.69/17.43 | | | | | | End of split
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | Case 2:
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | (687) all_56_15 = e3
% 114.69/17.43 | | | | | | (688) ~ (all_56_9 = e0)
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | COMBINE_EQS: (115), (687) imply:
% 114.69/17.43 | | | | | | (689) all_4_2 = e3
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | SIMP: (689) implies:
% 114.69/17.43 | | | | | | (690) all_4_2 = e3
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (91), (688) imply:
% 114.69/17.43 | | | | | | (691) ~ (all_52_3 = e0)
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (156), (690) imply:
% 114.69/17.43 | | | | | | (692) ~ (all_52_3 = e3)
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (23), (690) imply:
% 114.69/17.43 | | | | | | (693) ~ (all_52_7 = e3)
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (119), (690) imply:
% 114.69/17.43 | | | | | | (694) ~ (all_52_11 = e3)
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (46), (690) imply:
% 114.69/17.43 | | | | | | (695) op(all_4_1, e3) = all_4_0
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | REDUCE: (147), (690) imply:
% 114.69/17.43 | | | | | | (696) op(e0, e3) = all_4_1
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | BETA: splitting (54) gives:
% 114.69/17.43 | | | | | |
% 114.69/17.43 | | | | | | Case 1:
% 114.69/17.43 | | | | | | |
% 114.69/17.43 | | | | | | | (697) ~ (all_56_3 = e2)
% 114.69/17.43 | | | | | | |
% 114.69/17.43 | | | | | | | REDUCE: (16), (697) imply:
% 114.69/17.43 | | | | | | | (698) ~ (all_52_1 = e2)
% 114.69/17.43 | | | | | | |
% 114.69/17.43 | | | | | | | BETA: splitting (10) gives:
% 114.69/17.43 | | | | | | |
% 114.69/17.43 | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | (699) ~ (all_56_6 = e1)
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | REDUCE: (159), (699) imply:
% 114.69/17.43 | | | | | | | | (700) ~ (all_52_2 = e1)
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | GROUND_INST: instantiating (49) with all_52_3, all_4_1, e3, e0,
% 114.69/17.43 | | | | | | | | simplifying with (103), (696) gives:
% 114.69/17.43 | | | | | | | | (701) all_52_3 = all_4_1
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | COMBINE_EQS: (163), (701) imply:
% 114.69/17.43 | | | | | | | | (702) all_58_12 = all_4_1
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | REDUCE: (692), (701) imply:
% 114.69/17.43 | | | | | | | | (703) ~ (all_4_1 = e3)
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | BETA: splitting (94) gives:
% 114.69/17.43 | | | | | | | |
% 114.69/17.43 | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | |
% 114.69/17.43 | | | | | | | | | (704) ~ (all_56_8 = e1)
% 114.69/17.43 | | | | | | | | |
% 114.69/17.43 | | | | | | | | | REDUCE: (178), (704) imply:
% 114.69/17.43 | | | | | | | | | (705) ~ (all_52_14 = e1)
% 114.69/17.43 | | | | | | | | |
% 114.69/17.43 | | | | | | | | | BETA: splitting (137) gives:
% 114.69/17.43 | | | | | | | | |
% 114.69/17.43 | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | (706) all_58_6 = e1
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | REF_CLOSE: (111), (700), (706) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | #452.
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | (707) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | BETA: splitting (707) gives:
% 114.69/17.43 | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | (708) all_58_7 = e1
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | COMBINE_EQS: (6), (708) imply:
% 114.69/17.43 | | | | | | | | | | | (709) all_52_6 = e1
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | REDUCE: (195), (709) imply:
% 114.69/17.43 | | | | | | | | | | | (710) ~ (all_52_7 = e1)
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | SIMP: (710) implies:
% 114.69/17.43 | | | | | | | | | | | (711) ~ (all_52_7 = e1)
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | REDUCE: (123), (709) imply:
% 114.69/17.43 | | | | | | | | | | | (712) ~ (all_8_2 = e1)
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | SIMP: (712) implies:
% 114.69/17.43 | | | | | | | | | | | (713) ~ (all_8_2 = e1)
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | REDUCE: (157), (709) imply:
% 114.69/17.43 | | | | | | | | | | | (714) ~ (all_6_2 = e1)
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | BETA: splitting (85) gives:
% 114.69/17.43 | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | (715) ~ (all_56_5 = e2)
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | REDUCE: (154), (715) imply:
% 114.69/17.43 | | | | | | | | | | | | (716) ~ (all_52_13 = e2)
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | BETA: splitting (184) gives:
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | (717) all_58_2 = e2
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | REF_CLOSE: (99), (698), (717) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | | | | #335.
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | (718) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | BETA: splitting (718) gives:
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | (719) all_58_3 = e2
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | COMBINE_EQS: (64), (719) imply:
% 114.69/17.43 | | | | | | | | | | | | | | (720) all_8_2 = e2
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | REDUCE: (133), (720) imply:
% 114.69/17.43 | | | | | | | | | | | | | | (721) $false
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | CLOSE: (721) is inconsistent.
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | (722) all_58_5 = e2 | all_58_10 = e2
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | (723) all_58_5 = e2
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | COMBINE_EQS: (89), (723) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | (724) all_52_9 = e2
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | SIMP: (724) implies:
% 114.69/17.43 | | | | | | | | | | | | | | | (725) all_52_9 = e2
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | COMBINE_EQS: (152), (725) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | (726) all_56_4 = e2
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | REDUCE: (166), (725) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | (727) ~ (all_52_8 = e2)
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | (728) ~ (all_56_4 = e2)
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | REDUCE: (726), (728) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | (729) $false
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | CLOSE: (729) is inconsistent.
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | (730) ~ (all_56_12 = e1)
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | REDUCE: (34), (730) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | (731) ~ (all_10_2 = e1)
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | (732) all_54_0 = e3
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (104), (732) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | | | | | | | | #451.
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | (733) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | (734) all_54_0 = e2
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (429), (734) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | | | | | | | | | #450.
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | (735) ~ (all_54_0 = e2)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | (736) all_54_0 = e1 | all_54_0 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives:
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | Case 1:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (737) all_54_0 = e1
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (731), (737) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | #449.
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (738) all_54_0 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (738) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (739) all_10_2 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | SIMP: (739) implies:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (740) all_10_2 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (741) all_58_0 = e0
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (742) ~ (all_52_1 = e0)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (181), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (743) ~ (all_52_4 = e0)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (1), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (744) ~ (all_52_8 = e0)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (429), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (745) ~ (e2 = e0)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | SIMP: (745) implies:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (746) ~ (e2 = e0)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (425), (740) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (747) op(e3, e0) = e1
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (49) with all_52_12, e1, e0, e3,
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | simplifying with (57), (747) gives:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (748) all_52_12 = e1
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (144), (748) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (749) ~ (all_52_4 = e1)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REDUCE: (177), (748) imply:
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (750) ~ (all_52_8 = e1)
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (19), (28), (31), (33), (37), (39),
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (49), (61), (80), (86), (88), (99), (114), (125),
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (129), (132), (138), (158), (182), (190), (204),
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (693), (695), (698), (702), (703), (711), (713),
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (727), (741), (742), (743), (744), (746), (749),
% 114.69/17.43 | | | | | | | | | | | | | | | | | | | (750) are inconsistent by sub-proof #208.
% 114.69/17.43 | | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | (751) all_58_10 = e2
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | | REF_CLOSE: (117), (716), (751) are inconsistent by sub-proof
% 114.69/17.43 | | | | | | | | | | | | | | | #95.
% 114.69/17.43 | | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | End of split
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | Case 2:
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | (752) all_56_5 = e2
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | COMBINE_EQS: (154), (752) imply:
% 114.69/17.43 | | | | | | | | | | | | (753) all_52_13 = e2
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | SIMP: (753) implies:
% 114.69/17.43 | | | | | | | | | | | | (754) all_52_13 = e2
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.43 | | | | | | | | | | | | REDUCE: (118), (754) imply:
% 114.69/17.43 | | | | | | | | | | | | (755) ~ (all_8_2 = e2)
% 114.69/17.43 | | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 114.69/17.44 | | | | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (43),
% 114.69/17.44 | | | | | | | | | | | | (45), (47), (49), (50), (51), (53), (56), (59),
% 114.69/17.44 | | | | | | | | | | | | (64), (69), (70), (71), (74), (78), (80), (82),
% 114.69/17.44 | | | | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 114.69/17.44 | | | | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 114.69/17.44 | | | | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 114.69/17.44 | | | | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 114.69/17.44 | | | | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 114.69/17.44 | | | | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 114.69/17.44 | | | | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 114.69/17.44 | | | | | | | | | | | | (429), (691), (692), (693), (694), (695), (696),
% 114.69/17.44 | | | | | | | | | | | | (698), (700), (752) are inconsistent by sub-proof
% 114.69/17.44 | | | | | | | | | | | | #113.
% 114.69/17.44 | | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | | End of split
% 114.69/17.44 | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | Case 2:
% 114.69/17.44 | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | | (756) all_58_8 = e1 | all_58_11 = e1
% 114.69/17.44 | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | | REF_CLOSE: (70), (148), (194), (705), (756) are inconsistent
% 114.69/17.44 | | | | | | | | | | | by sub-proof #445.
% 114.69/17.44 | | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | | End of split
% 114.69/17.44 | | | | | | | | | |
% 114.69/17.44 | | | | | | | | | End of split
% 114.69/17.44 | | | | | | | | |
% 114.69/17.44 | | | | | | | | Case 2:
% 114.69/17.44 | | | | | | | | |
% 114.69/17.44 | | | | | | | | | (757) all_56_8 = e1
% 114.69/17.44 | | | | | | | | |
% 114.69/17.44 | | | | | | | | | COMBINE_EQS: (178), (757) imply:
% 114.69/17.44 | | | | | | | | | (758) all_52_14 = e1
% 114.69/17.44 | | | | | | | | |
% 114.69/17.44 | | | | | | | | | SIMP: (758) implies:
% 114.69/17.44 | | | | | | | | | (759) all_52_14 = e1
% 114.69/17.44 | | | | | | | | |
% 114.69/17.44 | | | | | | | | | REDUCE: (40), (759) imply:
% 114.69/17.44 | | | | | | | | | (760) ~ (all_6_2 = e1)
% 114.69/17.44 | | | | | | | | |
% 114.82/17.44 | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (12), (15), (18), (19),
% 114.82/17.44 | | | | | | | | | (24), (31), (33), (34), (36), (37), (39), (41),
% 114.82/17.44 | | | | | | | | | (43), (45), (47), (49), (50), (51), (53), (56),
% 114.82/17.44 | | | | | | | | | (59), (64), (69), (70), (74), (78), (80), (82),
% 114.82/17.44 | | | | | | | | | (85), (86), (87), (89), (94), (99), (100), (101),
% 114.82/17.44 | | | | | | | | | (103), (104), (108), (111), (113), (114), (117),
% 114.82/17.44 | | | | | | | | | (118), (122), (123), (130), (132), (133), (134),
% 114.82/17.44 | | | | | | | | | (137), (140), (142), (145), (146), (148), (149),
% 114.82/17.44 | | | | | | | | | (152), (154), (155), (158), (162), (163), (166),
% 114.82/17.44 | | | | | | | | | (167), (170), (173), (178), (183), (184), (190),
% 114.82/17.44 | | | | | | | | | (193), (194), (196), (197), (198), (201), (204),
% 114.82/17.44 | | | | | | | | | (429), (691), (692), (693), (694), (695), (696),
% 114.82/17.44 | | | | | | | | | (698), (700), (757) are inconsistent by sub-proof
% 114.82/17.44 | | | | | | | | | #100.
% 114.82/17.44 | | | | | | | | |
% 114.82/17.44 | | | | | | | | End of split
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | Case 2:
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | (761) ~ (all_56_15 = e3)
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | REDUCE: (687), (761) imply:
% 114.82/17.44 | | | | | | | | (762) $false
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | CLOSE: (762) is inconsistent.
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | End of split
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | Case 2:
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | (763) ~ (all_56_15 = e3)
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | REDUCE: (687), (763) imply:
% 114.82/17.44 | | | | | | | (764) $false
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | CLOSE: (764) is inconsistent.
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | End of split
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | End of split
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | Case 2:
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | (765) all_56_12 = e2
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | COMBINE_EQS: (34), (765) imply:
% 114.82/17.44 | | | | | (766) all_10_2 = e2
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | SIMP: (766) implies:
% 114.82/17.44 | | | | | (767) all_10_2 = e2
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | COMBINE_EQS: (52), (767) imply:
% 114.82/17.44 | | | | | (768) all_32_2 = e2
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (4), (767) imply:
% 114.82/17.44 | | | | | (769) ~ (all_52_2 = e2)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (181), (767) imply:
% 114.82/17.44 | | | | | (770) ~ (all_52_4 = e2)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (1), (767) imply:
% 114.82/17.44 | | | | | (771) ~ (all_52_8 = e2)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (425), (767) imply:
% 114.82/17.44 | | | | | (772) op(e3, e2) = e1
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (424), (767) imply:
% 114.82/17.44 | | | | | (773) op(e1, e2) = all_10_0
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REF_CLOSE: (6), (10), (13), (14), (21), (23), (38), (44), (47), (49),
% 114.82/17.44 | | | | | (50), (51), (56), (59), (60), (64), (67), (68), (72), (87),
% 114.82/17.44 | | | | | (89), (95), (96), (106), (115), (125), (128), (133), (134),
% 114.82/17.44 | | | | | (135), (139), (140), (148), (152), (157), (159), (165),
% 114.82/17.44 | | | | | (192), (194), (195), (422), (427), (765), (768), (769),
% 114.82/17.44 | | | | | (770), (771), (772), (773) are inconsistent by sub-proof
% 114.82/17.44 | | | | | #293.
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | End of split
% 114.82/17.44 | | | |
% 114.82/17.44 | | | Case 2:
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | (774) all_56_14 = e2
% 114.82/17.44 | | | | (775) ~ (all_56_10 = e0)
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | REF_CLOSE: (9), (13), (15), (16), (24), (25), (30), (33), (36), (43),
% 114.82/17.44 | | | | (48), (49), (54), (59), (60), (62), (64), (71), (78), (79),
% 114.82/17.44 | | | | (80), (89), (91), (98), (99), (102), (104), (106), (112),
% 114.82/17.44 | | | | (114), (115), (117), (118), (125), (126), (127), (128),
% 114.82/17.44 | | | | (130), (132), (133), (140), (146), (151), (153), (154),
% 114.82/17.44 | | | | (155), (160), (162), (163), (166), (168), (173), (176),
% 114.82/17.44 | | | | (184), (185), (188), (189), (192), (193), (200), (774), (775)
% 114.82/17.44 | | | | are inconsistent by sub-proof #104.
% 114.82/17.44 | | | |
% 114.82/17.44 | | | End of split
% 114.82/17.44 | | |
% 114.82/17.44 | | End of split
% 114.82/17.44 | |
% 114.82/17.44 | Case 2:
% 114.82/17.44 | |
% 114.82/17.44 | | (776) all_26_0 = e1
% 114.82/17.44 | | (777) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 114.82/17.44 | |
% 114.82/17.44 | | COMBINE_EQS: (202), (776) imply:
% 114.82/17.44 | | (778) all_4_0 = e1
% 114.82/17.44 | |
% 114.82/17.44 | | SIMP: (778) implies:
% 114.82/17.44 | | (779) all_4_0 = e1
% 114.82/17.44 | |
% 114.82/17.44 | | REDUCE: (90), (779) imply:
% 114.82/17.44 | | (780) ~ (e3 = e1)
% 114.82/17.44 | |
% 114.82/17.44 | | REDUCE: (46), (779) imply:
% 114.82/17.44 | | (781) op(all_4_1, all_4_2) = e1
% 114.82/17.44 | |
% 114.82/17.44 | | BETA: splitting (7) gives:
% 114.82/17.44 | |
% 114.82/17.44 | | Case 1:
% 114.82/17.44 | | |
% 114.82/17.44 | | | (782) ~ (all_32_1 = e1)
% 114.82/17.44 | | |
% 114.82/17.44 | | | REDUCE: (107), (782) imply:
% 114.82/17.44 | | | (783) ~ (all_10_1 = e1)
% 114.82/17.44 | | |
% 114.82/17.44 | | | BETA: splitting (55) gives:
% 114.82/17.44 | | |
% 114.82/17.44 | | | Case 1:
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | (784) ~ (all_38_1 = e2)
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | REDUCE: (17), (784) imply:
% 114.82/17.44 | | | | (785) ~ (all_10_1 = e2)
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | BETA: splitting (92) gives:
% 114.82/17.44 | | | |
% 114.82/17.44 | | | | Case 1:
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | (786) ~ (all_56_15 = e1)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (115), (786) imply:
% 114.82/17.44 | | | | | (787) ~ (all_4_2 = e1)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | BETA: splitting (183) gives:
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | Case 1:
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | (788) ~ (all_56_12 = e1)
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | REDUCE: (34), (788) imply:
% 114.82/17.44 | | | | | | (789) ~ (all_10_2 = e1)
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | BETA: splitting (79) gives:
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | Case 1:
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | (790) ~ (all_56_13 = e1)
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | REDUCE: (130), (790) imply:
% 114.82/17.44 | | | | | | | (791) ~ (all_8_2 = e1)
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | BETA: splitting (172) gives:
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | Case 1:
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | (792) ~ (all_56_15 = e2)
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | REDUCE: (115), (792) imply:
% 114.82/17.44 | | | | | | | | (793) ~ (all_4_2 = e2)
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | REF_CLOSE: (6), (10), (13), (14), (15), (18), (20), (22), (24),
% 114.82/17.44 | | | | | | | | (27), (29), (32), (34), (38), (40), (47), (49), (56),
% 114.82/17.44 | | | | | | | | (57), (60), (61), (64), (67), (70), (76), (77), (79),
% 114.82/17.44 | | | | | | | | (85), (89), (91), (94), (95), (98), (99), (104),
% 114.82/17.44 | | | | | | | | (106), (111), (113), (115), (117), (121), (125),
% 114.82/17.44 | | | | | | | | (128), (129), (130), (133), (137), (138), (139),
% 114.82/17.44 | | | | | | | | (148), (149), (150), (152), (154), (157), (159),
% 114.82/17.44 | | | | | | | | (163), (169), (178), (181), (184), (185), (186),
% 114.82/17.44 | | | | | | | | (188), (191), (192), (194), (783), (785), (787),
% 114.82/17.44 | | | | | | | | (789), (793) are inconsistent by sub-proof #416.
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | Case 2:
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | (794) all_56_15 = e2
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (15), (18), (20), (22),
% 114.82/17.44 | | | | | | | | (24), (27), (29), (32), (33), (34), (35), (38), (40),
% 114.82/17.44 | | | | | | | | (47), (49), (51), (56), (61), (62), (64), (67), (70),
% 114.82/17.44 | | | | | | | | (76), (77), (79), (85), (89), (91), (94), (95), (97),
% 114.82/17.44 | | | | | | | | (98), (99), (104), (105), (106), (111), (113), (114),
% 114.82/17.44 | | | | | | | | (115), (117), (121), (125), (126), (128), (129),
% 114.82/17.44 | | | | | | | | (130), (133), (137), (138), (139), (148), (149),
% 114.82/17.44 | | | | | | | | (150), (152), (154), (157), (159), (163), (168),
% 114.82/17.44 | | | | | | | | (169), (178), (181), (184), (185), (186), (188),
% 114.82/17.44 | | | | | | | | (191), (193), (194), (783), (789), (791), (794) are
% 114.82/17.44 | | | | | | | | inconsistent by sub-proof #94.
% 114.82/17.44 | | | | | | | |
% 114.82/17.44 | | | | | | | End of split
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | Case 2:
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | (795) all_56_13 = e1
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | COMBINE_EQS: (130), (795) imply:
% 114.82/17.44 | | | | | | | (796) all_8_2 = e1
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | REF_CLOSE: (9), (49), (155), (193), (796) are inconsistent by
% 114.82/17.44 | | | | | | | sub-proof #109.
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | End of split
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | Case 2:
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | (797) all_56_12 = e1
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | REF_CLOSE: (1), (5), (8), (9), (13), (16), (20), (25), (27), (29),
% 114.82/17.44 | | | | | | (33), (34), (45), (49), (59), (60), (62), (64), (67),
% 114.82/17.44 | | | | | | (73), (76), (81), (82), (89), (99), (100), (114), (117),
% 114.82/17.44 | | | | | | (119), (121), (126), (127), (128), (130), (131), (132),
% 114.82/17.44 | | | | | | (133), (146), (148), (150), (152), (158), (160), (169),
% 114.82/17.44 | | | | | | (177), (184), (192), (194), (197), (785), (787), (797)
% 114.82/17.44 | | | | | | are inconsistent by sub-proof #281.
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | End of split
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | Case 2:
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | (798) all_56_15 = e1
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | COMBINE_EQS: (115), (798) imply:
% 114.82/17.44 | | | | | (799) all_4_2 = e1
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | SIMP: (799) implies:
% 114.82/17.44 | | | | | (800) all_4_2 = e1
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (119), (800) imply:
% 114.82/17.44 | | | | | (801) ~ (all_52_11 = e1)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | REDUCE: (110), (800) imply:
% 114.82/17.44 | | | | | (802) ~ (all_52_14 = e1)
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | BETA: splitting (112) gives:
% 114.82/17.44 | | | | |
% 114.82/17.44 | | | | | Case 1:
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | (803) ~ (all_56_1 = e3)
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | REDUCE: (146), (803) imply:
% 114.82/17.44 | | | | | | (804) ~ (all_52_8 = e3)
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | BETA: splitting (165) gives:
% 114.82/17.44 | | | | | |
% 114.82/17.44 | | | | | | Case 1:
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | (805) ~ (all_56_4 = e2)
% 114.82/17.44 | | | | | | |
% 114.82/17.44 | | | | | | | REDUCE: (152), (805) imply:
% 114.82/17.44 | | | | | | | (806) ~ (all_52_9 = e2)
% 114.82/17.44 | | | | | | |
% 114.82/17.45 | | | | | | | BETA: splitting (108) gives:
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | | Case 1:
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | | (807) ~ (all_56_14 = e2)
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (15), (16),
% 114.82/17.45 | | | | | | | | (18), (24), (26), (29), (32), (33), (34), (35), (36),
% 114.82/17.45 | | | | | | | | (39), (40), (43), (45), (47), (49), (53), (54), (56),
% 114.82/17.45 | | | | | | | | (59), (60), (62), (63), (64), (65), (66), (70), (71),
% 114.82/17.45 | | | | | | | | (74), (75), (77), (78), (80), (81), (83), (84), (85),
% 114.82/17.45 | | | | | | | | (86), (88), (89), (91), (93), (94), (95), (97), (98),
% 114.82/17.45 | | | | | | | | (99), (101), (103), (104), (106), (110), (111),
% 114.82/17.45 | | | | | | | | (112), (113), (114), (115), (116), (117), (118),
% 114.82/17.45 | | | | | | | | (119), (123), (124), (125), (126), (127), (128),
% 114.82/17.45 | | | | | | | | (130), (132), (133), (137), (139), (140), (142),
% 114.82/17.45 | | | | | | | | (143), (145), (146), (147), (148), (149), (151),
% 114.82/17.45 | | | | | | | | (152), (153), (154), (155), (156), (157), (159),
% 114.82/17.45 | | | | | | | | (160), (161), (162), (163), (167), (168), (170),
% 114.82/17.45 | | | | | | | | (171), (172), (173), (174), (175), (176), (178),
% 114.82/17.45 | | | | | | | | (180), (183), (184), (187), (188), (190), (192),
% 114.82/17.45 | | | | | | | | (193), (194), (196), (197), (198), (201), (777),
% 114.82/17.45 | | | | | | | | (781), (801), (802), (806), (807) are inconsistent by
% 114.82/17.45 | | | | | | | | sub-proof #88.
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | Case 2:
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | | (808) all_56_14 = e2
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (15), (18), (22), (24),
% 114.82/17.45 | | | | | | | | (29), (32), (34), (36), (38), (42), (47), (49), (56),
% 114.82/17.45 | | | | | | | | (59), (61), (62), (64), (67), (70), (76), (77), (79),
% 114.82/17.45 | | | | | | | | (85), (89), (91), (95), (98), (99), (104), (106),
% 114.82/17.45 | | | | | | | | (111), (113), (117), (121), (125), (128), (129),
% 114.82/17.45 | | | | | | | | (130), (133), (137), (138), (139), (148), (149),
% 114.82/17.45 | | | | | | | | (150), (152), (153), (154), (157), (163), (176),
% 114.82/17.45 | | | | | | | | (181), (184), (185), (186), (188), (189), (191),
% 114.82/17.45 | | | | | | | | (194), (783), (802), (804), (808) are inconsistent by
% 114.82/17.45 | | | | | | | | sub-proof #87.
% 114.82/17.45 | | | | | | | |
% 114.82/17.45 | | | | | | | End of split
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | Case 2:
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | | (809) ~ (all_56_15 = e1)
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | | REDUCE: (798), (809) imply:
% 114.82/17.45 | | | | | | | (810) $false
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | | CLOSE: (810) is inconsistent.
% 114.82/17.45 | | | | | | |
% 114.82/17.45 | | | | | | End of split
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | Case 2:
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | (811) ~ (all_56_15 = e1)
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | REDUCE: (798), (811) imply:
% 114.82/17.45 | | | | | | (812) $false
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | CLOSE: (812) is inconsistent.
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | End of split
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | End of split
% 114.82/17.45 | | | |
% 114.82/17.45 | | | Case 2:
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | (813) all_38_1 = e2
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | COMBINE_EQS: (17), (813) imply:
% 114.82/17.45 | | | | (814) all_10_1 = e2
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | REDUCE: (121), (814) imply:
% 114.82/17.45 | | | | (815) op(e3, all_10_2) = e2
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | BETA: splitting (108) gives:
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | Case 1:
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | (816) ~ (all_56_14 = e2)
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | REDUCE: (15), (816) imply:
% 114.82/17.45 | | | | | (817) ~ (all_6_2 = e2)
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | BETA: splitting (109) gives:
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | Case 1:
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | (818) ~ (all_56_12 = e2)
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | REDUCE: (34), (818) imply:
% 114.82/17.45 | | | | | | (819) ~ (all_10_2 = e2)
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (15), (16), (18),
% 114.82/17.45 | | | | | | (24), (26), (29), (32), (33), (34), (35), (36), (39),
% 114.82/17.45 | | | | | | (40), (43), (45), (47), (49), (53), (54), (56), (59),
% 114.82/17.45 | | | | | | (60), (62), (63), (64), (65), (66), (70), (71), (74),
% 114.82/17.45 | | | | | | (75), (77), (78), (80), (81), (83), (84), (85), (86),
% 114.82/17.45 | | | | | | (88), (89), (91), (93), (94), (97), (98), (99), (103),
% 114.82/17.45 | | | | | | (104), (106), (110), (111), (112), (113), (114), (115),
% 114.82/17.45 | | | | | | (116), (117), (118), (119), (123), (124), (125), (126),
% 114.82/17.45 | | | | | | (127), (128), (130), (132), (133), (137), (139), (140),
% 114.82/17.45 | | | | | | (142), (143), (145), (146), (147), (148), (149), (151),
% 114.82/17.45 | | | | | | (152), (153), (154), (155), (156), (157), (159), (160),
% 114.82/17.45 | | | | | | (161), (162), (163), (167), (168), (170), (171), (172),
% 114.82/17.45 | | | | | | (173), (174), (175), (176), (178), (180), (183), (184),
% 114.82/17.45 | | | | | | (187), (188), (190), (192), (193), (194), (196), (197),
% 114.82/17.45 | | | | | | (198), (201), (777), (781), (817), (819) are inconsistent
% 114.82/17.45 | | | | | | by sub-proof #91.
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | Case 2:
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | (820) all_56_12 = e2
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | | REF_CLOSE: (14), (34), (49), (181), (815), (820) are inconsistent by
% 114.82/17.45 | | | | | | sub-proof #300.
% 114.82/17.45 | | | | | |
% 114.82/17.45 | | | | | End of split
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | Case 2:
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | (821) all_56_14 = e2
% 114.82/17.45 | | | | | (822) ~ (all_56_10 = e0)
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | REF_CLOSE: (9), (13), (15), (16), (24), (25), (30), (33), (36), (43),
% 114.82/17.45 | | | | | (48), (49), (54), (59), (60), (62), (64), (71), (78), (79),
% 114.82/17.45 | | | | | (80), (89), (91), (98), (99), (102), (104), (106), (112),
% 114.82/17.45 | | | | | (114), (115), (117), (118), (125), (126), (127), (128),
% 114.82/17.45 | | | | | (130), (132), (133), (140), (146), (151), (153), (154),
% 114.82/17.45 | | | | | (155), (160), (162), (163), (166), (168), (173), (176),
% 114.82/17.45 | | | | | (184), (185), (188), (189), (192), (193), (200), (821),
% 114.82/17.45 | | | | | (822) are inconsistent by sub-proof #104.
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | End of split
% 114.82/17.45 | | | |
% 114.82/17.45 | | | End of split
% 114.82/17.45 | | |
% 114.82/17.45 | | Case 2:
% 114.82/17.45 | | |
% 114.82/17.45 | | | (823) all_32_1 = e1
% 114.82/17.45 | | | (824) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 114.82/17.45 | | |
% 114.82/17.45 | | | COMBINE_EQS: (107), (823) imply:
% 114.82/17.45 | | | (825) all_10_1 = e1
% 114.82/17.45 | | |
% 114.82/17.45 | | | REDUCE: (76), (825) imply:
% 114.82/17.45 | | | (826) op(e1, all_10_2) = all_10_0
% 114.82/17.45 | | |
% 114.82/17.45 | | | REDUCE: (121), (825) imply:
% 114.82/17.45 | | | (827) op(e3, all_10_2) = e1
% 114.82/17.45 | | |
% 114.82/17.45 | | | BETA: splitting (108) gives:
% 114.82/17.45 | | |
% 114.82/17.45 | | | Case 1:
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | (828) ~ (all_56_14 = e2)
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | REDUCE: (15), (828) imply:
% 114.82/17.45 | | | | (829) ~ (all_6_2 = e2)
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | BETA: splitting (109) gives:
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | Case 1:
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | (830) ~ (all_56_12 = e2)
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | REDUCE: (34), (830) imply:
% 114.82/17.45 | | | | | (831) ~ (all_10_2 = e2)
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (15), (16), (18),
% 114.82/17.45 | | | | | (24), (26), (29), (32), (33), (34), (35), (36), (39), (40),
% 114.82/17.45 | | | | | (43), (45), (47), (49), (53), (54), (56), (59), (60), (62),
% 114.82/17.45 | | | | | (63), (64), (65), (66), (70), (71), (74), (75), (77), (78),
% 114.82/17.45 | | | | | (80), (81), (83), (84), (85), (86), (88), (89), (91), (93),
% 114.82/17.45 | | | | | (94), (97), (98), (99), (103), (104), (106), (110), (111),
% 114.82/17.45 | | | | | (112), (113), (114), (115), (116), (117), (118), (119),
% 114.82/17.45 | | | | | (123), (124), (125), (126), (127), (128), (130), (132),
% 114.82/17.45 | | | | | (133), (137), (139), (140), (142), (143), (145), (146),
% 114.82/17.45 | | | | | (147), (148), (149), (151), (152), (153), (154), (155),
% 114.82/17.45 | | | | | (156), (157), (159), (160), (161), (162), (163), (167),
% 114.82/17.45 | | | | | (168), (170), (171), (172), (173), (174), (175), (176),
% 114.82/17.45 | | | | | (178), (180), (183), (184), (187), (188), (190), (192),
% 114.82/17.45 | | | | | (193), (194), (196), (197), (198), (201), (777), (781),
% 114.82/17.45 | | | | | (829), (831) are inconsistent by sub-proof #91.
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | Case 2:
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | (832) all_56_12 = e2
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | | REF_CLOSE: (1), (4), (6), (10), (13), (14), (21), (23), (34), (38),
% 114.82/17.45 | | | | | (44), (47), (49), (50), (51), (52), (56), (59), (60), (64),
% 114.82/17.45 | | | | | (67), (68), (72), (87), (89), (95), (96), (106), (115),
% 114.82/17.45 | | | | | (125), (128), (133), (134), (135), (139), (140), (148),
% 114.82/17.45 | | | | | (152), (157), (159), (165), (181), (192), (194), (195),
% 114.82/17.45 | | | | | (824), (826), (827), (829), (832) are inconsistent by
% 114.82/17.45 | | | | | sub-proof #291.
% 114.82/17.45 | | | | |
% 114.82/17.45 | | | | End of split
% 114.82/17.45 | | | |
% 114.82/17.45 | | | Case 2:
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | (833) all_56_14 = e2
% 114.82/17.45 | | | | (834) ~ (all_56_10 = e0)
% 114.82/17.45 | | | |
% 114.82/17.45 | | | | REF_CLOSE: (9), (13), (15), (16), (24), (25), (30), (33), (36), (43),
% 114.82/17.45 | | | | (48), (49), (54), (59), (60), (62), (64), (71), (78), (79),
% 114.82/17.45 | | | | (80), (89), (91), (98), (99), (102), (104), (106), (112),
% 114.82/17.45 | | | | (114), (115), (117), (118), (125), (126), (127), (128),
% 114.82/17.45 | | | | (130), (132), (133), (140), (146), (151), (153), (154),
% 114.82/17.45 | | | | (155), (160), (162), (163), (166), (168), (173), (176),
% 114.82/17.45 | | | | (184), (185), (188), (189), (192), (193), (200), (833), (834)
% 114.82/17.45 | | | | are inconsistent by sub-proof #104.
% 114.82/17.45 | | | |
% 114.82/17.45 | | | End of split
% 114.82/17.45 | | |
% 114.82/17.45 | | End of split
% 114.82/17.45 | |
% 114.82/17.45 | End of split
% 114.82/17.45 |
% 114.82/17.45 End of proof
% 114.82/17.45
% 114.82/17.45 Sub-proof #87 shows that the following formulas are inconsistent:
% 114.82/17.45 ----------------------------------------------------------------
% 114.82/17.45 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 114.82/17.45 (2) ~ (all_52_2 = all_10_2)
% 114.82/17.45 (3) all_58_7 = all_52_6
% 114.82/17.45 (4) ~ (all_4_2 = e0)
% 114.82/17.45 (5) op(e3, e2) = all_52_4
% 114.82/17.45 (6) all_56_14 = all_6_2
% 114.82/17.45 (7) all_54_0 = all_10_2
% 114.82/17.45 (8) op(e0, e2) = all_52_7
% 114.82/17.45 (9) all_56_11 = all_52_11
% 114.82/17.45 (10) ~ (all_52_12 = all_10_2)
% 114.82/17.45 (11) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 114.82/17.45 (12) all_56_12 = all_10_2
% 114.82/17.45 (13) all_56_14 = e2
% 114.82/17.45 (14) all_58_0 = all_10_2
% 114.82/17.45 (15) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 114.82/17.45 (16) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 114.82/17.45 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.46 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 114.82/17.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 114.82/17.46 (19) all_54_10 = all_6_2
% 114.82/17.46 (20) ~ (all_52_14 = e1)
% 114.82/17.46 (21) all_58_4 = all_52_8
% 114.82/17.46 (22) ~ (all_52_4 = all_52_7)
% 114.82/17.46 (23) all_56_2 = all_52_12
% 114.82/17.46 (24) all_58_3 = all_8_2
% 114.82/17.46 (25) ~ (all_10_0 = e2)
% 114.82/17.46 (26) all_58_11 = all_52_14
% 114.82/17.46 (27) op(all_10_1, all_10_2) = all_10_0
% 114.82/17.46 (28) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 114.82/17.46 (29) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 114.82/17.46 (30) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 114.82/17.46 (31) all_58_5 = all_52_9
% 114.82/17.46 (32) all_56_9 = all_52_3
% 114.82/17.46 (33) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 114.82/17.46 (34) all_58_15 = all_4_2
% 114.82/17.46 (35) all_58_2 = all_52_1
% 114.82/17.46 (36) ~ (all_10_2 = e3)
% 114.82/17.46 (37) all_58_13 = all_52_7
% 114.82/17.46 (38) all_58_6 = all_52_2
% 114.82/17.46 (39) ~ (all_52_1 = all_10_2)
% 114.82/17.46 (40) all_58_10 = all_52_13
% 114.82/17.46 (41) op(e3, all_10_2) = all_10_1
% 114.82/17.46 (42) all_58_1 = all_52_4
% 114.82/17.46 (43) all_58_14 = all_52_11
% 114.82/17.46 (44) all_54_1 = all_52_4
% 114.82/17.46 (45) all_56_13 = all_8_2
% 114.82/17.46 (46) ~ (all_52_8 = e3)
% 114.82/17.46 (47) ~ (all_8_2 = e2)
% 114.82/17.46 (48) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.46 (49) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 114.82/17.46 (50) all_56_7 = all_52_6
% 114.82/17.46 (51) all_58_8 = all_6_2
% 114.82/17.46 (52) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.82/17.46 (53) ~ (all_10_0 = e1)
% 114.82/17.46 (54) all_56_4 = all_52_9
% 114.82/17.46 (55) all_58_9 = all_52_12
% 114.82/17.46 (56) all_56_5 = all_52_13
% 114.82/17.46 (57) ~ (all_52_6 = all_6_2)
% 114.82/17.46 (58) all_58_12 = all_52_3
% 114.82/17.46 (59) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 114.82/17.46 (60) ~ (all_52_4 = all_10_2)
% 114.82/17.46 (61) ~ (all_10_1 = e1)
% 114.82/17.46 (62) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 114.82/17.46 (63) all_56_0 = all_52_4
% 114.82/17.46 (64) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 114.82/17.46 (65) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 114.82/17.46 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 114.82/17.46 (66) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 114.82/17.46 (67) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 114.82/17.46 (68) ~ (all_6_2 = e1)
% 114.82/17.46
% 114.82/17.46 Begin of proof
% 114.82/17.46 |
% 114.82/17.46 | BETA: splitting (16) gives:
% 114.82/17.46 |
% 114.82/17.46 | Case 1:
% 114.82/17.46 | |
% 114.82/17.46 | | (69) ~ (all_56_7 = e1)
% 114.82/17.46 | |
% 114.82/17.46 | | REDUCE: (50), (69) imply:
% 114.82/17.46 | | (70) ~ (all_52_6 = e1)
% 114.82/17.46 | |
% 114.82/17.46 | | BETA: splitting (66) gives:
% 114.82/17.46 | |
% 114.82/17.46 | | Case 1:
% 114.82/17.46 | | |
% 114.82/17.46 | | | (71) ~ (all_56_0 = e3)
% 114.82/17.46 | | |
% 114.82/17.46 | | | REDUCE: (63), (71) imply:
% 114.82/17.46 | | | (72) ~ (all_52_4 = e3)
% 114.82/17.46 | | |
% 114.82/17.46 | | | BETA: splitting (48) gives:
% 114.82/17.46 | | |
% 114.82/17.46 | | | Case 1:
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | (73) all_58_6 = e1
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | COMBINE_EQS: (38), (73) imply:
% 114.82/17.46 | | | | (74) all_52_2 = e1
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | SIMP: (74) implies:
% 114.82/17.46 | | | | (75) all_52_2 = e1
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | REDUCE: (2), (75) imply:
% 114.82/17.46 | | | | (76) ~ (all_10_2 = e1)
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | SIMP: (76) implies:
% 114.82/17.46 | | | | (77) ~ (all_10_2 = e1)
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | BETA: splitting (59) gives:
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | Case 1:
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | (78) all_58_0 = e3
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | COMBINE_EQS: (14), (78) imply:
% 114.82/17.46 | | | | | (79) all_10_2 = e3
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | REDUCE: (36), (79) imply:
% 114.82/17.46 | | | | | (80) $false
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | CLOSE: (80) is inconsistent.
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | Case 2:
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | (81) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | BETA: splitting (81) gives:
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | | Case 1:
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | (82) all_58_1 = e3
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | COMBINE_EQS: (42), (82) imply:
% 114.82/17.46 | | | | | | (83) all_52_4 = e3
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | REDUCE: (72), (83) imply:
% 114.82/17.46 | | | | | | (84) $false
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | CLOSE: (84) is inconsistent.
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | Case 2:
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | (85) all_58_4 = e3 | all_58_9 = e3
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | BETA: splitting (85) gives:
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | | Case 1:
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | (86) all_58_4 = e3
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | REF_CLOSE: (21), (46), (86) are inconsistent by sub-proof #331.
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | Case 2:
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | (87) all_58_9 = e3
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | COMBINE_EQS: (55), (87) imply:
% 114.82/17.46 | | | | | | | (88) all_52_12 = e3
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | SIMP: (88) implies:
% 114.82/17.46 | | | | | | | (89) all_52_12 = e3
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | COMBINE_EQS: (23), (89) imply:
% 114.82/17.46 | | | | | | | (90) all_56_2 = e3
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | REDUCE: (10), (89) imply:
% 114.82/17.46 | | | | | | | (91) ~ (all_10_2 = e3)
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 114.82/17.46 | | | | | | | (15), (17), (18), (19), (22), (24), (25), (27), (28),
% 114.82/17.46 | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 114.82/17.46 | | | | | | | (39), (40), (41), (42), (43), (44), (45), (47), (49),
% 114.82/17.46 | | | | | | | (50), (52), (53), (54), (56), (57), (58), (60), (61),
% 114.82/17.46 | | | | | | | (62), (63), (64), (65), (67), (68), (77), (90) are
% 114.82/17.46 | | | | | | | inconsistent by sub-proof #356.
% 114.82/17.46 | | | | | | |
% 114.82/17.46 | | | | | | End of split
% 114.82/17.46 | | | | | |
% 114.82/17.46 | | | | | End of split
% 114.82/17.46 | | | | |
% 114.82/17.46 | | | | End of split
% 114.82/17.46 | | | |
% 114.82/17.46 | | | Case 2:
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | (92) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.46 | | | |
% 114.82/17.46 | | | | REF_CLOSE: (3), (20), (26), (51), (68), (70), (92) are inconsistent by
% 114.82/17.46 | | | | sub-proof #354.
% 114.82/17.46 | | | |
% 114.82/17.46 | | | End of split
% 114.82/17.46 | | |
% 114.82/17.46 | | Case 2:
% 114.82/17.46 | | |
% 114.82/17.46 | | | (93) ~ (all_56_14 = e2)
% 114.82/17.46 | | |
% 114.82/17.46 | | | REDUCE: (13), (93) imply:
% 114.82/17.46 | | | (94) $false
% 114.82/17.46 | | |
% 114.82/17.46 | | | CLOSE: (94) is inconsistent.
% 114.82/17.46 | | |
% 114.82/17.46 | | End of split
% 114.82/17.46 | |
% 114.82/17.46 | Case 2:
% 114.82/17.46 | |
% 114.82/17.46 | | (95) ~ (all_56_14 = e2)
% 114.82/17.46 | |
% 114.82/17.46 | | REDUCE: (13), (95) imply:
% 114.82/17.46 | | (96) $false
% 114.82/17.46 | |
% 114.82/17.46 | | CLOSE: (96) is inconsistent.
% 114.82/17.46 | |
% 114.82/17.46 | End of split
% 114.82/17.46 |
% 114.82/17.46 End of proof
% 114.82/17.46
% 114.82/17.46 Sub-proof #88 shows that the following formulas are inconsistent:
% 114.82/17.46 ----------------------------------------------------------------
% 114.82/17.46 (1) ~ (all_52_8 = all_10_2)
% 114.82/17.46 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 114.82/17.46 (3) ~ (all_52_2 = all_10_2)
% 114.82/17.46 (4) ~ (all_52_9 = e2)
% 114.82/17.46 (5) all_58_7 = all_52_6
% 114.82/17.46 (6) ~ (all_52_9 = all_8_2)
% 114.82/17.46 (7) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 114.82/17.46 (8) ~ (all_4_2 = e0)
% 114.82/17.46 (9) all_56_14 = all_6_2
% 114.82/17.46 (10) all_56_3 = all_52_1
% 114.82/17.46 (11) all_54_0 = all_10_2
% 114.82/17.46 (12) all_56_11 = all_52_11
% 114.82/17.46 (13) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 114.82/17.46 (14) ~ (all_52_12 = all_10_2)
% 114.82/17.46 (15) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 114.82/17.46 (16) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 114.82/17.46 (17) all_56_12 = all_10_2
% 114.82/17.46 (18) ~ (all_56_14 = e2)
% 114.82/17.46 (19) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 114.82/17.46 (20) all_58_0 = all_10_2
% 114.82/17.46 (21) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 114.82/17.46 (22) ~ (all_52_14 = all_6_2)
% 114.82/17.46 (23) all_56_10 = all_52_7
% 114.82/17.46 (24) all_54_14 = all_52_11
% 114.82/17.46 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.46 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 114.82/17.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 114.82/17.47 (27) ~ (all_52_1 = all_52_9)
% 114.82/17.47 (28) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 114.82/17.47 (29) all_54_10 = all_6_2
% 114.82/17.47 (30) ~ (all_52_14 = e1)
% 114.82/17.47 (31) all_58_4 = all_52_8
% 114.82/17.47 (32) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 114.82/17.47 (33) all_56_2 = all_52_12
% 114.82/17.47 (34) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 114.82/17.47 (35) all_58_3 = all_8_2
% 114.82/17.47 (36) all_54_6 = all_52_9
% 114.82/17.47 (37) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 114.82/17.47 (38) all_58_11 = all_52_14
% 114.82/17.47 (39) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 114.82/17.47 (40) ~ (all_52_2 = all_52_3)
% 114.82/17.47 (41) all_54_7 = all_52_13
% 114.82/17.47 (42) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 114.82/17.47 (43) ~ (all_52_11 = all_6_2)
% 114.82/17.47 (44) op(e2, e3) = all_52_1
% 114.82/17.47 (45) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 114.82/17.47 (46) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 114.82/17.47 (47) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 114.82/17.47 (48) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 114.82/17.47 (49) ~ (all_52_7 = all_8_2)
% 114.82/17.47 (50) ~ (all_52_4 = all_8_2)
% 114.82/17.47 (51) all_58_5 = all_52_9
% 114.82/17.47 (52) op(all_4_1, all_4_2) = e1
% 114.82/17.47 (53) all_56_9 = all_52_3
% 114.82/17.47 (54) op(e1, all_6_2) = all_6_1
% 114.82/17.47 (55) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 114.82/17.47 (56) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 114.82/17.47 (57) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 114.82/17.47 (58) all_58_15 = all_4_2
% 114.82/17.47 (59) all_58_2 = all_52_1
% 114.82/17.47 (60) ~ (all_52_1 = all_52_13)
% 114.82/17.47 (61) op(e0, e3) = all_52_3
% 114.82/17.47 (62) ~ (all_10_2 = e3)
% 114.82/17.47 (63) all_58_13 = all_52_7
% 114.82/17.47 (64) ~ (all_52_14 = all_4_2)
% 114.82/17.47 (65) all_58_6 = all_52_2
% 114.82/17.47 (66) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 114.82/17.47 (67) ~ (all_52_1 = all_10_2)
% 114.82/17.47 (68) all_54_5 = all_8_2
% 114.82/17.47 (69) all_56_15 = all_4_2
% 114.82/17.47 (70) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 114.82/17.47 (71) all_58_10 = all_52_13
% 114.82/17.47 (72) ~ (all_52_13 = all_8_2)
% 114.82/17.47 (73) ~ (all_52_11 = all_4_2)
% 114.82/17.47 (74) ~ (all_52_6 = all_8_2)
% 114.82/17.47 (75) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 114.82/17.47 (76) all_58_1 = all_52_4
% 114.82/17.47 (77) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 114.82/17.47 (78) ~ (all_52_9 = all_52_11)
% 114.82/17.47 (79) all_58_14 = all_52_11
% 114.82/17.47 (80) all_56_13 = all_8_2
% 114.82/17.47 (81) ~ (all_52_1 = all_8_2)
% 114.82/17.47 (82) ~ (all_8_2 = e2)
% 114.82/17.47 (83) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 114.82/17.47 (84) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.47 (85) all_56_7 = all_52_6
% 114.82/17.47 (86) ~ (all_52_9 = all_6_2)
% 114.82/17.47 (87) ~ (all_52_1 = all_52_2)
% 114.82/17.47 (88) all_26_2 = all_4_2
% 114.82/17.47 (89) ~ (all_52_1 = all_52_3)
% 114.82/17.47 (90) all_56_1 = all_52_8
% 114.82/17.47 (91) op(e0, all_4_2) = all_4_1
% 114.82/17.47 (92) all_58_8 = all_6_2
% 114.82/17.47 (93) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.82/17.47 (94) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 114.82/17.47 (95) all_56_4 = all_52_9
% 114.82/17.47 (96) all_58_9 = all_52_12
% 114.82/17.47 (97) all_56_5 = all_52_13
% 114.82/17.47 (98) op(e2, e1) = all_52_9
% 114.82/17.47 (99) ~ (all_52_3 = all_4_2)
% 114.82/17.47 (100) ~ (all_52_6 = all_6_2)
% 114.82/17.47 (101) all_56_6 = all_52_2
% 114.82/17.47 (102) ~ (all_52_13 = all_4_2)
% 114.82/17.47 (103) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 114.82/17.47 (104) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 114.82/17.47 (105) all_58_12 = all_52_3
% 114.82/17.47 (106) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 114.82/17.47 (107) op(e2, e0) = all_52_13
% 114.82/17.47 (108) ~ (all_52_3 = all_10_2)
% 114.82/17.47 (109) op(e1, e3) = all_52_2
% 114.82/17.47 (110) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 114.82/17.47 (111) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 114.82/17.47 (112) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 114.82/17.47 (113) op(e1, e1) = all_6_2
% 114.82/17.47 (114) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 114.82/17.47 (115) all_56_8 = all_52_14
% 114.82/17.47 (116) all_26_1 = all_4_1
% 114.82/17.47 (117) ~ (all_52_11 = e1)
% 114.82/17.47 (118) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 114.82/17.47 (119) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 114.82/17.47 (120) ~ (e3 = e2)
% 114.82/17.47 (121) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 114.82/17.47 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 114.82/17.47 (122) all_54_4 = all_52_1
% 114.82/17.47 (123) all_54_15 = all_4_2
% 114.82/17.47 (124) op(e2, all_8_2) = e1
% 114.82/17.47 (125) ~ (all_6_2 = e1)
% 114.82/17.47 (126) ~ (all_52_3 = all_52_11)
% 114.82/17.47 (127) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 114.82/17.47 (128) all_54_12 = all_52_3
% 114.82/17.47 (129) ~ (all_52_3 = all_52_7)
% 114.82/17.47
% 114.82/17.47 Begin of proof
% 114.82/17.47 |
% 114.82/17.47 | REDUCE: (9), (18) imply:
% 114.82/17.47 | (130) ~ (all_6_2 = e2)
% 114.82/17.47 |
% 114.82/17.47 | BETA: splitting (112) gives:
% 114.82/17.47 |
% 114.82/17.47 | Case 1:
% 114.82/17.47 | |
% 114.82/17.47 | | (131) ~ (all_56_5 = e2)
% 114.82/17.47 | |
% 114.82/17.47 | | REDUCE: (97), (131) imply:
% 114.82/17.47 | | (132) ~ (all_52_13 = e2)
% 114.82/17.47 | |
% 114.82/17.47 | | BETA: splitting (119) gives:
% 114.82/17.47 | |
% 114.82/17.47 | | Case 1:
% 114.82/17.47 | | |
% 114.82/17.47 | | | (133) all_58_2 = e2
% 114.82/17.47 | | |
% 114.82/17.47 | | | COMBINE_EQS: (59), (133) imply:
% 114.82/17.47 | | | (134) all_52_1 = e2
% 114.82/17.47 | | |
% 114.82/17.47 | | | SIMP: (134) implies:
% 114.82/17.47 | | | (135) all_52_1 = e2
% 114.82/17.47 | | |
% 114.82/17.47 | | | REDUCE: (67), (135) imply:
% 114.82/17.47 | | | (136) ~ (all_10_2 = e2)
% 114.82/17.47 | | |
% 114.82/17.47 | | | SIMP: (136) implies:
% 114.82/17.47 | | | (137) ~ (all_10_2 = e2)
% 114.82/17.47 | | |
% 114.82/17.47 | | | REDUCE: (81), (135) imply:
% 114.82/17.47 | | | (138) ~ (all_8_2 = e2)
% 114.82/17.47 | | |
% 114.82/17.47 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 114.82/17.47 | | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 114.82/17.47 | | | (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 114.82/17.47 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 114.82/17.47 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 114.82/17.47 | | | (57), (58), (59), (61), (62), (63), (64), (65), (66), (67),
% 114.82/17.47 | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 114.82/17.47 | | | (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 114.82/17.47 | | | (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 114.82/17.47 | | | (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 114.82/17.47 | | | (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 114.82/17.47 | | | (116), (118), (119), (120), (121), (122), (123), (124), (125),
% 114.82/17.47 | | | (126), (127), (128), (129), (130), (137) are inconsistent by
% 114.82/17.47 | | | sub-proof #91.
% 114.82/17.47 | | |
% 114.82/17.47 | | Case 2:
% 114.82/17.47 | | |
% 114.82/17.47 | | | (139) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 114.82/17.47 | | |
% 114.82/17.47 | | | REF_CLOSE: (4), (35), (51), (71), (82), (132), (139) are inconsistent by
% 114.82/17.47 | | | sub-proof #401.
% 114.82/17.47 | | |
% 114.82/17.47 | | End of split
% 114.82/17.47 | |
% 114.82/17.47 | Case 2:
% 114.82/17.47 | |
% 114.82/17.48 | | (140) all_56_5 = e2
% 114.82/17.48 | | (141) ~ (all_56_12 = e0)
% 114.82/17.48 | |
% 114.82/17.48 | | REF_CLOSE: (1), (5), (6), (9), (11), (16), (17), (21), (25), (26), (27),
% 114.82/17.48 | | (29), (30), (31), (34), (38), (39), (44), (45), (48), (51), (56),
% 114.82/17.48 | | (59), (60), (62), (65), (67), (68), (72), (79), (80), (81), (84),
% 114.82/17.48 | | (85), (92), (93), (97), (101), (111), (117), (122), (124), (125),
% 114.82/17.48 | | (130), (140), (141) are inconsistent by sub-proof #89.
% 114.82/17.48 | |
% 114.82/17.48 | End of split
% 114.82/17.48 |
% 114.82/17.48 End of proof
% 114.82/17.48
% 114.82/17.48 Sub-proof #89 shows that the following formulas are inconsistent:
% 114.82/17.48 ----------------------------------------------------------------
% 114.82/17.48 (1) ~ (all_52_8 = all_10_2)
% 114.82/17.48 (2) all_58_7 = all_52_6
% 114.82/17.48 (3) ~ (all_52_9 = all_8_2)
% 114.82/17.48 (4) all_56_14 = all_6_2
% 114.82/17.48 (5) all_54_0 = all_10_2
% 114.82/17.48 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 114.82/17.48 (7) all_56_12 = all_10_2
% 114.82/17.48 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 114.82/17.48 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.48 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 114.82/17.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 114.82/17.48 (11) ~ (all_52_1 = all_52_9)
% 114.82/17.48 (12) all_54_10 = all_6_2
% 114.82/17.48 (13) ~ (all_52_14 = e1)
% 114.82/17.48 (14) all_58_4 = all_52_8
% 114.82/17.48 (15) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 114.82/17.48 (16) all_58_11 = all_52_14
% 114.82/17.48 (17) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 114.82/17.48 (18) op(e2, e3) = all_52_1
% 114.82/17.48 (19) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 114.82/17.48 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 114.82/17.48 (21) all_58_5 = all_52_9
% 114.82/17.48 (22) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 114.82/17.48 (23) all_58_2 = all_52_1
% 114.82/17.48 (24) ~ (all_52_1 = all_52_13)
% 114.82/17.48 (25) ~ (all_10_2 = e3)
% 114.82/17.48 (26) ~ (all_56_12 = e0)
% 114.82/17.48 (27) all_58_6 = all_52_2
% 114.82/17.48 (28) ~ (all_52_1 = all_10_2)
% 114.82/17.48 (29) all_54_5 = all_8_2
% 114.82/17.48 (30) ~ (all_52_13 = all_8_2)
% 114.82/17.48 (31) all_56_5 = e2
% 114.82/17.48 (32) all_58_14 = all_52_11
% 114.82/17.48 (33) all_56_13 = all_8_2
% 114.82/17.48 (34) ~ (all_52_1 = all_8_2)
% 114.82/17.48 (35) ~ (all_6_2 = e2)
% 114.82/17.48 (36) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.48 (37) all_56_7 = all_52_6
% 114.82/17.48 (38) all_58_8 = all_6_2
% 114.82/17.48 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.82/17.48 (40) all_56_5 = all_52_13
% 114.82/17.48 (41) all_56_6 = all_52_2
% 114.82/17.48 (42) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 114.82/17.48 (43) ~ (all_52_11 = e1)
% 114.82/17.48 (44) all_54_4 = all_52_1
% 114.82/17.48 (45) op(e2, all_8_2) = e1
% 114.82/17.48 (46) ~ (all_6_2 = e1)
% 114.82/17.48
% 114.82/17.48 Begin of proof
% 114.82/17.48 |
% 114.82/17.48 | COMBINE_EQS: (31), (40) imply:
% 114.82/17.48 | (47) all_52_13 = e2
% 114.82/17.48 |
% 114.82/17.48 | REDUCE: (7), (26) imply:
% 114.82/17.48 | (48) ~ (all_10_2 = e0)
% 114.82/17.48 |
% 114.82/17.48 | REDUCE: (24), (47) imply:
% 114.82/17.48 | (49) ~ (all_52_1 = e2)
% 114.82/17.48 |
% 114.82/17.48 | REDUCE: (30), (47) imply:
% 114.82/17.48 | (50) ~ (all_8_2 = e2)
% 114.82/17.48 |
% 114.82/17.48 | SIMP: (50) implies:
% 114.82/17.48 | (51) ~ (all_8_2 = e2)
% 114.82/17.48 |
% 114.82/17.48 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 114.82/17.48 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 114.82/17.48 | (25), (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 114.82/17.48 | (38), (39), (41), (42), (43), (44), (45), (46), (48), (49), (51)
% 114.82/17.48 | are inconsistent by sub-proof #90.
% 114.82/17.48 |
% 114.82/17.48 End of proof
% 114.82/17.48
% 114.82/17.48 Sub-proof #90 shows that the following formulas are inconsistent:
% 114.82/17.48 ----------------------------------------------------------------
% 114.82/17.48 (1) ~ (all_52_8 = all_10_2)
% 114.82/17.48 (2) all_58_7 = all_52_6
% 114.82/17.48 (3) ~ (all_52_9 = all_8_2)
% 114.82/17.48 (4) ~ (all_52_1 = e2)
% 114.82/17.48 (5) all_56_14 = all_6_2
% 114.82/17.48 (6) all_54_0 = all_10_2
% 114.82/17.48 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 114.82/17.48 (8) all_56_12 = all_10_2
% 114.82/17.48 (9) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 114.82/17.48 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.48 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 114.82/17.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 114.82/17.48 (12) ~ (all_52_1 = all_52_9)
% 114.82/17.48 (13) all_54_10 = all_6_2
% 114.82/17.48 (14) ~ (all_52_14 = e1)
% 114.82/17.48 (15) all_58_4 = all_52_8
% 114.82/17.48 (16) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 114.82/17.48 (17) all_58_11 = all_52_14
% 114.82/17.48 (18) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 114.82/17.48 (19) op(e2, e3) = all_52_1
% 114.82/17.48 (20) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 114.82/17.48 (21) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 114.82/17.48 (22) all_58_5 = all_52_9
% 114.82/17.48 (23) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 114.82/17.48 (24) all_58_2 = all_52_1
% 114.82/17.48 (25) ~ (all_10_2 = e3)
% 114.82/17.48 (26) all_58_6 = all_52_2
% 114.82/17.48 (27) ~ (all_52_1 = all_10_2)
% 114.82/17.48 (28) all_54_5 = all_8_2
% 114.82/17.48 (29) all_56_5 = e2
% 114.82/17.48 (30) all_58_14 = all_52_11
% 114.82/17.48 (31) all_56_13 = all_8_2
% 114.82/17.48 (32) ~ (all_52_1 = all_8_2)
% 114.82/17.48 (33) ~ (all_8_2 = e2)
% 114.82/17.48 (34) ~ (all_6_2 = e2)
% 114.82/17.48 (35) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.48 (36) ~ (all_10_2 = e0)
% 114.82/17.48 (37) all_56_7 = all_52_6
% 114.82/17.48 (38) all_58_8 = all_6_2
% 114.82/17.48 (39) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.82/17.48 (40) all_56_6 = all_52_2
% 114.82/17.48 (41) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 114.82/17.48 (42) ~ (all_52_11 = e1)
% 114.82/17.48 (43) all_54_4 = all_52_1
% 114.82/17.48 (44) op(e2, all_8_2) = e1
% 114.82/17.48 (45) ~ (all_6_2 = e1)
% 114.82/17.48
% 114.82/17.48 Begin of proof
% 114.82/17.48 |
% 114.82/17.48 | BETA: splitting (21) gives:
% 114.82/17.48 |
% 114.82/17.48 | Case 1:
% 114.82/17.48 | |
% 114.82/17.48 | | (46) ~ (all_56_5 = e2)
% 114.82/17.48 | |
% 114.82/17.48 | | REDUCE: (29), (46) imply:
% 114.82/17.48 | | (47) $false
% 114.82/17.48 | |
% 114.82/17.48 | | CLOSE: (47) is inconsistent.
% 114.82/17.48 | |
% 114.82/17.48 | Case 2:
% 114.82/17.48 | |
% 114.82/17.48 | | (48) ~ (all_56_14 = e0)
% 114.82/17.48 | |
% 114.82/17.48 | | REDUCE: (5), (48) imply:
% 114.82/17.48 | | (49) ~ (all_6_2 = e0)
% 114.82/17.48 | |
% 114.82/17.48 | | BETA: splitting (18) gives:
% 114.82/17.48 | |
% 114.82/17.48 | | Case 1:
% 114.82/17.48 | | |
% 114.82/17.48 | | | (50) ~ (all_56_5 = e2)
% 114.82/17.48 | | |
% 114.82/17.48 | | | REDUCE: (29), (50) imply:
% 114.82/17.48 | | | (51) $false
% 114.82/17.48 | | |
% 114.82/17.48 | | | CLOSE: (51) is inconsistent.
% 114.82/17.48 | | |
% 114.82/17.48 | | Case 2:
% 114.82/17.48 | | |
% 114.82/17.48 | | | (52) ~ (all_56_13 = e0)
% 114.82/17.48 | | |
% 114.82/17.48 | | | REDUCE: (31), (52) imply:
% 114.82/17.48 | | | (53) ~ (all_8_2 = e0)
% 114.82/17.48 | | |
% 114.82/17.48 | | | BETA: splitting (10) gives:
% 114.82/17.48 | | |
% 114.82/17.48 | | | Case 1:
% 114.82/17.48 | | | |
% 114.82/17.48 | | | | (54) all_54_10 = e3
% 114.82/17.48 | | | |
% 114.82/17.48 | | | | COMBINE_EQS: (13), (54) imply:
% 114.82/17.48 | | | | (55) all_6_2 = e3
% 114.82/17.48 | | | |
% 114.82/17.48 | | | | COMBINE_EQS: (5), (55) imply:
% 114.82/17.49 | | | | (56) all_56_14 = e3
% 114.82/17.49 | | | |
% 114.82/17.49 | | | | BETA: splitting (16) gives:
% 114.82/17.49 | | | |
% 114.82/17.49 | | | | Case 1:
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | (57) ~ (all_56_6 = e1)
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | REDUCE: (40), (57) imply:
% 114.82/17.49 | | | | | (58) ~ (all_52_2 = e1)
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | BETA: splitting (35) gives:
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | Case 1:
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | | (59) all_58_6 = e1
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | | REF_CLOSE: (26), (58), (59) are inconsistent by sub-proof #452.
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | Case 2:
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | | (60) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | | BETA: splitting (60) gives:
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | | Case 1:
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | (61) all_58_7 = e1
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | COMBINE_EQS: (2), (61) imply:
% 114.82/17.49 | | | | | | | (62) all_52_6 = e1
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | COMBINE_EQS: (37), (62) imply:
% 114.82/17.49 | | | | | | | (63) all_56_7 = e1
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | BETA: splitting (23) gives:
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | Case 1:
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | (64) ~ (all_56_7 = e1)
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | REDUCE: (63), (64) imply:
% 114.82/17.49 | | | | | | | | (65) $false
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | CLOSE: (65) is inconsistent.
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | Case 2:
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | (66) ~ (all_56_12 = e2)
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | REDUCE: (8), (66) imply:
% 114.82/17.49 | | | | | | | | (67) ~ (all_10_2 = e2)
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (15), (19),
% 114.82/17.49 | | | | | | | | (20), (22), (24), (25), (27), (28), (30), (32), (33),
% 114.82/17.49 | | | | | | | | (36), (38), (39), (41), (42), (43), (44), (45), (53),
% 114.82/17.49 | | | | | | | | (67) are inconsistent by sub-proof #124.
% 114.82/17.49 | | | | | | | |
% 114.82/17.49 | | | | | | | End of split
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | Case 2:
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | (68) all_58_8 = e1 | all_58_11 = e1
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | | REF_CLOSE: (14), (17), (38), (45), (68) are inconsistent by
% 114.82/17.49 | | | | | | | sub-proof #445.
% 114.82/17.49 | | | | | | |
% 114.82/17.49 | | | | | | End of split
% 114.82/17.49 | | | | | |
% 114.82/17.49 | | | | | End of split
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | Case 2:
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | (69) ~ (all_56_14 = e3)
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | REDUCE: (56), (69) imply:
% 114.82/17.49 | | | | | (70) $false
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | | CLOSE: (70) is inconsistent.
% 114.82/17.49 | | | | |
% 114.82/17.49 | | | | End of split
% 114.82/17.49 | | | |
% 114.82/17.49 | | | Case 2:
% 114.82/17.49 | | | |
% 114.82/17.49 | | | | (71) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.49 | | | |
% 114.82/17.49 | | | | REF_CLOSE: (13), (34), (45), (49), (71) are inconsistent by sub-proof
% 114.82/17.49 | | | | #435.
% 114.82/17.49 | | | |
% 114.82/17.49 | | | End of split
% 114.82/17.49 | | |
% 114.82/17.49 | | End of split
% 114.82/17.49 | |
% 114.82/17.49 | End of split
% 114.82/17.49 |
% 114.82/17.49 End of proof
% 114.82/17.49
% 114.82/17.49 Sub-proof #91 shows that the following formulas are inconsistent:
% 114.82/17.49 ----------------------------------------------------------------
% 114.82/17.49 (1) ~ (all_52_8 = all_10_2)
% 114.82/17.49 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 114.82/17.49 (3) ~ (all_52_2 = all_10_2)
% 114.82/17.49 (4) all_58_7 = all_52_6
% 114.82/17.49 (5) ~ (all_52_9 = all_8_2)
% 114.82/17.49 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 114.82/17.49 (7) ~ (all_4_2 = e0)
% 114.82/17.49 (8) all_56_14 = all_6_2
% 114.82/17.49 (9) all_56_3 = all_52_1
% 114.82/17.49 (10) all_54_0 = all_10_2
% 114.82/17.49 (11) all_56_11 = all_52_11
% 114.82/17.49 (12) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 114.82/17.49 (13) ~ (all_52_12 = all_10_2)
% 114.82/17.49 (14) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 114.82/17.49 (15) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 114.82/17.49 (16) all_56_12 = all_10_2
% 114.82/17.49 (17) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 114.82/17.49 (18) all_58_0 = all_10_2
% 114.82/17.49 (19) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 114.82/17.49 (20) ~ (all_52_14 = all_6_2)
% 114.82/17.49 (21) all_56_10 = all_52_7
% 114.82/17.49 (22) all_54_14 = all_52_11
% 114.82/17.49 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 114.82/17.49 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 114.82/17.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 114.82/17.49 (25) ~ (all_52_1 = all_52_9)
% 114.82/17.49 (26) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 114.82/17.49 (27) ~ (all_10_2 = e2)
% 114.82/17.49 (28) all_54_10 = all_6_2
% 114.82/17.49 (29) all_58_4 = all_52_8
% 114.82/17.49 (30) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 114.82/17.49 (31) all_56_2 = all_52_12
% 114.82/17.49 (32) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 114.82/17.49 (33) all_58_3 = all_8_2
% 114.82/17.49 (34) all_54_6 = all_52_9
% 114.82/17.49 (35) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 114.82/17.49 (36) all_58_11 = all_52_14
% 114.82/17.49 (37) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 114.82/17.49 (38) ~ (all_52_2 = all_52_3)
% 114.82/17.49 (39) all_54_7 = all_52_13
% 114.82/17.49 (40) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 114.82/17.49 (41) ~ (all_52_11 = all_6_2)
% 114.82/17.49 (42) op(e2, e3) = all_52_1
% 114.82/17.49 (43) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 114.82/17.49 (44) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 114.82/17.49 (45) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 114.82/17.49 (46) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 114.82/17.49 (47) ~ (all_52_7 = all_8_2)
% 114.82/17.49 (48) ~ (all_52_4 = all_8_2)
% 114.82/17.49 (49) all_58_5 = all_52_9
% 114.82/17.49 (50) op(all_4_1, all_4_2) = e1
% 114.82/17.49 (51) all_56_9 = all_52_3
% 114.82/17.49 (52) op(e1, all_6_2) = all_6_1
% 114.82/17.49 (53) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 114.82/17.49 (54) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 114.82/17.49 (55) all_58_15 = all_4_2
% 114.82/17.49 (56) all_58_2 = all_52_1
% 114.82/17.49 (57) op(e0, e3) = all_52_3
% 114.82/17.49 (58) ~ (all_10_2 = e3)
% 114.82/17.49 (59) all_58_13 = all_52_7
% 114.82/17.49 (60) ~ (all_52_14 = all_4_2)
% 114.82/17.49 (61) all_58_6 = all_52_2
% 114.82/17.49 (62) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 114.82/17.49 (63) ~ (all_52_1 = all_10_2)
% 114.82/17.49 (64) all_54_5 = all_8_2
% 114.82/17.49 (65) all_56_15 = all_4_2
% 114.82/17.49 (66) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 114.82/17.49 (67) all_58_10 = all_52_13
% 114.82/17.49 (68) ~ (all_52_13 = all_8_2)
% 114.82/17.49 (69) ~ (all_52_11 = all_4_2)
% 114.82/17.49 (70) ~ (all_52_6 = all_8_2)
% 114.82/17.49 (71) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 114.82/17.49 (72) all_58_1 = all_52_4
% 114.82/17.49 (73) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 114.82/17.49 (74) ~ (all_52_9 = all_52_11)
% 114.82/17.49 (75) all_58_14 = all_52_11
% 114.82/17.49 (76) all_56_13 = all_8_2
% 114.82/17.49 (77) ~ (all_52_1 = all_8_2)
% 114.82/17.49 (78) ~ (all_8_2 = e2)
% 114.82/17.49 (79) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 114.82/17.49 (80) ~ (all_6_2 = e2)
% 114.82/17.49 (81) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 114.82/17.49 (82) all_56_7 = all_52_6
% 114.82/17.49 (83) ~ (all_52_9 = all_6_2)
% 114.82/17.49 (84) ~ (all_52_1 = all_52_2)
% 114.82/17.49 (85) all_26_2 = all_4_2
% 114.82/17.49 (86) ~ (all_52_1 = all_52_3)
% 114.82/17.49 (87) all_56_1 = all_52_8
% 114.82/17.49 (88) op(e0, all_4_2) = all_4_1
% 114.82/17.49 (89) all_58_8 = all_6_2
% 114.82/17.49 (90) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 114.82/17.49 (91) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 114.82/17.49 (92) all_56_4 = all_52_9
% 114.82/17.49 (93) all_58_9 = all_52_12
% 114.82/17.49 (94) all_56_5 = all_52_13
% 114.82/17.49 (95) op(e2, e1) = all_52_9
% 115.06/17.49 (96) ~ (all_52_3 = all_4_2)
% 115.06/17.49 (97) ~ (all_52_6 = all_6_2)
% 115.06/17.49 (98) all_56_6 = all_52_2
% 115.06/17.49 (99) ~ (all_52_13 = all_4_2)
% 115.06/17.49 (100) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 115.06/17.50 (101) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.06/17.50 (102) all_58_12 = all_52_3
% 115.06/17.50 (103) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.06/17.50 (104) op(e2, e0) = all_52_13
% 115.06/17.50 (105) ~ (all_52_3 = all_10_2)
% 115.06/17.50 (106) op(e1, e3) = all_52_2
% 115.06/17.50 (107) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 115.06/17.50 (108) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.06/17.50 (109) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 115.06/17.50 (110) op(e1, e1) = all_6_2
% 115.06/17.50 (111) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.06/17.50 (112) all_56_8 = all_52_14
% 115.06/17.50 (113) all_26_1 = all_4_1
% 115.06/17.50 (114) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.06/17.50 (115) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.06/17.50 (116) ~ (e3 = e2)
% 115.06/17.50 (117) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.06/17.50 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.06/17.50 (118) all_54_4 = all_52_1
% 115.06/17.50 (119) all_54_15 = all_4_2
% 115.06/17.50 (120) op(e2, all_8_2) = e1
% 115.06/17.50 (121) ~ (all_6_2 = e1)
% 115.06/17.50 (122) ~ (all_52_3 = all_52_11)
% 115.06/17.50 (123) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.06/17.50 (124) all_54_12 = all_52_3
% 115.06/17.50 (125) ~ (all_52_3 = all_52_7)
% 115.06/17.50
% 115.06/17.50 Begin of proof
% 115.06/17.50 |
% 115.06/17.50 | BETA: splitting (91) gives:
% 115.06/17.50 |
% 115.06/17.50 | Case 1:
% 115.06/17.50 | |
% 115.06/17.50 | | (126) ~ (all_56_15 = e3)
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (65), (126) imply:
% 115.06/17.50 | | (127) ~ (all_4_2 = e3)
% 115.06/17.50 | |
% 115.06/17.50 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 115.06/17.50 | | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 115.06/17.50 | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 115.06/17.50 | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 115.06/17.50 | | (49), (51), (53), (54), (55), (56), (58), (59), (60), (61), (62),
% 115.06/17.50 | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 115.06/17.50 | | (75), (76), (77), (78), (80), (81), (82), (86), (87), (89), (90),
% 115.06/17.50 | | (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 115.06/17.50 | | (102), (103), (104), (105), (107), (108), (110), (111), (112),
% 115.06/17.50 | | (114), (115), (116), (117), (118), (119), (120), (121), (124),
% 115.06/17.50 | | (125), (127) are inconsistent by sub-proof #120.
% 115.06/17.50 | |
% 115.06/17.50 | Case 2:
% 115.06/17.50 | |
% 115.06/17.50 | | (128) all_56_15 = e3
% 115.06/17.50 | | (129) ~ (all_56_9 = e0)
% 115.06/17.50 | |
% 115.06/17.50 | | COMBINE_EQS: (65), (128) imply:
% 115.06/17.50 | | (130) all_4_2 = e3
% 115.06/17.50 | |
% 115.06/17.50 | | SIMP: (130) implies:
% 115.06/17.50 | | (131) all_4_2 = e3
% 115.06/17.50 | |
% 115.06/17.50 | | COMBINE_EQS: (85), (131) imply:
% 115.06/17.50 | | (132) all_26_2 = e3
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (51), (129) imply:
% 115.06/17.50 | | (133) ~ (all_52_3 = e0)
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (96), (131) imply:
% 115.06/17.50 | | (134) ~ (all_52_3 = e3)
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (69), (131) imply:
% 115.06/17.50 | | (135) ~ (all_52_11 = e3)
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (50), (131) imply:
% 115.06/17.50 | | (136) op(all_4_1, e3) = e1
% 115.06/17.50 | |
% 115.06/17.50 | | REDUCE: (88), (131) imply:
% 115.06/17.50 | | (137) op(e0, e3) = all_4_1
% 115.06/17.50 | |
% 115.06/17.50 | | BETA: splitting (26) gives:
% 115.06/17.50 | |
% 115.06/17.50 | | Case 1:
% 115.06/17.50 | | |
% 115.06/17.50 | | | (138) ~ (all_56_3 = e2)
% 115.06/17.50 | | |
% 115.06/17.50 | | | REDUCE: (9), (138) imply:
% 115.06/17.50 | | | (139) ~ (all_52_1 = e2)
% 115.06/17.50 | | |
% 115.06/17.50 | | | BETA: splitting (79) gives:
% 115.06/17.50 | | |
% 115.06/17.50 | | | Case 1:
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | (140) ~ (all_26_1 = e2)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (113), (140) imply:
% 115.06/17.50 | | | | (141) ~ (all_4_1 = e2)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | GROUND_INST: instantiating (24) with all_52_3, all_4_1, e3, e0,
% 115.06/17.50 | | | | simplifying with (57), (137) gives:
% 115.06/17.50 | | | | (142) all_52_3 = all_4_1
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | COMBINE_EQS: (124), (142) imply:
% 115.06/17.50 | | | | (143) all_54_12 = all_4_1
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | COMBINE_EQS: (102), (142) imply:
% 115.06/17.50 | | | | (144) all_58_12 = all_4_1
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (38), (142) imply:
% 115.06/17.50 | | | | (145) ~ (all_52_2 = all_4_1)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (122), (142) imply:
% 115.06/17.50 | | | | (146) ~ (all_52_11 = all_4_1)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | SIMP: (146) implies:
% 115.06/17.50 | | | | (147) ~ (all_52_11 = all_4_1)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (105), (142) imply:
% 115.06/17.50 | | | | (148) ~ (all_10_2 = all_4_1)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | SIMP: (148) implies:
% 115.06/17.50 | | | | (149) ~ (all_10_2 = all_4_1)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (134), (142) imply:
% 115.06/17.50 | | | | (150) ~ (all_4_1 = e3)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | REDUCE: (133), (142) imply:
% 115.06/17.50 | | | | (151) ~ (all_4_1 = e0)
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | BETA: splitting (103) gives:
% 115.06/17.50 | | | |
% 115.06/17.50 | | | | Case 1:
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | (152) all_54_12 = e3
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | COMBINE_EQS: (143), (152) imply:
% 115.06/17.50 | | | | | (153) all_4_1 = e3
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | REDUCE: (150), (153) imply:
% 115.06/17.50 | | | | | (154) $false
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | CLOSE: (154) is inconsistent.
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | Case 2:
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | (155) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | BETA: splitting (155) gives:
% 115.06/17.50 | | | | |
% 115.06/17.50 | | | | | Case 1:
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | (156) all_54_12 = e2
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | COMBINE_EQS: (143), (156) imply:
% 115.06/17.50 | | | | | | (157) all_4_1 = e2
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | REDUCE: (141), (157) imply:
% 115.06/17.50 | | | | | | (158) $false
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | CLOSE: (158) is inconsistent.
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | Case 2:
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | (159) ~ (all_54_12 = e2)
% 115.06/17.50 | | | | | | (160) all_54_12 = e1 | all_54_12 = e0
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | BETA: splitting (160) gives:
% 115.06/17.50 | | | | | |
% 115.06/17.50 | | | | | | Case 1:
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | (161) all_54_12 = e1
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | COMBINE_EQS: (143), (161) imply:
% 115.06/17.50 | | | | | | | (162) all_4_1 = e1
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | COMBINE_EQS: (144), (162) imply:
% 115.06/17.50 | | | | | | | (163) all_58_12 = e1
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | REDUCE: (145), (162) imply:
% 115.06/17.50 | | | | | | | (164) ~ (all_52_2 = e1)
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | REDUCE: (147), (162) imply:
% 115.06/17.50 | | | | | | | (165) ~ (all_52_11 = e1)
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | REDUCE: (149), (162) imply:
% 115.06/17.50 | | | | | | | (166) ~ (all_10_2 = e1)
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | REDUCE: (141), (162) imply:
% 115.06/17.50 | | | | | | | (167) ~ (e2 = e1)
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | SIMP: (167) implies:
% 115.06/17.50 | | | | | | | (168) ~ (e2 = e1)
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | REDUCE: (136), (162) imply:
% 115.06/17.50 | | | | | | | (169) op(e1, e3) = e1
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | BETA: splitting (6) gives:
% 115.06/17.50 | | | | | | |
% 115.06/17.50 | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | (170) all_58_0 = e2
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | COMBINE_EQS: (18), (170) imply:
% 115.06/17.50 | | | | | | | | (171) all_10_2 = e2
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | REDUCE: (27), (171) imply:
% 115.06/17.50 | | | | | | | | (172) $false
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | CLOSE: (172) is inconsistent.
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | Case 2:
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | (173) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | BETA: splitting (173) gives:
% 115.06/17.50 | | | | | | | |
% 115.06/17.50 | | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | (174) all_58_2 = e2
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | COMBINE_EQS: (56), (174) imply:
% 115.06/17.50 | | | | | | | | | (175) all_52_1 = e2
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | REDUCE: (139), (175) imply:
% 115.06/17.50 | | | | | | | | | (176) $false
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | CLOSE: (176) is inconsistent.
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | Case 2:
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | (177) all_58_6 = e2 | all_58_12 = e2
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | BETA: splitting (177) gives:
% 115.06/17.50 | | | | | | | | |
% 115.06/17.50 | | | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | (178) all_58_6 = e2
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | COMBINE_EQS: (61), (178) imply:
% 115.06/17.50 | | | | | | | | | | (179) all_52_2 = e2
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | REDUCE: (3), (179) imply:
% 115.06/17.50 | | | | | | | | | | (180) ~ (all_10_2 = e2)
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | REDUCE: (106), (179) imply:
% 115.06/17.50 | | | | | | | | | | (181) op(e1, e3) = e2
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | BETA: splitting (90) gives:
% 115.06/17.50 | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | (182) all_54_0 = e3
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | REF_CLOSE: (10), (58), (182) are inconsistent by sub-proof
% 115.06/17.50 | | | | | | | | | | | #451.
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | Case 2:
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | (183) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | BETA: splitting (183) gives:
% 115.06/17.50 | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | (184) all_54_0 = e2
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | REF_CLOSE: (10), (27), (184) are inconsistent by sub-proof
% 115.06/17.50 | | | | | | | | | | | | #450.
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | Case 2:
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | (185) all_54_0 = e1 | all_54_0 = e0
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | BETA: splitting (185) gives:
% 115.06/17.50 | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | Case 1:
% 115.06/17.50 | | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | | (186) all_54_0 = e1
% 115.06/17.50 | | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | | REF_CLOSE: (10), (166), (186) are inconsistent by sub-proof
% 115.06/17.50 | | | | | | | | | | | | | #449.
% 115.06/17.50 | | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | Case 2:
% 115.06/17.50 | | | | | | | | | | | | |
% 115.06/17.50 | | | | | | | | | | | | | (187) all_54_0 = e0
% 115.06/17.50 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | COMBINE_EQS: (10), (187) imply:
% 115.06/17.51 | | | | | | | | | | | | | (188) all_10_2 = e0
% 115.06/17.51 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | SIMP: (188) implies:
% 115.06/17.51 | | | | | | | | | | | | | (189) all_10_2 = e0
% 115.06/17.51 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | COMBINE_EQS: (16), (189) imply:
% 115.06/17.51 | | | | | | | | | | | | | (190) all_56_12 = e0
% 115.06/17.51 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | BETA: splitting (109) gives:
% 115.06/17.51 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | (191) ~ (all_56_5 = e2)
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | REDUCE: (94), (191) imply:
% 115.06/17.51 | | | | | | | | | | | | | | (192) ~ (all_52_13 = e2)
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | (193) all_58_2 = e2
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | COMBINE_EQS: (56), (193) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | (194) all_52_1 = e2
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | REDUCE: (139), (194) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | (195) $false
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | (196) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | (197) all_58_3 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (197) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | (198) all_8_2 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | REDUCE: (78), (198) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | (199) $false
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | (200) all_58_5 = e2 | all_58_10 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | (201) all_58_5 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (201) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (202) all_52_9 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | REDUCE: (74), (202) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (203) ~ (all_52_11 = e2)
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | SIMP: (203) implies:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (204) ~ (all_52_11 = e2)
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | REDUCE: (83), (202) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (205) ~ (all_6_2 = e2)
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | (206) all_54_14 = e3
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (135), (206) are inconsistent by sub-proof
% 115.06/17.51 | | | | | | | | | | | | | | | | | | #93.
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | (207) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | (208) all_54_14 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (204), (208) are inconsistent by sub-proof
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | #92.
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | (209) all_54_14 = e1 | all_54_14 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (210) all_54_14 = e1
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (165), (210) are inconsistent by sub-proof
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | #141.
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (211) all_54_14 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (211) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (212) all_52_11 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (213) all_52_11 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (213) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (214) ~ (all_6_2 = e0)
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | (215) ~ (all_6_2 = e0)
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (216) all_54_10 = e3
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (216) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (217) all_6_2 = e3
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | SIMP: (217) implies:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (218) all_6_2 = e3
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (218) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (219) op(e1, e3) = all_6_1
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with e2, all_6_1, e3, e1,
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | simplifying with (181), (219) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (220) all_6_1 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with e1, all_6_1, e3, e1,
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | simplifying with (169), (219) gives:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (221) all_6_1 = e1
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (221) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (222) e2 = e1
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (223) e2 = e1
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (223) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (224) $false
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | (225) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (80), (121), (215), (225) are inconsistent
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | | by sub-proof #435.
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | (226) all_58_10 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (226) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (227) all_52_13 = e2
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | REDUCE: (192), (227) imply:
% 115.06/17.51 | | | | | | | | | | | | | | | | | (228) $false
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 115.06/17.51 | | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | (229) ~ (all_56_12 = e0)
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | REDUCE: (190), (229) imply:
% 115.06/17.51 | | | | | | | | | | | | | | (230) $false
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 115.06/17.51 | | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | Case 2:
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | (231) all_58_12 = e2
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | COMBINE_EQS: (163), (231) imply:
% 115.06/17.51 | | | | | | | | | | (232) e2 = e1
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | SIMP: (232) implies:
% 115.06/17.51 | | | | | | | | | | (233) e2 = e1
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | REDUCE: (168), (233) imply:
% 115.06/17.51 | | | | | | | | | | (234) $false
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | | CLOSE: (234) is inconsistent.
% 115.06/17.51 | | | | | | | | | |
% 115.06/17.51 | | | | | | | | | End of split
% 115.06/17.51 | | | | | | | | |
% 115.06/17.51 | | | | | | | | End of split
% 115.06/17.51 | | | | | | | |
% 115.06/17.51 | | | | | | | End of split
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | Case 2:
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | | (235) all_54_12 = e0
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | | COMBINE_EQS: (143), (235) imply:
% 115.06/17.51 | | | | | | | (236) all_4_1 = e0
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | | REDUCE: (151), (236) imply:
% 115.06/17.51 | | | | | | | (237) $false
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | | CLOSE: (237) is inconsistent.
% 115.06/17.51 | | | | | | |
% 115.06/17.51 | | | | | | End of split
% 115.06/17.51 | | | | | |
% 115.06/17.51 | | | | | End of split
% 115.06/17.51 | | | | |
% 115.06/17.51 | | | | End of split
% 115.06/17.51 | | | |
% 115.06/17.51 | | | Case 2:
% 115.06/17.51 | | | |
% 115.06/17.51 | | | | (238) ~ (all_26_2 = e3)
% 115.06/17.51 | | | |
% 115.06/17.51 | | | | REDUCE: (132), (238) imply:
% 115.06/17.51 | | | | (239) $false
% 115.06/17.51 | | | |
% 115.06/17.51 | | | | CLOSE: (239) is inconsistent.
% 115.06/17.51 | | | |
% 115.06/17.51 | | | End of split
% 115.06/17.51 | | |
% 115.06/17.51 | | Case 2:
% 115.06/17.51 | | |
% 115.06/17.51 | | | (240) ~ (all_56_15 = e3)
% 115.06/17.51 | | |
% 115.06/17.51 | | | REDUCE: (128), (240) imply:
% 115.06/17.51 | | | (241) $false
% 115.06/17.51 | | |
% 115.06/17.51 | | | CLOSE: (241) is inconsistent.
% 115.06/17.51 | | |
% 115.06/17.51 | | End of split
% 115.06/17.51 | |
% 115.06/17.51 | End of split
% 115.06/17.51 |
% 115.06/17.51 End of proof
% 115.06/17.51
% 115.06/17.51 Sub-proof #92 shows that the following formulas are inconsistent:
% 115.06/17.51 ----------------------------------------------------------------
% 115.06/17.51 (1) all_54_14 = all_52_11
% 115.06/17.51 (2) all_54_14 = e2
% 115.06/17.51 (3) ~ (all_52_11 = e2)
% 115.06/17.51
% 115.06/17.51 Begin of proof
% 115.06/17.51 |
% 115.06/17.51 | COMBINE_EQS: (1), (2) imply:
% 115.06/17.51 | (4) all_52_11 = e2
% 115.06/17.51 |
% 115.06/17.51 | SIMP: (4) implies:
% 115.06/17.51 | (5) all_52_11 = e2
% 115.06/17.51 |
% 115.06/17.51 | REDUCE: (3), (5) imply:
% 115.06/17.51 | (6) $false
% 115.06/17.51 |
% 115.06/17.51 | CLOSE: (6) is inconsistent.
% 115.06/17.51 |
% 115.06/17.51 End of proof
% 115.06/17.51
% 115.06/17.51 Sub-proof #93 shows that the following formulas are inconsistent:
% 115.06/17.51 ----------------------------------------------------------------
% 115.06/17.51 (1) all_54_14 = all_52_11
% 115.06/17.51 (2) all_54_14 = e3
% 115.06/17.51 (3) ~ (all_52_11 = e3)
% 115.06/17.51
% 115.06/17.51 Begin of proof
% 115.06/17.51 |
% 115.06/17.51 | COMBINE_EQS: (1), (2) imply:
% 115.06/17.51 | (4) all_52_11 = e3
% 115.06/17.51 |
% 115.06/17.51 | SIMP: (4) implies:
% 115.06/17.51 | (5) all_52_11 = e3
% 115.06/17.51 |
% 115.06/17.51 | REDUCE: (3), (5) imply:
% 115.06/17.51 | (6) $false
% 115.06/17.51 |
% 115.06/17.51 | CLOSE: (6) is inconsistent.
% 115.06/17.51 |
% 115.06/17.51 End of proof
% 115.06/17.51
% 115.06/17.51 Sub-proof #94 shows that the following formulas are inconsistent:
% 115.06/17.51 ----------------------------------------------------------------
% 115.06/17.51 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 115.06/17.51 (2) ~ (all_52_2 = all_10_2)
% 115.06/17.51 (3) all_58_7 = all_52_6
% 115.06/17.51 (4) ~ (all_4_2 = e0)
% 115.06/17.51 (5) op(e3, e2) = all_52_4
% 115.06/17.51 (6) all_56_14 = all_6_2
% 115.06/17.51 (7) all_54_0 = all_10_2
% 115.06/17.51 (8) all_54_3 = all_52_12
% 115.06/17.51 (9) op(e0, e2) = all_52_7
% 115.06/17.51 (10) all_56_11 = all_52_11
% 115.06/17.51 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 115.06/17.51 (12) ~ (all_52_12 = all_10_2)
% 115.06/17.51 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.06/17.51 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.06/17.51 (15) all_56_12 = all_10_2
% 115.06/17.51 (16) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 115.06/17.51 (17) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 115.06/17.51 (18) ~ (all_52_14 = all_6_2)
% 115.06/17.51 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.06/17.51 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.06/17.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.06/17.51 (21) ~ (all_52_2 = all_6_2)
% 115.06/17.51 (22) all_54_10 = all_6_2
% 115.06/17.51 (23) ~ (all_52_4 = all_52_7)
% 115.06/17.51 (24) all_56_2 = all_52_12
% 115.06/17.51 (25) all_58_3 = all_8_2
% 115.06/17.51 (26) ~ (all_10_0 = e2)
% 115.06/17.51 (27) all_58_11 = all_52_14
% 115.06/17.51 (28) op(all_10_1, all_10_2) = all_10_0
% 115.06/17.51 (29) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 115.06/17.52 (30) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 115.06/17.52 (31) ~ (all_10_2 = e1)
% 115.06/17.52 (32) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.06/17.52 (33) all_58_5 = all_52_9
% 115.06/17.52 (34) all_56_9 = all_52_3
% 115.06/17.52 (35) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.06/17.52 (36) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 115.06/17.52 (37) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 115.06/17.52 (38) all_58_15 = all_4_2
% 115.06/17.52 (39) all_58_2 = all_52_1
% 115.06/17.52 (40) ~ (all_10_2 = e3)
% 115.06/17.52 (41) ~ (all_52_12 = all_52_13)
% 115.06/17.52 (42) all_58_13 = all_52_7
% 115.06/17.52 (43) all_58_6 = all_52_2
% 115.06/17.52 (44) ~ (all_52_1 = all_10_2)
% 115.06/17.52 (45) all_54_5 = all_8_2
% 115.06/17.52 (46) all_56_15 = all_4_2
% 115.06/17.52 (47) all_58_10 = all_52_13
% 115.06/17.52 (48) op(e3, all_10_2) = all_10_1
% 115.06/17.52 (49) all_58_1 = all_52_4
% 115.06/17.52 (50) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.06/17.52 (51) ~ (all_8_2 = e1)
% 115.06/17.52 (52) all_58_14 = all_52_11
% 115.06/17.52 (53) all_54_1 = all_52_4
% 115.06/17.52 (54) all_56_13 = all_8_2
% 115.06/17.52 (55) ~ (all_8_2 = e2)
% 115.06/17.52 (56) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.06/17.52 (57) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 115.06/17.52 (58) all_56_7 = all_52_6
% 115.06/17.52 (59) all_58_8 = all_6_2
% 115.06/17.52 (60) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.52 (61) ~ (all_10_0 = e1)
% 115.06/17.52 (62) all_56_4 = all_52_9
% 115.06/17.52 (63) all_56_5 = all_52_13
% 115.06/17.52 (64) ~ (all_52_6 = all_6_2)
% 115.06/17.52 (65) all_56_6 = all_52_2
% 115.06/17.52 (66) all_58_12 = all_52_3
% 115.06/17.52 (67) op(e2, e0) = all_52_13
% 115.06/17.52 (68) ~ (all_52_12 = all_4_2)
% 115.06/17.52 (69) all_56_15 = e2
% 115.06/17.52 (70) all_56_8 = all_52_14
% 115.06/17.52 (71) ~ (all_52_4 = all_10_2)
% 115.06/17.52 (72) ~ (all_10_1 = e1)
% 115.06/17.52 (73) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.06/17.52 (74) all_56_0 = all_52_4
% 115.06/17.52 (75) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 115.06/17.52 (76) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.06/17.52 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.06/17.52 (77) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 115.06/17.52 (78) op(e2, all_8_2) = e1
% 115.06/17.52 (79) ~ (all_6_2 = e1)
% 115.06/17.52
% 115.06/17.52 Begin of proof
% 115.06/17.52 |
% 115.06/17.52 | COMBINE_EQS: (46), (69) imply:
% 115.06/17.52 | (80) all_4_2 = e2
% 115.06/17.52 |
% 115.06/17.52 | SIMP: (80) implies:
% 115.06/17.52 | (81) all_4_2 = e2
% 115.06/17.52 |
% 115.06/17.52 | REDUCE: (68), (81) imply:
% 115.06/17.52 | (82) ~ (all_52_12 = e2)
% 115.06/17.52 |
% 115.06/17.52 | BETA: splitting (16) gives:
% 115.06/17.52 |
% 115.06/17.52 | Case 1:
% 115.06/17.52 | |
% 115.06/17.52 | | (83) ~ (all_56_7 = e1)
% 115.06/17.52 | |
% 115.06/17.52 | | REDUCE: (58), (83) imply:
% 115.06/17.52 | | (84) ~ (all_52_6 = e1)
% 115.06/17.52 | |
% 115.06/17.52 | | BETA: splitting (50) gives:
% 115.06/17.52 | |
% 115.06/17.52 | | Case 1:
% 115.06/17.52 | | |
% 115.06/17.52 | | | (85) ~ (all_56_2 = e3)
% 115.06/17.52 | | |
% 115.06/17.52 | | | REDUCE: (24), (85) imply:
% 115.06/17.52 | | | (86) ~ (all_52_12 = e3)
% 115.06/17.52 | | |
% 115.06/17.52 | | | BETA: splitting (37) gives:
% 115.06/17.52 | | |
% 115.06/17.52 | | | Case 1:
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | (87) ~ (all_56_6 = e1)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | REDUCE: (65), (87) imply:
% 115.06/17.52 | | | | (88) ~ (all_52_2 = e1)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (13), (15), (17), (18),
% 115.06/17.52 | | | | (19), (20), (22), (23), (25), (26), (27), (28), (29), (30),
% 115.06/17.52 | | | | (31), (32), (33), (34), (35), (36), (38), (39), (40), (42),
% 115.06/17.52 | | | | (43), (44), (47), (48), (49), (52), (53), (54), (55), (56),
% 115.06/17.52 | | | | (57), (58), (59), (60), (61), (62), (63), (64), (66), (70),
% 115.06/17.52 | | | | (71), (72), (73), (74), (75), (76), (77), (79), (84), (88)
% 115.06/17.52 | | | | are inconsistent by sub-proof #371.
% 115.06/17.52 | | | |
% 115.06/17.52 | | | Case 2:
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | (89) all_56_6 = e1
% 115.06/17.52 | | | | (90) ~ (all_56_13 = e3)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | COMBINE_EQS: (65), (89) imply:
% 115.06/17.52 | | | | (91) all_52_2 = e1
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | REDUCE: (54), (90) imply:
% 115.06/17.52 | | | | (92) ~ (all_8_2 = e3)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | REDUCE: (2), (91) imply:
% 115.06/17.52 | | | | (93) ~ (all_10_2 = e1)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | REDUCE: (21), (91) imply:
% 115.06/17.52 | | | | (94) ~ (all_6_2 = e1)
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | BETA: splitting (14) gives:
% 115.06/17.52 | | | |
% 115.06/17.52 | | | | Case 1:
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | | (95) all_54_5 = e3
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | | REF_CLOSE: (45), (92), (95) are inconsistent by sub-proof #339.
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | Case 2:
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | | (96) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | | BETA: splitting (96) gives:
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | | Case 1:
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | | (97) all_54_5 = e2
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | | REF_CLOSE: (45), (55), (97) are inconsistent by sub-proof #338.
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | Case 2:
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | | (98) ~ (all_54_5 = e2)
% 115.06/17.52 | | | | | | (99) all_54_5 = e1 | all_54_5 = e0
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | | BETA: splitting (99) gives:
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | | Case 1:
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | (100) all_54_5 = e1
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | REF_CLOSE: (45), (51), (100) are inconsistent by sub-proof #337.
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | Case 2:
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | (101) all_54_5 = e0
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | COMBINE_EQS: (45), (101) imply:
% 115.06/17.52 | | | | | | | (102) all_8_2 = e0
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | SIMP: (102) implies:
% 115.06/17.52 | | | | | | | (103) all_8_2 = e0
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | REDUCE: (78), (103) imply:
% 115.06/17.52 | | | | | | | (104) op(e2, e0) = e1
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | GROUND_INST: instantiating (20) with all_52_13, e1, e0, e2,
% 115.06/17.52 | | | | | | | simplifying with (67), (104) gives:
% 115.06/17.52 | | | | | | | (105) all_52_13 = e1
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | REDUCE: (41), (105) imply:
% 115.06/17.52 | | | | | | | (106) ~ (all_52_12 = e1)
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | BETA: splitting (11) gives:
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | | Case 1:
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | | (107) all_54_3 = e3
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | | REF_CLOSE: (8), (86), (107) are inconsistent by sub-proof #224.
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | Case 2:
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | | (108) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | | BETA: splitting (108) gives:
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | | Case 1:
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | | (109) all_54_3 = e2
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | | REF_CLOSE: (8), (82), (109) are inconsistent by sub-proof
% 115.06/17.52 | | | | | | | | | #285.
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | Case 2:
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | | (110) all_54_3 = e1 | all_54_3 = e0
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | | BETA: splitting (110) gives:
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | | Case 1:
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | (111) all_54_3 = e1
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | REF_CLOSE: (8), (106), (111) are inconsistent by sub-proof
% 115.06/17.52 | | | | | | | | | | #284.
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | Case 2:
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | (112) all_54_3 = e0
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | COMBINE_EQS: (8), (112) imply:
% 115.06/17.52 | | | | | | | | | | (113) all_52_12 = e0
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | SIMP: (113) implies:
% 115.06/17.52 | | | | | | | | | | (114) all_52_12 = e0
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | REDUCE: (12), (114) imply:
% 115.06/17.52 | | | | | | | | | | (115) ~ (all_10_2 = e0)
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | SIMP: (115) implies:
% 115.06/17.52 | | | | | | | | | | (116) ~ (all_10_2 = e0)
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (13), (15),
% 115.06/17.52 | | | | | | | | | | (17), (19), (20), (22), (23), (25), (26), (28),
% 115.06/17.52 | | | | | | | | | | (29), (30), (31), (32), (33), (34), (36), (38),
% 115.06/17.52 | | | | | | | | | | (39), (40), (42), (44), (47), (48), (49), (52),
% 115.06/17.52 | | | | | | | | | | (53), (54), (55), (57), (58), (60), (61), (62),
% 115.06/17.52 | | | | | | | | | | (63), (64), (66), (71), (72), (73), (74), (75),
% 115.06/17.52 | | | | | | | | | | (76), (77), (79), (116) are inconsistent by
% 115.06/17.52 | | | | | | | | | | sub-proof #422.
% 115.06/17.52 | | | | | | | | | |
% 115.06/17.52 | | | | | | | | | End of split
% 115.06/17.52 | | | | | | | | |
% 115.06/17.52 | | | | | | | | End of split
% 115.06/17.52 | | | | | | | |
% 115.06/17.52 | | | | | | | End of split
% 115.06/17.52 | | | | | | |
% 115.06/17.52 | | | | | | End of split
% 115.06/17.52 | | | | | |
% 115.06/17.52 | | | | | End of split
% 115.06/17.52 | | | | |
% 115.06/17.52 | | | | End of split
% 115.06/17.52 | | | |
% 115.06/17.52 | | | End of split
% 115.06/17.52 | | |
% 115.06/17.52 | | Case 2:
% 115.06/17.52 | | |
% 115.06/17.52 | | | (117) all_56_2 = e3
% 115.06/17.52 | | |
% 115.06/17.52 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (13), (15), (17),
% 115.06/17.52 | | | (19), (20), (22), (23), (25), (26), (28), (29), (30), (31),
% 115.06/17.52 | | | (32), (33), (34), (36), (38), (39), (40), (42), (44), (47),
% 115.06/17.52 | | | (48), (49), (52), (53), (54), (55), (57), (58), (60), (61),
% 115.06/17.52 | | | (62), (63), (64), (66), (71), (72), (73), (74), (75), (76),
% 115.06/17.52 | | | (77), (79), (117) are inconsistent by sub-proof #356.
% 115.06/17.52 | | |
% 115.06/17.52 | | End of split
% 115.06/17.52 | |
% 115.06/17.52 | Case 2:
% 115.06/17.52 | |
% 115.06/17.52 | | (118) ~ (all_56_15 = e2)
% 115.06/17.52 | |
% 115.06/17.52 | | REDUCE: (69), (118) imply:
% 115.06/17.52 | | (119) $false
% 115.06/17.52 | |
% 115.06/17.52 | | CLOSE: (119) is inconsistent.
% 115.06/17.52 | |
% 115.06/17.52 | End of split
% 115.06/17.52 |
% 115.06/17.52 End of proof
% 115.06/17.52
% 115.06/17.52 Sub-proof #95 shows that the following formulas are inconsistent:
% 115.06/17.52 ----------------------------------------------------------------
% 115.06/17.52 (1) all_58_10 = all_52_13
% 115.06/17.52 (2) all_58_10 = e2
% 115.06/17.52 (3) ~ (all_52_13 = e2)
% 115.06/17.52
% 115.06/17.52 Begin of proof
% 115.06/17.52 |
% 115.06/17.52 | COMBINE_EQS: (1), (2) imply:
% 115.06/17.52 | (4) all_52_13 = e2
% 115.06/17.52 |
% 115.06/17.52 | SIMP: (4) implies:
% 115.06/17.52 | (5) all_52_13 = e2
% 115.06/17.52 |
% 115.06/17.52 | REDUCE: (3), (5) imply:
% 115.06/17.52 | (6) $false
% 115.06/17.52 |
% 115.06/17.52 | CLOSE: (6) is inconsistent.
% 115.06/17.52 |
% 115.06/17.52 End of proof
% 115.06/17.52
% 115.06/17.52 Sub-proof #96 shows that the following formulas are inconsistent:
% 115.06/17.52 ----------------------------------------------------------------
% 115.06/17.52 (1) ~ (all_52_8 = all_10_2)
% 115.06/17.53 (2) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 115.06/17.53 (3) all_54_2 = all_52_8
% 115.06/17.53 (4) ~ (all_52_8 = all_52_11)
% 115.06/17.53 (5) all_54_0 = all_10_2
% 115.06/17.53 (6) op(e3, all_10_2) = e1
% 115.06/17.53 (7) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.53 (8) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.06/17.53 (9) all_58_0 = all_10_2
% 115.06/17.53 (10) all_54_14 = all_52_11
% 115.06/17.53 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.06/17.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.06/17.53 (12) ~ (all_10_2 = e2)
% 115.06/17.53 (13) all_58_4 = all_52_8
% 115.06/17.53 (14) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.06/17.53 (15) op(e3, e1) = all_52_8
% 115.06/17.53 (16) ~ (all_52_8 = e3)
% 115.06/17.53 (17) ~ (all_10_2 = e0)
% 115.06/17.53 (18) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.06/17.53 (19) ~ (all_52_11 = e1)
% 115.06/17.53 (20) ~ (all_52_11 = e0)
% 115.06/17.53
% 115.06/17.53 Begin of proof
% 115.06/17.53 |
% 115.06/17.53 | BETA: splitting (8) gives:
% 115.06/17.53 |
% 115.06/17.53 | Case 1:
% 115.06/17.53 | |
% 115.06/17.53 | | (21) all_54_14 = e2
% 115.06/17.53 | |
% 115.06/17.53 | | COMBINE_EQS: (10), (21) imply:
% 115.06/17.53 | | (22) all_52_11 = e2
% 115.06/17.53 | |
% 115.06/17.53 | | REDUCE: (4), (22) imply:
% 115.06/17.53 | | (23) ~ (all_52_8 = e2)
% 115.06/17.53 | |
% 115.06/17.53 | | BETA: splitting (7) gives:
% 115.06/17.53 | |
% 115.06/17.53 | | Case 1:
% 115.06/17.53 | | |
% 115.06/17.53 | | | (24) all_54_0 = e2
% 115.06/17.53 | | |
% 115.06/17.53 | | | REF_CLOSE: (5), (12), (24) are inconsistent by sub-proof #450.
% 115.06/17.53 | | |
% 115.06/17.53 | | Case 2:
% 115.06/17.53 | | |
% 115.06/17.53 | | | (25) all_54_0 = e1 | all_54_0 = e0
% 115.06/17.53 | | |
% 115.06/17.53 | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (11), (13), (14), (15), (16),
% 115.06/17.53 | | | (17), (18), (23), (25) are inconsistent by sub-proof #99.
% 115.06/17.53 | | |
% 115.06/17.53 | | End of split
% 115.06/17.53 | |
% 115.06/17.53 | Case 2:
% 115.06/17.53 | |
% 115.06/17.53 | | (26) all_54_14 = e1 | all_54_14 = e0
% 115.06/17.53 | |
% 115.06/17.53 | | REF_CLOSE: (10), (19), (20), (26) are inconsistent by sub-proof #139.
% 115.06/17.53 | |
% 115.06/17.53 | End of split
% 115.06/17.53 |
% 115.06/17.53 End of proof
% 115.06/17.53
% 115.06/17.53 Sub-proof #97 shows that the following formulas are inconsistent:
% 115.06/17.53 ----------------------------------------------------------------
% 115.06/17.53 (1) ~ (all_52_8 = all_10_2)
% 115.06/17.53 (2) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 115.06/17.53 (3) all_54_2 = all_52_8
% 115.06/17.53 (4) all_58_7 = all_52_6
% 115.06/17.53 (5) ~ (all_4_2 = e0)
% 115.06/17.53 (6) all_56_14 = all_6_2
% 115.06/17.53 (7) all_54_0 = all_10_2
% 115.06/17.53 (8) ~ (all_52_7 = all_4_2)
% 115.06/17.53 (9) all_56_11 = all_52_11
% 115.06/17.53 (10) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 115.06/17.53 (11) ~ (all_52_4 = all_52_8)
% 115.06/17.53 (12) op(e3, all_10_2) = e1
% 115.06/17.53 (13) all_56_12 = all_10_2
% 115.06/17.53 (14) all_58_0 = all_10_2
% 115.06/17.53 (15) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 115.06/17.53 (16) all_56_10 = all_52_7
% 115.06/17.53 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.06/17.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.06/17.53 (18) ~ (all_10_2 = e2)
% 115.06/17.53 (19) all_58_4 = all_52_8
% 115.06/17.53 (20) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.06/17.53 (21) all_58_3 = all_8_2
% 115.06/17.53 (22) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.06/17.53 (23) all_58_11 = all_52_14
% 115.06/17.53 (24) op(e3, e1) = all_52_8
% 115.06/17.53 (25) ~ (all_52_2 = all_52_3)
% 115.06/17.53 (26) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.06/17.53 (27) ~ (all_4_2 = e3)
% 115.06/17.53 (28) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.06/17.53 (29) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.06/17.53 (30) all_58_15 = all_4_2
% 115.06/17.53 (31) ~ (all_10_2 = e3)
% 115.06/17.53 (32) all_58_13 = all_52_7
% 115.06/17.53 (33) ~ (all_52_14 = all_4_2)
% 115.06/17.53 (34) all_58_6 = all_52_2
% 115.06/17.53 (35) all_56_15 = all_4_2
% 115.06/17.53 (36) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 115.06/17.53 (37) all_58_1 = all_52_4
% 115.06/17.53 (38) all_58_14 = all_52_11
% 115.06/17.53 (39) ~ (all_8_2 = e2)
% 115.06/17.53 (40) all_56_1 = all_52_8
% 115.06/17.53 (41) all_58_8 = all_6_2
% 115.06/17.53 (42) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.53 (43) ~ (all_52_3 = all_4_2)
% 115.06/17.53 (44) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.06/17.53 (45) all_58_12 = all_52_3
% 115.06/17.53 (46) ~ (all_52_3 = all_10_2)
% 115.06/17.53 (47) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 115.06/17.53 (48) all_56_8 = all_52_14
% 115.06/17.53 (49) ~ (all_52_6 = e1)
% 115.06/17.53 (50) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.06/17.53 (51) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.06/17.53 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.06/17.53 (52) all_54_15 = all_4_2
% 115.06/17.53 (53) ~ (all_6_2 = e1)
% 115.06/17.53
% 115.06/17.53 Begin of proof
% 115.06/17.53 |
% 115.06/17.53 | BETA: splitting (28) gives:
% 115.06/17.53 |
% 115.06/17.53 | Case 1:
% 115.06/17.53 | |
% 115.06/17.53 | | (54) all_58_7 = e1
% 115.06/17.53 | |
% 115.06/17.53 | | COMBINE_EQS: (4), (54) imply:
% 115.06/17.53 | | (55) all_52_6 = e1
% 115.06/17.53 | |
% 115.06/17.53 | | REDUCE: (49), (55) imply:
% 115.06/17.53 | | (56) $false
% 115.06/17.53 | |
% 115.06/17.53 | | CLOSE: (56) is inconsistent.
% 115.06/17.53 | |
% 115.06/17.53 | Case 2:
% 115.06/17.53 | |
% 115.06/17.53 | | (57) all_58_8 = e1 | all_58_11 = e1
% 115.06/17.53 | |
% 115.06/17.53 | | BETA: splitting (57) gives:
% 115.06/17.53 | |
% 115.06/17.53 | | Case 1:
% 115.06/17.53 | | |
% 115.06/17.53 | | | (58) all_58_8 = e1
% 115.06/17.53 | | |
% 115.06/17.53 | | | COMBINE_EQS: (41), (58) imply:
% 115.06/17.53 | | | (59) all_6_2 = e1
% 115.06/17.53 | | |
% 115.06/17.53 | | | REDUCE: (53), (59) imply:
% 115.06/17.53 | | | (60) $false
% 115.06/17.53 | | |
% 115.06/17.53 | | | CLOSE: (60) is inconsistent.
% 115.06/17.53 | | |
% 115.06/17.53 | | Case 2:
% 115.06/17.53 | | |
% 115.06/17.53 | | | (61) all_58_11 = e1
% 115.06/17.53 | | |
% 115.06/17.53 | | | COMBINE_EQS: (23), (61) imply:
% 115.06/17.53 | | | (62) all_52_14 = e1
% 115.06/17.53 | | |
% 115.06/17.53 | | | COMBINE_EQS: (48), (62) imply:
% 115.06/17.53 | | | (63) all_56_8 = e1
% 115.06/17.53 | | |
% 115.06/17.53 | | | REDUCE: (33), (62) imply:
% 115.06/17.53 | | | (64) ~ (all_4_2 = e1)
% 115.06/17.53 | | |
% 115.06/17.53 | | | SIMP: (64) implies:
% 115.06/17.53 | | | (65) ~ (all_4_2 = e1)
% 115.06/17.53 | | |
% 115.06/17.53 | | | BETA: splitting (10) gives:
% 115.06/17.53 | | |
% 115.06/17.53 | | | Case 1:
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | (66) ~ (all_56_8 = e1)
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | REDUCE: (63), (66) imply:
% 115.06/17.53 | | | | (67) $false
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | CLOSE: (67) is inconsistent.
% 115.06/17.53 | | | |
% 115.06/17.53 | | | Case 2:
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | (68) ~ (all_56_14 = e0)
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | REDUCE: (6), (68) imply:
% 115.06/17.53 | | | | (69) ~ (all_6_2 = e0)
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | BETA: splitting (20) gives:
% 115.06/17.53 | | | |
% 115.06/17.53 | | | | Case 1:
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | | (70) all_54_15 = e3
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | | REF_CLOSE: (27), (52), (70) are inconsistent by sub-proof #312.
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | Case 2:
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | | (71) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | | BETA: splitting (29) gives:
% 115.06/17.53 | | | | |
% 115.06/17.53 | | | | | Case 1:
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | (72) ~ (all_56_8 = e1)
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | REDUCE: (63), (72) imply:
% 115.06/17.53 | | | | | | (73) $false
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | CLOSE: (73) is inconsistent.
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | Case 2:
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | (74) ~ (all_56_12 = e0)
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | REDUCE: (13), (74) imply:
% 115.06/17.53 | | | | | | (75) ~ (all_10_2 = e0)
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | BETA: splitting (71) gives:
% 115.06/17.53 | | | | | |
% 115.06/17.53 | | | | | | Case 1:
% 115.06/17.53 | | | | | | |
% 115.06/17.53 | | | | | | | (76) all_54_15 = e2
% 115.06/17.53 | | | | | | |
% 115.06/17.53 | | | | | | | COMBINE_EQS: (52), (76) imply:
% 115.06/17.54 | | | | | | | (77) all_4_2 = e2
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | SIMP: (77) implies:
% 115.06/17.54 | | | | | | | (78) all_4_2 = e2
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | COMBINE_EQS: (35), (78) imply:
% 115.06/17.54 | | | | | | | (79) all_56_15 = e2
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | COMBINE_EQS: (30), (78) imply:
% 115.06/17.54 | | | | | | | (80) all_58_15 = e2
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | REDUCE: (43), (78) imply:
% 115.06/17.54 | | | | | | | (81) ~ (all_52_3 = e2)
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | REDUCE: (8), (78) imply:
% 115.06/17.54 | | | | | | | (82) ~ (all_52_7 = e2)
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | REDUCE: (5), (78) imply:
% 115.06/17.54 | | | | | | | (83) ~ (e2 = e0)
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | BETA: splitting (47) gives:
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | (84) ~ (all_56_15 = e2)
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | REDUCE: (79), (84) imply:
% 115.06/17.54 | | | | | | | | (85) $false
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | CLOSE: (85) is inconsistent.
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | (86) ~ (all_56_10 = e0)
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | REDUCE: (16), (86) imply:
% 115.06/17.54 | | | | | | | | (87) ~ (all_52_7 = e0)
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | BETA: splitting (42) gives:
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | | (88) all_54_0 = e3
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | | REF_CLOSE: (7), (31), (88) are inconsistent by sub-proof #451.
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | | (89) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | | BETA: splitting (89) gives:
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | (90) all_54_0 = e2
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | REF_CLOSE: (7), (18), (90) are inconsistent by sub-proof
% 115.06/17.54 | | | | | | | | | | #450.
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | (91) all_54_0 = e1 | all_54_0 = e0
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | BETA: splitting (91) gives:
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | (92) all_54_0 = e1
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | COMBINE_EQS: (7), (92) imply:
% 115.06/17.54 | | | | | | | | | | | (93) all_10_2 = e1
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | SIMP: (93) implies:
% 115.06/17.54 | | | | | | | | | | | (94) all_10_2 = e1
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | COMBINE_EQS: (13), (94) imply:
% 115.06/17.54 | | | | | | | | | | | (95) all_56_12 = e1
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | REDUCE: (46), (94) imply:
% 115.06/17.54 | | | | | | | | | | | (96) ~ (all_52_3 = e1)
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | BETA: splitting (50) gives:
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | (97) ~ (all_56_12 = e1)
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | REDUCE: (95), (97) imply:
% 115.06/17.54 | | | | | | | | | | | | (98) $false
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | CLOSE: (98) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | (99) ~ (all_56_11 = e0)
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | REDUCE: (9), (99) imply:
% 115.06/17.54 | | | | | | | | | | | | (100) ~ (all_52_11 = e0)
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | BETA: splitting (51) gives:
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | (101) all_58_15 = e0
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | COMBINE_EQS: (80), (101) imply:
% 115.06/17.54 | | | | | | | | | | | | | (102) e2 = e0
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | REDUCE: (83), (102) imply:
% 115.06/17.54 | | | | | | | | | | | | | (103) $false
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | (104) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 115.06/17.54 | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 115.06/17.54 | | | | | | | | | | | | | e0)
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | ALPHA: (104) implies:
% 115.06/17.54 | | | | | | | | | | | | | (105) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | BETA: splitting (105) gives:
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | (106) all_58_12 = e0
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | COMBINE_EQS: (45), (106) imply:
% 115.06/17.54 | | | | | | | | | | | | | | (107) all_52_3 = e0
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | SIMP: (107) implies:
% 115.06/17.54 | | | | | | | | | | | | | | (108) all_52_3 = e0
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | REDUCE: (25), (108) imply:
% 115.06/17.54 | | | | | | | | | | | | | | (109) ~ (all_52_2 = e0)
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | REDUCE: (81), (108) imply:
% 115.06/17.54 | | | | | | | | | | | | | | (110) ~ (e2 = e0)
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | REDUCE: (96), (108) imply:
% 115.06/17.54 | | | | | | | | | | | | | | (111) ~ (e1 = e0)
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | SIMP: (111) implies:
% 115.06/17.54 | | | | | | | | | | | | | | (112) ~ (e1 = e0)
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | (113) all_58_6 = e0
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | COMBINE_EQS: (34), (113) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | (114) all_52_2 = e0
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | SIMP: (114) implies:
% 115.06/17.54 | | | | | | | | | | | | | | | (115) all_52_2 = e0
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | REDUCE: (109), (115) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | (116) $false
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | (117) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | (118) all_58_7 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (118) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | (119) all_52_6 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | (120) ~ (all_56_1 = e3)
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | REDUCE: (40), (120) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (121) ~ (all_52_8 = e3)
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (122) all_58_1 = e2
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (122) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (123) all_52_4 = e2
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | REDUCE: (11), (123) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (124) ~ (all_52_8 = e2)
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (125) ~ (all_52_8 = e2)
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (7), (12), (14), (17), (19), (22),
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (24), (44), (75), (91), (121), (125) are
% 115.06/17.54 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #99.
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | (126) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (32), (39), (82), (83), (118), (126) are
% 115.06/17.54 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98.
% 115.06/17.54 | | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | (127) ~ (all_56_12 = e1)
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | REDUCE: (95), (127) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (128) $false
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | (129) all_58_8 = e0 | all_58_11 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | Case 1:
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | (130) all_58_8 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (130) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (131) all_6_2 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | REDUCE: (69), (131) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (132) $false
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | (133) all_58_11 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (133) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (134) e1 = e0
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | REDUCE: (112), (134) imply:
% 115.06/17.54 | | | | | | | | | | | | | | | | | (135) $false
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 115.06/17.54 | | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | (136) all_58_13 = e0 | all_58_14 = e0
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | | REF_CLOSE: (32), (38), (87), (100), (136) are inconsistent by
% 115.06/17.54 | | | | | | | | | | | | | | sub-proof #428.
% 115.06/17.54 | | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | Case 2:
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | (137) all_54_0 = e0
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | | REF_CLOSE: (7), (75), (137) are inconsistent by sub-proof
% 115.06/17.54 | | | | | | | | | | | #424.
% 115.06/17.54 | | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | | |
% 115.06/17.54 | | | | | | | | | End of split
% 115.06/17.54 | | | | | | | | |
% 115.06/17.54 | | | | | | | | End of split
% 115.06/17.54 | | | | | | | |
% 115.06/17.54 | | | | | | | End of split
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | Case 2:
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | (138) all_54_15 = e1 | all_54_15 = e0
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | | REF_CLOSE: (5), (52), (65), (138) are inconsistent by sub-proof
% 115.06/17.54 | | | | | | | #418.
% 115.06/17.54 | | | | | | |
% 115.06/17.54 | | | | | | End of split
% 115.06/17.54 | | | | | |
% 115.06/17.54 | | | | | End of split
% 115.06/17.54 | | | | |
% 115.06/17.54 | | | | End of split
% 115.06/17.54 | | | |
% 115.06/17.54 | | | End of split
% 115.06/17.54 | | |
% 115.06/17.54 | | End of split
% 115.06/17.54 | |
% 115.06/17.54 | End of split
% 115.06/17.54 |
% 115.06/17.54 End of proof
% 115.06/17.54
% 115.06/17.54 Sub-proof #98 shows that the following formulas are inconsistent:
% 115.06/17.54 ----------------------------------------------------------------
% 115.06/17.54 (1) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 115.06/17.54 (2) all_58_3 = all_8_2
% 115.06/17.54 (3) all_58_13 = all_52_7
% 115.06/17.54 (4) ~ (all_52_7 = e2)
% 115.06/17.54 (5) ~ (all_8_2 = e2)
% 115.06/17.54 (6) all_58_7 = e0
% 115.06/17.54 (7) ~ (e2 = e0)
% 115.06/17.54
% 115.06/17.54 Begin of proof
% 115.06/17.54 |
% 115.06/17.54 | BETA: splitting (1) gives:
% 115.06/17.54 |
% 115.06/17.54 | Case 1:
% 115.06/17.54 | |
% 115.06/17.54 | | (8) all_58_3 = e2
% 115.06/17.54 | |
% 115.06/17.54 | | COMBINE_EQS: (2), (8) imply:
% 115.06/17.54 | | (9) all_8_2 = e2
% 115.06/17.54 | |
% 115.06/17.54 | | REDUCE: (5), (9) imply:
% 115.06/17.54 | | (10) $false
% 115.06/17.54 | |
% 115.06/17.54 | | CLOSE: (10) is inconsistent.
% 115.06/17.54 | |
% 115.06/17.54 | Case 2:
% 115.06/17.54 | |
% 115.06/17.54 | | (11) all_58_7 = e2 | all_58_13 = e2
% 115.06/17.54 | |
% 115.06/17.54 | | BETA: splitting (11) gives:
% 115.06/17.54 | |
% 115.06/17.54 | | Case 1:
% 115.06/17.54 | | |
% 115.06/17.54 | | | (12) all_58_7 = e2
% 115.06/17.54 | | |
% 115.06/17.54 | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #376.
% 115.06/17.54 | | |
% 115.06/17.54 | | Case 2:
% 115.06/17.54 | | |
% 115.06/17.54 | | | (13) all_58_13 = e2
% 115.06/17.54 | | |
% 115.06/17.54 | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #265.
% 115.06/17.54 | | |
% 115.06/17.54 | | End of split
% 115.06/17.54 | |
% 115.06/17.54 | End of split
% 115.06/17.54 |
% 115.06/17.54 End of proof
% 115.06/17.54
% 115.06/17.54 Sub-proof #99 shows that the following formulas are inconsistent:
% 115.06/17.54 ----------------------------------------------------------------
% 115.06/17.54 (1) ~ (all_52_8 = all_10_2)
% 115.06/17.54 (2) all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 115.06/17.54 (3) all_54_2 = all_52_8
% 115.06/17.54 (4) all_54_0 = all_10_2
% 115.06/17.54 (5) op(e3, all_10_2) = e1
% 115.06/17.54 (6) all_58_0 = all_10_2
% 115.06/17.54 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.06/17.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.06/17.54 (8) all_58_4 = all_52_8
% 115.06/17.54 (9) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.06/17.55 (10) op(e3, e1) = all_52_8
% 115.06/17.55 (11) all_54_0 = e1 | all_54_0 = e0
% 115.06/17.55 (12) ~ (all_52_8 = e2)
% 115.06/17.55 (13) ~ (all_52_8 = e3)
% 115.06/17.55 (14) ~ (all_10_2 = e0)
% 115.06/17.55 (15) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.06/17.55
% 115.06/17.55 Begin of proof
% 115.06/17.55 |
% 115.06/17.55 | BETA: splitting (2) gives:
% 115.06/17.55 |
% 115.06/17.55 | Case 1:
% 115.06/17.55 | |
% 115.06/17.55 | | (16) all_58_0 = e1
% 115.06/17.55 | |
% 115.06/17.55 | | COMBINE_EQS: (6), (16) imply:
% 115.06/17.55 | | (17) all_10_2 = e1
% 115.06/17.55 | |
% 115.06/17.55 | | REDUCE: (1), (17) imply:
% 115.06/17.55 | | (18) ~ (all_52_8 = e1)
% 115.06/17.55 | |
% 115.06/17.55 | | REDUCE: (5), (17) imply:
% 115.06/17.55 | | (19) op(e3, e1) = e1
% 115.06/17.55 | |
% 115.06/17.55 | | BETA: splitting (15) gives:
% 115.06/17.55 | |
% 115.06/17.55 | | Case 1:
% 115.06/17.55 | | |
% 115.06/17.55 | | | (20) all_54_2 = e3
% 115.06/17.55 | | |
% 115.06/17.55 | | | REF_CLOSE: (3), (13), (20) are inconsistent by sub-proof #179.
% 115.06/17.55 | | |
% 115.06/17.55 | | Case 2:
% 115.06/17.55 | | |
% 115.06/17.55 | | | (21) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.06/17.55 | | |
% 115.06/17.55 | | | BETA: splitting (9) gives:
% 115.06/17.55 | | |
% 115.06/17.55 | | | Case 1:
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | (22) all_58_4 = e0
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | COMBINE_EQS: (8), (22) imply:
% 115.06/17.55 | | | | (23) all_52_8 = e0
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | REDUCE: (18), (23) imply:
% 115.06/17.55 | | | | (24) ~ (e1 = e0)
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | SIMP: (24) implies:
% 115.06/17.55 | | | | (25) ~ (e1 = e0)
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | REDUCE: (10), (23) imply:
% 115.06/17.55 | | | | (26) op(e3, e1) = e0
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | GROUND_INST: instantiating (7) with e0, e1, e1, e3, simplifying with
% 115.06/17.55 | | | | (19), (26) gives:
% 115.06/17.55 | | | | (27) e1 = e0
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | REDUCE: (25), (27) imply:
% 115.06/17.55 | | | | (28) $false
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | CLOSE: (28) is inconsistent.
% 115.06/17.55 | | | |
% 115.06/17.55 | | | Case 2:
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | (29) ~ (all_58_4 = e0)
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | REDUCE: (8), (29) imply:
% 115.06/17.55 | | | | (30) ~ (all_52_8 = e0)
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | BETA: splitting (21) gives:
% 115.06/17.55 | | | |
% 115.06/17.55 | | | | Case 1:
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | | (31) all_54_2 = e2
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | | REF_CLOSE: (3), (12), (31) are inconsistent by sub-proof #212.
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | Case 2:
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | | (32) all_54_2 = e1 | all_54_2 = e0
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | | REF_CLOSE: (3), (18), (30), (32) are inconsistent by sub-proof #210.
% 115.06/17.55 | | | | |
% 115.06/17.55 | | | | End of split
% 115.06/17.55 | | | |
% 115.06/17.55 | | | End of split
% 115.06/17.55 | | |
% 115.06/17.55 | | End of split
% 115.06/17.55 | |
% 115.06/17.55 | Case 2:
% 115.06/17.55 | |
% 115.06/17.55 | | (33) ~ (all_58_0 = e1)
% 115.06/17.55 | |
% 115.06/17.55 | | REDUCE: (6), (33) imply:
% 115.06/17.55 | | (34) ~ (all_10_2 = e1)
% 115.06/17.55 | |
% 115.06/17.55 | | REF_CLOSE: (4), (11), (14), (34) are inconsistent by sub-proof #127.
% 115.06/17.55 | |
% 115.06/17.55 | End of split
% 115.06/17.55 |
% 115.06/17.55 End of proof
% 115.06/17.55
% 115.06/17.55 Sub-proof #100 shows that the following formulas are inconsistent:
% 115.06/17.55 ----------------------------------------------------------------
% 115.06/17.55 (1) ~ (all_52_2 = all_10_2)
% 115.06/17.55 (2) ~ (all_52_3 = e0)
% 115.06/17.55 (3) all_54_2 = all_52_8
% 115.06/17.55 (4) all_58_7 = all_52_6
% 115.06/17.55 (5) ~ (all_52_8 = all_52_11)
% 115.06/17.55 (6) ~ (all_52_9 = all_8_2)
% 115.06/17.55 (7) ~ (all_52_1 = e2)
% 115.06/17.55 (8) ~ (all_52_3 = e3)
% 115.06/17.55 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 115.06/17.55 (10) all_56_14 = all_6_2
% 115.06/17.55 (11) all_54_0 = all_10_2
% 115.06/17.55 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.06/17.55 (13) all_56_11 = all_52_11
% 115.06/17.55 (14) ~ (all_4_0 = e1)
% 115.06/17.55 (15) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.06/17.55 (16) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.06/17.55 (17) all_56_12 = all_10_2
% 115.06/17.55 (18) all_58_0 = all_10_2
% 115.06/17.55 (19) all_54_13 = all_52_7
% 115.06/17.55 (20) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.06/17.55 (21) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 115.06/17.55 (22) all_56_10 = all_52_7
% 115.06/17.55 (23) all_54_14 = all_52_11
% 115.06/17.55 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.06/17.55 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.06/17.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.06/17.55 (26) all_54_8 = all_52_2
% 115.06/17.55 (27) ~ (all_52_2 = all_6_2)
% 115.06/17.55 (28) op(e0, e3) = all_4_1
% 115.06/17.55 (29) ~ (all_52_1 = all_52_9)
% 115.06/17.55 (30) ~ (all_52_7 = e3)
% 115.06/17.55 (31) all_56_8 = e1
% 115.06/17.55 (32) ~ (all_10_2 = e2)
% 115.06/17.55 (33) all_54_10 = all_6_2
% 115.06/17.55 (34) all_58_4 = all_52_8
% 115.06/17.55 (35) all_58_3 = all_8_2
% 115.06/17.55 (36) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.06/17.55 (37) all_58_11 = all_52_14
% 115.06/17.55 (38) ~ (all_52_2 = all_52_3)
% 115.06/17.55 (39) ~ (all_52_11 = all_6_2)
% 115.06/17.55 (40) op(e2, e3) = all_52_1
% 115.06/17.55 (41) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.06/17.55 (42) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.06/17.55 (43) ~ (all_52_7 = all_8_2)
% 115.06/17.55 (44) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.06/17.55 (45) all_58_5 = all_52_9
% 115.06/17.55 (46) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.06/17.55 (47) all_58_2 = all_52_1
% 115.06/17.55 (48) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.06/17.55 (49) ~ (all_52_1 = all_52_13)
% 115.06/17.55 (50) op(e0, e3) = all_52_3
% 115.06/17.55 (51) ~ (all_10_2 = e3)
% 115.06/17.55 (52) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.06/17.55 (53) all_58_6 = all_52_2
% 115.06/17.55 (54) ~ (all_52_2 = e1)
% 115.06/17.55 (55) ~ (all_52_1 = all_10_2)
% 115.06/17.55 (56) all_54_5 = all_8_2
% 115.06/17.55 (57) all_58_10 = all_52_13
% 115.06/17.55 (58) ~ (all_52_13 = all_8_2)
% 115.06/17.55 (59) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.06/17.55 (60) ~ (all_52_6 = all_8_2)
% 115.06/17.55 (61) all_56_13 = all_8_2
% 115.06/17.55 (62) ~ (all_52_1 = all_8_2)
% 115.06/17.55 (63) ~ (all_8_2 = e2)
% 115.06/17.55 (64) op(all_4_1, e3) = all_4_0
% 115.06/17.55 (65) ~ (all_52_7 = all_52_11)
% 115.06/17.55 (66) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.06/17.55 (67) ~ (all_52_9 = all_6_2)
% 115.06/17.55 (68) ~ (all_52_1 = all_52_2)
% 115.06/17.55 (69) ~ (all_52_1 = all_52_3)
% 115.06/17.55 (70) all_56_1 = all_52_8
% 115.06/17.55 (71) all_58_8 = all_6_2
% 115.06/17.55 (72) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.06/17.55 (73) all_56_4 = all_52_9
% 115.06/17.55 (74) all_56_5 = all_52_13
% 115.06/17.55 (75) op(e2, e1) = all_52_9
% 115.06/17.55 (76) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.06/17.55 (77) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.06/17.55 (78) all_58_12 = all_52_3
% 115.06/17.55 (79) ~ (all_52_8 = all_52_9)
% 115.06/17.55 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.06/17.55 (81) ~ (all_52_3 = all_10_2)
% 115.06/17.55 (82) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.06/17.55 (83) all_56_8 = all_52_14
% 115.30/17.55 (84) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.30/17.55 (85) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.30/17.55 (86) all_54_4 = all_52_1
% 115.30/17.56 (87) ~ (all_52_11 = e3)
% 115.30/17.56 (88) op(e2, all_8_2) = e1
% 115.30/17.56 (89) ~ (all_6_2 = e1)
% 115.30/17.56 (90) ~ (all_52_3 = all_52_11)
% 115.30/17.56 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.30/17.56 (92) all_54_12 = all_52_3
% 115.30/17.56 (93) ~ (all_52_3 = all_52_7)
% 115.30/17.56
% 115.30/17.56 Begin of proof
% 115.30/17.56 |
% 115.30/17.56 | BETA: splitting (21) gives:
% 115.30/17.56 |
% 115.30/17.56 | Case 1:
% 115.30/17.56 | |
% 115.30/17.56 | | (94) ~ (all_56_8 = e1)
% 115.30/17.56 | |
% 115.30/17.56 | | REDUCE: (31), (94) imply:
% 115.30/17.56 | | (95) $false
% 115.30/17.56 | |
% 115.30/17.56 | | CLOSE: (95) is inconsistent.
% 115.30/17.56 | |
% 115.30/17.56 | Case 2:
% 115.30/17.56 | |
% 115.30/17.56 | | (96) ~ (all_56_13 = e0)
% 115.30/17.56 | |
% 115.30/17.56 | | REDUCE: (61), (96) imply:
% 115.30/17.56 | | (97) ~ (all_8_2 = e0)
% 115.30/17.56 | |
% 115.30/17.56 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 115.30/17.56 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 115.30/17.56 | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 115.30/17.56 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 115.30/17.56 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 115.30/17.56 | | (59), (60), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 115.30/17.56 | | (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 115.30/17.56 | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 115.30/17.56 | | (93), (97) are inconsistent by sub-proof #114.
% 115.30/17.56 | |
% 115.30/17.56 | End of split
% 115.30/17.56 |
% 115.30/17.56 End of proof
% 115.30/17.56
% 115.30/17.56 Sub-proof #101 shows that the following formulas are inconsistent:
% 115.30/17.56 ----------------------------------------------------------------
% 115.30/17.56 (1) ~ (all_52_4 = e1)
% 115.31/17.56 (2) ~ (all_52_4 = e0)
% 115.31/17.56 (3) all_54_1 = all_52_4
% 115.31/17.56 (4) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 115.31/17.56 (5) ~ (all_52_4 = e2)
% 115.31/17.56
% 115.31/17.56 Begin of proof
% 115.31/17.56 |
% 115.31/17.56 | BETA: splitting (4) gives:
% 115.31/17.56 |
% 115.31/17.56 | Case 1:
% 115.31/17.56 | |
% 115.31/17.56 | | (6) all_54_1 = e2
% 115.31/17.56 | |
% 115.31/17.56 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #221.
% 115.31/17.56 | |
% 115.31/17.56 | Case 2:
% 115.31/17.56 | |
% 115.31/17.56 | | (7) all_54_1 = e1 | all_54_1 = e0
% 115.31/17.56 | |
% 115.31/17.56 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #213.
% 115.31/17.56 | |
% 115.31/17.56 | End of split
% 115.31/17.56 |
% 115.31/17.56 End of proof
% 115.31/17.56
% 115.31/17.56 Sub-proof #102 shows that the following formulas are inconsistent:
% 115.31/17.56 ----------------------------------------------------------------
% 115.31/17.56 (1) all_56_14 = all_6_2
% 115.31/17.56 (2) all_56_3 = all_52_1
% 115.31/17.56 (3) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.31/17.56 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.56 (5) all_58_3 = all_8_2
% 115.31/17.56 (6) all_58_5 = all_52_9
% 115.31/17.56 (7) all_58_2 = all_52_1
% 115.31/17.56 (8) all_54_5 = all_8_2
% 115.31/17.56 (9) ~ (all_52_13 = e2)
% 115.31/17.56 (10) op(e1, e1) = e3
% 115.31/17.56 (11) all_58_10 = all_52_13
% 115.31/17.56 (12) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 115.31/17.56 (13) all_56_13 = all_8_2
% 115.31/17.56 (14) ~ (all_8_2 = e2)
% 115.31/17.56 (15) all_54_5 = e1
% 115.31/17.56 (16) all_56_4 = all_52_9
% 115.31/17.56 (17) op(e1, e1) = all_6_2
% 115.31/17.56 (18) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.56
% 115.31/17.56 Begin of proof
% 115.31/17.56 |
% 115.31/17.56 | COMBINE_EQS: (8), (15) imply:
% 115.31/17.56 | (19) all_8_2 = e1
% 115.31/17.56 |
% 115.31/17.56 | SIMP: (19) implies:
% 115.31/17.56 | (20) all_8_2 = e1
% 115.31/17.56 |
% 115.31/17.56 | COMBINE_EQS: (13), (20) imply:
% 115.31/17.56 | (21) all_56_13 = e1
% 115.31/17.56 |
% 115.31/17.56 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 115.31/17.56 | (16), (17), (18), (21) are inconsistent by sub-proof #103.
% 115.31/17.56 |
% 115.31/17.56 End of proof
% 115.31/17.56
% 115.31/17.56 Sub-proof #103 shows that the following formulas are inconsistent:
% 115.31/17.56 ----------------------------------------------------------------
% 115.31/17.56 (1) all_56_14 = all_6_2
% 115.31/17.56 (2) all_56_3 = all_52_1
% 115.31/17.56 (3) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.31/17.56 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.56 (5) all_58_3 = all_8_2
% 115.31/17.56 (6) all_58_5 = all_52_9
% 115.31/17.56 (7) all_58_2 = all_52_1
% 115.31/17.56 (8) ~ (all_52_13 = e2)
% 115.31/17.56 (9) op(e1, e1) = e3
% 115.31/17.56 (10) all_58_10 = all_52_13
% 115.31/17.56 (11) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 115.31/17.56 (12) ~ (all_8_2 = e2)
% 115.31/17.56 (13) all_56_13 = e1
% 115.31/17.56 (14) all_56_4 = all_52_9
% 115.31/17.56 (15) op(e1, e1) = all_6_2
% 115.31/17.56 (16) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.56
% 115.31/17.56 Begin of proof
% 115.31/17.56 |
% 115.31/17.56 | BETA: splitting (3) gives:
% 115.31/17.56 |
% 115.31/17.56 | Case 1:
% 115.31/17.56 | |
% 115.31/17.56 | | (17) ~ (all_56_4 = e2)
% 115.31/17.56 | |
% 115.31/17.56 | | REDUCE: (14), (17) imply:
% 115.31/17.56 | | (18) ~ (all_52_9 = e2)
% 115.31/17.56 | |
% 115.31/17.56 | | BETA: splitting (16) gives:
% 115.31/17.56 | |
% 115.31/17.56 | | Case 1:
% 115.31/17.56 | | |
% 115.31/17.56 | | | (19) all_58_2 = e2
% 115.31/17.56 | | |
% 115.31/17.56 | | | COMBINE_EQS: (7), (19) imply:
% 115.31/17.56 | | | (20) all_52_1 = e2
% 115.31/17.56 | | |
% 115.31/17.56 | | | COMBINE_EQS: (2), (20) imply:
% 115.31/17.56 | | | (21) all_56_3 = e2
% 115.31/17.56 | | |
% 115.31/17.56 | | | REF_CLOSE: (1), (4), (9), (11), (15), (21) are inconsistent by sub-proof
% 115.31/17.56 | | | #121.
% 115.31/17.56 | | |
% 115.31/17.56 | | Case 2:
% 115.31/17.56 | | |
% 115.31/17.56 | | | (22) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.56 | | |
% 115.31/17.56 | | | REF_CLOSE: (5), (6), (8), (10), (12), (18), (22) are inconsistent by
% 115.31/17.56 | | | sub-proof #401.
% 115.31/17.56 | | |
% 115.31/17.56 | | End of split
% 115.31/17.56 | |
% 115.31/17.56 | Case 2:
% 115.31/17.56 | |
% 115.31/17.56 | | (23) ~ (all_56_13 = e1)
% 115.31/17.56 | |
% 115.31/17.56 | | REDUCE: (13), (23) imply:
% 115.31/17.56 | | (24) $false
% 115.31/17.56 | |
% 115.31/17.56 | | CLOSE: (24) is inconsistent.
% 115.31/17.56 | |
% 115.31/17.56 | End of split
% 115.31/17.56 |
% 115.31/17.56 End of proof
% 115.31/17.56
% 115.31/17.56 Sub-proof #104 shows that the following formulas are inconsistent:
% 115.31/17.56 ----------------------------------------------------------------
% 115.31/17.56 (1) ~ (all_52_9 = all_8_2)
% 115.31/17.56 (2) ~ (all_4_2 = e0)
% 115.31/17.56 (3) all_56_14 = all_6_2
% 115.31/17.56 (4) all_56_3 = all_52_1
% 115.31/17.56 (5) all_56_11 = all_52_11
% 115.31/17.56 (6) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 115.31/17.56 (7) ~ (e3 = e1)
% 115.31/17.56 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.56 (9) all_56_14 = e2
% 115.31/17.56 (10) all_58_0 = all_10_2
% 115.31/17.56 (11) all_56_10 = all_52_7
% 115.31/17.56 (12) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 115.31/17.56 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.56 (14) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 115.31/17.56 (15) all_58_4 = all_52_8
% 115.31/17.56 (16) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.31/17.56 (17) all_56_2 = all_52_12
% 115.31/17.56 (18) all_58_3 = all_8_2
% 115.31/17.56 (19) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.31/17.56 (20) ~ (all_52_11 = all_6_2)
% 115.31/17.56 (21) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 115.31/17.56 (22) op(e2, e3) = all_52_1
% 115.31/17.56 (23) ~ (all_56_10 = e0)
% 115.31/17.56 (24) all_58_5 = all_52_9
% 115.31/17.56 (25) all_56_9 = all_52_3
% 115.31/17.56 (26) all_58_15 = all_4_2
% 115.31/17.56 (27) all_58_2 = all_52_1
% 115.31/17.56 (28) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 115.31/17.56 (29) ~ (all_10_2 = e3)
% 115.31/17.56 (30) all_58_13 = all_52_7
% 115.31/17.56 (31) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 115.31/17.56 (32) all_54_5 = all_8_2
% 115.31/17.56 (33) all_56_15 = all_4_2
% 115.31/17.56 (34) all_58_10 = all_52_13
% 115.31/17.56 (35) ~ (all_52_13 = all_8_2)
% 115.31/17.56 (36) all_58_1 = all_52_4
% 115.31/17.56 (37) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.31/17.56 (38) ~ (all_52_9 = all_52_11)
% 115.31/17.56 (39) all_58_14 = all_52_11
% 115.31/17.56 (40) all_56_13 = all_8_2
% 115.31/17.56 (41) ~ (all_52_1 = all_8_2)
% 115.31/17.56 (42) ~ (all_8_2 = e2)
% 115.31/17.56 (43) ~ (all_52_9 = all_6_2)
% 115.31/17.56 (44) all_56_1 = all_52_8
% 115.31/17.56 (45) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 115.31/17.56 (46) all_58_9 = all_52_12
% 115.31/17.56 (47) all_56_5 = all_52_13
% 115.31/17.57 (48) op(e2, e1) = all_52_9
% 115.31/17.57 (49) ~ (all_52_13 = all_4_2)
% 115.31/17.57 (50) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.31/17.57 (51) all_58_12 = all_52_3
% 115.31/17.57 (52) ~ (all_52_8 = all_52_9)
% 115.31/17.57 (53) op(e2, e0) = all_52_13
% 115.31/17.57 (54) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.31/17.57 (55) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.31/17.57 (56) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.57 (57) all_56_0 = all_52_4
% 115.31/17.57 (58) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.31/17.57 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.31/17.57 (59) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 115.31/17.57 (60) all_54_15 = all_4_2
% 115.31/17.57 (61) op(e2, all_8_2) = e1
% 115.31/17.57 (62) ~ (e1 = e0)
% 115.31/17.57
% 115.31/17.57 Begin of proof
% 115.31/17.57 |
% 115.31/17.57 | COMBINE_EQS: (3), (9) imply:
% 115.31/17.57 | (63) all_6_2 = e2
% 115.31/17.57 |
% 115.31/17.57 | SIMP: (63) implies:
% 115.31/17.57 | (64) all_6_2 = e2
% 115.31/17.57 |
% 115.31/17.57 | REDUCE: (11), (23) imply:
% 115.31/17.57 | (65) ~ (all_52_7 = e0)
% 115.31/17.57 |
% 115.31/17.57 | REDUCE: (43), (64) imply:
% 115.31/17.57 | (66) ~ (all_52_9 = e2)
% 115.31/17.57 |
% 115.31/17.57 | REDUCE: (20), (64) imply:
% 115.31/17.57 | (67) ~ (all_52_11 = e2)
% 115.31/17.57 |
% 115.31/17.57 | BETA: splitting (59) gives:
% 115.31/17.57 |
% 115.31/17.57 | Case 1:
% 115.31/17.57 | |
% 115.31/17.57 | | (68) ~ (all_56_0 = e3)
% 115.31/17.57 | |
% 115.31/17.57 | | REDUCE: (57), (68) imply:
% 115.31/17.57 | | (69) ~ (all_52_4 = e3)
% 115.31/17.57 | |
% 115.31/17.57 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 115.31/17.57 | | (16), (17), (18), (19), (21), (22), (24), (25), (26), (27), (28),
% 115.31/17.57 | | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 115.31/17.57 | | (40), (41), (42), (44), (45), (46), (47), (48), (49), (50), (51),
% 115.31/17.57 | | (52), (53), (54), (55), (56), (58), (60), (61), (62), (65), (66),
% 115.31/17.57 | | (67), (69) are inconsistent by sub-proof #105.
% 115.31/17.57 | |
% 115.31/17.57 | Case 2:
% 115.31/17.57 | |
% 115.31/17.57 | | (70) ~ (all_56_14 = e2)
% 115.31/17.57 | |
% 115.31/17.57 | | REDUCE: (9), (70) imply:
% 115.31/17.57 | | (71) $false
% 115.31/17.57 | |
% 115.31/17.57 | | CLOSE: (71) is inconsistent.
% 115.31/17.57 | |
% 115.31/17.57 | End of split
% 115.31/17.57 |
% 115.31/17.57 End of proof
% 115.31/17.57
% 115.31/17.57 Sub-proof #105 shows that the following formulas are inconsistent:
% 115.31/17.57 ----------------------------------------------------------------
% 115.31/17.57 (1) ~ (all_52_9 = e2)
% 115.31/17.57 (2) ~ (all_52_9 = all_8_2)
% 115.31/17.57 (3) ~ (all_4_2 = e0)
% 115.31/17.57 (4) all_56_3 = all_52_1
% 115.31/17.57 (5) all_56_11 = all_52_11
% 115.31/17.57 (6) ~ (all_52_4 = e3)
% 115.31/17.57 (7) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 115.31/17.57 (8) ~ (e3 = e1)
% 115.31/17.57 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.57 (10) all_58_0 = all_10_2
% 115.31/17.57 (11) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 115.31/17.57 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.57 (13) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 115.31/17.57 (14) all_58_4 = all_52_8
% 115.31/17.57 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.31/17.57 (16) all_56_2 = all_52_12
% 115.31/17.57 (17) all_58_3 = all_8_2
% 115.31/17.57 (18) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.31/17.57 (19) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 115.31/17.57 (20) op(e2, e3) = all_52_1
% 115.31/17.57 (21) all_58_5 = all_52_9
% 115.31/17.57 (22) all_56_9 = all_52_3
% 115.31/17.57 (23) all_58_15 = all_4_2
% 115.31/17.57 (24) all_58_2 = all_52_1
% 115.31/17.57 (25) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 115.31/17.57 (26) ~ (all_10_2 = e3)
% 115.31/17.57 (27) all_58_13 = all_52_7
% 115.31/17.57 (28) ~ (all_52_7 = e0)
% 115.31/17.57 (29) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 115.31/17.57 (30) all_54_5 = all_8_2
% 115.31/17.57 (31) ~ (all_52_11 = e2)
% 115.31/17.57 (32) all_56_15 = all_4_2
% 115.31/17.57 (33) all_58_10 = all_52_13
% 115.31/17.57 (34) ~ (all_52_13 = all_8_2)
% 115.31/17.57 (35) all_58_1 = all_52_4
% 115.31/17.57 (36) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.31/17.57 (37) ~ (all_52_9 = all_52_11)
% 115.31/17.57 (38) all_58_14 = all_52_11
% 115.31/17.57 (39) all_56_13 = all_8_2
% 115.31/17.57 (40) ~ (all_52_1 = all_8_2)
% 115.31/17.57 (41) ~ (all_8_2 = e2)
% 115.31/17.57 (42) all_56_1 = all_52_8
% 115.31/17.57 (43) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 115.31/17.57 (44) all_58_9 = all_52_12
% 115.31/17.57 (45) all_56_5 = all_52_13
% 115.31/17.57 (46) op(e2, e1) = all_52_9
% 115.31/17.57 (47) ~ (all_52_13 = all_4_2)
% 115.31/17.57 (48) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.31/17.57 (49) all_58_12 = all_52_3
% 115.31/17.57 (50) ~ (all_52_8 = all_52_9)
% 115.31/17.57 (51) op(e2, e0) = all_52_13
% 115.31/17.57 (52) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.31/17.57 (53) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.31/17.57 (54) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.57 (55) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.31/17.57 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.31/17.57 (56) all_54_15 = all_4_2
% 115.31/17.57 (57) op(e2, all_8_2) = e1
% 115.31/17.57 (58) ~ (e1 = e0)
% 115.31/17.57
% 115.31/17.57 Begin of proof
% 115.31/17.57 |
% 115.31/17.57 | BETA: splitting (43) gives:
% 115.31/17.57 |
% 115.31/17.57 | Case 1:
% 115.31/17.57 | |
% 115.31/17.57 | | (59) ~ (all_56_15 = e3)
% 115.31/17.57 | |
% 115.31/17.57 | | REDUCE: (32), (59) imply:
% 115.31/17.57 | | (60) ~ (all_4_2 = e3)
% 115.31/17.57 | |
% 115.31/17.57 | | BETA: splitting (25) gives:
% 115.31/17.57 | |
% 115.31/17.57 | | Case 1:
% 115.31/17.57 | | |
% 115.31/17.57 | | | (61) ~ (all_56_13 = e3)
% 115.31/17.57 | | |
% 115.31/17.57 | | | REDUCE: (39), (61) imply:
% 115.31/17.57 | | | (62) ~ (all_8_2 = e3)
% 115.31/17.57 | | |
% 115.31/17.57 | | | BETA: splitting (53) gives:
% 115.31/17.57 | | |
% 115.31/17.57 | | | Case 1:
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | (63) all_58_0 = e3
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | COMBINE_EQS: (10), (63) imply:
% 115.31/17.57 | | | | (64) all_10_2 = e3
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | REDUCE: (26), (64) imply:
% 115.31/17.57 | | | | (65) $false
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | CLOSE: (65) is inconsistent.
% 115.31/17.57 | | | |
% 115.31/17.57 | | | Case 2:
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | (66) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | BETA: splitting (66) gives:
% 115.31/17.57 | | | |
% 115.31/17.57 | | | | Case 1:
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | (67) all_58_1 = e3
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | COMBINE_EQS: (35), (67) imply:
% 115.31/17.57 | | | | | (68) all_52_4 = e3
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | REDUCE: (6), (68) imply:
% 115.31/17.57 | | | | | (69) $false
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | CLOSE: (69) is inconsistent.
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | Case 2:
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | (70) all_58_4 = e3 | all_58_9 = e3
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | BETA: splitting (70) gives:
% 115.31/17.57 | | | | |
% 115.31/17.57 | | | | | Case 1:
% 115.31/17.57 | | | | | |
% 115.31/17.57 | | | | | | (71) all_58_4 = e3
% 115.31/17.57 | | | | | |
% 115.31/17.57 | | | | | | COMBINE_EQS: (14), (71) imply:
% 115.31/17.57 | | | | | | (72) all_52_8 = e3
% 115.31/17.57 | | | | | |
% 115.31/17.57 | | | | | | COMBINE_EQS: (42), (72) imply:
% 115.31/17.57 | | | | | | (73) all_56_1 = e3
% 115.31/17.57 | | | | | |
% 115.31/17.57 | | | | | | REDUCE: (50), (72) imply:
% 115.31/17.57 | | | | | | (74) ~ (all_52_9 = e3)
% 115.31/17.57 | | | | | |
% 115.31/17.57 | | | | | | SIMP: (74) implies:
% 115.31/17.57 | | | | | | (75) ~ (all_52_9 = e3)
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | BETA: splitting (29) gives:
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | Case 1:
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | (76) ~ (all_56_1 = e3)
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | REDUCE: (73), (76) imply:
% 115.31/17.58 | | | | | | | (77) $false
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | CLOSE: (77) is inconsistent.
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | Case 2:
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | (78) ~ (all_56_15 = e1)
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | REDUCE: (32), (78) imply:
% 115.31/17.58 | | | | | | | (79) ~ (all_4_2 = e1)
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | BETA: splitting (15) gives:
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | | Case 1:
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | (80) all_54_15 = e3
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | COMBINE_EQS: (56), (80) imply:
% 115.31/17.58 | | | | | | | | (81) all_4_2 = e3
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | REDUCE: (60), (81) imply:
% 115.31/17.58 | | | | | | | | (82) $false
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | CLOSE: (82) is inconsistent.
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | Case 2:
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | (83) ~ (all_54_15 = e3)
% 115.31/17.58 | | | | | | | | (84) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | BETA: splitting (84) gives:
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | | Case 1:
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | (85) all_54_15 = e2
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | COMBINE_EQS: (56), (85) imply:
% 115.31/17.58 | | | | | | | | | (86) all_4_2 = e2
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | REDUCE: (47), (86) imply:
% 115.31/17.58 | | | | | | | | | (87) ~ (all_52_13 = e2)
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | REDUCE: (60), (86) imply:
% 115.31/17.58 | | | | | | | | | (88) ~ (e3 = e2)
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | SIMP: (88) implies:
% 115.31/17.58 | | | | | | | | | (89) ~ (e3 = e2)
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | REF_CLOSE: (1), (8), (9), (11), (12), (17), (21), (24), (30),
% 115.31/17.58 | | | | | | | | | (33), (34), (39), (40), (41), (48), (51), (54),
% 115.31/17.58 | | | | | | | | | (57), (62), (73), (75), (87), (89) are inconsistent
% 115.31/17.58 | | | | | | | | | by sub-proof #111.
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | Case 2:
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | (90) all_54_15 = e1 | all_54_15 = e0
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | | REF_CLOSE: (3), (56), (79), (90) are inconsistent by sub-proof
% 115.31/17.58 | | | | | | | | | #418.
% 115.31/17.58 | | | | | | | | |
% 115.31/17.58 | | | | | | | | End of split
% 115.31/17.58 | | | | | | | |
% 115.31/17.58 | | | | | | | End of split
% 115.31/17.58 | | | | | | |
% 115.31/17.58 | | | | | | End of split
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | Case 2:
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | (91) all_58_9 = e3
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | COMBINE_EQS: (44), (91) imply:
% 115.31/17.58 | | | | | | (92) all_52_12 = e3
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | COMBINE_EQS: (16), (92) imply:
% 115.31/17.58 | | | | | | (93) all_56_2 = e3
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | REF_CLOSE: (2), (9), (12), (30), (36), (39), (41), (46), (57), (62),
% 115.31/17.58 | | | | | | (93) are inconsistent by sub-proof #107.
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | End of split
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | End of split
% 115.31/17.58 | | | |
% 115.31/17.58 | | | End of split
% 115.31/17.58 | | |
% 115.31/17.58 | | Case 2:
% 115.31/17.58 | | |
% 115.31/17.58 | | | (94) all_56_13 = e3
% 115.31/17.58 | | | (95) ~ (all_56_9 = e0)
% 115.31/17.58 | | |
% 115.31/17.58 | | | REDUCE: (22), (95) imply:
% 115.31/17.58 | | | (96) ~ (all_52_3 = e0)
% 115.31/17.58 | | |
% 115.31/17.58 | | | BETA: splitting (55) gives:
% 115.31/17.58 | | |
% 115.31/17.58 | | | Case 1:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | (97) all_58_15 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | COMBINE_EQS: (23), (97) imply:
% 115.31/17.58 | | | | (98) all_4_2 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | REDUCE: (3), (98) imply:
% 115.31/17.58 | | | | (99) $false
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | CLOSE: (99) is inconsistent.
% 115.31/17.58 | | | |
% 115.31/17.58 | | | Case 2:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | (100) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 115.31/17.58 | | | | = e0 | all_58_13 = e0 | all_58_14 = e0)
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | ALPHA: (100) implies:
% 115.31/17.58 | | | | (101) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | BETA: splitting (101) gives:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | Case 1:
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | (102) all_58_12 = e0
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | REF_CLOSE: (49), (96), (102) are inconsistent by sub-proof #362.
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | Case 2:
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | (103) all_58_13 = e0 | all_58_14 = e0
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | BETA: splitting (7) gives:
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | Case 1:
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | (104) ~ (all_56_3 = e2)
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | REDUCE: (4), (104) imply:
% 115.31/17.58 | | | | | | (105) ~ (all_52_1 = e2)
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | REF_CLOSE: (1), (5), (9), (12), (17), (18), (19), (20), (21), (24),
% 115.31/17.58 | | | | | | (27), (28), (30), (31), (33), (34), (37), (38), (39),
% 115.31/17.58 | | | | | | (41), (45), (52), (54), (57), (58), (103), (105) are
% 115.31/17.58 | | | | | | inconsistent by sub-proof #106.
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | Case 2:
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | (106) ~ (all_56_13 = e3)
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | REDUCE: (94), (106) imply:
% 115.31/17.58 | | | | | | (107) $false
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | | CLOSE: (107) is inconsistent.
% 115.31/17.58 | | | | | |
% 115.31/17.58 | | | | | End of split
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | End of split
% 115.31/17.58 | | | |
% 115.31/17.58 | | | End of split
% 115.31/17.58 | | |
% 115.31/17.58 | | End of split
% 115.31/17.58 | |
% 115.31/17.58 | Case 2:
% 115.31/17.58 | |
% 115.31/17.58 | | (108) all_56_15 = e3
% 115.31/17.58 | | (109) ~ (all_56_9 = e0)
% 115.31/17.58 | |
% 115.31/17.58 | | COMBINE_EQS: (32), (108) imply:
% 115.31/17.58 | | (110) all_4_2 = e3
% 115.31/17.58 | |
% 115.31/17.58 | | SIMP: (110) implies:
% 115.31/17.58 | | (111) all_4_2 = e3
% 115.31/17.58 | |
% 115.31/17.58 | | COMBINE_EQS: (23), (111) imply:
% 115.31/17.58 | | (112) all_58_15 = e3
% 115.31/17.58 | |
% 115.31/17.58 | | REDUCE: (22), (109) imply:
% 115.31/17.58 | | (113) ~ (all_52_3 = e0)
% 115.31/17.58 | |
% 115.31/17.58 | | REDUCE: (3), (111) imply:
% 115.31/17.58 | | (114) ~ (e3 = e0)
% 115.31/17.58 | |
% 115.31/17.58 | | BETA: splitting (13) gives:
% 115.31/17.58 | |
% 115.31/17.58 | | Case 1:
% 115.31/17.58 | | |
% 115.31/17.58 | | | (115) ~ (all_56_3 = e2)
% 115.31/17.58 | | |
% 115.31/17.58 | | | REDUCE: (4), (115) imply:
% 115.31/17.58 | | | (116) ~ (all_52_1 = e2)
% 115.31/17.58 | | |
% 115.31/17.58 | | | BETA: splitting (55) gives:
% 115.31/17.58 | | |
% 115.31/17.58 | | | Case 1:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | (117) all_58_15 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | COMBINE_EQS: (112), (117) imply:
% 115.31/17.58 | | | | (118) e3 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | REDUCE: (114), (118) imply:
% 115.31/17.58 | | | | (119) $false
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | CLOSE: (119) is inconsistent.
% 115.31/17.58 | | | |
% 115.31/17.58 | | | Case 2:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | (120) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 115.31/17.58 | | | | = e0 | all_58_13 = e0 | all_58_14 = e0)
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | ALPHA: (120) implies:
% 115.31/17.58 | | | | (121) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | BETA: splitting (121) gives:
% 115.31/17.58 | | | |
% 115.31/17.58 | | | | Case 1:
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | (122) all_58_12 = e0
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | REF_CLOSE: (49), (113), (122) are inconsistent by sub-proof #362.
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | Case 2:
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | (123) all_58_13 = e0 | all_58_14 = e0
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | | REF_CLOSE: (1), (5), (9), (12), (17), (18), (19), (20), (21), (24),
% 115.31/17.58 | | | | | (27), (28), (30), (31), (33), (34), (37), (38), (39), (41),
% 115.31/17.58 | | | | | (45), (52), (54), (57), (58), (116), (123) are inconsistent
% 115.31/17.58 | | | | | by sub-proof #106.
% 115.31/17.58 | | | | |
% 115.31/17.58 | | | | End of split
% 115.31/17.58 | | | |
% 115.31/17.58 | | | End of split
% 115.31/17.58 | | |
% 115.31/17.58 | | Case 2:
% 115.31/17.58 | | |
% 115.31/17.58 | | | (124) ~ (all_56_15 = e3)
% 115.31/17.58 | | |
% 115.31/17.58 | | | REDUCE: (108), (124) imply:
% 115.31/17.58 | | | (125) $false
% 115.31/17.58 | | |
% 115.31/17.58 | | | CLOSE: (125) is inconsistent.
% 115.31/17.58 | | |
% 115.31/17.58 | | End of split
% 115.31/17.58 | |
% 115.31/17.58 | End of split
% 115.31/17.58 |
% 115.31/17.58 End of proof
% 115.31/17.58
% 115.31/17.58 Sub-proof #106 shows that the following formulas are inconsistent:
% 115.31/17.58 ----------------------------------------------------------------
% 115.31/17.58 (1) ~ (all_52_9 = e2)
% 115.31/17.58 (2) ~ (all_52_1 = e2)
% 115.31/17.58 (3) all_56_11 = all_52_11
% 115.31/17.58 (4) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.58 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.58 (6) all_58_3 = all_8_2
% 115.31/17.58 (7) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.31/17.58 (8) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 115.31/17.58 (9) op(e2, e3) = all_52_1
% 115.31/17.58 (10) all_58_5 = all_52_9
% 115.31/17.58 (11) all_58_2 = all_52_1
% 115.31/17.58 (12) all_58_13 = all_52_7
% 115.31/17.58 (13) ~ (all_52_7 = e0)
% 115.31/17.58 (14) all_54_5 = all_8_2
% 115.31/17.58 (15) ~ (all_52_11 = e2)
% 115.31/17.58 (16) all_58_10 = all_52_13
% 115.31/17.58 (17) ~ (all_52_13 = all_8_2)
% 115.31/17.58 (18) ~ (all_52_9 = all_52_11)
% 115.31/17.58 (19) all_58_14 = all_52_11
% 115.31/17.58 (20) all_56_13 = all_8_2
% 115.31/17.58 (21) ~ (all_8_2 = e2)
% 115.31/17.58 (22) all_56_5 = all_52_13
% 115.31/17.58 (23) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.31/17.58 (24) all_58_13 = e0 | all_58_14 = e0
% 115.31/17.58 (25) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.58 (26) op(e2, all_8_2) = e1
% 115.31/17.58 (27) ~ (e1 = e0)
% 115.31/17.58
% 115.31/17.58 Begin of proof
% 115.31/17.58 |
% 115.31/17.58 | BETA: splitting (24) gives:
% 115.31/17.58 |
% 115.31/17.58 | Case 1:
% 115.31/17.58 | |
% 115.31/17.58 | | (28) all_58_13 = e0
% 115.31/17.58 | |
% 115.31/17.58 | | REF_CLOSE: (12), (13), (28) are inconsistent by sub-proof #430.
% 115.31/17.58 | |
% 115.31/17.58 | Case 2:
% 115.31/17.58 | |
% 115.31/17.58 | | (29) all_58_14 = e0
% 115.31/17.58 | |
% 115.31/17.58 | | COMBINE_EQS: (19), (29) imply:
% 115.31/17.58 | | (30) all_52_11 = e0
% 115.31/17.58 | |
% 115.31/17.58 | | SIMP: (30) implies:
% 115.31/17.58 | | (31) all_52_11 = e0
% 115.31/17.58 | |
% 115.31/17.58 | | COMBINE_EQS: (3), (31) imply:
% 115.31/17.58 | | (32) all_56_11 = e0
% 115.31/17.58 | |
% 115.31/17.58 | | REDUCE: (18), (31) imply:
% 115.31/17.58 | | (33) ~ (all_52_9 = e0)
% 115.31/17.58 | |
% 115.31/17.58 | | REDUCE: (15), (31) imply:
% 115.31/17.58 | | (34) ~ (e2 = e0)
% 115.31/17.58 | |
% 115.31/17.58 | | SIMP: (34) implies:
% 115.31/17.59 | | (35) ~ (e2 = e0)
% 115.31/17.59 | |
% 115.31/17.59 | | BETA: splitting (8) gives:
% 115.31/17.59 | |
% 115.31/17.59 | | Case 1:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (36) ~ (all_56_13 = e1)
% 115.31/17.59 | | |
% 115.31/17.59 | | | REDUCE: (20), (36) imply:
% 115.31/17.59 | | | (37) ~ (all_8_2 = e1)
% 115.31/17.59 | | |
% 115.31/17.59 | | | BETA: splitting (25) gives:
% 115.31/17.59 | | |
% 115.31/17.59 | | | Case 1:
% 115.31/17.59 | | | |
% 115.31/17.59 | | | | (38) all_58_2 = e2
% 115.31/17.59 | | | |
% 115.31/17.59 | | | | REF_CLOSE: (2), (11), (38) are inconsistent by sub-proof #335.
% 115.31/17.59 | | | |
% 115.31/17.59 | | | Case 2:
% 115.31/17.59 | | | |
% 115.31/17.59 | | | | (39) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.59 | | | |
% 115.31/17.59 | | | | BETA: splitting (39) gives:
% 115.31/17.59 | | | |
% 115.31/17.59 | | | | Case 1:
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | (40) all_58_3 = e2
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | COMBINE_EQS: (6), (40) imply:
% 115.31/17.59 | | | | | (41) all_8_2 = e2
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | REDUCE: (21), (41) imply:
% 115.31/17.59 | | | | | (42) $false
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | CLOSE: (42) is inconsistent.
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | Case 2:
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | (43) all_58_5 = e2 | all_58_10 = e2
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | BETA: splitting (43) gives:
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | | Case 1:
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | (44) all_58_5 = e2
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | REF_CLOSE: (1), (10), (44) are inconsistent by sub-proof #119.
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | Case 2:
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | (45) all_58_10 = e2
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | COMBINE_EQS: (16), (45) imply:
% 115.31/17.59 | | | | | | (46) all_52_13 = e2
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | COMBINE_EQS: (22), (46) imply:
% 115.31/17.59 | | | | | | (47) all_56_5 = e2
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | REDUCE: (17), (46) imply:
% 115.31/17.59 | | | | | | (48) ~ (all_8_2 = e2)
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (11), (14), (20), (21),
% 115.31/17.59 | | | | | | (23), (26), (27), (33), (35), (37), (45), (47) are
% 115.31/17.59 | | | | | | inconsistent by sub-proof #131.
% 115.31/17.59 | | | | | |
% 115.31/17.59 | | | | | End of split
% 115.31/17.59 | | | | |
% 115.31/17.59 | | | | End of split
% 115.31/17.59 | | | |
% 115.31/17.59 | | | End of split
% 115.31/17.59 | | |
% 115.31/17.59 | | Case 2:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (49) ~ (all_56_11 = e0)
% 115.31/17.59 | | |
% 115.31/17.59 | | | REDUCE: (32), (49) imply:
% 115.31/17.59 | | | (50) $false
% 115.31/17.59 | | |
% 115.31/17.59 | | | CLOSE: (50) is inconsistent.
% 115.31/17.59 | | |
% 115.31/17.59 | | End of split
% 115.31/17.59 | |
% 115.31/17.59 | End of split
% 115.31/17.59 |
% 115.31/17.59 End of proof
% 115.31/17.59
% 115.31/17.59 Sub-proof #107 shows that the following formulas are inconsistent:
% 115.31/17.59 ----------------------------------------------------------------
% 115.31/17.59 (1) ~ (all_52_9 = all_8_2)
% 115.31/17.59 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.59 (4) ~ (all_8_2 = e3)
% 115.31/17.59 (5) all_54_5 = all_8_2
% 115.31/17.59 (6) all_56_2 = e3
% 115.31/17.59 (7) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.31/17.59 (8) all_56_13 = all_8_2
% 115.31/17.59 (9) ~ (all_8_2 = e2)
% 115.31/17.59 (10) op(e2, e1) = all_52_9
% 115.31/17.59 (11) op(e2, all_8_2) = e1
% 115.31/17.59
% 115.31/17.59 Begin of proof
% 115.31/17.59 |
% 115.31/17.59 | BETA: splitting (7) gives:
% 115.31/17.59 |
% 115.31/17.59 | Case 1:
% 115.31/17.59 | |
% 115.31/17.59 | | (12) ~ (all_56_2 = e3)
% 115.31/17.59 | |
% 115.31/17.59 | | REDUCE: (6), (12) imply:
% 115.31/17.59 | | (13) $false
% 115.31/17.59 | |
% 115.31/17.59 | | CLOSE: (13) is inconsistent.
% 115.31/17.59 | |
% 115.31/17.59 | Case 2:
% 115.31/17.59 | |
% 115.31/17.59 | | (14) ~ (all_56_13 = e0)
% 115.31/17.59 | |
% 115.31/17.59 | | REDUCE: (8), (14) imply:
% 115.31/17.59 | | (15) ~ (all_8_2 = e0)
% 115.31/17.59 | |
% 115.31/17.59 | | BETA: splitting (2) gives:
% 115.31/17.59 | |
% 115.31/17.59 | | Case 1:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (16) all_54_5 = e3
% 115.31/17.59 | | |
% 115.31/17.59 | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #339.
% 115.31/17.59 | | |
% 115.31/17.59 | | Case 2:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (17) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.59 | | |
% 115.31/17.59 | | | REF_CLOSE: (1), (3), (5), (9), (10), (11), (15), (17) are inconsistent by
% 115.31/17.59 | | | sub-proof #108.
% 115.31/17.59 | | |
% 115.31/17.59 | | End of split
% 115.31/17.59 | |
% 115.31/17.59 | End of split
% 115.31/17.59 |
% 115.31/17.59 End of proof
% 115.31/17.59
% 115.31/17.59 Sub-proof #108 shows that the following formulas are inconsistent:
% 115.31/17.59 ----------------------------------------------------------------
% 115.31/17.59 (1) ~ (all_52_9 = all_8_2)
% 115.31/17.59 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.59 (4) ~ (all_8_2 = e0)
% 115.31/17.59 (5) all_54_5 = all_8_2
% 115.31/17.59 (6) ~ (all_8_2 = e2)
% 115.31/17.59 (7) op(e2, e1) = all_52_9
% 115.31/17.59 (8) op(e2, all_8_2) = e1
% 115.31/17.59
% 115.31/17.59 Begin of proof
% 115.31/17.59 |
% 115.31/17.59 | BETA: splitting (2) gives:
% 115.31/17.59 |
% 115.31/17.59 | Case 1:
% 115.31/17.59 | |
% 115.31/17.59 | | (9) all_54_5 = e2
% 115.31/17.59 | |
% 115.31/17.59 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #338.
% 115.31/17.59 | |
% 115.31/17.59 | Case 2:
% 115.31/17.59 | |
% 115.31/17.59 | | (10) all_54_5 = e1 | all_54_5 = e0
% 115.31/17.59 | |
% 115.31/17.59 | | BETA: splitting (10) gives:
% 115.31/17.59 | |
% 115.31/17.59 | | Case 1:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (11) all_54_5 = e1
% 115.31/17.59 | | |
% 115.31/17.59 | | | COMBINE_EQS: (5), (11) imply:
% 115.31/17.59 | | | (12) all_8_2 = e1
% 115.31/17.59 | | |
% 115.31/17.59 | | | REF_CLOSE: (1), (3), (7), (8), (12) are inconsistent by sub-proof #109.
% 115.31/17.59 | | |
% 115.31/17.59 | | Case 2:
% 115.31/17.59 | | |
% 115.31/17.59 | | | (13) all_54_5 = e0
% 115.31/17.59 | | |
% 115.31/17.59 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #311.
% 115.31/17.59 | | |
% 115.31/17.59 | | End of split
% 115.31/17.59 | |
% 115.31/17.59 | End of split
% 115.31/17.59 |
% 115.31/17.59 End of proof
% 115.31/17.59
% 115.31/17.59 Sub-proof #109 shows that the following formulas are inconsistent:
% 115.31/17.59 ----------------------------------------------------------------
% 115.31/17.59 (1) ~ (all_52_9 = all_8_2)
% 115.31/17.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.59 (3) all_8_2 = e1
% 115.31/17.59 (4) op(e2, e1) = all_52_9
% 115.31/17.59 (5) op(e2, all_8_2) = e1
% 115.31/17.59
% 115.31/17.59 Begin of proof
% 115.31/17.59 |
% 115.31/17.59 | SIMP: (3) implies:
% 115.31/17.59 | (6) all_8_2 = e1
% 115.31/17.59 |
% 115.31/17.59 | REDUCE: (1), (6) imply:
% 115.31/17.59 | (7) ~ (all_52_9 = e1)
% 115.31/17.59 |
% 115.31/17.59 | REDUCE: (5), (6) imply:
% 115.31/17.59 | (8) op(e2, e1) = e1
% 115.31/17.59 |
% 115.31/17.59 | REF_CLOSE: (2), (4), (7), (8) are inconsistent by sub-proof #110.
% 115.31/17.59 |
% 115.31/17.59 End of proof
% 115.31/17.59
% 115.31/17.59 Sub-proof #110 shows that the following formulas are inconsistent:
% 115.31/17.59 ----------------------------------------------------------------
% 115.31/17.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.59 (2) op(e2, e1) = all_52_9
% 115.31/17.59 (3) op(e2, e1) = e1
% 115.31/17.59 (4) ~ (all_52_9 = e1)
% 115.31/17.59
% 115.31/17.59 Begin of proof
% 115.31/17.59 |
% 115.31/17.59 | GROUND_INST: instantiating (1) with all_52_9, e1, e1, e2, simplifying with
% 115.31/17.59 | (2), (3) gives:
% 115.31/17.59 | (5) all_52_9 = e1
% 115.31/17.59 |
% 115.31/17.59 | REDUCE: (4), (5) imply:
% 115.31/17.59 | (6) $false
% 115.31/17.59 |
% 115.31/17.59 | CLOSE: (6) is inconsistent.
% 115.31/17.59 |
% 115.31/17.59 End of proof
% 115.31/17.59
% 115.31/17.59 Sub-proof #111 shows that the following formulas are inconsistent:
% 115.31/17.59 ----------------------------------------------------------------
% 115.31/17.59 (1) ~ (all_52_9 = e2)
% 115.31/17.59 (2) ~ (all_52_9 = e3)
% 115.31/17.59 (3) ~ (e3 = e1)
% 115.31/17.59 (4) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.59 (5) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 115.31/17.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.31/17.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.31/17.59 (7) all_58_3 = all_8_2
% 115.31/17.59 (8) ~ (all_8_2 = e3)
% 115.31/17.59 (9) all_58_5 = all_52_9
% 115.31/17.59 (10) all_58_2 = all_52_1
% 115.31/17.59 (11) all_54_5 = all_8_2
% 115.31/17.59 (12) ~ (all_52_13 = e2)
% 115.31/17.59 (13) all_58_10 = all_52_13
% 115.31/17.59 (14) ~ (all_52_13 = all_8_2)
% 115.31/17.59 (15) all_56_13 = all_8_2
% 115.31/17.59 (16) ~ (all_52_1 = all_8_2)
% 115.31/17.59 (17) ~ (all_8_2 = e2)
% 115.31/17.59 (18) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.31/17.59 (19) all_56_1 = e3
% 115.31/17.59 (20) op(e2, e0) = all_52_13
% 115.31/17.59 (21) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.31/17.59 (22) ~ (e3 = e2)
% 115.31/17.59 (23) op(e2, all_8_2) = e1
% 115.31/17.59
% 115.31/17.59 Begin of proof
% 115.31/17.59 |
% 115.31/17.59 | BETA: splitting (21) gives:
% 115.31/17.59 |
% 115.31/17.59 | Case 1:
% 115.31/17.59 | |
% 115.31/17.59 | | (24) all_58_2 = e2
% 115.31/17.59 | |
% 115.31/17.59 | | COMBINE_EQS: (10), (24) imply:
% 115.31/17.59 | | (25) all_52_1 = e2
% 115.31/17.59 | |
% 115.31/17.59 | | SIMP: (25) implies:
% 115.31/17.59 | | (26) all_52_1 = e2
% 115.31/17.59 | |
% 115.31/17.59 | | REDUCE: (16), (26) imply:
% 115.31/17.60 | | (27) ~ (all_8_2 = e2)
% 115.31/17.60 | |
% 115.31/17.60 | | BETA: splitting (18) gives:
% 115.31/17.60 | |
% 115.31/17.60 | | Case 1:
% 115.31/17.60 | | |
% 115.31/17.60 | | | (28) all_58_2 = e3
% 115.31/17.60 | | |
% 115.31/17.60 | | | COMBINE_EQS: (24), (28) imply:
% 115.31/17.60 | | | (29) e3 = e2
% 115.31/17.60 | | |
% 115.31/17.60 | | | REDUCE: (22), (29) imply:
% 115.31/17.60 | | | (30) $false
% 115.31/17.60 | | |
% 115.31/17.60 | | | CLOSE: (30) is inconsistent.
% 115.31/17.60 | | |
% 115.31/17.60 | | Case 2:
% 115.31/17.60 | | |
% 115.31/17.60 | | | (31) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.31/17.60 | | |
% 115.31/17.60 | | | BETA: splitting (5) gives:
% 115.31/17.60 | | |
% 115.31/17.60 | | | Case 1:
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | (32) ~ (all_56_1 = e3)
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | REDUCE: (19), (32) imply:
% 115.31/17.60 | | | | (33) $false
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | CLOSE: (33) is inconsistent.
% 115.31/17.60 | | | |
% 115.31/17.60 | | | Case 2:
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | (34) ~ (all_56_13 = e1)
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | REDUCE: (15), (34) imply:
% 115.31/17.60 | | | | (35) ~ (all_8_2 = e1)
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | BETA: splitting (31) gives:
% 115.31/17.60 | | | |
% 115.31/17.60 | | | | Case 1:
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | (36) all_58_3 = e3
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | COMBINE_EQS: (7), (36) imply:
% 115.31/17.60 | | | | | (37) all_8_2 = e3
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | REDUCE: (8), (37) imply:
% 115.31/17.60 | | | | | (38) $false
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | CLOSE: (38) is inconsistent.
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | Case 2:
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | (39) all_58_5 = e3 | all_58_10 = e3
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | BETA: splitting (39) gives:
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | | Case 1:
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | (40) all_58_5 = e3
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | REF_CLOSE: (2), (9), (40) are inconsistent by sub-proof #175.
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | Case 2:
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | (41) all_58_10 = e3
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | COMBINE_EQS: (13), (41) imply:
% 115.31/17.60 | | | | | | (42) all_52_13 = e3
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | REDUCE: (14), (42) imply:
% 115.31/17.60 | | | | | | (43) ~ (all_8_2 = e3)
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | REDUCE: (20), (42) imply:
% 115.31/17.60 | | | | | | (44) op(e2, e0) = e3
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | BETA: splitting (4) gives:
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | | Case 1:
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | | (45) all_54_5 = e3
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | | REF_CLOSE: (8), (11), (45) are inconsistent by sub-proof #339.
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | Case 2:
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | | (46) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | | BETA: splitting (46) gives:
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | | Case 1:
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | | (47) all_54_5 = e2
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | | REF_CLOSE: (11), (17), (47) are inconsistent by sub-proof #338.
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | Case 2:
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | | (48) all_54_5 = e1 | all_54_5 = e0
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | | BETA: splitting (48) gives:
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | | Case 1:
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | (49) all_54_5 = e1
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | REF_CLOSE: (11), (35), (49) are inconsistent by sub-proof
% 115.31/17.60 | | | | | | | | | #337.
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | Case 2:
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | (50) all_54_5 = e0
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | COMBINE_EQS: (11), (50) imply:
% 115.31/17.60 | | | | | | | | | (51) all_8_2 = e0
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | SIMP: (51) implies:
% 115.31/17.60 | | | | | | | | | (52) all_8_2 = e0
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | REDUCE: (23), (52) imply:
% 115.31/17.60 | | | | | | | | | (53) op(e2, e0) = e1
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | | REF_CLOSE: (3), (6), (44), (53) are inconsistent by sub-proof
% 115.31/17.60 | | | | | | | | | #133.
% 115.31/17.60 | | | | | | | | |
% 115.31/17.60 | | | | | | | | End of split
% 115.31/17.60 | | | | | | | |
% 115.31/17.60 | | | | | | | End of split
% 115.31/17.60 | | | | | | |
% 115.31/17.60 | | | | | | End of split
% 115.31/17.60 | | | | | |
% 115.31/17.60 | | | | | End of split
% 115.31/17.60 | | | | |
% 115.31/17.60 | | | | End of split
% 115.31/17.60 | | | |
% 115.31/17.60 | | | End of split
% 115.31/17.60 | | |
% 115.31/17.60 | | End of split
% 115.31/17.60 | |
% 115.31/17.60 | Case 2:
% 115.31/17.60 | |
% 115.48/17.60 | | (54) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.48/17.60 | |
% 115.48/17.60 | | REF_CLOSE: (1), (7), (9), (12), (13), (17), (54) are inconsistent by
% 115.48/17.60 | | sub-proof #401.
% 115.48/17.60 | |
% 115.48/17.60 | End of split
% 115.48/17.60 |
% 115.48/17.60 End of proof
% 115.48/17.60
% 115.48/17.60 Sub-proof #112 shows that the following formulas are inconsistent:
% 115.48/17.60 ----------------------------------------------------------------
% 115.48/17.60 (1) ~ (all_52_2 = all_10_2)
% 115.48/17.60 (2) ~ (all_52_3 = e0)
% 115.48/17.60 (3) all_58_10 = e2
% 115.48/17.60 (4) all_54_2 = all_52_8
% 115.48/17.60 (5) all_58_7 = all_52_6
% 115.48/17.60 (6) ~ (all_52_8 = all_52_11)
% 115.48/17.60 (7) ~ (all_52_9 = all_8_2)
% 115.48/17.60 (8) ~ (all_52_1 = e2)
% 115.48/17.60 (9) ~ (all_52_3 = e3)
% 115.48/17.60 (10) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 115.48/17.60 (11) all_56_14 = all_6_2
% 115.48/17.60 (12) all_54_0 = all_10_2
% 115.48/17.60 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.48/17.60 (14) all_56_11 = all_52_11
% 115.48/17.60 (15) ~ (all_4_0 = e1)
% 115.48/17.60 (16) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.48/17.60 (17) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.48/17.60 (18) all_56_12 = all_10_2
% 115.48/17.60 (19) all_58_0 = all_10_2
% 115.48/17.60 (20) all_54_13 = all_52_7
% 115.48/17.60 (21) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.48/17.60 (22) all_56_10 = all_52_7
% 115.48/17.60 (23) all_54_14 = all_52_11
% 115.48/17.60 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.48/17.60 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.48/17.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.48/17.60 (26) all_54_8 = all_52_2
% 115.48/17.60 (27) ~ (all_52_2 = all_6_2)
% 115.48/17.60 (28) op(e0, e3) = all_4_1
% 115.48/17.60 (29) ~ (all_52_1 = all_52_9)
% 115.48/17.60 (30) ~ (all_52_7 = e3)
% 115.48/17.60 (31) ~ (all_10_2 = e2)
% 115.48/17.60 (32) all_54_10 = all_6_2
% 115.48/17.60 (33) all_58_4 = all_52_8
% 115.48/17.60 (34) all_58_3 = all_8_2
% 115.48/17.60 (35) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.48/17.60 (36) all_58_11 = all_52_14
% 115.48/17.60 (37) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.48/17.60 (38) ~ (all_52_2 = all_52_3)
% 115.48/17.60 (39) ~ (all_52_11 = all_6_2)
% 115.48/17.60 (40) op(e2, e3) = all_52_1
% 115.48/17.60 (41) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.48/17.60 (42) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.48/17.60 (43) ~ (all_52_7 = all_8_2)
% 115.48/17.60 (44) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.48/17.60 (45) all_58_5 = all_52_9
% 115.48/17.60 (46) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.48/17.60 (47) all_58_2 = all_52_1
% 115.48/17.60 (48) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.48/17.60 (49) ~ (all_52_1 = all_52_13)
% 115.48/17.60 (50) op(e0, e3) = all_52_3
% 115.48/17.60 (51) ~ (all_10_2 = e3)
% 115.48/17.60 (52) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.48/17.60 (53) all_58_6 = all_52_2
% 115.48/17.60 (54) ~ (all_52_2 = e1)
% 115.48/17.60 (55) ~ (all_52_1 = all_10_2)
% 115.48/17.60 (56) all_54_5 = all_8_2
% 115.48/17.60 (57) all_58_10 = all_52_13
% 115.48/17.60 (58) ~ (all_52_13 = all_8_2)
% 115.48/17.60 (59) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.48/17.60 (60) ~ (all_52_6 = all_8_2)
% 115.48/17.60 (61) all_56_13 = all_8_2
% 115.48/17.60 (62) ~ (all_52_1 = all_8_2)
% 115.48/17.60 (63) ~ (all_8_2 = e2)
% 115.48/17.60 (64) op(all_4_1, e3) = all_4_0
% 115.48/17.60 (65) ~ (all_52_7 = all_52_11)
% 115.48/17.60 (66) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.48/17.60 (67) ~ (all_52_9 = all_6_2)
% 115.48/17.60 (68) ~ (all_52_1 = all_52_2)
% 115.48/17.60 (69) ~ (all_52_1 = all_52_3)
% 115.48/17.60 (70) all_56_1 = all_52_8
% 115.48/17.60 (71) all_58_8 = all_6_2
% 115.48/17.60 (72) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.48/17.60 (73) all_56_4 = all_52_9
% 115.48/17.60 (74) all_56_5 = all_52_13
% 115.48/17.60 (75) op(e2, e1) = all_52_9
% 115.48/17.60 (76) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.48/17.60 (77) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.48/17.60 (78) all_58_12 = all_52_3
% 115.48/17.60 (79) ~ (all_52_8 = all_52_9)
% 115.48/17.60 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.48/17.60 (81) ~ (all_52_3 = all_10_2)
% 115.48/17.61 (82) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.48/17.61 (83) all_56_8 = all_52_14
% 115.48/17.61 (84) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.48/17.61 (85) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.48/17.61 (86) all_54_4 = all_52_1
% 115.48/17.61 (87) ~ (all_52_11 = e3)
% 115.48/17.61 (88) op(e2, all_8_2) = e1
% 115.48/17.61 (89) ~ (all_6_2 = e1)
% 115.48/17.61 (90) ~ (all_52_3 = all_52_11)
% 115.48/17.61 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.48/17.61 (92) all_54_12 = all_52_3
% 115.48/17.61 (93) ~ (all_52_3 = all_52_7)
% 115.48/17.61
% 115.48/17.61 Begin of proof
% 115.48/17.61 |
% 115.48/17.61 | COMBINE_EQS: (3), (57) imply:
% 115.48/17.61 | (94) all_52_13 = e2
% 115.48/17.61 |
% 115.48/17.61 | COMBINE_EQS: (74), (94) imply:
% 115.48/17.61 | (95) all_56_5 = e2
% 115.48/17.61 |
% 115.48/17.61 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 115.48/17.61 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 115.48/17.61 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 115.48/17.61 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 115.48/17.61 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 115.48/17.61 | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 115.48/17.61 | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 115.48/17.61 | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 115.48/17.61 | (91), (92), (93), (95) are inconsistent by sub-proof #113.
% 115.48/17.61 |
% 115.48/17.61 End of proof
% 115.48/17.61
% 115.48/17.61 Sub-proof #113 shows that the following formulas are inconsistent:
% 115.48/17.61 ----------------------------------------------------------------
% 115.48/17.61 (1) ~ (all_52_2 = all_10_2)
% 115.48/17.61 (2) ~ (all_52_3 = e0)
% 115.48/17.61 (3) all_54_2 = all_52_8
% 115.48/17.61 (4) all_58_7 = all_52_6
% 115.48/17.61 (5) ~ (all_52_8 = all_52_11)
% 115.48/17.61 (6) ~ (all_52_9 = all_8_2)
% 115.48/17.61 (7) ~ (all_52_1 = e2)
% 115.48/17.61 (8) ~ (all_52_3 = e3)
% 115.48/17.61 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 115.48/17.61 (10) all_56_14 = all_6_2
% 115.48/17.61 (11) all_54_0 = all_10_2
% 115.48/17.61 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.48/17.61 (13) all_56_11 = all_52_11
% 115.48/17.61 (14) ~ (all_4_0 = e1)
% 115.48/17.61 (15) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.48/17.61 (16) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.48/17.61 (17) all_56_12 = all_10_2
% 115.48/17.61 (18) all_58_0 = all_10_2
% 115.48/17.61 (19) all_54_13 = all_52_7
% 115.48/17.61 (20) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.48/17.61 (21) all_56_10 = all_52_7
% 115.48/17.61 (22) all_54_14 = all_52_11
% 115.48/17.61 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.48/17.61 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.48/17.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.48/17.61 (25) all_54_8 = all_52_2
% 115.48/17.61 (26) ~ (all_52_2 = all_6_2)
% 115.48/17.61 (27) op(e0, e3) = all_4_1
% 115.48/17.61 (28) ~ (all_52_1 = all_52_9)
% 115.48/17.61 (29) ~ (all_52_7 = e3)
% 115.48/17.61 (30) ~ (all_10_2 = e2)
% 115.48/17.61 (31) all_54_10 = all_6_2
% 115.48/17.61 (32) all_58_4 = all_52_8
% 115.48/17.61 (33) all_58_3 = all_8_2
% 115.48/17.61 (34) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.48/17.61 (35) all_58_11 = all_52_14
% 115.48/17.61 (36) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.48/17.61 (37) ~ (all_52_2 = all_52_3)
% 115.48/17.61 (38) ~ (all_52_11 = all_6_2)
% 115.48/17.61 (39) op(e2, e3) = all_52_1
% 115.48/17.61 (40) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.48/17.61 (41) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.48/17.61 (42) ~ (all_52_7 = all_8_2)
% 115.48/17.61 (43) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.48/17.61 (44) all_58_5 = all_52_9
% 115.48/17.61 (45) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.48/17.61 (46) all_58_2 = all_52_1
% 115.48/17.61 (47) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.48/17.61 (48) ~ (all_52_1 = all_52_13)
% 115.48/17.61 (49) op(e0, e3) = all_52_3
% 115.48/17.61 (50) ~ (all_10_2 = e3)
% 115.48/17.61 (51) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.48/17.61 (52) all_58_6 = all_52_2
% 115.48/17.61 (53) ~ (all_52_2 = e1)
% 115.48/17.61 (54) ~ (all_52_1 = all_10_2)
% 115.48/17.61 (55) all_54_5 = all_8_2
% 115.48/17.61 (56) all_58_10 = all_52_13
% 115.48/17.61 (57) ~ (all_52_13 = all_8_2)
% 115.48/17.61 (58) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.48/17.61 (59) ~ (all_52_6 = all_8_2)
% 115.48/17.61 (60) all_56_5 = e2
% 115.48/17.61 (61) all_56_13 = all_8_2
% 115.48/17.61 (62) ~ (all_52_1 = all_8_2)
% 115.48/17.61 (63) ~ (all_8_2 = e2)
% 115.48/17.61 (64) op(all_4_1, e3) = all_4_0
% 115.48/17.61 (65) ~ (all_52_7 = all_52_11)
% 115.48/17.61 (66) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.48/17.61 (67) ~ (all_52_9 = all_6_2)
% 115.48/17.61 (68) ~ (all_52_1 = all_52_2)
% 115.48/17.61 (69) ~ (all_52_1 = all_52_3)
% 115.48/17.61 (70) all_56_1 = all_52_8
% 115.48/17.61 (71) all_58_8 = all_6_2
% 115.48/17.61 (72) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.48/17.61 (73) all_56_4 = all_52_9
% 115.48/17.61 (74) all_56_5 = all_52_13
% 115.48/17.61 (75) op(e2, e1) = all_52_9
% 115.48/17.61 (76) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.48/17.61 (77) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.48/17.61 (78) all_58_12 = all_52_3
% 115.48/17.61 (79) ~ (all_52_8 = all_52_9)
% 115.48/17.61 (80) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.48/17.61 (81) ~ (all_52_3 = all_10_2)
% 115.48/17.61 (82) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.48/17.61 (83) all_56_8 = all_52_14
% 115.48/17.61 (84) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.48/17.61 (85) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.48/17.61 (86) all_54_4 = all_52_1
% 115.48/17.61 (87) ~ (all_52_11 = e3)
% 115.48/17.61 (88) op(e2, all_8_2) = e1
% 115.48/17.61 (89) ~ (all_6_2 = e1)
% 115.48/17.61 (90) ~ (all_52_3 = all_52_11)
% 115.48/17.61 (91) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.48/17.61 (92) all_54_12 = all_52_3
% 115.48/17.61 (93) ~ (all_52_3 = all_52_7)
% 115.48/17.61
% 115.48/17.61 Begin of proof
% 115.48/17.61 |
% 115.48/17.61 | BETA: splitting (36) gives:
% 115.48/17.61 |
% 115.48/17.61 | Case 1:
% 115.48/17.61 | |
% 115.48/17.61 | | (94) ~ (all_56_5 = e2)
% 115.48/17.61 | |
% 115.48/17.61 | | REDUCE: (60), (94) imply:
% 115.48/17.61 | | (95) $false
% 115.48/17.61 | |
% 115.48/17.61 | | CLOSE: (95) is inconsistent.
% 115.48/17.61 | |
% 115.48/17.61 | Case 2:
% 115.48/17.61 | |
% 115.48/17.61 | | (96) ~ (all_56_13 = e0)
% 115.48/17.61 | |
% 115.48/17.61 | | REDUCE: (61), (96) imply:
% 115.48/17.61 | | (97) ~ (all_8_2 = e0)
% 115.48/17.61 | |
% 115.48/17.61 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 115.48/17.61 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 115.48/17.61 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 115.48/17.61 | | (35), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 115.48/17.62 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 115.48/17.62 | | (58), (59), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 115.48/17.62 | | (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 115.48/17.62 | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 115.48/17.62 | | (93), (97) are inconsistent by sub-proof #114.
% 115.48/17.62 | |
% 115.48/17.62 | End of split
% 115.48/17.62 |
% 115.48/17.62 End of proof
% 115.48/17.62
% 115.48/17.62 Sub-proof #114 shows that the following formulas are inconsistent:
% 115.48/17.62 ----------------------------------------------------------------
% 115.48/17.62 (1) ~ (all_52_2 = all_10_2)
% 115.48/17.62 (2) ~ (all_52_3 = e0)
% 115.48/17.62 (3) all_54_2 = all_52_8
% 115.48/17.62 (4) all_58_7 = all_52_6
% 115.48/17.62 (5) ~ (all_52_8 = all_52_11)
% 115.48/17.62 (6) ~ (all_52_9 = all_8_2)
% 115.48/17.62 (7) ~ (all_52_1 = e2)
% 115.48/17.62 (8) ~ (all_52_3 = e3)
% 115.48/17.62 (9) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 115.48/17.62 (10) all_56_14 = all_6_2
% 115.48/17.62 (11) all_54_0 = all_10_2
% 115.48/17.62 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.48/17.62 (13) all_56_11 = all_52_11
% 115.48/17.62 (14) ~ (all_4_0 = e1)
% 115.48/17.62 (15) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.48/17.62 (16) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.48/17.62 (17) all_56_12 = all_10_2
% 115.48/17.62 (18) all_58_0 = all_10_2
% 115.48/17.62 (19) all_54_13 = all_52_7
% 115.48/17.62 (20) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.48/17.62 (21) all_56_10 = all_52_7
% 115.48/17.62 (22) all_54_14 = all_52_11
% 115.48/17.62 (23) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.48/17.62 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.48/17.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.48/17.62 (25) all_54_8 = all_52_2
% 115.48/17.62 (26) ~ (all_52_2 = all_6_2)
% 115.48/17.62 (27) op(e0, e3) = all_4_1
% 115.48/17.62 (28) ~ (all_52_1 = all_52_9)
% 115.48/17.62 (29) ~ (all_52_7 = e3)
% 115.48/17.62 (30) ~ (all_10_2 = e2)
% 115.48/17.62 (31) all_54_10 = all_6_2
% 115.48/17.62 (32) all_58_4 = all_52_8
% 115.48/17.62 (33) all_58_3 = all_8_2
% 115.48/17.62 (34) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.48/17.62 (35) all_58_11 = all_52_14
% 115.48/17.62 (36) ~ (all_52_2 = all_52_3)
% 115.48/17.62 (37) ~ (all_8_2 = e0)
% 115.48/17.62 (38) ~ (all_52_11 = all_6_2)
% 115.48/17.62 (39) op(e2, e3) = all_52_1
% 115.48/17.62 (40) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.48/17.62 (41) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.48/17.62 (42) ~ (all_52_7 = all_8_2)
% 115.48/17.62 (43) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.48/17.62 (44) all_58_5 = all_52_9
% 115.48/17.62 (45) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.48/17.62 (46) all_58_2 = all_52_1
% 115.48/17.62 (47) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.48/17.62 (48) ~ (all_52_1 = all_52_13)
% 115.48/17.62 (49) op(e0, e3) = all_52_3
% 115.48/17.62 (50) ~ (all_10_2 = e3)
% 115.48/17.62 (51) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.48/17.62 (52) all_58_6 = all_52_2
% 115.48/17.62 (53) ~ (all_52_2 = e1)
% 115.48/17.62 (54) ~ (all_52_1 = all_10_2)
% 115.48/17.62 (55) all_54_5 = all_8_2
% 115.48/17.62 (56) all_58_10 = all_52_13
% 115.48/17.62 (57) ~ (all_52_13 = all_8_2)
% 115.48/17.62 (58) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.48/17.62 (59) ~ (all_52_6 = all_8_2)
% 115.48/17.62 (60) ~ (all_52_1 = all_8_2)
% 115.48/17.62 (61) ~ (all_8_2 = e2)
% 115.48/17.62 (62) op(all_4_1, e3) = all_4_0
% 115.48/17.62 (63) ~ (all_52_7 = all_52_11)
% 115.48/17.62 (64) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.48/17.62 (65) ~ (all_52_9 = all_6_2)
% 115.48/17.62 (66) ~ (all_52_1 = all_52_2)
% 115.48/17.62 (67) ~ (all_52_1 = all_52_3)
% 115.48/17.62 (68) all_56_1 = all_52_8
% 115.48/17.62 (69) all_58_8 = all_6_2
% 115.48/17.62 (70) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.48/17.62 (71) all_56_4 = all_52_9
% 115.48/17.62 (72) all_56_5 = all_52_13
% 115.48/17.62 (73) op(e2, e1) = all_52_9
% 115.48/17.62 (74) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.48/17.62 (75) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.48/17.62 (76) all_58_12 = all_52_3
% 115.48/17.62 (77) ~ (all_52_8 = all_52_9)
% 115.48/17.62 (78) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.48/17.62 (79) ~ (all_52_3 = all_10_2)
% 115.48/17.62 (80) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.48/17.62 (81) all_56_8 = all_52_14
% 115.48/17.62 (82) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.48/17.62 (83) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.48/17.62 (84) all_54_4 = all_52_1
% 115.48/17.62 (85) ~ (all_52_11 = e3)
% 115.48/17.62 (86) op(e2, all_8_2) = e1
% 115.48/17.62 (87) ~ (all_6_2 = e1)
% 115.48/17.62 (88) ~ (all_52_3 = all_52_11)
% 115.48/17.62 (89) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.48/17.62 (90) all_54_12 = all_52_3
% 115.48/17.62 (91) ~ (all_52_3 = all_52_7)
% 115.48/17.62
% 115.48/17.62 Begin of proof
% 115.48/17.62 |
% 115.48/17.62 | GROUND_INST: instantiating (24) with all_52_3, all_4_1, e3, e0, simplifying
% 115.48/17.62 | with (27), (49) gives:
% 115.48/17.62 | (92) all_52_3 = all_4_1
% 115.48/17.62 |
% 115.48/17.62 | COMBINE_EQS: (90), (92) imply:
% 115.48/17.62 | (93) all_54_12 = all_4_1
% 115.48/17.62 |
% 115.48/17.62 | COMBINE_EQS: (76), (92) imply:
% 115.48/17.62 | (94) all_58_12 = all_4_1
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (67), (92) imply:
% 115.48/17.62 | (95) ~ (all_52_1 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (36), (92) imply:
% 115.48/17.62 | (96) ~ (all_52_2 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (91), (92) imply:
% 115.48/17.62 | (97) ~ (all_52_7 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | SIMP: (97) implies:
% 115.48/17.62 | (98) ~ (all_52_7 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (88), (92) imply:
% 115.48/17.62 | (99) ~ (all_52_11 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | SIMP: (99) implies:
% 115.48/17.62 | (100) ~ (all_52_11 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (79), (92) imply:
% 115.48/17.62 | (101) ~ (all_10_2 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | SIMP: (101) implies:
% 115.48/17.62 | (102) ~ (all_10_2 = all_4_1)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (8), (92) imply:
% 115.48/17.62 | (103) ~ (all_4_1 = e3)
% 115.48/17.62 |
% 115.48/17.62 | REDUCE: (2), (92) imply:
% 115.48/17.62 | (104) ~ (all_4_1 = e0)
% 115.48/17.62 |
% 115.48/17.62 | BETA: splitting (82) gives:
% 115.48/17.62 |
% 115.48/17.62 | Case 1:
% 115.48/17.62 | |
% 115.48/17.62 | | (105) ~ (all_56_12 = e1)
% 115.48/17.62 | |
% 115.48/17.62 | | REDUCE: (17), (105) imply:
% 115.48/17.62 | | (106) ~ (all_10_2 = e1)
% 115.48/17.62 | |
% 115.48/17.62 | | BETA: splitting (70) gives:
% 115.48/17.62 | |
% 115.48/17.62 | | Case 1:
% 115.48/17.62 | | |
% 115.48/17.62 | | | (107) all_54_0 = e3
% 115.48/17.62 | | |
% 115.48/17.62 | | | REF_CLOSE: (11), (50), (107) are inconsistent by sub-proof #451.
% 115.48/17.62 | | |
% 115.48/17.62 | | Case 2:
% 115.48/17.62 | | |
% 115.48/17.62 | | | (108) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.48/17.62 | | |
% 115.48/17.62 | | | BETA: splitting (108) gives:
% 115.48/17.62 | | |
% 115.48/17.62 | | | Case 1:
% 115.48/17.62 | | | |
% 115.48/17.62 | | | | (109) all_54_0 = e2
% 115.48/17.62 | | | |
% 115.48/17.62 | | | | REF_CLOSE: (11), (30), (109) are inconsistent by sub-proof #450.
% 115.48/17.62 | | | |
% 115.48/17.62 | | | Case 2:
% 115.48/17.62 | | | |
% 115.48/17.62 | | | | (110) ~ (all_54_0 = e2)
% 115.48/17.62 | | | | (111) all_54_0 = e1 | all_54_0 = e0
% 115.48/17.62 | | | |
% 115.48/17.62 | | | | BETA: splitting (111) gives:
% 115.48/17.62 | | | |
% 115.48/17.62 | | | | Case 1:
% 115.48/17.62 | | | | |
% 115.48/17.62 | | | | | (112) all_54_0 = e1
% 115.48/17.62 | | | | |
% 115.48/17.62 | | | | | REF_CLOSE: (11), (106), (112) are inconsistent by sub-proof #449.
% 115.48/17.62 | | | | |
% 115.48/17.62 | | | | Case 2:
% 115.48/17.62 | | | | |
% 115.48/17.62 | | | | | (113) all_54_0 = e0
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | COMBINE_EQS: (11), (113) imply:
% 115.48/17.63 | | | | | (114) all_10_2 = e0
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | SIMP: (114) implies:
% 115.48/17.63 | | | | | (115) all_10_2 = e0
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | COMBINE_EQS: (17), (115) imply:
% 115.48/17.63 | | | | | (116) all_56_12 = e0
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | COMBINE_EQS: (18), (115) imply:
% 115.48/17.63 | | | | | (117) all_58_0 = e0
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | REDUCE: (54), (115) imply:
% 115.48/17.63 | | | | | (118) ~ (all_52_1 = e0)
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | REDUCE: (30), (115) imply:
% 115.48/17.63 | | | | | (119) ~ (e2 = e0)
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | SIMP: (119) implies:
% 115.48/17.63 | | | | | (120) ~ (e2 = e0)
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | BETA: splitting (45) gives:
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | | Case 1:
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | (121) ~ (all_56_8 = e1)
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | REDUCE: (81), (121) imply:
% 115.48/17.63 | | | | | | (122) ~ (all_52_14 = e1)
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | BETA: splitting (64) gives:
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | Case 1:
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | | (123) all_58_6 = e1
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | | REF_CLOSE: (52), (53), (123) are inconsistent by sub-proof #452.
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | Case 2:
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | | (124) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | | BETA: splitting (124) gives:
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | | Case 1:
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | (125) all_58_7 = e1
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | COMBINE_EQS: (4), (125) imply:
% 115.48/17.63 | | | | | | | | (126) all_52_6 = e1
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | REDUCE: (59), (126) imply:
% 115.48/17.63 | | | | | | | | (127) ~ (all_8_2 = e1)
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | SIMP: (127) implies:
% 115.48/17.63 | | | | | | | | (128) ~ (all_8_2 = e1)
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | BETA: splitting (16) gives:
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | Case 1:
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | (129) all_54_5 = e3
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | COMBINE_EQS: (55), (129) imply:
% 115.48/17.63 | | | | | | | | | (130) all_8_2 = e3
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | SIMP: (130) implies:
% 115.48/17.63 | | | | | | | | | (131) all_8_2 = e3
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | REDUCE: (60), (131) imply:
% 115.48/17.63 | | | | | | | | | (132) ~ (all_52_1 = e3)
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | REDUCE: (61), (131) imply:
% 115.48/17.63 | | | | | | | | | (133) ~ (e3 = e2)
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | REDUCE: (37), (131) imply:
% 115.48/17.63 | | | | | | | | | (134) ~ (e3 = e0)
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | REF_CLOSE: (7), (9), (14), (15), (20), (24), (39), (46), (62),
% 115.48/17.63 | | | | | | | | | (84), (94), (103), (117), (118), (120), (132),
% 115.48/17.63 | | | | | | | | | (133), (134) are inconsistent by sub-proof #322.
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | Case 2:
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | (135) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | | REF_CLOSE: (37), (55), (61), (128), (135) are inconsistent by
% 115.48/17.63 | | | | | | | | | sub-proof #310.
% 115.48/17.63 | | | | | | | | |
% 115.48/17.63 | | | | | | | | End of split
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | Case 2:
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | (136) all_58_8 = e1 | all_58_11 = e1
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | | REF_CLOSE: (35), (69), (87), (122), (136) are inconsistent by
% 115.48/17.63 | | | | | | | | sub-proof #445.
% 115.48/17.63 | | | | | | | |
% 115.48/17.63 | | | | | | | End of split
% 115.48/17.63 | | | | | | |
% 115.48/17.63 | | | | | | End of split
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | Case 2:
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | (137) ~ (all_56_12 = e0)
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | REDUCE: (116), (137) imply:
% 115.48/17.63 | | | | | | (138) $false
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | | CLOSE: (138) is inconsistent.
% 115.48/17.63 | | | | | |
% 115.48/17.63 | | | | | End of split
% 115.48/17.63 | | | | |
% 115.48/17.63 | | | | End of split
% 115.48/17.63 | | | |
% 115.48/17.63 | | | End of split
% 115.48/17.63 | | |
% 115.48/17.63 | | End of split
% 115.48/17.63 | |
% 115.48/17.63 | Case 2:
% 115.48/17.63 | |
% 115.48/17.63 | | (139) all_56_12 = e1
% 115.48/17.63 | | (140) ~ (all_56_11 = e0)
% 115.48/17.63 | |
% 115.48/17.63 | | COMBINE_EQS: (17), (139) imply:
% 115.48/17.63 | | (141) all_10_2 = e1
% 115.48/17.63 | |
% 115.48/17.63 | | SIMP: (141) implies:
% 115.48/17.63 | | (142) all_10_2 = e1
% 115.48/17.63 | |
% 115.48/17.63 | | COMBINE_EQS: (18), (142) imply:
% 115.48/17.63 | | (143) all_58_0 = e1
% 115.48/17.63 | |
% 115.48/17.63 | | REDUCE: (13), (140) imply:
% 115.48/17.63 | | (144) ~ (all_52_11 = e0)
% 115.48/17.63 | |
% 115.48/17.63 | | REDUCE: (54), (142) imply:
% 115.48/17.63 | | (145) ~ (all_52_1 = e1)
% 115.48/17.63 | |
% 115.48/17.63 | | REDUCE: (102), (142) imply:
% 115.48/17.63 | | (146) ~ (all_4_1 = e1)
% 115.48/17.63 | |
% 115.48/17.63 | | SIMP: (146) implies:
% 115.48/17.63 | | (147) ~ (all_4_1 = e1)
% 115.48/17.63 | |
% 115.48/17.63 | | REF_CLOSE: (3), (5), (6), (10), (12), (14), (15), (16), (19), (20), (21),
% 115.48/17.63 | | (22), (23), (24), (25), (26), (28), (29), (31), (32), (33), (34),
% 115.48/17.63 | | (38), (40), (41), (42), (43), (44), (46), (47), (48), (51), (53),
% 115.48/17.63 | | (55), (56), (57), (58), (60), (61), (62), (63), (65), (66), (68),
% 115.48/17.63 | | (71), (72), (73), (74), (75), (77), (78), (80), (83), (84), (85),
% 115.48/17.63 | | (86), (89), (93), (95), (96), (98), (100), (103), (104), (139),
% 115.48/17.63 | | (143), (144), (145), (147) are inconsistent by sub-proof #115.
% 115.48/17.63 | |
% 115.48/17.63 | End of split
% 115.48/17.63 |
% 115.48/17.63 End of proof
% 115.48/17.63
% 115.48/17.63 Sub-proof #115 shows that the following formulas are inconsistent:
% 115.48/17.63 ----------------------------------------------------------------
% 115.48/17.63 (1) all_54_2 = all_52_8
% 115.48/17.63 (2) ~ (all_52_8 = all_52_11)
% 115.48/17.63 (3) ~ (all_52_9 = all_8_2)
% 115.48/17.63 (4) all_56_14 = all_6_2
% 115.48/17.63 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.48/17.63 (6) ~ (all_4_0 = e1)
% 115.48/17.63 (7) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.48/17.63 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.48/17.63 (9) all_54_13 = all_52_7
% 115.48/17.63 (10) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.48/17.63 (11) all_56_10 = all_52_7
% 115.48/17.63 (12) all_54_14 = all_52_11
% 115.48/17.63 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.48/17.63 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.48/17.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.48/17.63 (15) all_54_8 = all_52_2
% 115.48/17.63 (16) ~ (all_52_2 = all_6_2)
% 115.48/17.63 (17) ~ (all_52_1 = all_52_9)
% 115.48/17.63 (18) ~ (all_52_7 = e3)
% 115.48/17.63 (19) all_54_10 = all_6_2
% 115.48/17.63 (20) all_58_4 = all_52_8
% 115.48/17.63 (21) all_58_3 = all_8_2
% 115.48/17.63 (22) all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.48/17.63 (23) all_58_0 = e1
% 115.48/17.63 (24) ~ (all_52_11 = all_6_2)
% 115.48/17.63 (25) ~ (all_52_7 = all_4_1)
% 115.48/17.63 (26) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.48/17.63 (27) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.48/17.63 (28) ~ (all_52_7 = all_8_2)
% 115.48/17.63 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.48/17.63 (30) all_58_5 = all_52_9
% 115.48/17.63 (31) all_58_2 = all_52_1
% 115.48/17.63 (32) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.48/17.63 (33) ~ (all_52_1 = all_52_13)
% 115.48/17.63 (34) ~ (all_4_1 = e0)
% 115.48/17.63 (35) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.48/17.63 (36) ~ (all_52_2 = e1)
% 115.48/17.63 (37) all_54_5 = all_8_2
% 115.48/17.63 (38) all_58_10 = all_52_13
% 115.48/17.63 (39) ~ (all_52_13 = all_8_2)
% 115.48/17.63 (40) all_56_12 = e1
% 115.48/17.63 (41) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.48/17.63 (42) ~ (all_52_1 = all_8_2)
% 115.48/17.63 (43) ~ (all_8_2 = e2)
% 115.48/17.63 (44) op(all_4_1, e3) = all_4_0
% 115.48/17.63 (45) ~ (all_52_7 = all_52_11)
% 115.48/17.63 (46) ~ (all_52_9 = all_6_2)
% 115.48/17.63 (47) ~ (all_52_1 = all_52_2)
% 115.48/17.63 (48) all_56_1 = all_52_8
% 115.48/17.63 (49) all_56_4 = all_52_9
% 115.48/17.63 (50) all_56_5 = all_52_13
% 115.48/17.63 (51) ~ (all_52_2 = all_4_1)
% 115.48/17.63 (52) op(e2, e1) = all_52_9
% 115.48/17.63 (53) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.48/17.63 (54) all_54_12 = all_4_1
% 115.48/17.63 (55) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.48/17.63 (56) ~ (all_52_8 = all_52_9)
% 115.48/17.63 (57) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.48/17.63 (58) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.48/17.63 (59) ~ (all_4_1 = e1)
% 115.48/17.63 (60) ~ (all_52_1 = all_4_1)
% 115.48/17.63 (61) ~ (all_52_11 = all_4_1)
% 115.48/17.63 (62) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.48/17.63 (63) ~ (all_52_1 = e1)
% 115.48/17.63 (64) ~ (all_4_1 = e3)
% 115.48/17.63 (65) ~ (all_52_11 = e0)
% 115.48/17.63 (66) all_54_4 = all_52_1
% 115.48/17.63 (67) ~ (all_52_11 = e3)
% 115.48/17.64 (68) op(e2, all_8_2) = e1
% 115.48/17.64 (69) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.48/17.64
% 115.48/17.64 Begin of proof
% 115.48/17.64 |
% 115.48/17.64 | BETA: splitting (57) gives:
% 115.48/17.64 |
% 115.48/17.64 | Case 1:
% 115.48/17.64 | |
% 115.48/17.64 | | (70) all_54_12 = e3
% 115.48/17.64 | |
% 115.48/17.64 | | COMBINE_EQS: (54), (70) imply:
% 115.48/17.64 | | (71) all_4_1 = e3
% 115.48/17.64 | |
% 115.48/17.64 | | REDUCE: (64), (71) imply:
% 115.48/17.64 | | (72) $false
% 115.48/17.64 | |
% 115.48/17.64 | | CLOSE: (72) is inconsistent.
% 115.48/17.64 | |
% 115.48/17.64 | Case 2:
% 115.48/17.64 | |
% 115.48/17.64 | | (73) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.48/17.64 | |
% 115.48/17.64 | | BETA: splitting (73) gives:
% 115.48/17.64 | |
% 115.48/17.64 | | Case 1:
% 115.48/17.64 | | |
% 115.48/17.64 | | | (74) all_54_12 = e2
% 115.48/17.64 | | |
% 115.48/17.64 | | | COMBINE_EQS: (54), (74) imply:
% 115.48/17.64 | | | (75) all_4_1 = e2
% 115.48/17.64 | | |
% 115.48/17.64 | | | REDUCE: (60), (75) imply:
% 115.48/17.64 | | | (76) ~ (all_52_1 = e2)
% 115.48/17.64 | | |
% 115.48/17.64 | | | REDUCE: (51), (75) imply:
% 115.48/17.64 | | | (77) ~ (all_52_2 = e2)
% 115.48/17.64 | | |
% 115.48/17.64 | | | REDUCE: (25), (75) imply:
% 115.48/17.64 | | | (78) ~ (all_52_7 = e2)
% 115.48/17.64 | | |
% 115.48/17.64 | | | REDUCE: (61), (75) imply:
% 115.48/17.64 | | | (79) ~ (all_52_11 = e2)
% 115.48/17.64 | | |
% 115.48/17.64 | | | REDUCE: (44), (75) imply:
% 115.48/17.64 | | | (80) op(e2, e3) = all_4_0
% 115.48/17.64 | | |
% 115.48/17.64 | | | BETA: splitting (69) gives:
% 115.48/17.64 | | |
% 115.48/17.64 | | | Case 1:
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | (81) all_54_14 = e3
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | COMBINE_EQS: (12), (81) imply:
% 115.48/17.64 | | | | (82) all_52_11 = e3
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | REDUCE: (67), (82) imply:
% 115.48/17.64 | | | | (83) $false
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | CLOSE: (83) is inconsistent.
% 115.48/17.64 | | | |
% 115.48/17.64 | | | Case 2:
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | (84) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | BETA: splitting (84) gives:
% 115.48/17.64 | | | |
% 115.48/17.64 | | | | Case 1:
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | (85) all_54_14 = e2
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | COMBINE_EQS: (12), (85) imply:
% 115.48/17.64 | | | | | (86) all_52_11 = e2
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | REDUCE: (79), (86) imply:
% 115.48/17.64 | | | | | (87) $false
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | CLOSE: (87) is inconsistent.
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | Case 2:
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | (88) all_54_14 = e1 | all_54_14 = e0
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | BETA: splitting (88) gives:
% 115.48/17.64 | | | | |
% 115.48/17.64 | | | | | Case 1:
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | (89) all_54_14 = e1
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | COMBINE_EQS: (12), (89) imply:
% 115.48/17.64 | | | | | | (90) all_52_11 = e1
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | REDUCE: (45), (90) imply:
% 115.48/17.64 | | | | | | (91) ~ (all_52_7 = e1)
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | REDUCE: (2), (90) imply:
% 115.48/17.64 | | | | | | (92) ~ (all_52_8 = e1)
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | REDUCE: (24), (90) imply:
% 115.48/17.64 | | | | | | (93) ~ (all_6_2 = e1)
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | SIMP: (93) implies:
% 115.48/17.64 | | | | | | (94) ~ (all_6_2 = e1)
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | BETA: splitting (5) gives:
% 115.48/17.64 | | | | | |
% 115.48/17.64 | | | | | | Case 1:
% 115.48/17.64 | | | | | | |
% 115.48/17.64 | | | | | | | (95) all_54_13 = e3
% 115.48/17.64 | | | | | | |
% 115.48/17.64 | | | | | | | COMBINE_EQS: (9), (95) imply:
% 115.48/17.64 | | | | | | | (96) all_52_7 = e3
% 115.48/17.64 | | | | | | |
% 115.48/17.64 | | | | | | | REDUCE: (18), (96) imply:
% 115.48/17.64 | | | | | | | (97) $false
% 115.48/17.64 | | | | | | |
% 115.48/17.64 | | | | | | | CLOSE: (97) is inconsistent.
% 115.48/17.64 | | | | | | |
% 115.48/17.64 | | | | | | Case 2:
% 115.48/17.64 | | | | | | |
% 115.61/17.64 | | | | | | | (98) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.61/17.64 | | | | | | |
% 115.61/17.64 | | | | | | | BETA: splitting (26) gives:
% 115.61/17.64 | | | | | | |
% 115.61/17.64 | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | |
% 115.61/17.64 | | | | | | | | (99) ~ (all_56_1 = e3)
% 115.61/17.64 | | | | | | | |
% 115.61/17.64 | | | | | | | | REDUCE: (48), (99) imply:
% 115.61/17.64 | | | | | | | | (100) ~ (all_52_8 = e3)
% 115.61/17.64 | | | | | | | |
% 115.61/17.64 | | | | | | | | BETA: splitting (32) gives:
% 115.61/17.64 | | | | | | | |
% 115.61/17.64 | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | |
% 115.61/17.64 | | | | | | | | | (101) ~ (all_56_4 = e2)
% 115.61/17.64 | | | | | | | | |
% 115.61/17.64 | | | | | | | | | REDUCE: (49), (101) imply:
% 115.61/17.64 | | | | | | | | | (102) ~ (all_52_9 = e2)
% 115.61/17.64 | | | | | | | | |
% 115.61/17.64 | | | | | | | | | BETA: splitting (62) gives:
% 115.61/17.64 | | | | | | | | |
% 115.61/17.64 | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | (103) all_58_2 = e2
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | REF_CLOSE: (31), (76), (103) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | #335.
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | (104) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | BETA: splitting (104) gives:
% 115.61/17.64 | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | (105) all_58_3 = e2
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | COMBINE_EQS: (21), (105) imply:
% 115.61/17.64 | | | | | | | | | | | (106) all_8_2 = e2
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | REDUCE: (43), (106) imply:
% 115.61/17.64 | | | | | | | | | | | (107) $false
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | (108) all_58_5 = e2 | all_58_10 = e2
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | BETA: splitting (98) gives:
% 115.61/17.64 | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | (109) all_54_13 = e2
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | COMBINE_EQS: (9), (109) imply:
% 115.61/17.64 | | | | | | | | | | | | (110) all_52_7 = e2
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | REDUCE: (78), (110) imply:
% 115.61/17.64 | | | | | | | | | | | | (111) $false
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | (112) ~ (all_54_13 = e2)
% 115.61/17.64 | | | | | | | | | | | | (113) all_54_13 = e1 | all_54_13 = e0
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | BETA: splitting (113) gives:
% 115.61/17.64 | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | (114) all_54_13 = e1
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | COMBINE_EQS: (9), (114) imply:
% 115.61/17.64 | | | | | | | | | | | | | (115) all_52_7 = e1
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | REDUCE: (91), (115) imply:
% 115.61/17.64 | | | | | | | | | | | | | (116) $false
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | (117) all_54_13 = e0
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | COMBINE_EQS: (9), (117) imply:
% 115.61/17.64 | | | | | | | | | | | | | (118) all_52_7 = e0
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | COMBINE_EQS: (11), (118) imply:
% 115.61/17.64 | | | | | | | | | | | | | (119) all_56_10 = e0
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | REDUCE: (28), (118) imply:
% 115.61/17.64 | | | | | | | | | | | | | (120) ~ (all_8_2 = e0)
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | SIMP: (120) implies:
% 115.61/17.64 | | | | | | | | | | | | | (121) ~ (all_8_2 = e0)
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | REDUCE: (78), (118) imply:
% 115.61/17.64 | | | | | | | | | | | | | (122) ~ (e2 = e0)
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | SIMP: (122) implies:
% 115.61/17.64 | | | | | | | | | | | | | (123) ~ (e2 = e0)
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | BETA: splitting (35) gives:
% 115.61/17.64 | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | (124) ~ (all_56_14 = e2)
% 115.61/17.64 | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | REDUCE: (4), (124) imply:
% 115.61/17.64 | | | | | | | | | | | | | | (125) ~ (all_6_2 = e2)
% 115.61/17.64 | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 115.61/17.64 | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | (126) all_54_2 = e3
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | REF_CLOSE: (1), (100), (126) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | | | | | | #179.
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | (127) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 115.61/17.64 | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | (128) all_58_5 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (102), (128) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | | | | | | | #119.
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | (129) all_58_10 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (129) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | (130) all_52_13 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (130) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | (131) all_56_5 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | REDUCE: (39), (130) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | (132) ~ (all_8_2 = e2)
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | (133) ~ (all_56_5 = e2)
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | REDUCE: (131), (133) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | (134) $false
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | (135) ~ (all_56_14 = e0)
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | REDUCE: (4), (135) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | (136) ~ (all_6_2 = e0)
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (137) all_54_10 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (137) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (138) all_6_2 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | SIMP: (138) implies:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (139) all_6_2 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | REDUCE: (16), (139) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (140) ~ (all_52_2 = e3)
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | REDUCE: (46), (139) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (141) ~ (all_52_9 = e3)
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | REDUCE: (125), (139) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (142) ~ (e3 = e2)
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | REDUCE: (94), (139) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (143) ~ (e3 = e1)
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | REDUCE: (136), (139) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | (144) ~ (e3 = e0)
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | (145) all_54_8 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (140), (145) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | #399.
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | (146) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | (147) all_54_8 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (77), (147) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | #382.
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | (148) ~ (all_54_8 = e2)
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | (149) all_54_8 = e1 | all_54_8 = e0
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | (150) all_58_0 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (143), (150) are inconsistent by sub-proof
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | #319.
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | (151) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | (152) all_54_2 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (152) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | (153) all_52_8 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | SIMP: (153) implies:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | (154) all_52_8 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (154) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | (155) all_58_4 = e2
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | (156) all_58_2 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (156) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | (157) all_52_1 = e3
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (157) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | (158) ~ (all_52_9 = e3)
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (157) imply:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | (159) ~ (all_8_2 = e3)
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | (160) ~ (all_8_2 = e3)
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (161) all_54_5 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (160), (161) are inconsistent by sub-proof
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | #339.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (162) ~ (all_54_5 = e3)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (163) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_58_4 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (164) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (165) e2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (165) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (166) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (167) ~ (all_58_4 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_58_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (169) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) e3 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (170) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_58_2 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (173) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) e3 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (174) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_58_3 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (177) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_8_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (178) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_58_3 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_5 = e0 | all_58_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_54_5 = e2
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (43), (182) are inconsistent by sub-proof
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #338.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_54_5 = e1 | all_54_5 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_58_3 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (184) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_8_2 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (185) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) ~ (all_52_9 = e1)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (185) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) op(e2, e1) = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_5 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (188) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_52_9 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (186), (189) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) ~ (e1 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) ~ (e1 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (189) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) op(e2, e1) = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with e0, e1, e1, e2,
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (187), (192) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) e1 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (193) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) ~ (all_58_5 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (195) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) ~ (all_52_9 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (123), (129), (181), (196) are inconsistent
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #173.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_58_3 = e1)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (197) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_8_2 = e1)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (121), (183), (198) are inconsistent by
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #174.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (30), (129), (141), (142), (160), (199) are
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (all_58_2 = e3)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (200) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (all_52_1 = e3)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (21), (30), (31), (55), (68), (80),
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (129), (141), (142), (201) are inconsistent by
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | (202) all_54_2 = e1 | all_54_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (203) all_54_8 = e1
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (36), (203) are inconsistent by sub-proof
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | #397.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_8 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (204) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (205) all_52_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (206) all_52_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (206) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | (207) ~ (all_52_1 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (208) all_54_4 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (208) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (209) all_52_1 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_1 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (210) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_2 = e3
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_58_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (212) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | (213) e3 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (213) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | (214) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_3 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (216) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_8_2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (217) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_5 = e0 | all_58_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_5 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (220) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_52_9 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (221) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) ~ (all_52_8 = e0)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (92), (202), (222) are inconsistent by
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #210.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (223) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) e2 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (224) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) $false
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (226) ~ (all_54_4 = e3)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (226) imply:
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_52_1 = e3)
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (21), (30), (31), (55), (68), (80),
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | (129), (141), (142), (227) are inconsistent by
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | (228) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.61/17.65 | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (94), (125), (136), (228) are inconsistent
% 115.61/17.65 | | | | | | | | | | | | | | | | | | by sub-proof #435.
% 115.61/17.65 | | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | (229) ~ (all_56_10 = e0)
% 115.61/17.65 | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | REDUCE: (119), (229) imply:
% 115.61/17.65 | | | | | | | | | | | | | | (230) $false
% 115.61/17.65 | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 115.61/17.65 | | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | | |
% 115.61/17.65 | | | | | | | | | End of split
% 115.61/17.65 | | | | | | | | |
% 115.61/17.65 | | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | | |
% 115.61/17.65 | | | | | | | | | (231) ~ (all_56_12 = e1)
% 115.61/17.65 | | | | | | | | |
% 115.61/17.65 | | | | | | | | | REDUCE: (40), (231) imply:
% 115.61/17.65 | | | | | | | | | (232) $false
% 115.61/17.65 | | | | | | | | |
% 115.61/17.65 | | | | | | | | | CLOSE: (232) is inconsistent.
% 115.61/17.65 | | | | | | | | |
% 115.61/17.65 | | | | | | | | End of split
% 115.61/17.65 | | | | | | | |
% 115.61/17.65 | | | | | | | Case 2:
% 115.61/17.65 | | | | | | | |
% 115.61/17.65 | | | | | | | | (233) ~ (all_56_12 = e1)
% 115.61/17.65 | | | | | | | |
% 115.61/17.65 | | | | | | | | REDUCE: (40), (233) imply:
% 115.61/17.65 | | | | | | | | (234) $false
% 115.61/17.65 | | | | | | | |
% 115.61/17.65 | | | | | | | | CLOSE: (234) is inconsistent.
% 115.61/17.65 | | | | | | | |
% 115.61/17.65 | | | | | | | End of split
% 115.61/17.65 | | | | | | |
% 115.61/17.65 | | | | | | End of split
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | Case 2:
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | | (235) all_54_14 = e0
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | | COMBINE_EQS: (12), (235) imply:
% 115.61/17.65 | | | | | | (236) all_52_11 = e0
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | | REDUCE: (65), (236) imply:
% 115.61/17.65 | | | | | | (237) $false
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | | CLOSE: (237) is inconsistent.
% 115.61/17.65 | | | | | |
% 115.61/17.65 | | | | | End of split
% 115.61/17.65 | | | | |
% 115.61/17.65 | | | | End of split
% 115.61/17.65 | | | |
% 115.61/17.65 | | | End of split
% 115.61/17.65 | | |
% 115.61/17.65 | | Case 2:
% 115.61/17.65 | | |
% 115.61/17.65 | | | (238) all_54_12 = e1 | all_54_12 = e0
% 115.61/17.65 | | |
% 115.61/17.65 | | | REF_CLOSE: (34), (54), (59), (238) are inconsistent by sub-proof #315.
% 115.61/17.65 | | |
% 115.61/17.65 | | End of split
% 115.61/17.65 | |
% 115.61/17.65 | End of split
% 115.61/17.65 |
% 115.61/17.65 End of proof
% 115.61/17.65
% 115.61/17.65 Sub-proof #116 shows that the following formulas are inconsistent:
% 115.61/17.65 ----------------------------------------------------------------
% 115.61/17.65 (1) all_58_10 = e2
% 115.61/17.65 (2) ~ (all_52_9 = e3)
% 115.61/17.65 (3) ~ (all_4_0 = e1)
% 115.61/17.65 (4) ~ (all_52_1 = e3)
% 115.61/17.66 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.66 (6) all_58_3 = all_8_2
% 115.61/17.66 (7) all_58_5 = all_52_9
% 115.61/17.66 (8) all_58_2 = all_52_1
% 115.61/17.66 (9) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 (10) op(e2, e3) = all_4_0
% 115.61/17.66 (11) ~ (e3 = e2)
% 115.61/17.66 (12) op(e2, all_8_2) = e1
% 115.61/17.66
% 115.61/17.66 Begin of proof
% 115.61/17.66 |
% 115.61/17.66 | BETA: splitting (9) gives:
% 115.61/17.66 |
% 115.61/17.66 | Case 1:
% 115.61/17.66 | |
% 115.61/17.66 | | (13) all_58_2 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | COMBINE_EQS: (8), (13) imply:
% 115.61/17.66 | | (14) all_52_1 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | REDUCE: (4), (14) imply:
% 115.61/17.66 | | (15) $false
% 115.61/17.66 | |
% 115.61/17.66 | | CLOSE: (15) is inconsistent.
% 115.61/17.66 | |
% 115.61/17.66 | Case 2:
% 115.61/17.66 | |
% 115.61/17.66 | | (16) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | BETA: splitting (16) gives:
% 115.61/17.66 | |
% 115.61/17.66 | | Case 1:
% 115.61/17.66 | | |
% 115.61/17.66 | | | (17) all_58_3 = e3
% 115.61/17.66 | | |
% 115.61/17.66 | | | COMBINE_EQS: (6), (17) imply:
% 115.61/17.66 | | | (18) all_8_2 = e3
% 115.61/17.66 | | |
% 115.61/17.66 | | | REDUCE: (12), (18) imply:
% 115.61/17.66 | | | (19) op(e2, e3) = e1
% 115.61/17.66 | | |
% 115.61/17.66 | | | REF_CLOSE: (3), (5), (10), (19) are inconsistent by sub-proof #325.
% 115.61/17.66 | | |
% 115.61/17.66 | | Case 2:
% 115.61/17.66 | | |
% 115.61/17.66 | | | (20) all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 | | |
% 115.61/17.66 | | | REF_CLOSE: (1), (2), (7), (11), (20) are inconsistent by sub-proof #118.
% 115.61/17.66 | | |
% 115.61/17.66 | | End of split
% 115.61/17.66 | |
% 115.61/17.66 | End of split
% 115.61/17.66 |
% 115.61/17.66 End of proof
% 115.61/17.66
% 115.61/17.66 Sub-proof #117 shows that the following formulas are inconsistent:
% 115.61/17.66 ----------------------------------------------------------------
% 115.61/17.66 (1) all_58_10 = e2
% 115.61/17.66 (2) ~ (all_52_9 = e3)
% 115.61/17.66 (3) all_58_3 = all_8_2
% 115.61/17.66 (4) ~ (all_8_2 = e3)
% 115.61/17.66 (5) all_58_5 = all_52_9
% 115.61/17.66 (6) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 (7) ~ (e3 = e2)
% 115.61/17.66
% 115.61/17.66 Begin of proof
% 115.61/17.66 |
% 115.61/17.66 | BETA: splitting (6) gives:
% 115.61/17.66 |
% 115.61/17.66 | Case 1:
% 115.61/17.66 | |
% 115.61/17.66 | | (8) all_58_3 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | COMBINE_EQS: (3), (8) imply:
% 115.61/17.66 | | (9) all_8_2 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | REDUCE: (4), (9) imply:
% 115.61/17.66 | | (10) $false
% 115.61/17.66 | |
% 115.61/17.66 | | CLOSE: (10) is inconsistent.
% 115.61/17.66 | |
% 115.61/17.66 | Case 2:
% 115.61/17.66 | |
% 115.61/17.66 | | (11) all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #118.
% 115.61/17.66 | |
% 115.61/17.66 | End of split
% 115.61/17.66 |
% 115.61/17.66 End of proof
% 115.61/17.66
% 115.61/17.66 Sub-proof #118 shows that the following formulas are inconsistent:
% 115.61/17.66 ----------------------------------------------------------------
% 115.61/17.66 (1) all_58_10 = e2
% 115.61/17.66 (2) ~ (all_52_9 = e3)
% 115.61/17.66 (3) all_58_5 = e3 | all_58_10 = e3
% 115.61/17.66 (4) all_58_5 = all_52_9
% 115.61/17.66 (5) ~ (e3 = e2)
% 115.61/17.66
% 115.61/17.66 Begin of proof
% 115.61/17.66 |
% 115.61/17.66 | BETA: splitting (3) gives:
% 115.61/17.66 |
% 115.61/17.66 | Case 1:
% 115.61/17.66 | |
% 115.61/17.66 | | (6) all_58_5 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | COMBINE_EQS: (4), (6) imply:
% 115.61/17.66 | | (7) all_52_9 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | REDUCE: (2), (7) imply:
% 115.61/17.66 | | (8) $false
% 115.61/17.66 | |
% 115.61/17.66 | | CLOSE: (8) is inconsistent.
% 115.61/17.66 | |
% 115.61/17.66 | Case 2:
% 115.61/17.66 | |
% 115.61/17.66 | | (9) all_58_10 = e3
% 115.61/17.66 | |
% 115.61/17.66 | | COMBINE_EQS: (1), (9) imply:
% 115.61/17.66 | | (10) e3 = e2
% 115.61/17.66 | |
% 115.61/17.66 | | SIMP: (10) implies:
% 115.61/17.66 | | (11) e3 = e2
% 115.61/17.66 | |
% 115.61/17.66 | | REDUCE: (5), (11) imply:
% 115.61/17.66 | | (12) $false
% 115.61/17.66 | |
% 115.61/17.66 | | CLOSE: (12) is inconsistent.
% 115.61/17.66 | |
% 115.61/17.66 | End of split
% 115.61/17.66 |
% 115.61/17.66 End of proof
% 115.61/17.66
% 115.61/17.66 Sub-proof #119 shows that the following formulas are inconsistent:
% 115.61/17.66 ----------------------------------------------------------------
% 115.61/17.66 (1) all_58_5 = all_52_9
% 115.61/17.66 (2) all_58_5 = e2
% 115.61/17.66 (3) ~ (all_52_9 = e2)
% 115.61/17.66
% 115.61/17.66 Begin of proof
% 115.61/17.66 |
% 115.61/17.66 | COMBINE_EQS: (1), (2) imply:
% 115.61/17.66 | (4) all_52_9 = e2
% 115.61/17.66 |
% 115.61/17.66 | SIMP: (4) implies:
% 115.61/17.66 | (5) all_52_9 = e2
% 115.61/17.66 |
% 115.61/17.66 | REDUCE: (3), (5) imply:
% 115.61/17.66 | (6) $false
% 115.61/17.66 |
% 115.61/17.66 | CLOSE: (6) is inconsistent.
% 115.61/17.66 |
% 115.61/17.66 End of proof
% 115.61/17.66
% 115.61/17.66 Sub-proof #120 shows that the following formulas are inconsistent:
% 115.61/17.66 ----------------------------------------------------------------
% 115.61/17.66 (1) ~ (all_52_8 = all_10_2)
% 115.61/17.66 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 115.61/17.66 (3) ~ (all_52_2 = all_10_2)
% 115.61/17.66 (4) all_58_7 = all_52_6
% 115.61/17.66 (5) ~ (all_52_9 = all_8_2)
% 115.61/17.66 (6) ~ (all_4_2 = e0)
% 115.61/17.66 (7) all_56_14 = all_6_2
% 115.61/17.66 (8) all_56_3 = all_52_1
% 115.61/17.66 (9) all_54_0 = all_10_2
% 115.61/17.66 (10) all_56_11 = all_52_11
% 115.61/17.66 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 115.61/17.66 (12) ~ (all_52_12 = all_10_2)
% 115.61/17.66 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.61/17.66 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.66 (15) all_56_12 = all_10_2
% 115.61/17.66 (16) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 115.61/17.66 (17) all_58_0 = all_10_2
% 115.61/17.66 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.66 (19) ~ (all_52_14 = all_6_2)
% 115.61/17.66 (20) all_56_10 = all_52_7
% 115.61/17.66 (21) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.61/17.66 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.66 (23) ~ (all_52_1 = all_52_9)
% 115.61/17.66 (24) ~ (all_10_2 = e2)
% 115.61/17.66 (25) all_54_10 = all_6_2
% 115.61/17.66 (26) all_58_4 = all_52_8
% 115.61/17.66 (27) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.66 (28) all_56_2 = all_52_12
% 115.61/17.66 (29) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 115.61/17.66 (30) all_58_3 = all_8_2
% 115.61/17.66 (31) all_54_6 = all_52_9
% 115.61/17.66 (32) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 115.61/17.66 (33) all_58_11 = all_52_14
% 115.61/17.66 (34) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.61/17.66 (35) ~ (all_52_2 = all_52_3)
% 115.61/17.66 (36) all_54_7 = all_52_13
% 115.61/17.66 (37) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 115.61/17.66 (38) ~ (all_52_11 = all_6_2)
% 115.61/17.66 (39) op(e2, e3) = all_52_1
% 115.61/17.66 (40) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.66 (41) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 115.61/17.66 (42) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 115.61/17.66 (43) ~ (all_4_2 = e3)
% 115.61/17.66 (44) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.61/17.66 (45) ~ (all_52_7 = all_8_2)
% 115.61/17.66 (46) ~ (all_52_4 = all_8_2)
% 115.61/17.66 (47) all_58_5 = all_52_9
% 115.61/17.66 (48) all_56_9 = all_52_3
% 115.61/17.66 (49) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.61/17.66 (50) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 115.61/17.66 (51) all_58_15 = all_4_2
% 115.61/17.66 (52) all_58_2 = all_52_1
% 115.61/17.66 (53) ~ (all_10_2 = e3)
% 115.61/17.66 (54) all_58_13 = all_52_7
% 115.61/17.66 (55) ~ (all_52_14 = all_4_2)
% 115.61/17.66 (56) all_58_6 = all_52_2
% 115.61/17.66 (57) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 115.61/17.66 (58) ~ (all_52_1 = all_10_2)
% 115.61/17.66 (59) all_54_5 = all_8_2
% 115.61/17.66 (60) all_56_15 = all_4_2
% 115.61/17.66 (61) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 115.61/17.66 (62) all_58_10 = all_52_13
% 115.61/17.66 (63) ~ (all_52_13 = all_8_2)
% 115.61/17.66 (64) ~ (all_52_11 = all_4_2)
% 115.61/17.66 (65) ~ (all_52_6 = all_8_2)
% 115.61/17.66 (66) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 115.61/17.66 (67) all_58_1 = all_52_4
% 115.61/17.66 (68) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.61/17.66 (69) all_58_14 = all_52_11
% 115.61/17.66 (70) all_56_13 = all_8_2
% 115.61/17.66 (71) ~ (all_52_1 = all_8_2)
% 115.61/17.66 (72) ~ (all_8_2 = e2)
% 115.61/17.66 (73) ~ (all_6_2 = e2)
% 115.61/17.66 (74) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.61/17.67 (75) all_56_7 = all_52_6
% 115.61/17.67 (76) ~ (all_52_1 = all_52_3)
% 115.61/17.67 (77) all_56_1 = all_52_8
% 115.61/17.67 (78) all_58_8 = all_6_2
% 115.61/17.67 (79) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.67 (80) all_56_4 = all_52_9
% 115.61/17.67 (81) all_58_9 = all_52_12
% 115.61/17.67 (82) all_56_5 = all_52_13
% 115.61/17.67 (83) op(e2, e1) = all_52_9
% 115.61/17.67 (84) ~ (all_52_3 = all_4_2)
% 115.61/17.67 (85) ~ (all_52_6 = all_6_2)
% 115.61/17.67 (86) all_56_6 = all_52_2
% 115.61/17.67 (87) ~ (all_52_13 = all_4_2)
% 115.61/17.67 (88) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 115.61/17.67 (89) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.67 (90) all_58_12 = all_52_3
% 115.61/17.67 (91) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.61/17.67 (92) op(e2, e0) = all_52_13
% 115.61/17.67 (93) ~ (all_52_3 = all_10_2)
% 115.61/17.67 (94) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 115.61/17.67 (95) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.67 (96) op(e1, e1) = all_6_2
% 115.61/17.67 (97) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.61/17.67 (98) all_56_8 = all_52_14
% 115.61/17.67 (99) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.61/17.67 (100) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.61/17.67 (101) ~ (e3 = e2)
% 115.61/17.67 (102) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.61/17.67 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.61/17.67 (103) all_54_4 = all_52_1
% 115.61/17.67 (104) all_54_15 = all_4_2
% 115.61/17.67 (105) op(e2, all_8_2) = e1
% 115.61/17.67 (106) ~ (all_6_2 = e1)
% 115.61/17.67 (107) all_54_12 = all_52_3
% 115.61/17.67 (108) ~ (all_52_3 = all_52_7)
% 115.61/17.67
% 115.61/17.67 Begin of proof
% 115.61/17.67 |
% 115.61/17.67 | BETA: splitting (16) gives:
% 115.61/17.67 |
% 115.61/17.67 | Case 1:
% 115.61/17.67 | |
% 115.61/17.67 | | (109) ~ (all_56_7 = e1)
% 115.61/17.67 | |
% 115.61/17.67 | | REDUCE: (75), (109) imply:
% 115.61/17.67 | | (110) ~ (all_52_6 = e1)
% 115.61/17.67 | |
% 115.61/17.67 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 115.61/17.67 | | (19), (20), (21), (22), (24), (25), (27), (28), (29), (30), (31),
% 115.61/17.67 | | (32), (33), (35), (37), (38), (41), (42), (43), (44), (45), (47),
% 115.61/17.67 | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (59), (60),
% 115.61/17.67 | | (62), (69), (70), (72), (73), (74), (76), (78), (79), (80), (81),
% 115.61/17.67 | | (82), (83), (84), (86), (88), (89), (90), (91), (93), (94), (98),
% 115.61/17.67 | | (99), (100), (101), (102), (104), (105), (106), (107), (108),
% 115.61/17.67 | | (110) are inconsistent by sub-proof #134.
% 115.61/17.67 | |
% 115.61/17.67 | Case 2:
% 115.61/17.67 | |
% 115.61/17.67 | | (111) all_56_7 = e1
% 115.61/17.67 | | (112) ~ (all_56_15 = e2)
% 115.61/17.67 | |
% 115.61/17.67 | | COMBINE_EQS: (75), (111) imply:
% 115.61/17.67 | | (113) all_52_6 = e1
% 115.61/17.67 | |
% 115.61/17.67 | | REDUCE: (60), (112) imply:
% 115.61/17.67 | | (114) ~ (all_4_2 = e2)
% 115.61/17.67 | |
% 115.61/17.67 | | REDUCE: (65), (113) imply:
% 115.61/17.67 | | (115) ~ (all_8_2 = e1)
% 115.61/17.67 | |
% 115.61/17.67 | | SIMP: (115) implies:
% 115.61/17.67 | | (116) ~ (all_8_2 = e1)
% 115.61/17.67 | |
% 115.61/17.67 | | REDUCE: (85), (113) imply:
% 115.61/17.67 | | (117) ~ (all_6_2 = e1)
% 115.61/17.67 | |
% 115.61/17.67 | | BETA: splitting (27) gives:
% 115.61/17.67 | |
% 115.61/17.67 | | Case 1:
% 115.61/17.67 | | |
% 115.61/17.67 | | | (118) all_54_15 = e3
% 115.61/17.67 | | |
% 115.61/17.67 | | | REF_CLOSE: (43), (104), (118) are inconsistent by sub-proof #312.
% 115.61/17.67 | | |
% 115.61/17.67 | | Case 2:
% 115.61/17.67 | | |
% 115.61/17.67 | | | (119) ~ (all_54_15 = e3)
% 115.61/17.67 | | | (120) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.67 | | |
% 115.61/17.67 | | | BETA: splitting (120) gives:
% 115.61/17.67 | | |
% 115.61/17.67 | | | Case 1:
% 115.61/17.67 | | | |
% 115.61/17.67 | | | | (121) all_54_15 = e2
% 115.61/17.67 | | | |
% 115.61/17.67 | | | | REF_CLOSE: (104), (114), (121) are inconsistent by sub-proof #420.
% 115.61/17.67 | | | |
% 115.61/17.67 | | | Case 2:
% 115.61/17.67 | | | |
% 115.61/17.67 | | | | (122) ~ (all_54_15 = e2)
% 115.61/17.67 | | | | (123) all_54_15 = e1 | all_54_15 = e0
% 115.61/17.67 | | | |
% 115.61/17.67 | | | | BETA: splitting (123) gives:
% 115.61/17.67 | | | |
% 115.61/17.67 | | | | Case 1:
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | (124) all_54_15 = e1
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | COMBINE_EQS: (104), (124) imply:
% 115.61/17.67 | | | | | (125) all_4_2 = e1
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | SIMP: (125) implies:
% 115.61/17.67 | | | | | (126) all_4_2 = e1
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | COMBINE_EQS: (60), (126) imply:
% 115.61/17.67 | | | | | (127) all_56_15 = e1
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | REDUCE: (87), (126) imply:
% 115.61/17.67 | | | | | (128) ~ (all_52_13 = e1)
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | BETA: splitting (57) gives:
% 115.61/17.67 | | | | |
% 115.61/17.67 | | | | | Case 1:
% 115.61/17.67 | | | | | |
% 115.61/17.67 | | | | | | (129) ~ (all_56_1 = e3)
% 115.61/17.67 | | | | | |
% 115.61/17.67 | | | | | | REDUCE: (77), (129) imply:
% 115.61/17.67 | | | | | | (130) ~ (all_52_8 = e3)
% 115.61/17.67 | | | | | |
% 115.61/17.67 | | | | | | BETA: splitting (2) gives:
% 115.61/17.67 | | | | | |
% 115.61/17.67 | | | | | | Case 1:
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | (131) ~ (all_56_2 = e3)
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | REDUCE: (28), (131) imply:
% 115.61/17.67 | | | | | | | (132) ~ (all_52_12 = e3)
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | BETA: splitting (97) gives:
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | (133) all_58_0 = e3
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | COMBINE_EQS: (17), (133) imply:
% 115.61/17.67 | | | | | | | | (134) all_10_2 = e3
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | REDUCE: (53), (134) imply:
% 115.61/17.67 | | | | | | | | (135) $false
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | CLOSE: (135) is inconsistent.
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | (136) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | BETA: splitting (136) gives:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | (137) all_58_1 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | COMBINE_EQS: (67), (137) imply:
% 115.61/17.67 | | | | | | | | | (138) all_52_4 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | REDUCE: (46), (138) imply:
% 115.61/17.67 | | | | | | | | | (139) ~ (all_8_2 = e3)
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | SIMP: (139) implies:
% 115.61/17.67 | | | | | | | | | (140) ~ (all_8_2 = e3)
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | BETA: splitting (14) gives:
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | (141) all_54_5 = e3
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | REF_CLOSE: (59), (140), (141) are inconsistent by sub-proof
% 115.61/17.67 | | | | | | | | | | #339.
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | (142) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | REF_CLOSE: (5), (14), (22), (30), (34), (36), (39), (47),
% 115.61/17.67 | | | | | | | | | | (52), (59), (61), (62), (63), (70), (72), (82),
% 115.61/17.67 | | | | | | | | | | (92), (95), (105), (116), (128), (142) are
% 115.61/17.67 | | | | | | | | | | inconsistent by sub-proof #129.
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | End of split
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | (143) all_58_4 = e3 | all_58_9 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | REF_CLOSE: (26), (81), (130), (132), (143) are inconsistent by
% 115.61/17.67 | | | | | | | | | sub-proof #184.
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | End of split
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | End of split
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | Case 2:
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | (144) all_56_2 = e3
% 115.61/17.67 | | | | | | | (145) ~ (all_56_12 = e0)
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | COMBINE_EQS: (28), (144) imply:
% 115.61/17.67 | | | | | | | (146) all_52_12 = e3
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | REDUCE: (15), (145) imply:
% 115.61/17.67 | | | | | | | (147) ~ (all_10_2 = e0)
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | REDUCE: (12), (146) imply:
% 115.61/17.67 | | | | | | | (148) ~ (all_10_2 = e3)
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | BETA: splitting (32) gives:
% 115.61/17.67 | | | | | | |
% 115.61/17.67 | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | (149) ~ (all_56_2 = e3)
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | REDUCE: (144), (149) imply:
% 115.61/17.67 | | | | | | | | (150) $false
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | CLOSE: (150) is inconsistent.
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | (151) ~ (all_56_14 = e0)
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | REDUCE: (7), (151) imply:
% 115.61/17.67 | | | | | | | | (152) ~ (all_6_2 = e0)
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | BETA: splitting (21) gives:
% 115.61/17.67 | | | | | | | |
% 115.61/17.67 | | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | (153) all_54_10 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | COMBINE_EQS: (25), (153) imply:
% 115.61/17.67 | | | | | | | | | (154) all_6_2 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | SIMP: (154) implies:
% 115.61/17.67 | | | | | | | | | (155) all_6_2 = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | REDUCE: (96), (155) imply:
% 115.61/17.67 | | | | | | | | | (156) op(e1, e1) = e3
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | BETA: splitting (66) gives:
% 115.61/17.67 | | | | | | | | |
% 115.61/17.67 | | | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | (157) ~ (all_56_3 = e2)
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | REDUCE: (8), (157) imply:
% 115.61/17.67 | | | | | | | | | | (158) ~ (all_52_1 = e2)
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | BETA: splitting (68) gives:
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | Case 1:
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | (159) ~ (all_56_2 = e3)
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | REDUCE: (144), (159) imply:
% 115.61/17.67 | | | | | | | | | | | (160) $false
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | (161) ~ (all_56_13 = e0)
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | REDUCE: (70), (161) imply:
% 115.61/17.67 | | | | | | | | | | | (162) ~ (all_8_2 = e0)
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (18), (22), (23), (24),
% 115.61/17.67 | | | | | | | | | | | (26), (27), (39), (40), (43), (47), (52), (53),
% 115.61/17.67 | | | | | | | | | | | (58), (59), (64), (69), (71), (72), (78), (79),
% 115.61/17.67 | | | | | | | | | | | (95), (103), (104), (105), (106), (114), (147),
% 115.61/17.67 | | | | | | | | | | | (158), (162) are inconsistent by sub-proof #122.
% 115.61/17.67 | | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | | End of split
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.67 | | | | | | | | | Case 2:
% 115.61/17.67 | | | | | | | | | |
% 115.61/17.68 | | | | | | | | | | (163) all_56_3 = e2
% 115.61/17.68 | | | | | | | | | |
% 115.61/17.68 | | | | | | | | | | REF_CLOSE: (7), (22), (66), (96), (156), (163) are
% 115.61/17.68 | | | | | | | | | | inconsistent by sub-proof #121.
% 115.61/17.68 | | | | | | | | | |
% 115.61/17.68 | | | | | | | | | End of split
% 115.61/17.68 | | | | | | | | |
% 115.61/17.68 | | | | | | | | Case 2:
% 115.61/17.68 | | | | | | | | |
% 115.61/17.68 | | | | | | | | | (164) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.61/17.68 | | | | | | | | |
% 115.61/17.68 | | | | | | | | | REF_CLOSE: (25), (73), (106), (152), (164) are inconsistent by
% 115.61/17.68 | | | | | | | | | sub-proof #435.
% 115.61/17.68 | | | | | | | | |
% 115.61/17.68 | | | | | | | | End of split
% 115.61/17.68 | | | | | | | |
% 115.61/17.68 | | | | | | | End of split
% 115.61/17.68 | | | | | | |
% 115.61/17.68 | | | | | | End of split
% 115.61/17.68 | | | | | |
% 115.61/17.68 | | | | | Case 2:
% 115.61/17.68 | | | | | |
% 115.61/17.68 | | | | | | (165) ~ (all_56_15 = e1)
% 115.61/17.68 | | | | | |
% 115.61/17.68 | | | | | | REDUCE: (127), (165) imply:
% 115.61/17.68 | | | | | | (166) $false
% 115.61/17.68 | | | | | |
% 115.61/17.68 | | | | | | CLOSE: (166) is inconsistent.
% 115.61/17.68 | | | | | |
% 115.61/17.68 | | | | | End of split
% 115.61/17.68 | | | | |
% 115.61/17.68 | | | | Case 2:
% 115.61/17.68 | | | | |
% 115.61/17.68 | | | | | (167) all_54_15 = e0
% 115.61/17.68 | | | | |
% 115.61/17.68 | | | | | REF_CLOSE: (6), (104), (167) are inconsistent by sub-proof #419.
% 115.61/17.68 | | | | |
% 115.61/17.68 | | | | End of split
% 115.61/17.68 | | | |
% 115.61/17.68 | | | End of split
% 115.61/17.68 | | |
% 115.61/17.68 | | End of split
% 115.61/17.68 | |
% 115.61/17.68 | End of split
% 115.61/17.68 |
% 115.61/17.68 End of proof
% 115.61/17.68
% 115.61/17.68 Sub-proof #121 shows that the following formulas are inconsistent:
% 115.61/17.68 ----------------------------------------------------------------
% 115.61/17.68 (1) all_56_14 = all_6_2
% 115.61/17.68 (2) all_56_3 = e2
% 115.61/17.68 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.68 (4) op(e1, e1) = e3
% 115.61/17.68 (5) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 115.61/17.68 (6) op(e1, e1) = all_6_2
% 115.61/17.68
% 115.61/17.68 Begin of proof
% 115.61/17.68 |
% 115.61/17.68 | BETA: splitting (5) gives:
% 115.61/17.68 |
% 115.61/17.68 | Case 1:
% 115.61/17.68 | |
% 115.61/17.68 | | (7) ~ (all_56_3 = e2)
% 115.61/17.68 | |
% 115.61/17.68 | | REDUCE: (2), (7) imply:
% 115.61/17.68 | | (8) $false
% 115.61/17.68 | |
% 115.61/17.68 | | CLOSE: (8) is inconsistent.
% 115.61/17.68 | |
% 115.61/17.68 | Case 2:
% 115.61/17.68 | |
% 115.61/17.68 | | (9) ~ (all_56_14 = e3)
% 115.61/17.68 | |
% 115.61/17.68 | | REDUCE: (1), (9) imply:
% 115.61/17.68 | | (10) ~ (all_6_2 = e3)
% 115.61/17.68 | |
% 115.61/17.68 | | GROUND_INST: instantiating (3) with all_6_2, e3, e1, e1, simplifying with
% 115.61/17.68 | | (4), (6) gives:
% 115.61/17.68 | | (11) all_6_2 = e3
% 115.61/17.68 | |
% 115.61/17.68 | | REDUCE: (10), (11) imply:
% 115.61/17.68 | | (12) $false
% 115.61/17.68 | |
% 115.61/17.68 | | CLOSE: (12) is inconsistent.
% 115.61/17.68 | |
% 115.61/17.68 | End of split
% 115.61/17.68 |
% 115.61/17.68 End of proof
% 115.61/17.68
% 115.61/17.68 Sub-proof #122 shows that the following formulas are inconsistent:
% 115.61/17.68 ----------------------------------------------------------------
% 115.61/17.68 (1) ~ (all_52_8 = all_10_2)
% 115.61/17.68 (2) ~ (all_52_9 = all_8_2)
% 115.61/17.68 (3) ~ (all_52_1 = e2)
% 115.61/17.68 (4) ~ (all_4_2 = e0)
% 115.61/17.68 (5) all_54_0 = all_10_2
% 115.61/17.68 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.68 (7) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.68 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.68 (9) ~ (all_52_1 = all_52_9)
% 115.61/17.68 (10) ~ (all_10_2 = e2)
% 115.61/17.68 (11) all_58_4 = all_52_8
% 115.61/17.68 (12) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.68 (13) ~ (all_8_2 = e0)
% 115.61/17.68 (14) op(e2, e3) = all_52_1
% 115.61/17.68 (15) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.68 (16) ~ (all_4_2 = e3)
% 115.61/17.68 (17) all_58_5 = all_52_9
% 115.61/17.68 (18) all_58_2 = all_52_1
% 115.61/17.68 (19) ~ (all_10_2 = e3)
% 115.61/17.68 (20) ~ (all_52_1 = all_10_2)
% 115.61/17.68 (21) all_54_5 = all_8_2
% 115.61/17.68 (22) ~ (all_52_11 = all_4_2)
% 115.61/17.68 (23) all_58_14 = all_52_11
% 115.61/17.68 (24) ~ (all_52_1 = all_8_2)
% 115.61/17.68 (25) ~ (all_8_2 = e2)
% 115.61/17.68 (26) ~ (all_10_2 = e0)
% 115.61/17.68 (27) all_58_8 = all_6_2
% 115.61/17.68 (28) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.68 (29) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.68 (30) ~ (all_4_2 = e2)
% 115.61/17.68 (31) all_54_4 = all_52_1
% 115.61/17.68 (32) all_54_15 = all_4_2
% 115.61/17.68 (33) op(e2, all_8_2) = e1
% 115.61/17.68 (34) ~ (all_6_2 = e1)
% 115.61/17.68
% 115.61/17.68 Begin of proof
% 115.61/17.68 |
% 115.61/17.68 | BETA: splitting (12) gives:
% 115.61/17.68 |
% 115.61/17.68 | Case 1:
% 115.61/17.68 | |
% 115.61/17.68 | | (35) all_54_15 = e3
% 115.61/17.68 | |
% 115.61/17.68 | | REF_CLOSE: (16), (32), (35) are inconsistent by sub-proof #312.
% 115.61/17.68 | |
% 115.61/17.68 | Case 2:
% 115.61/17.68 | |
% 115.61/17.68 | | (36) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.68 | |
% 115.61/17.68 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 115.61/17.68 | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 115.61/17.68 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (36) are
% 115.61/17.68 | | inconsistent by sub-proof #123.
% 115.61/17.68 | |
% 115.61/17.68 | End of split
% 115.61/17.68 |
% 115.61/17.68 End of proof
% 115.61/17.68
% 115.61/17.68 Sub-proof #123 shows that the following formulas are inconsistent:
% 115.61/17.68 ----------------------------------------------------------------
% 115.61/17.68 (1) ~ (all_52_8 = all_10_2)
% 115.61/17.68 (2) ~ (all_52_9 = all_8_2)
% 115.61/17.68 (3) ~ (all_52_1 = e2)
% 115.61/17.68 (4) ~ (all_4_2 = e0)
% 115.61/17.68 (5) all_54_0 = all_10_2
% 115.61/17.68 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.68 (7) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.68 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.68 (9) ~ (all_52_1 = all_52_9)
% 115.61/17.68 (10) ~ (all_10_2 = e2)
% 115.61/17.68 (11) all_58_4 = all_52_8
% 115.61/17.68 (12) ~ (all_8_2 = e0)
% 115.61/17.68 (13) op(e2, e3) = all_52_1
% 115.61/17.68 (14) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.68 (15) all_58_5 = all_52_9
% 115.61/17.68 (16) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.68 (17) all_58_2 = all_52_1
% 115.61/17.68 (18) ~ (all_10_2 = e3)
% 115.61/17.68 (19) ~ (all_52_1 = all_10_2)
% 115.61/17.68 (20) all_54_5 = all_8_2
% 115.61/17.68 (21) ~ (all_52_11 = all_4_2)
% 115.61/17.68 (22) all_58_14 = all_52_11
% 115.61/17.68 (23) ~ (all_52_1 = all_8_2)
% 115.61/17.68 (24) ~ (all_8_2 = e2)
% 115.61/17.68 (25) ~ (all_10_2 = e0)
% 115.61/17.68 (26) all_58_8 = all_6_2
% 115.61/17.68 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.68 (28) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.68 (29) ~ (all_4_2 = e2)
% 115.61/17.68 (30) all_54_4 = all_52_1
% 115.61/17.68 (31) all_54_15 = all_4_2
% 115.61/17.68 (32) op(e2, all_8_2) = e1
% 115.61/17.68 (33) ~ (all_6_2 = e1)
% 115.61/17.68
% 115.61/17.68 Begin of proof
% 115.61/17.68 |
% 115.61/17.68 | BETA: splitting (16) gives:
% 115.61/17.68 |
% 115.61/17.68 | Case 1:
% 115.61/17.68 | |
% 115.61/17.68 | | (34) all_54_15 = e2
% 115.61/17.68 | |
% 115.61/17.68 | | REF_CLOSE: (29), (31), (34) are inconsistent by sub-proof #420.
% 115.61/17.68 | |
% 115.61/17.68 | Case 2:
% 115.61/17.68 | |
% 115.61/17.68 | | (35) all_54_15 = e1 | all_54_15 = e0
% 115.61/17.68 | |
% 115.61/17.68 | | BETA: splitting (35) gives:
% 115.61/17.68 | |
% 115.61/17.68 | | Case 1:
% 115.61/17.68 | | |
% 115.61/17.68 | | | (36) all_54_15 = e1
% 115.61/17.68 | | |
% 115.61/17.68 | | | COMBINE_EQS: (31), (36) imply:
% 115.61/17.68 | | | (37) all_4_2 = e1
% 115.61/17.68 | | |
% 115.61/17.68 | | | SIMP: (37) implies:
% 115.61/17.68 | | | (38) all_4_2 = e1
% 115.61/17.68 | | |
% 115.61/17.68 | | | REDUCE: (21), (38) imply:
% 115.61/17.68 | | | (39) ~ (all_52_11 = e1)
% 115.61/17.68 | | |
% 115.61/17.68 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 115.61/17.68 | | | (14), (15), (17), (18), (19), (20), (22), (23), (24), (25),
% 115.61/17.68 | | | (26), (27), (28), (30), (32), (33), (39) are inconsistent by
% 115.61/17.68 | | | sub-proof #124.
% 115.61/17.68 | | |
% 115.61/17.68 | | Case 2:
% 115.61/17.68 | | |
% 115.61/17.68 | | | (40) all_54_15 = e0
% 115.61/17.68 | | |
% 115.61/17.68 | | | REF_CLOSE: (4), (31), (40) are inconsistent by sub-proof #419.
% 115.61/17.68 | | |
% 115.61/17.68 | | End of split
% 115.61/17.68 | |
% 115.61/17.68 | End of split
% 115.61/17.68 |
% 115.61/17.68 End of proof
% 115.61/17.68
% 115.61/17.68 Sub-proof #124 shows that the following formulas are inconsistent:
% 115.61/17.68 ----------------------------------------------------------------
% 115.61/17.68 (1) ~ (all_52_8 = all_10_2)
% 115.61/17.68 (2) ~ (all_52_9 = all_8_2)
% 115.61/17.68 (3) ~ (all_52_1 = e2)
% 115.61/17.68 (4) all_54_0 = all_10_2
% 115.61/17.68 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.68 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.68 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.68 (8) ~ (all_52_1 = all_52_9)
% 115.61/17.68 (9) ~ (all_10_2 = e2)
% 115.61/17.68 (10) all_58_4 = all_52_8
% 115.61/17.68 (11) ~ (all_8_2 = e0)
% 115.61/17.68 (12) op(e2, e3) = all_52_1
% 115.61/17.68 (13) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.68 (14) all_58_5 = all_52_9
% 115.61/17.68 (15) all_58_2 = all_52_1
% 115.61/17.68 (16) ~ (all_10_2 = e3)
% 115.61/17.68 (17) ~ (all_52_1 = all_10_2)
% 115.61/17.68 (18) all_54_5 = all_8_2
% 115.61/17.68 (19) all_58_14 = all_52_11
% 115.61/17.68 (20) ~ (all_52_1 = all_8_2)
% 115.61/17.69 (21) ~ (all_8_2 = e2)
% 115.61/17.69 (22) ~ (all_10_2 = e0)
% 115.61/17.69 (23) all_58_8 = all_6_2
% 115.61/17.69 (24) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.69 (25) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.69 (26) ~ (all_52_11 = e1)
% 115.61/17.69 (27) all_54_4 = all_52_1
% 115.61/17.69 (28) op(e2, all_8_2) = e1
% 115.61/17.69 (29) ~ (all_6_2 = e1)
% 115.61/17.69
% 115.61/17.69 Begin of proof
% 115.61/17.69 |
% 115.61/17.69 | BETA: splitting (24) gives:
% 115.61/17.69 |
% 115.61/17.69 | Case 1:
% 115.61/17.69 | |
% 115.61/17.69 | | (30) all_54_0 = e3
% 115.61/17.69 | |
% 115.61/17.69 | | REF_CLOSE: (4), (16), (30) are inconsistent by sub-proof #451.
% 115.61/17.69 | |
% 115.61/17.69 | Case 2:
% 115.61/17.69 | |
% 115.61/17.69 | | (31) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.69 | |
% 115.61/17.69 | | BETA: splitting (31) gives:
% 115.61/17.69 | |
% 115.61/17.69 | | Case 1:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (32) all_54_0 = e2
% 115.61/17.69 | | |
% 115.61/17.69 | | | REF_CLOSE: (4), (9), (32) are inconsistent by sub-proof #450.
% 115.61/17.69 | | |
% 115.61/17.69 | | Case 2:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (33) all_54_0 = e1 | all_54_0 = e0
% 115.61/17.69 | | |
% 115.61/17.69 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 115.61/17.69 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (25),
% 115.61/17.69 | | | (26), (27), (28), (29), (33) are inconsistent by sub-proof
% 115.61/17.69 | | | #125.
% 115.61/17.69 | | |
% 115.61/17.69 | | End of split
% 115.61/17.69 | |
% 115.61/17.69 | End of split
% 115.61/17.69 |
% 115.61/17.69 End of proof
% 115.61/17.69
% 115.61/17.69 Sub-proof #125 shows that the following formulas are inconsistent:
% 115.61/17.69 ----------------------------------------------------------------
% 115.61/17.69 (1) ~ (all_52_8 = all_10_2)
% 115.61/17.69 (2) ~ (all_52_9 = all_8_2)
% 115.61/17.69 (3) ~ (all_52_1 = e2)
% 115.61/17.69 (4) all_54_0 = all_10_2
% 115.61/17.69 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.69 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.69 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.69 (8) ~ (all_52_1 = all_52_9)
% 115.61/17.69 (9) all_58_4 = all_52_8
% 115.61/17.69 (10) ~ (all_8_2 = e0)
% 115.61/17.69 (11) op(e2, e3) = all_52_1
% 115.61/17.69 (12) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.69 (13) all_54_0 = e1 | all_54_0 = e0
% 115.61/17.69 (14) all_58_5 = all_52_9
% 115.61/17.69 (15) all_58_2 = all_52_1
% 115.61/17.69 (16) ~ (all_52_1 = all_10_2)
% 115.61/17.69 (17) all_54_5 = all_8_2
% 115.61/17.69 (18) all_58_14 = all_52_11
% 115.61/17.69 (19) ~ (all_52_1 = all_8_2)
% 115.61/17.69 (20) ~ (all_8_2 = e2)
% 115.61/17.69 (21) ~ (all_10_2 = e0)
% 115.61/17.69 (22) all_58_8 = all_6_2
% 115.61/17.69 (23) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.69 (24) ~ (all_52_11 = e1)
% 115.61/17.69 (25) all_54_4 = all_52_1
% 115.61/17.69 (26) op(e2, all_8_2) = e1
% 115.61/17.69 (27) ~ (all_6_2 = e1)
% 115.61/17.69
% 115.61/17.69 Begin of proof
% 115.61/17.69 |
% 115.61/17.69 | BETA: splitting (13) gives:
% 115.61/17.69 |
% 115.61/17.69 | Case 1:
% 115.61/17.69 | |
% 115.61/17.69 | | (28) all_54_0 = e1
% 115.61/17.69 | |
% 115.61/17.69 | | COMBINE_EQS: (4), (28) imply:
% 115.61/17.69 | | (29) all_10_2 = e1
% 115.61/17.69 | |
% 115.61/17.69 | | SIMP: (29) implies:
% 115.61/17.69 | | (30) all_10_2 = e1
% 115.61/17.69 | |
% 115.61/17.69 | | REDUCE: (1), (30) imply:
% 115.61/17.69 | | (31) ~ (all_52_8 = e1)
% 115.61/17.69 | |
% 115.61/17.69 | | BETA: splitting (12) gives:
% 115.61/17.69 | |
% 115.61/17.69 | | Case 1:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (32) all_58_4 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | COMBINE_EQS: (9), (32) imply:
% 115.61/17.69 | | | (33) all_52_8 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | REDUCE: (31), (33) imply:
% 115.61/17.69 | | | (34) $false
% 115.61/17.69 | | |
% 115.61/17.69 | | | CLOSE: (34) is inconsistent.
% 115.61/17.69 | | |
% 115.61/17.69 | | Case 2:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (35) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | BETA: splitting (35) gives:
% 115.61/17.69 | | |
% 115.61/17.69 | | | Case 1:
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | (36) all_58_5 = e1
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | COMBINE_EQS: (14), (36) imply:
% 115.61/17.69 | | | | (37) all_52_9 = e1
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | REDUCE: (8), (37) imply:
% 115.61/17.69 | | | | (38) ~ (all_52_1 = e1)
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | REDUCE: (2), (37) imply:
% 115.61/17.69 | | | | (39) ~ (all_8_2 = e1)
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | SIMP: (39) implies:
% 115.61/17.69 | | | | (40) ~ (all_8_2 = e1)
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | BETA: splitting (5) gives:
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | Case 1:
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | (41) all_54_5 = e3
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | COMBINE_EQS: (17), (41) imply:
% 115.61/17.69 | | | | | (42) all_8_2 = e3
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | SIMP: (42) implies:
% 115.61/17.69 | | | | | (43) all_8_2 = e3
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | REDUCE: (19), (43) imply:
% 115.61/17.69 | | | | | (44) ~ (all_52_1 = e3)
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | REDUCE: (26), (43) imply:
% 115.61/17.69 | | | | | (45) op(e2, e3) = e1
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | BETA: splitting (23) gives:
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | Case 1:
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | (46) all_58_2 = e0
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | REF_CLOSE: (7), (11), (15), (38), (45), (46) are inconsistent by
% 115.61/17.69 | | | | | | sub-proof #128.
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | Case 2:
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | (47) ~ (all_58_2 = e0)
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | REDUCE: (15), (47) imply:
% 115.61/17.69 | | | | | | (48) ~ (all_52_1 = e0)
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | BETA: splitting (6) gives:
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | | Case 1:
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | | (49) all_54_4 = e3
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | | REF_CLOSE: (25), (44), (49) are inconsistent by sub-proof #329.
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | Case 2:
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | | (50) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | | REF_CLOSE: (3), (4), (13), (16), (21), (25), (48), (50) are
% 115.61/17.69 | | | | | | | inconsistent by sub-proof #126.
% 115.61/17.69 | | | | | | |
% 115.61/17.69 | | | | | | End of split
% 115.61/17.69 | | | | | |
% 115.61/17.69 | | | | | End of split
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | Case 2:
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | (51) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | | REF_CLOSE: (10), (17), (20), (40), (51) are inconsistent by sub-proof
% 115.61/17.69 | | | | | #310.
% 115.61/17.69 | | | | |
% 115.61/17.69 | | | | End of split
% 115.61/17.69 | | | |
% 115.61/17.69 | | | Case 2:
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | (52) all_58_8 = e1 | all_58_14 = e1
% 115.61/17.69 | | | |
% 115.61/17.69 | | | | REF_CLOSE: (18), (22), (24), (27), (52) are inconsistent by sub-proof
% 115.61/17.69 | | | | #219.
% 115.61/17.69 | | | |
% 115.61/17.69 | | | End of split
% 115.61/17.69 | | |
% 115.61/17.69 | | End of split
% 115.61/17.69 | |
% 115.61/17.69 | Case 2:
% 115.61/17.69 | |
% 115.61/17.69 | | (53) all_54_0 = e0
% 115.61/17.69 | |
% 115.61/17.69 | | REF_CLOSE: (4), (21), (53) are inconsistent by sub-proof #424.
% 115.61/17.69 | |
% 115.61/17.69 | End of split
% 115.61/17.69 |
% 115.61/17.69 End of proof
% 115.61/17.69
% 115.61/17.69 Sub-proof #126 shows that the following formulas are inconsistent:
% 115.61/17.69 ----------------------------------------------------------------
% 115.61/17.69 (1) ~ (all_52_1 = e2)
% 115.61/17.69 (2) all_54_0 = all_10_2
% 115.61/17.69 (3) all_54_0 = e1 | all_54_0 = e0
% 115.61/17.69 (4) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.61/17.69 (5) ~ (all_52_1 = all_10_2)
% 115.61/17.69 (6) ~ (all_52_1 = e0)
% 115.61/17.69 (7) ~ (all_10_2 = e0)
% 115.61/17.69 (8) all_54_4 = all_52_1
% 115.61/17.69
% 115.61/17.69 Begin of proof
% 115.61/17.69 |
% 115.61/17.69 | BETA: splitting (4) gives:
% 115.61/17.69 |
% 115.61/17.69 | Case 1:
% 115.61/17.69 | |
% 115.61/17.69 | | (9) all_54_4 = e2
% 115.61/17.69 | |
% 115.61/17.69 | | REF_CLOSE: (1), (8), (9) are inconsistent by sub-proof #328.
% 115.61/17.69 | |
% 115.61/17.69 | Case 2:
% 115.61/17.69 | |
% 115.61/17.69 | | (10) all_54_4 = e1 | all_54_4 = e0
% 115.61/17.69 | |
% 115.61/17.69 | | BETA: splitting (10) gives:
% 115.61/17.69 | |
% 115.61/17.69 | | Case 1:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (11) all_54_4 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | COMBINE_EQS: (8), (11) imply:
% 115.61/17.69 | | | (12) all_52_1 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | SIMP: (12) implies:
% 115.61/17.69 | | | (13) all_52_1 = e1
% 115.61/17.69 | | |
% 115.61/17.69 | | | REDUCE: (5), (13) imply:
% 115.61/17.69 | | | (14) ~ (all_10_2 = e1)
% 115.61/17.69 | | |
% 115.61/17.69 | | | SIMP: (14) implies:
% 115.61/17.69 | | | (15) ~ (all_10_2 = e1)
% 115.61/17.69 | | |
% 115.61/17.69 | | | REF_CLOSE: (2), (3), (7), (15) are inconsistent by sub-proof #127.
% 115.61/17.69 | | |
% 115.61/17.69 | | Case 2:
% 115.61/17.69 | | |
% 115.61/17.69 | | | (16) all_54_4 = e0
% 115.61/17.69 | | |
% 115.61/17.69 | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #323.
% 115.61/17.69 | | |
% 115.61/17.69 | | End of split
% 115.61/17.69 | |
% 115.61/17.69 | End of split
% 115.61/17.69 |
% 115.61/17.69 End of proof
% 115.61/17.69
% 115.61/17.69 Sub-proof #127 shows that the following formulas are inconsistent:
% 115.61/17.69 ----------------------------------------------------------------
% 115.61/17.69 (1) all_54_0 = e1 | all_54_0 = e0
% 115.61/17.70 (2) all_54_0 = all_10_2
% 115.61/17.70 (3) ~ (all_10_2 = e1)
% 115.61/17.70 (4) ~ (all_10_2 = e0)
% 115.61/17.70
% 115.61/17.70 Begin of proof
% 115.61/17.70 |
% 115.61/17.70 | BETA: splitting (1) gives:
% 115.61/17.70 |
% 115.61/17.70 | Case 1:
% 115.61/17.70 | |
% 115.61/17.70 | | (5) all_54_0 = e1
% 115.61/17.70 | |
% 115.61/17.70 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #449.
% 115.61/17.70 | |
% 115.61/17.70 | Case 2:
% 115.61/17.70 | |
% 115.61/17.70 | | (6) all_54_0 = e0
% 115.61/17.70 | |
% 115.61/17.70 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #424.
% 115.61/17.70 | |
% 115.61/17.70 | End of split
% 115.61/17.70 |
% 115.61/17.70 End of proof
% 115.61/17.70
% 115.61/17.70 Sub-proof #128 shows that the following formulas are inconsistent:
% 115.61/17.70 ----------------------------------------------------------------
% 115.61/17.70 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.70 (2) op(e2, e3) = e1
% 115.61/17.70 (3) op(e2, e3) = all_52_1
% 115.61/17.70 (4) all_58_2 = all_52_1
% 115.61/17.70 (5) all_58_2 = e0
% 115.61/17.70 (6) ~ (all_52_1 = e1)
% 115.61/17.70
% 115.61/17.70 Begin of proof
% 115.61/17.70 |
% 115.61/17.70 | COMBINE_EQS: (4), (5) imply:
% 115.61/17.70 | (7) all_52_1 = e0
% 115.61/17.70 |
% 115.61/17.70 | REDUCE: (6), (7) imply:
% 115.61/17.70 | (8) ~ (e1 = e0)
% 115.61/17.70 |
% 115.61/17.70 | SIMP: (8) implies:
% 115.61/17.70 | (9) ~ (e1 = e0)
% 115.61/17.70 |
% 115.61/17.70 | REF_CLOSE: (1), (2), (3), (7), (9) are inconsistent by sub-proof #132.
% 115.61/17.70 |
% 115.61/17.70 End of proof
% 115.61/17.70
% 115.61/17.70 Sub-proof #129 shows that the following formulas are inconsistent:
% 115.61/17.70 ----------------------------------------------------------------
% 115.61/17.70 (1) ~ (all_52_9 = all_8_2)
% 115.61/17.70 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.70 (3) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.70 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.70 (5) all_58_3 = all_8_2
% 115.61/17.70 (6) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.61/17.70 (7) all_54_7 = all_52_13
% 115.61/17.70 (8) op(e2, e3) = all_52_1
% 115.61/17.70 (9) all_58_5 = all_52_9
% 115.61/17.70 (10) all_58_2 = all_52_1
% 115.61/17.70 (11) ~ (all_52_13 = e1)
% 115.61/17.70 (12) all_54_5 = all_8_2
% 115.61/17.70 (13) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 115.61/17.70 (14) all_58_10 = all_52_13
% 115.61/17.70 (15) ~ (all_52_13 = all_8_2)
% 115.61/17.70 (16) ~ (all_8_2 = e1)
% 115.61/17.70 (17) all_56_13 = all_8_2
% 115.61/17.70 (18) ~ (all_8_2 = e2)
% 115.61/17.70 (19) all_56_5 = all_52_13
% 115.61/17.70 (20) op(e2, e0) = all_52_13
% 115.61/17.70 (21) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.70 (22) op(e2, all_8_2) = e1
% 115.61/17.70
% 115.61/17.70 Begin of proof
% 115.61/17.70 |
% 115.61/17.70 | BETA: splitting (2) gives:
% 115.61/17.70 |
% 115.61/17.70 | Case 1:
% 115.61/17.70 | |
% 115.61/17.70 | | (23) all_54_5 = e2
% 115.61/17.70 | |
% 115.61/17.70 | | REF_CLOSE: (12), (18), (23) are inconsistent by sub-proof #338.
% 115.61/17.70 | |
% 115.61/17.70 | Case 2:
% 115.61/17.70 | |
% 115.61/17.70 | | (24) ~ (all_54_5 = e2)
% 115.61/17.70 | | (25) all_54_5 = e1 | all_54_5 = e0
% 115.61/17.70 | |
% 115.61/17.70 | | BETA: splitting (25) gives:
% 115.61/17.70 | |
% 115.61/17.70 | | Case 1:
% 115.61/17.70 | | |
% 115.61/17.70 | | | (26) all_54_5 = e1
% 115.61/17.70 | | |
% 115.61/17.70 | | | REF_CLOSE: (12), (16), (26) are inconsistent by sub-proof #337.
% 115.61/17.70 | | |
% 115.61/17.70 | | Case 2:
% 115.61/17.70 | | |
% 115.61/17.70 | | | (27) all_54_5 = e0
% 115.61/17.70 | | |
% 115.61/17.70 | | | COMBINE_EQS: (12), (27) imply:
% 115.61/17.70 | | | (28) all_8_2 = e0
% 115.61/17.70 | | |
% 115.61/17.70 | | | SIMP: (28) implies:
% 115.61/17.70 | | | (29) all_8_2 = e0
% 115.61/17.70 | | |
% 115.61/17.70 | | | REDUCE: (1), (29) imply:
% 115.61/17.70 | | | (30) ~ (all_52_9 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | REDUCE: (15), (29) imply:
% 115.61/17.70 | | | (31) ~ (all_52_13 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | REDUCE: (18), (29) imply:
% 115.61/17.70 | | | (32) ~ (e2 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | SIMP: (32) implies:
% 115.61/17.70 | | | (33) ~ (e2 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | REDUCE: (16), (29) imply:
% 115.61/17.70 | | | (34) ~ (e1 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | SIMP: (34) implies:
% 115.61/17.70 | | | (35) ~ (e1 = e0)
% 115.61/17.70 | | |
% 115.61/17.70 | | | REDUCE: (22), (29) imply:
% 115.61/17.70 | | | (36) op(e2, e0) = e1
% 115.61/17.70 | | |
% 115.61/17.70 | | | BETA: splitting (13) gives:
% 115.61/17.70 | | |
% 115.61/17.70 | | | Case 1:
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | (37) all_54_7 = e3
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | COMBINE_EQS: (7), (37) imply:
% 115.61/17.70 | | | | (38) all_52_13 = e3
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | SIMP: (38) implies:
% 115.61/17.70 | | | | (39) all_52_13 = e3
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | REDUCE: (11), (39) imply:
% 115.61/17.70 | | | | (40) ~ (e3 = e1)
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | REDUCE: (20), (39) imply:
% 115.61/17.70 | | | | (41) op(e2, e0) = e3
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | REF_CLOSE: (4), (36), (40), (41) are inconsistent by sub-proof #133.
% 115.61/17.70 | | | |
% 115.61/17.70 | | | Case 2:
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | (42) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | BETA: splitting (42) gives:
% 115.61/17.70 | | | |
% 115.61/17.70 | | | | Case 1:
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | (43) all_54_7 = e2
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | COMBINE_EQS: (7), (43) imply:
% 115.61/17.70 | | | | | (44) all_52_13 = e2
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | SIMP: (44) implies:
% 115.61/17.70 | | | | | (45) all_52_13 = e2
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | COMBINE_EQS: (19), (45) imply:
% 115.61/17.70 | | | | | (46) all_56_5 = e2
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | COMBINE_EQS: (14), (45) imply:
% 115.61/17.70 | | | | | (47) all_58_10 = e2
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (12), (16), (17), (18),
% 115.61/17.70 | | | | | (21), (22), (30), (33), (35), (46), (47) are inconsistent
% 115.61/17.70 | | | | | by sub-proof #131.
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | Case 2:
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | (48) all_54_7 = e1 | all_54_7 = e0
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | BETA: splitting (48) gives:
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | | Case 1:
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | | (49) all_54_7 = e1
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | | REF_CLOSE: (7), (11), (49) are inconsistent by sub-proof #349.
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | Case 2:
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | | (50) all_54_7 = e0
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | | REF_CLOSE: (7), (31), (50) are inconsistent by sub-proof #130.
% 115.61/17.70 | | | | | |
% 115.61/17.70 | | | | | End of split
% 115.61/17.70 | | | | |
% 115.61/17.70 | | | | End of split
% 115.61/17.70 | | | |
% 115.61/17.70 | | | End of split
% 115.61/17.70 | | |
% 115.61/17.70 | | End of split
% 115.61/17.70 | |
% 115.61/17.70 | End of split
% 115.61/17.70 |
% 115.61/17.70 End of proof
% 115.61/17.70
% 115.61/17.70 Sub-proof #130 shows that the following formulas are inconsistent:
% 115.61/17.70 ----------------------------------------------------------------
% 115.61/17.70 (1) all_54_7 = all_52_13
% 115.61/17.70 (2) all_54_7 = e0
% 115.61/17.70 (3) ~ (all_52_13 = e0)
% 115.61/17.70
% 115.61/17.70 Begin of proof
% 115.61/17.70 |
% 115.61/17.70 | COMBINE_EQS: (1), (2) imply:
% 115.61/17.70 | (4) all_52_13 = e0
% 115.61/17.70 |
% 115.61/17.70 | SIMP: (4) implies:
% 115.61/17.70 | (5) all_52_13 = e0
% 115.61/17.70 |
% 115.61/17.70 | REDUCE: (3), (5) imply:
% 115.61/17.70 | (6) $false
% 115.61/17.70 |
% 115.61/17.70 | CLOSE: (6) is inconsistent.
% 115.61/17.70 |
% 115.61/17.70 End of proof
% 115.61/17.70
% 115.61/17.70 Sub-proof #131 shows that the following formulas are inconsistent:
% 115.61/17.70 ----------------------------------------------------------------
% 115.61/17.70 (1) all_58_10 = e2
% 115.61/17.70 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.70 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.70 (4) all_58_3 = all_8_2
% 115.61/17.70 (5) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.61/17.70 (6) ~ (all_52_9 = e0)
% 115.61/17.70 (7) op(e2, e3) = all_52_1
% 115.61/17.70 (8) all_58_5 = all_52_9
% 115.61/17.70 (9) all_58_2 = all_52_1
% 115.61/17.70 (10) all_54_5 = all_8_2
% 115.61/17.70 (11) all_56_5 = e2
% 115.61/17.70 (12) ~ (all_8_2 = e1)
% 115.61/17.70 (13) all_56_13 = all_8_2
% 115.61/17.70 (14) ~ (all_8_2 = e2)
% 115.61/17.70 (15) ~ (e2 = e0)
% 115.61/17.70 (16) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.70 (17) op(e2, all_8_2) = e1
% 115.61/17.70 (18) ~ (e1 = e0)
% 115.61/17.70
% 115.61/17.70 Begin of proof
% 115.61/17.70 |
% 115.61/17.70 | BETA: splitting (5) gives:
% 115.61/17.70 |
% 115.61/17.70 | Case 1:
% 115.61/17.70 | |
% 115.61/17.70 | | (19) ~ (all_56_5 = e2)
% 115.61/17.70 | |
% 115.61/17.70 | | REDUCE: (11), (19) imply:
% 115.61/17.70 | | (20) $false
% 115.61/17.70 | |
% 115.61/17.70 | | CLOSE: (20) is inconsistent.
% 115.61/17.70 | |
% 115.61/17.70 | Case 2:
% 115.61/17.70 | |
% 115.61/17.70 | | (21) ~ (all_56_13 = e0)
% 115.61/17.70 | |
% 115.61/17.70 | | REDUCE: (13), (21) imply:
% 115.61/17.70 | | (22) ~ (all_8_2 = e0)
% 115.61/17.70 | |
% 115.61/17.70 | | BETA: splitting (2) gives:
% 115.61/17.70 | |
% 115.61/17.70 | | Case 1:
% 115.61/17.70 | | |
% 115.61/17.70 | | | (23) all_54_5 = e3
% 115.61/17.70 | | |
% 115.61/17.70 | | | COMBINE_EQS: (10), (23) imply:
% 115.61/17.70 | | | (24) all_8_2 = e3
% 115.61/17.70 | | |
% 115.61/17.70 | | | SIMP: (24) implies:
% 115.61/17.70 | | | (25) all_8_2 = e3
% 115.61/17.70 | | |
% 115.61/17.70 | | | COMBINE_EQS: (4), (25) imply:
% 115.61/17.71 | | | (26) all_58_3 = e3
% 115.61/17.71 | | |
% 115.61/17.71 | | | REDUCE: (22), (25) imply:
% 115.61/17.71 | | | (27) ~ (e3 = e0)
% 115.61/17.71 | | |
% 115.61/17.71 | | | REDUCE: (17), (25) imply:
% 115.61/17.71 | | | (28) op(e2, e3) = e1
% 115.61/17.71 | | |
% 115.61/17.71 | | | BETA: splitting (16) gives:
% 115.61/17.71 | | |
% 115.61/17.71 | | | Case 1:
% 115.61/17.71 | | | |
% 115.61/17.71 | | | | (29) all_58_2 = e0
% 115.61/17.71 | | | |
% 115.61/17.71 | | | | COMBINE_EQS: (9), (29) imply:
% 115.61/17.71 | | | | (30) all_52_1 = e0
% 115.61/17.71 | | | |
% 115.61/17.71 | | | | REF_CLOSE: (3), (7), (18), (28), (30) are inconsistent by sub-proof
% 115.61/17.71 | | | | #132.
% 115.61/17.71 | | | |
% 115.61/17.71 | | | Case 2:
% 115.61/17.71 | | | |
% 115.61/17.71 | | | | (31) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 115.61/17.71 | | | |
% 115.61/17.71 | | | | REF_CLOSE: (1), (6), (8), (15), (26), (27), (31) are inconsistent by
% 115.61/17.71 | | | | sub-proof #172.
% 115.61/17.71 | | | |
% 115.61/17.71 | | | End of split
% 115.61/17.71 | | |
% 115.61/17.71 | | Case 2:
% 115.61/17.71 | | |
% 115.61/17.71 | | | (32) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.71 | | |
% 115.61/17.71 | | | REF_CLOSE: (10), (12), (14), (22), (32) are inconsistent by sub-proof
% 115.61/17.71 | | | #310.
% 115.61/17.71 | | |
% 115.61/17.71 | | End of split
% 115.61/17.71 | |
% 115.61/17.71 | End of split
% 115.61/17.71 |
% 115.61/17.71 End of proof
% 115.61/17.71
% 115.61/17.71 Sub-proof #132 shows that the following formulas are inconsistent:
% 115.61/17.71 ----------------------------------------------------------------
% 115.61/17.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.71 (2) op(e2, e3) = e1
% 115.61/17.71 (3) op(e2, e3) = all_52_1
% 115.61/17.71 (4) all_52_1 = e0
% 115.61/17.71 (5) ~ (e1 = e0)
% 115.61/17.71
% 115.61/17.71 Begin of proof
% 115.61/17.71 |
% 115.61/17.71 | REDUCE: (3), (4) imply:
% 115.61/17.71 | (6) op(e2, e3) = e0
% 115.61/17.71 |
% 115.61/17.71 | GROUND_INST: instantiating (1) with e0, e1, e3, e2, simplifying with (2), (6)
% 115.61/17.71 | gives:
% 115.61/17.71 | (7) e1 = e0
% 115.61/17.71 |
% 115.61/17.71 | REDUCE: (5), (7) imply:
% 115.61/17.71 | (8) $false
% 115.61/17.71 |
% 115.61/17.71 | CLOSE: (8) is inconsistent.
% 115.61/17.71 |
% 115.61/17.71 End of proof
% 115.61/17.71
% 115.61/17.71 Sub-proof #133 shows that the following formulas are inconsistent:
% 115.61/17.71 ----------------------------------------------------------------
% 115.61/17.71 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.71 (2) op(e2, e0) = e3
% 115.61/17.71 (3) op(e2, e0) = e1
% 115.61/17.71 (4) ~ (e3 = e1)
% 115.61/17.71
% 115.61/17.71 Begin of proof
% 115.61/17.71 |
% 115.61/17.71 | GROUND_INST: instantiating (1) with e1, e3, e0, e2, simplifying with (2), (3)
% 115.61/17.71 | gives:
% 115.61/17.71 | (5) e3 = e1
% 115.61/17.71 |
% 115.61/17.71 | REDUCE: (4), (5) imply:
% 115.61/17.71 | (6) $false
% 115.61/17.71 |
% 115.61/17.71 | CLOSE: (6) is inconsistent.
% 115.61/17.71 |
% 115.61/17.71 End of proof
% 115.61/17.71
% 115.61/17.71 Sub-proof #134 shows that the following formulas are inconsistent:
% 115.61/17.71 ----------------------------------------------------------------
% 115.61/17.71 (1) ~ (all_52_2 = all_10_2)
% 115.61/17.71 (2) all_58_7 = all_52_6
% 115.61/17.71 (3) ~ (all_4_2 = e0)
% 115.61/17.71 (4) all_56_14 = all_6_2
% 115.61/17.71 (5) all_54_0 = all_10_2
% 115.61/17.71 (6) all_56_11 = all_52_11
% 115.61/17.71 (7) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 115.61/17.71 (8) ~ (all_52_12 = all_10_2)
% 115.61/17.71 (9) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.61/17.71 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.71 (11) all_56_12 = all_10_2
% 115.61/17.71 (12) ~ (all_52_14 = all_6_2)
% 115.61/17.71 (13) all_56_10 = all_52_7
% 115.61/17.71 (14) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.61/17.71 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.71 (16) ~ (all_10_2 = e2)
% 115.61/17.71 (17) all_54_10 = all_6_2
% 115.61/17.71 (18) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.61/17.71 (19) all_56_2 = all_52_12
% 115.61/17.71 (20) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 115.61/17.71 (21) all_58_3 = all_8_2
% 115.61/17.71 (22) all_54_6 = all_52_9
% 115.61/17.71 (23) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 115.61/17.71 (24) all_58_11 = all_52_14
% 115.61/17.71 (25) ~ (all_52_2 = all_52_3)
% 115.61/17.71 (26) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 115.61/17.71 (27) ~ (all_52_11 = all_6_2)
% 115.61/17.71 (28) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 115.61/17.71 (29) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 115.61/17.71 (30) ~ (all_4_2 = e3)
% 115.61/17.71 (31) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.61/17.71 (32) ~ (all_52_7 = all_8_2)
% 115.61/17.71 (33) all_58_5 = all_52_9
% 115.61/17.71 (34) all_56_9 = all_52_3
% 115.61/17.71 (35) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.61/17.71 (36) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 115.61/17.71 (37) all_58_15 = all_4_2
% 115.61/17.71 (38) all_58_2 = all_52_1
% 115.61/17.71 (39) ~ (all_10_2 = e3)
% 115.61/17.71 (40) all_58_13 = all_52_7
% 115.61/17.71 (41) ~ (all_52_14 = all_4_2)
% 115.61/17.71 (42) all_58_6 = all_52_2
% 115.61/17.71 (43) all_54_5 = all_8_2
% 115.61/17.71 (44) all_56_15 = all_4_2
% 115.61/17.71 (45) all_58_10 = all_52_13
% 115.61/17.71 (46) all_58_14 = all_52_11
% 115.61/17.71 (47) all_56_13 = all_8_2
% 115.61/17.71 (48) ~ (all_8_2 = e2)
% 115.61/17.71 (49) ~ (all_6_2 = e2)
% 115.61/17.71 (50) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.61/17.71 (51) ~ (all_52_1 = all_52_3)
% 115.61/17.71 (52) all_58_8 = all_6_2
% 115.61/17.71 (53) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.71 (54) all_56_4 = all_52_9
% 115.61/17.71 (55) all_58_9 = all_52_12
% 115.61/17.71 (56) all_56_5 = all_52_13
% 115.61/17.71 (57) op(e2, e1) = all_52_9
% 115.61/17.71 (58) ~ (all_52_3 = all_4_2)
% 115.61/17.71 (59) all_56_6 = all_52_2
% 115.61/17.71 (60) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 115.61/17.71 (61) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.71 (62) all_58_12 = all_52_3
% 115.61/17.71 (63) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.61/17.71 (64) ~ (all_52_3 = all_10_2)
% 115.61/17.71 (65) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 115.61/17.71 (66) all_56_8 = all_52_14
% 115.61/17.71 (67) ~ (all_52_6 = e1)
% 115.61/17.71 (68) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.61/17.71 (69) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.61/17.71 (70) ~ (e3 = e2)
% 115.61/17.71 (71) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.61/17.71 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.61/17.71 (72) all_54_15 = all_4_2
% 115.61/17.71 (73) op(e2, all_8_2) = e1
% 115.61/17.71 (74) ~ (all_6_2 = e1)
% 115.61/17.71 (75) all_54_12 = all_52_3
% 115.61/17.71 (76) ~ (all_52_3 = all_52_7)
% 115.61/17.71
% 115.61/17.71 Begin of proof
% 115.61/17.71 |
% 115.61/17.71 | BETA: splitting (26) gives:
% 115.61/17.71 |
% 115.61/17.71 | Case 1:
% 115.61/17.71 | |
% 115.61/17.71 | | (77) ~ (all_56_14 = e3)
% 115.61/17.71 | |
% 115.61/17.71 | | REDUCE: (4), (77) imply:
% 115.61/17.71 | | (78) ~ (all_6_2 = e3)
% 115.61/17.71 | |
% 115.61/17.71 | | BETA: splitting (14) gives:
% 115.61/17.71 | |
% 115.61/17.71 | | Case 1:
% 115.61/17.71 | | |
% 115.61/17.71 | | | (79) all_54_10 = e3
% 115.61/17.71 | | |
% 115.61/17.71 | | | COMBINE_EQS: (17), (79) imply:
% 115.61/17.71 | | | (80) all_6_2 = e3
% 115.61/17.71 | | |
% 115.61/17.71 | | | REDUCE: (78), (80) imply:
% 115.61/17.71 | | | (81) $false
% 115.61/17.71 | | |
% 115.61/17.71 | | | CLOSE: (81) is inconsistent.
% 115.61/17.71 | | |
% 115.61/17.71 | | Case 2:
% 115.61/17.71 | | |
% 115.61/17.72 | | | (82) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.61/17.72 | | |
% 115.61/17.72 | | | BETA: splitting (82) gives:
% 115.61/17.72 | | |
% 115.61/17.72 | | | Case 1:
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | (83) all_54_10 = e2
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | COMBINE_EQS: (17), (83) imply:
% 115.61/17.72 | | | | (84) all_6_2 = e2
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | REDUCE: (49), (84) imply:
% 115.61/17.72 | | | | (85) $false
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | CLOSE: (85) is inconsistent.
% 115.61/17.72 | | | |
% 115.61/17.72 | | | Case 2:
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | (86) ~ (all_54_10 = e2)
% 115.61/17.72 | | | | (87) all_54_10 = e1 | all_54_10 = e0
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | BETA: splitting (87) gives:
% 115.61/17.72 | | | |
% 115.61/17.72 | | | | Case 1:
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | (88) all_54_10 = e1
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | COMBINE_EQS: (17), (88) imply:
% 115.61/17.72 | | | | | (89) all_6_2 = e1
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | REDUCE: (74), (89) imply:
% 115.61/17.72 | | | | | (90) $false
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | CLOSE: (90) is inconsistent.
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | Case 2:
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | (91) all_54_10 = e0
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | COMBINE_EQS: (17), (91) imply:
% 115.61/17.72 | | | | | (92) all_6_2 = e0
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | COMBINE_EQS: (4), (92) imply:
% 115.61/17.72 | | | | | (93) all_56_14 = e0
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | REDUCE: (27), (92) imply:
% 115.61/17.72 | | | | | (94) ~ (all_52_11 = e0)
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | REDUCE: (12), (92) imply:
% 115.61/17.72 | | | | | (95) ~ (all_52_14 = e0)
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | BETA: splitting (7) gives:
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | | Case 1:
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | (96) ~ (all_56_8 = e1)
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | REDUCE: (66), (96) imply:
% 115.61/17.72 | | | | | | (97) ~ (all_52_14 = e1)
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | BETA: splitting (23) gives:
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | Case 1:
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | (98) ~ (all_56_2 = e3)
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | REDUCE: (19), (98) imply:
% 115.61/17.72 | | | | | | | (99) ~ (all_52_12 = e3)
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | BETA: splitting (31) gives:
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | Case 1:
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | (100) ~ (all_56_5 = e2)
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | REDUCE: (56), (100) imply:
% 115.61/17.72 | | | | | | | | (101) ~ (all_52_13 = e2)
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | BETA: splitting (50) gives:
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | Case 1:
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | (102) all_58_6 = e1
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | COMBINE_EQS: (42), (102) imply:
% 115.61/17.72 | | | | | | | | | (103) all_52_2 = e1
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | SIMP: (103) implies:
% 115.61/17.72 | | | | | | | | | (104) all_52_2 = e1
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | COMBINE_EQS: (59), (104) imply:
% 115.61/17.72 | | | | | | | | | (105) all_56_6 = e1
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | REDUCE: (25), (104) imply:
% 115.61/17.72 | | | | | | | | | (106) ~ (all_52_3 = e1)
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | SIMP: (106) implies:
% 115.61/17.72 | | | | | | | | | (107) ~ (all_52_3 = e1)
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | REDUCE: (1), (104) imply:
% 115.61/17.72 | | | | | | | | | (108) ~ (all_10_2 = e1)
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | SIMP: (108) implies:
% 115.61/17.72 | | | | | | | | | (109) ~ (all_10_2 = e1)
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | REF_CLOSE: (3), (5), (8), (9), (10), (11), (15), (16), (21),
% 115.61/17.72 | | | | | | | | | (22), (24), (28), (29), (32), (33), (35), (36),
% 115.61/17.72 | | | | | | | | | (37), (38), (39), (40), (43), (45), (46), (47),
% 115.61/17.72 | | | | | | | | | (48), (51), (53), (54), (55), (57), (58), (60),
% 115.61/17.72 | | | | | | | | | (61), (62), (63), (64), (66), (69), (70), (71),
% 115.61/17.72 | | | | | | | | | (73), (75), (76), (94), (95), (99), (101), (105),
% 115.61/17.72 | | | | | | | | | (107), (109) are inconsistent by sub-proof #135.
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | Case 2:
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | (110) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | | REF_CLOSE: (2), (24), (52), (67), (74), (97), (110) are
% 115.61/17.72 | | | | | | | | | inconsistent by sub-proof #354.
% 115.61/17.72 | | | | | | | | |
% 115.61/17.72 | | | | | | | | End of split
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | Case 2:
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | (111) all_56_5 = e2
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | | REF_CLOSE: (4), (17), (31), (49), (74), (82), (111) are
% 115.61/17.72 | | | | | | | | inconsistent by sub-proof #434.
% 115.61/17.72 | | | | | | | |
% 115.61/17.72 | | | | | | | End of split
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | Case 2:
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | (112) all_56_2 = e3
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | | REF_CLOSE: (4), (17), (23), (49), (74), (82), (112) are
% 115.61/17.72 | | | | | | | inconsistent by sub-proof #351.
% 115.61/17.72 | | | | | | |
% 115.61/17.72 | | | | | | End of split
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | Case 2:
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | (113) ~ (all_56_14 = e0)
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | REDUCE: (93), (113) imply:
% 115.61/17.72 | | | | | | (114) $false
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | | CLOSE: (114) is inconsistent.
% 115.61/17.72 | | | | | |
% 115.61/17.72 | | | | | End of split
% 115.61/17.72 | | | | |
% 115.61/17.72 | | | | End of split
% 115.61/17.72 | | | |
% 115.61/17.72 | | | End of split
% 115.61/17.72 | | |
% 115.61/17.72 | | End of split
% 115.61/17.72 | |
% 115.61/17.72 | Case 2:
% 115.61/17.72 | |
% 115.61/17.72 | | (115) all_56_14 = e3
% 115.61/17.72 | | (116) ~ (all_56_9 = e0)
% 115.61/17.72 | |
% 115.61/17.72 | | COMBINE_EQS: (4), (115) imply:
% 115.61/17.72 | | (117) all_6_2 = e3
% 115.61/17.72 | |
% 115.61/17.72 | | SIMP: (117) implies:
% 115.61/17.72 | | (118) all_6_2 = e3
% 115.61/17.72 | |
% 115.61/17.72 | | COMBINE_EQS: (52), (118) imply:
% 115.61/17.72 | | (119) all_58_8 = e3
% 115.61/17.72 | |
% 115.61/17.72 | | REDUCE: (34), (116) imply:
% 115.61/17.72 | | (120) ~ (all_52_3 = e0)
% 115.61/17.72 | |
% 115.61/17.72 | | REDUCE: (74), (118) imply:
% 115.61/17.72 | | (121) ~ (e3 = e1)
% 115.61/17.72 | |
% 115.61/17.72 | | REF_CLOSE: (2), (3), (5), (6), (11), (13), (16), (18), (20), (24), (30),
% 115.61/17.72 | | (35), (37), (39), (40), (41), (42), (44), (46), (50), (53), (59),
% 115.61/17.72 | | (62), (65), (66), (67), (68), (71), (72), (115), (119), (120),
% 115.61/17.72 | | (121) are inconsistent by sub-proof #359.
% 115.61/17.72 | |
% 115.61/17.72 | End of split
% 115.61/17.72 |
% 115.61/17.72 End of proof
% 115.61/17.72
% 115.61/17.72 Sub-proof #135 shows that the following formulas are inconsistent:
% 115.61/17.72 ----------------------------------------------------------------
% 115.61/17.72 (1) ~ (all_4_2 = e0)
% 115.61/17.72 (2) all_54_0 = all_10_2
% 115.61/17.72 (3) ~ (all_52_12 = all_10_2)
% 115.61/17.72 (4) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.61/17.72 (5) ~ (all_52_14 = e0)
% 115.61/17.72 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.72 (7) all_56_12 = all_10_2
% 115.61/17.72 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.61/17.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.61/17.72 (9) ~ (all_10_2 = e2)
% 115.61/17.72 (10) all_58_3 = all_8_2
% 115.61/17.72 (11) all_54_6 = all_52_9
% 115.61/17.72 (12) all_58_11 = all_52_14
% 115.61/17.72 (13) all_56_6 = e1
% 115.61/17.72 (14) ~ (all_10_2 = e1)
% 115.61/17.72 (15) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 115.61/17.72 (16) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 115.61/17.72 (17) ~ (all_52_7 = all_8_2)
% 115.61/17.72 (18) all_58_5 = all_52_9
% 115.61/17.72 (19) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.61/17.72 (20) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 115.61/17.72 (21) all_58_15 = all_4_2
% 115.61/17.72 (22) all_58_2 = all_52_1
% 115.61/17.72 (23) ~ (all_10_2 = e3)
% 115.61/17.72 (24) all_58_13 = all_52_7
% 115.61/17.72 (25) all_54_5 = all_8_2
% 115.61/17.72 (26) ~ (all_52_13 = e2)
% 115.61/17.72 (27) ~ (all_52_12 = e3)
% 115.61/17.72 (28) all_58_10 = all_52_13
% 115.61/17.72 (29) all_58_14 = all_52_11
% 115.61/17.72 (30) all_56_13 = all_8_2
% 115.61/17.72 (31) ~ (all_8_2 = e2)
% 115.61/17.72 (32) ~ (all_52_1 = all_52_3)
% 115.61/17.72 (33) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.72 (34) all_56_4 = all_52_9
% 115.61/17.72 (35) all_58_9 = all_52_12
% 115.61/17.72 (36) op(e2, e1) = all_52_9
% 115.61/17.72 (37) ~ (all_52_3 = all_4_2)
% 115.61/17.72 (38) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 115.61/17.72 (39) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.72 (40) all_58_12 = all_52_3
% 115.61/17.72 (41) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.61/17.72 (42) ~ (all_52_3 = all_10_2)
% 115.61/17.72 (43) ~ (all_52_3 = e1)
% 115.61/17.72 (44) all_56_8 = all_52_14
% 115.61/17.72 (45) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.61/17.72 (46) ~ (e3 = e2)
% 115.61/17.72 (47) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.61/17.72 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.61/17.72 (48) ~ (all_52_11 = e0)
% 115.61/17.72 (49) op(e2, all_8_2) = e1
% 115.61/17.72 (50) all_54_12 = all_52_3
% 115.61/17.72 (51) ~ (all_52_3 = all_52_7)
% 115.61/17.72
% 115.61/17.72 Begin of proof
% 115.61/17.72 |
% 115.61/17.72 | BETA: splitting (33) gives:
% 115.61/17.72 |
% 115.61/17.72 | Case 1:
% 115.61/17.72 | |
% 115.61/17.72 | | (52) all_54_0 = e3
% 115.61/17.72 | |
% 115.61/17.72 | | REF_CLOSE: (2), (23), (52) are inconsistent by sub-proof #451.
% 115.61/17.72 | |
% 115.61/17.72 | Case 2:
% 115.61/17.72 | |
% 115.61/17.72 | | (53) ~ (all_54_0 = e3)
% 115.61/17.72 | | (54) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.61/17.72 | |
% 115.61/17.72 | | BETA: splitting (54) gives:
% 115.61/17.72 | |
% 115.61/17.72 | | Case 1:
% 115.61/17.72 | | |
% 115.61/17.72 | | | (55) all_54_0 = e2
% 115.61/17.72 | | |
% 115.61/17.72 | | | REF_CLOSE: (2), (9), (55) are inconsistent by sub-proof #450.
% 115.61/17.72 | | |
% 115.61/17.72 | | Case 2:
% 115.61/17.72 | | |
% 115.61/17.72 | | | (56) ~ (all_54_0 = e2)
% 115.61/17.72 | | | (57) all_54_0 = e1 | all_54_0 = e0
% 115.61/17.72 | | |
% 115.61/17.73 | | | BETA: splitting (57) gives:
% 115.61/17.73 | | |
% 115.61/17.73 | | | Case 1:
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | (58) all_54_0 = e1
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | REF_CLOSE: (2), (14), (58) are inconsistent by sub-proof #449.
% 115.61/17.73 | | | |
% 115.61/17.73 | | | Case 2:
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | (59) all_54_0 = e0
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | COMBINE_EQS: (2), (59) imply:
% 115.61/17.73 | | | | (60) all_10_2 = e0
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | SIMP: (60) implies:
% 115.61/17.73 | | | | (61) all_10_2 = e0
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | REDUCE: (42), (61) imply:
% 115.61/17.73 | | | | (62) ~ (all_52_3 = e0)
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | REDUCE: (3), (61) imply:
% 115.61/17.73 | | | | (63) ~ (all_52_12 = e0)
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | REDUCE: (23), (61) imply:
% 115.61/17.73 | | | | (64) ~ (e3 = e0)
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | SIMP: (64) implies:
% 115.61/17.73 | | | | (65) ~ (e3 = e0)
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | BETA: splitting (20) gives:
% 115.61/17.73 | | | |
% 115.61/17.73 | | | | Case 1:
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | (66) ~ (all_56_6 = e1)
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | REDUCE: (13), (66) imply:
% 115.61/17.73 | | | | | (67) $false
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | CLOSE: (67) is inconsistent.
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | Case 2:
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | (68) ~ (all_56_13 = e3)
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | REDUCE: (30), (68) imply:
% 115.61/17.73 | | | | | (69) ~ (all_8_2 = e3)
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | BETA: splitting (47) gives:
% 115.61/17.73 | | | | |
% 115.61/17.73 | | | | | Case 1:
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | (70) all_58_15 = e0
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | COMBINE_EQS: (21), (70) imply:
% 115.61/17.73 | | | | | | (71) all_4_2 = e0
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | REDUCE: (1), (71) imply:
% 115.61/17.73 | | | | | | (72) $false
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | CLOSE: (72) is inconsistent.
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | Case 2:
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | (73) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.61/17.73 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | ALPHA: (73) implies:
% 115.61/17.73 | | | | | | (74) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.61/17.73 | | | | | | (75) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | BETA: splitting (74) gives:
% 115.61/17.73 | | | | | |
% 115.61/17.73 | | | | | | Case 1:
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | | (76) all_58_12 = e0
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | | REF_CLOSE: (40), (62), (76) are inconsistent by sub-proof #362.
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | Case 2:
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | | (77) all_58_13 = e0 | all_58_14 = e0
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | | BETA: splitting (77) gives:
% 115.61/17.73 | | | | | | |
% 115.61/17.73 | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | (78) all_58_13 = e0
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | COMBINE_EQS: (24), (78) imply:
% 115.61/17.73 | | | | | | | | (79) all_52_7 = e0
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | SIMP: (79) implies:
% 115.61/17.73 | | | | | | | | (80) all_52_7 = e0
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | REDUCE: (17), (80) imply:
% 115.61/17.73 | | | | | | | | (81) ~ (all_8_2 = e0)
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | SIMP: (81) implies:
% 115.61/17.73 | | | | | | | | (82) ~ (all_8_2 = e0)
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | BETA: splitting (6) gives:
% 115.61/17.73 | | | | | | | |
% 115.61/17.73 | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | | (83) all_54_5 = e3
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | | REF_CLOSE: (25), (69), (83) are inconsistent by sub-proof
% 115.61/17.73 | | | | | | | | | #339.
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | | (84) ~ (all_54_5 = e3)
% 115.61/17.73 | | | | | | | | | (85) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | | BETA: splitting (85) gives:
% 115.61/17.73 | | | | | | | | |
% 115.61/17.73 | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | (86) all_54_5 = e2
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | REF_CLOSE: (25), (31), (86) are inconsistent by sub-proof
% 115.61/17.73 | | | | | | | | | | #338.
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | (87) ~ (all_54_5 = e2)
% 115.61/17.73 | | | | | | | | | | (88) all_54_5 = e1 | all_54_5 = e0
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | BETA: splitting (16) gives:
% 115.61/17.73 | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | (89) all_58_9 = e3
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | COMBINE_EQS: (35), (89) imply:
% 115.61/17.73 | | | | | | | | | | | (90) all_52_12 = e3
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | REDUCE: (27), (90) imply:
% 115.61/17.73 | | | | | | | | | | | (91) $false
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | CLOSE: (91) is inconsistent.
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | (92) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | BETA: splitting (88) gives:
% 115.61/17.73 | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | (93) all_54_5 = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | COMBINE_EQS: (25), (93) imply:
% 115.61/17.73 | | | | | | | | | | | | (94) all_8_2 = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | SIMP: (94) implies:
% 115.61/17.73 | | | | | | | | | | | | (95) all_8_2 = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | COMBINE_EQS: (30), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (96) all_56_13 = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | COMBINE_EQS: (10), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (97) all_58_3 = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | REDUCE: (69), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (98) ~ (e3 = e1)
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | SIMP: (98) implies:
% 115.61/17.73 | | | | | | | | | | | | (99) ~ (e3 = e1)
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | REDUCE: (31), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (100) ~ (e2 = e1)
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | SIMP: (100) implies:
% 115.61/17.73 | | | | | | | | | | | | (101) ~ (e2 = e1)
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | REDUCE: (82), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (102) ~ (e1 = e0)
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | REDUCE: (49), (95) imply:
% 115.61/17.73 | | | | | | | | | | | | (103) op(e2, e1) = e1
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | BETA: splitting (4) gives:
% 115.61/17.73 | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | (104) ~ (all_56_4 = e2)
% 115.61/17.73 | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | REDUCE: (34), (104) imply:
% 115.61/17.73 | | | | | | | | | | | | | (105) ~ (all_52_9 = e2)
% 115.61/17.73 | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | BETA: splitting (38) gives:
% 115.61/17.73 | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | (106) all_54_6 = e3
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | COMBINE_EQS: (11), (106) imply:
% 115.61/17.73 | | | | | | | | | | | | | | (107) all_52_9 = e3
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | SIMP: (107) implies:
% 115.61/17.73 | | | | | | | | | | | | | | (108) all_52_9 = e3
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | REDUCE: (36), (108) imply:
% 115.61/17.73 | | | | | | | | | | | | | | (109) op(e2, e1) = e3
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | (110) all_58_2 = e2
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | COMBINE_EQS: (22), (110) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | (111) all_52_1 = e2
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | REDUCE: (32), (111) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | (112) ~ (all_52_3 = e2)
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | SIMP: (112) implies:
% 115.61/17.73 | | | | | | | | | | | | | | | (113) ~ (all_52_3 = e2)
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | (114) all_54_12 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (114) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | (115) all_52_3 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (115) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | (116) all_58_12 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | REDUCE: (37), (115) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | (117) ~ (all_4_2 = e3)
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | SIMP: (117) implies:
% 115.61/17.73 | | | | | | | | | | | | | | | | (118) ~ (all_4_2 = e3)
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | (119) all_58_10 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (35), (63), (65), (75), (119) are
% 115.61/17.73 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | (120) all_58_11 = e3 | all_58_15 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (121) all_58_11 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (121) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (122) all_52_14 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (122) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (123) all_56_8 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | (124) all_58_12 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (124) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | (125) e3 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (125) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | (126) all_56_8 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (9), (14), (19), (54), (126) are
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #385.
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | (127) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (128) all_58_13 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (128) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (129) e1 = e0
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | SIMP: (129) implies:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (130) e1 = e0
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (130) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (131) $false
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e1, e3, e1, e2, simplifying
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | with (103), (109) gives:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (132) e3 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (132) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | (133) all_56_8 = e1
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (9), (14), (19), (54), (133) are
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #385.
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (134) all_58_15 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (134) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (135) all_4_2 = e3
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | REDUCE: (118), (135) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | | | | (136) $false
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 115.61/17.73 | | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | (137) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (50), (62), (113), (137) are inconsistent by
% 115.61/17.73 | | | | | | | | | | | | | | | | sub-proof #406.
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | (138) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | (139) all_58_3 = e2
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | REF_CLOSE: (97), (101), (139) are inconsistent by sub-proof
% 115.61/17.73 | | | | | | | | | | | | | | | | #439.
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | (140) all_58_5 = e2 | all_58_10 = e2
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (26), (28), (105), (140) are inconsistent by
% 115.61/17.73 | | | | | | | | | | | | | | | | sub-proof #402.
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | End of split
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | Case 2:
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | (141) ~ (all_54_6 = e3)
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | REDUCE: (11), (141) imply:
% 115.61/17.73 | | | | | | | | | | | | | | (142) ~ (all_52_9 = e3)
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 115.61/17.73 | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | (143) all_58_2 = e2
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | COMBINE_EQS: (22), (143) imply:
% 115.61/17.73 | | | | | | | | | | | | | | | (144) all_52_1 = e2
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 115.61/17.73 | | | | | | | | | | | | | | |
% 115.61/17.73 | | | | | | | | | | | | | | | Case 1:
% 115.61/17.73 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | (145) all_58_2 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (145) imply:
% 115.61/17.74 | | | | | | | | | | | | | | | | (146) e3 = e2
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | SIMP: (146) implies:
% 115.61/17.74 | | | | | | | | | | | | | | | | (147) e3 = e2
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | REDUCE: (46), (147) imply:
% 115.61/17.74 | | | | | | | | | | | | | | | | (148) $false
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | Case 2:
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | (149) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | (150) all_58_3 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (99), (150) are inconsistent by sub-proof
% 115.61/17.74 | | | | | | | | | | | | | | | | | #266.
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | (151) all_58_5 = e3 | all_58_10 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | Case 1:
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | (152) all_58_5 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (152) imply:
% 115.61/17.74 | | | | | | | | | | | | | | | | | | (153) all_52_9 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | REDUCE: (142), (153) imply:
% 115.61/17.74 | | | | | | | | | | | | | | | | | | (154) $false
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | Case 2:
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | (155) all_58_10 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (155) imply:
% 115.61/17.74 | | | | | | | | | | | | | | | | | | (156) all_52_13 = e3
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (35), (63), (65), (75), (155) are
% 115.61/17.74 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #136.
% 115.61/17.74 | | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | | End of split
% 115.61/17.74 | | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | | End of split
% 115.61/17.74 | | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | | End of split
% 115.61/17.74 | | | | | | | | | | | | | | |
% 115.61/17.74 | | | | | | | | | | | | | | Case 2:
% 115.61/17.74 | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | (157) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.92/17.74 | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 115.92/17.74 | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | | (158) all_58_3 = e2
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | | REF_CLOSE: (97), (101), (158) are inconsistent by sub-proof
% 115.92/17.74 | | | | | | | | | | | | | | | | #439.
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | | (159) all_58_5 = e2 | all_58_10 = e2
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (26), (28), (105), (159) are inconsistent by
% 115.92/17.74 | | | | | | | | | | | | | | | | sub-proof #402.
% 115.92/17.74 | | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | Case 2:
% 115.92/17.74 | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | (160) ~ (all_56_13 = e1)
% 115.92/17.74 | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | REDUCE: (96), (160) imply:
% 115.92/17.74 | | | | | | | | | | | | | (161) $false
% 115.92/17.74 | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 115.92/17.74 | | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | Case 2:
% 115.92/17.74 | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | (162) all_54_5 = e0
% 115.92/17.74 | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | | REF_CLOSE: (25), (82), (162) are inconsistent by sub-proof
% 115.92/17.74 | | | | | | | | | | | | #311.
% 115.92/17.74 | | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | | |
% 115.92/17.74 | | | | | | | | | End of split
% 115.92/17.74 | | | | | | | | |
% 115.92/17.74 | | | | | | | | End of split
% 115.92/17.74 | | | | | | | |
% 115.92/17.74 | | | | | | | Case 2:
% 115.92/17.74 | | | | | | | |
% 115.92/17.74 | | | | | | | | (163) all_58_14 = e0
% 115.92/17.74 | | | | | | | |
% 115.92/17.74 | | | | | | | | REF_CLOSE: (29), (48), (163) are inconsistent by sub-proof #429.
% 115.92/17.74 | | | | | | | |
% 115.92/17.74 | | | | | | | End of split
% 115.92/17.74 | | | | | | |
% 115.92/17.74 | | | | | | End of split
% 115.92/17.74 | | | | | |
% 115.92/17.74 | | | | | End of split
% 115.92/17.74 | | | | |
% 115.92/17.74 | | | | End of split
% 115.92/17.74 | | | |
% 115.92/17.74 | | | End of split
% 115.92/17.74 | | |
% 115.92/17.74 | | End of split
% 115.92/17.74 | |
% 115.92/17.74 | End of split
% 115.92/17.74 |
% 115.92/17.74 End of proof
% 115.92/17.74
% 115.92/17.74 Sub-proof #136 shows that the following formulas are inconsistent:
% 115.92/17.74 ----------------------------------------------------------------
% 115.92/17.74 (1) ~ (all_52_14 = e0)
% 115.92/17.74 (2) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 115.92/17.74 (3) ~ (all_52_12 = e0)
% 115.92/17.74 (4) all_58_11 = all_52_14
% 115.92/17.74 (5) ~ (e3 = e0)
% 115.92/17.74 (6) all_58_10 = e3
% 115.92/17.74 (7) all_58_9 = all_52_12
% 115.92/17.74
% 115.92/17.74 Begin of proof
% 115.92/17.74 |
% 115.92/17.74 | BETA: splitting (2) gives:
% 115.92/17.74 |
% 115.92/17.74 | Case 1:
% 115.92/17.74 | |
% 115.92/17.74 | | (8) all_58_9 = e0
% 115.92/17.74 | |
% 115.92/17.74 | | COMBINE_EQS: (7), (8) imply:
% 115.92/17.74 | | (9) all_52_12 = e0
% 115.92/17.74 | |
% 115.92/17.74 | | REDUCE: (3), (9) imply:
% 115.92/17.74 | | (10) $false
% 115.92/17.74 | |
% 115.92/17.74 | | CLOSE: (10) is inconsistent.
% 115.92/17.74 | |
% 115.92/17.74 | Case 2:
% 115.92/17.74 | |
% 115.92/17.74 | | (11) all_58_10 = e0 | all_58_11 = e0
% 115.92/17.74 | |
% 115.92/17.74 | | BETA: splitting (11) gives:
% 115.92/17.74 | |
% 115.92/17.74 | | Case 1:
% 115.92/17.74 | | |
% 115.92/17.74 | | | (12) all_58_10 = e0
% 115.92/17.74 | | |
% 115.92/17.74 | | | COMBINE_EQS: (6), (12) imply:
% 115.92/17.74 | | | (13) e3 = e0
% 115.92/17.74 | | |
% 115.92/17.74 | | | REDUCE: (5), (13) imply:
% 115.92/17.74 | | | (14) $false
% 115.92/17.74 | | |
% 115.92/17.74 | | | CLOSE: (14) is inconsistent.
% 115.92/17.74 | | |
% 115.92/17.74 | | Case 2:
% 115.92/17.74 | | |
% 115.92/17.74 | | | (15) all_58_11 = e0
% 115.92/17.74 | | |
% 115.92/17.74 | | | COMBINE_EQS: (4), (15) imply:
% 115.92/17.74 | | | (16) all_52_14 = e0
% 115.92/17.74 | | |
% 115.92/17.74 | | | REDUCE: (1), (16) imply:
% 115.92/17.74 | | | (17) $false
% 115.92/17.74 | | |
% 115.92/17.74 | | | CLOSE: (17) is inconsistent.
% 115.92/17.74 | | |
% 115.92/17.74 | | End of split
% 115.92/17.74 | |
% 115.92/17.74 | End of split
% 115.92/17.74 |
% 115.92/17.74 End of proof
% 115.92/17.74
% 115.92/17.74 Sub-proof #137 shows that the following formulas are inconsistent:
% 115.92/17.74 ----------------------------------------------------------------
% 115.92/17.74 (1) ~ (all_52_8 = all_10_2)
% 115.92/17.74 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 115.92/17.74 (3) ~ (all_52_2 = all_10_2)
% 115.92/17.74 (4) ~ (all_52_6 = all_52_14)
% 115.92/17.74 (5) all_54_2 = all_52_8
% 115.92/17.74 (6) all_58_7 = all_52_6
% 115.92/17.74 (7) all_36_2 = all_6_2
% 115.92/17.74 (8) ~ (all_52_8 = all_52_11)
% 115.92/17.74 (9) ~ (all_52_9 = all_8_2)
% 115.92/17.74 (10) all_28_1 = all_6_1
% 115.92/17.74 (11) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 115.92/17.74 (12) ~ (all_52_13 = all_52_14)
% 115.92/17.74 (13) ~ (all_4_2 = e0)
% 115.92/17.74 (14) op(e3, e2) = all_52_4
% 115.92/17.74 (15) all_56_14 = all_6_2
% 115.92/17.74 (16) all_56_3 = all_52_1
% 115.92/17.74 (17) all_54_0 = all_10_2
% 115.92/17.74 (18) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 115.92/17.74 (19) all_54_3 = all_52_12
% 115.92/17.74 (20) ~ (all_52_2 = all_52_6)
% 115.92/17.74 (21) ~ (all_52_12 = all_52_14)
% 115.92/17.74 (22) op(e0, e2) = all_52_7
% 115.92/17.74 (23) ~ (all_52_7 = all_4_2)
% 115.92/17.74 (24) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 115.92/17.74 (25) all_56_11 = all_52_11
% 115.92/17.74 (26) all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 115.92/17.74 (27) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 115.92/17.74 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 115.92/17.74 (29) ~ (all_52_4 = all_52_8)
% 115.92/17.74 (30) ~ (all_52_12 = all_10_2)
% 115.92/17.74 (31) ~ (e3 = e1)
% 115.92/17.74 (32) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 115.92/17.74 (33) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 115.92/17.74 (34) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 115.92/17.74 (35) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.92/17.74 (36) all_56_12 = all_10_2
% 115.92/17.74 (37) all_58_0 = all_10_2
% 115.92/17.74 (38) op(all_6_1, all_6_2) = all_6_0
% 115.92/17.74 (39) all_54_11 = all_52_14
% 115.92/17.74 (40) all_54_13 = all_52_7
% 115.92/17.74 (41) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 115.92/17.74 (42) all_36_1 = all_6_1
% 115.92/17.74 (43) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.92/17.74 (44) ~ (all_52_14 = all_6_2)
% 115.92/17.74 (45) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 115.92/17.74 (46) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 115.92/17.74 (47) all_56_10 = all_52_7
% 115.92/17.74 (48) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 115.92/17.74 (49) all_54_14 = all_52_11
% 115.92/17.74 (50) op(all_4_1, all_4_2) = all_4_0
% 115.92/17.74 (51) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.92/17.74 (52) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 115.92/17.74 (53) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.92/17.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 115.92/17.74 (54) all_54_8 = all_52_2
% 115.92/17.74 (55) ~ (all_52_2 = all_6_2)
% 115.92/17.74 (56) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 115.92/17.74 (57) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 115.92/17.74 (58) all_44_2 = all_4_2
% 115.92/17.74 (59) all_54_10 = all_6_2
% 115.92/17.74 (60) ~ (e2 = e1)
% 115.92/17.74 (61) all_36_0 = all_6_0
% 115.92/17.74 (62) op(e3, e0) = all_52_12
% 115.92/17.74 (63) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 115.92/17.74 (64) ~ (all_52_8 = all_6_2)
% 115.92/17.74 (65) all_58_4 = all_52_8
% 115.92/17.74 (66) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 115.92/17.74 (67) all_50_1 = all_10_1
% 115.92/17.74 (68) ~ (all_52_4 = all_52_7)
% 115.92/17.74 (69) all_56_2 = all_52_12
% 115.92/17.74 (70) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 115.92/17.74 (71) all_58_3 = all_8_2
% 115.92/17.74 (72) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 115.92/17.74 (73) all_10_0 = e2
% 115.92/17.74 (74) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 115.92/17.74 (75) all_58_11 = all_52_14
% 115.92/17.74 (76) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 115.92/17.74 (77) all_54_9 = all_52_6
% 115.92/17.74 (78) op(e3, e1) = all_52_8
% 115.92/17.74 (79) ~ (all_52_2 = all_52_3)
% 115.92/17.74 (80) all_54_7 = all_52_13
% 115.92/17.74 (81) op(all_10_1, all_10_2) = all_10_0
% 115.92/17.74 (82) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 115.92/17.74 (83) ~ (all_52_11 = all_6_2)
% 115.92/17.74 (84) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 115.92/17.74 (85) op(e2, e3) = all_52_1
% 115.92/17.74 (86) all_28_2 = all_6_2
% 115.92/17.74 (87) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 115.92/17.74 (88) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 115.92/17.74 (89) all_44_0 = all_4_0
% 115.92/17.74 (90) all_50_2 = all_10_2
% 115.92/17.74 (91) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 115.92/17.74 (92) ~ (all_52_7 = all_8_2)
% 115.92/17.75 (93) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.92/17.75 (94) ~ (all_52_4 = all_8_2)
% 115.92/17.75 (95) op(e1, e0) = all_52_14
% 115.92/17.75 (96) all_58_5 = all_52_9
% 115.92/17.75 (97) ~ (all_52_9 = all_52_13)
% 115.92/17.75 (98) all_40_0 = all_6_0
% 115.92/17.75 (99) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 115.92/17.75 (100) all_56_9 = all_52_3
% 115.92/17.75 (101) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 115.92/17.75 (102) op(e1, all_6_2) = all_6_1
% 115.92/17.75 (103) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 115.92/17.75 (104) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 115.92/17.75 (105) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 115.92/17.75 (106) all_58_15 = all_4_2
% 115.92/17.75 (107) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 115.92/17.75 (108) all_58_2 = all_52_1
% 115.92/17.75 (109) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 115.92/17.75 (110) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 115.92/17.75 (111) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 115.92/17.75 (112) op(e0, e3) = all_52_3
% 115.92/17.75 (113) ~ (all_10_2 = e3)
% 115.92/17.75 (114) ~ (all_52_12 = all_52_13)
% 115.92/17.75 (115) all_58_13 = all_52_7
% 115.92/17.75 (116) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 115.92/17.75 (117) all_40_1 = all_6_1
% 115.92/17.75 (118) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 115.92/17.75 (119) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 115.92/17.75 (120) ~ (all_52_14 = all_4_2)
% 115.92/17.75 (121) all_58_6 = all_52_2
% 115.92/17.75 (122) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 115.92/17.75 (123) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 115.92/17.75 (124) ~ (all_52_1 = all_10_2)
% 115.92/17.75 (125) all_54_5 = all_8_2
% 115.92/17.75 (126) all_56_15 = all_4_2
% 115.92/17.75 (127) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 115.92/17.75 (128) all_58_10 = all_52_13
% 115.92/17.75 (129) ~ (all_52_13 = all_8_2)
% 115.92/17.75 (130) op(e2, all_8_2) = all_8_1
% 115.92/17.75 (131) ~ (all_52_11 = all_4_2)
% 115.92/17.75 (132) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 115.92/17.75 (133) op(e3, all_10_2) = all_10_1
% 115.92/17.75 (134) all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 115.92/17.75 (135) ~ (all_52_6 = all_8_2)
% 115.92/17.75 (136) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 115.92/17.75 (137) all_28_0 = all_6_0
% 115.92/17.75 (138) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 115.92/17.75 (139) all_58_1 = all_52_4
% 115.92/17.75 (140) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 115.92/17.75 (141) all_58_14 = all_52_11
% 115.92/17.75 (142) all_54_1 = all_52_4
% 115.92/17.75 (143) all_56_13 = all_8_2
% 115.92/17.75 (144) op(e0, e1) = all_52_11
% 115.92/17.75 (145) ~ (all_52_1 = all_8_2)
% 115.92/17.75 (146) ~ (all_8_2 = e2)
% 115.92/17.75 (147) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 115.92/17.75 (148) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 115.92/17.75 (149) op(e1, e2) = all_52_6
% 115.92/17.75 (150) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 115.92/17.75 (151) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.92/17.75 (152) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 115.92/17.75 (153) all_56_7 = all_52_6
% 115.92/17.75 (154) ~ (all_52_9 = all_6_2)
% 115.92/17.75 (155) ~ (all_52_4 = all_52_6)
% 115.92/17.75 (156) ~ (all_52_1 = all_52_2)
% 115.92/17.75 (157) all_26_2 = all_4_2
% 115.92/17.75 (158) ~ (all_52_4 = all_52_12)
% 115.92/17.75 (159) ~ (all_52_1 = all_52_3)
% 115.92/17.75 (160) all_56_1 = all_52_8
% 115.92/17.75 (161) op(e0, all_4_2) = all_4_1
% 115.92/17.75 (162) all_58_8 = all_6_2
% 115.92/17.75 (163) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.92/17.75 (164) all_50_0 = all_10_0
% 115.92/17.75 (165) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 115.92/17.75 (166) all_40_2 = all_6_2
% 115.92/17.75 (167) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 115.92/17.75 (168) all_56_4 = all_52_9
% 115.92/17.75 (169) all_58_9 = all_52_12
% 115.92/17.75 (170) all_56_5 = all_52_13
% 115.92/17.75 (171) op(e2, e1) = all_52_9
% 115.92/17.75 (172) ~ (all_52_3 = all_4_2)
% 115.92/17.75 (173) ~ (all_52_6 = all_6_2)
% 115.92/17.75 (174) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 115.92/17.75 (175) all_56_6 = all_52_2
% 115.92/17.75 (176) ~ (all_52_13 = all_4_2)
% 115.92/17.75 (177) all_58_12 = all_52_3
% 115.92/17.75 (178) ~ (all_52_2 = all_52_14)
% 115.92/17.75 (179) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 115.92/17.75 (180) ~ (all_52_8 = all_52_9)
% 115.92/17.75 (181) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 115.92/17.75 (182) op(e2, e0) = all_52_13
% 115.92/17.75 (183) ~ (all_52_12 = all_4_2)
% 115.92/17.75 (184) ~ (all_52_3 = all_10_2)
% 115.92/17.75 (185) op(e1, e3) = all_52_2
% 115.92/17.75 (186) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 115.92/17.75 (187) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 115.92/17.75 (188) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.92/17.75 (189) all_44_1 = all_4_1
% 115.92/17.75 (190) ~ (all_8_1 = e1)
% 115.92/17.75 (191) ~ (all_52_8 = all_52_12)
% 115.92/17.75 (192) all_56_8 = all_52_14
% 115.92/17.75 (193) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 115.92/17.75 (194) all_26_1 = all_4_1
% 115.92/17.75 (195) ~ (all_52_4 = all_10_2)
% 115.92/17.75 (196) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 115.92/17.75 (197) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.92/17.75 (198) all_56_0 = all_52_4
% 115.92/17.75 (199) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 115.92/17.75 (200) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 115.92/17.75 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 115.92/17.75 (201) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 115.92/17.75 (202) all_54_4 = all_52_1
% 115.92/17.75 (203) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 115.92/17.75 (204) all_54_15 = all_4_2
% 115.92/17.75 (205) ~ (all_6_2 = e1)
% 115.92/17.75 (206) ~ (all_6_1 = e2)
% 115.92/17.75 (207) ~ (all_52_6 = all_52_7)
% 115.92/17.75 (208) ~ (all_52_3 = all_52_11)
% 115.92/17.75 (209) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 115.92/17.75 (210) all_54_12 = all_52_3
% 115.92/17.75 (211) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 115.92/17.75 (212) ~ (all_52_3 = all_52_7)
% 115.92/17.75 (213) all_26_0 = all_4_0
% 115.92/17.75
% 115.92/17.75 Begin of proof
% 115.92/17.75 |
% 115.92/17.75 | COMBINE_EQS: (73), (164) imply:
% 115.92/17.75 | (214) all_50_0 = e2
% 115.92/17.75 |
% 115.92/17.75 | REDUCE: (73), (81) imply:
% 115.92/17.75 | (215) op(all_10_1, all_10_2) = e2
% 115.92/17.75 |
% 115.92/17.75 | BETA: splitting (193) gives:
% 115.92/17.75 |
% 115.92/17.75 | Case 1:
% 115.92/17.75 | |
% 115.92/17.75 | | (216) ~ (all_26_0 = e1)
% 115.92/17.75 | |
% 115.92/17.75 | | REDUCE: (213), (216) imply:
% 115.92/17.75 | | (217) ~ (all_4_0 = e1)
% 115.92/17.75 | |
% 115.92/17.75 | | BETA: splitting (123) gives:
% 115.92/17.75 | |
% 115.92/17.75 | | Case 1:
% 115.92/17.75 | | |
% 115.92/17.75 | | | (218) ~ (all_28_0 = e2)
% 115.92/17.75 | | |
% 115.92/17.75 | | | REDUCE: (137), (218) imply:
% 115.92/17.75 | | | (219) ~ (all_6_0 = e2)
% 115.92/17.75 | | |
% 115.92/17.75 | | | BETA: splitting (138) gives:
% 115.92/17.75 | | |
% 115.92/17.75 | | | Case 1:
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | (220) ~ (all_36_1 = e3)
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | REDUCE: (42), (220) imply:
% 115.92/17.75 | | | | (221) ~ (all_6_1 = e3)
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (12), (13), (14), (15), (16),
% 115.92/17.75 | | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 115.92/17.75 | | | | (28), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 115.92/17.75 | | | | (40), (41), (44), (45), (46), (47), (51), (53), (54), (55),
% 115.92/17.75 | | | | (57), (59), (62), (64), (67), (68), (69), (70), (71), (74),
% 115.92/17.75 | | | | (75), (77), (78), (82), (84), (90), (91), (92), (93), (95),
% 115.92/17.75 | | | | (96), (98), (100), (102), (103), (104), (105), (106), (108),
% 115.92/17.75 | | | | (109), (110), (111), (113), (114), (115), (116), (117),
% 115.92/17.75 | | | | (118), (119), (121), (124), (125), (126), (128), (133),
% 115.92/17.75 | | | | (135), (136), (139), (141), (142), (143), (146), (147),
% 115.92/17.75 | | | | (148), (149), (151), (152), (153), (155), (158), (161),
% 115.92/17.75 | | | | (162), (163), (166), (167), (168), (169), (170), (171),
% 115.92/17.75 | | | | (173), (174), (175), (176), (177), (178), (179), (180),
% 115.92/17.75 | | | | (182), (187), (188), (192), (195), (196), (197), (198),
% 115.92/17.75 | | | | (199), (200), (201), (203), (205), (206), (207), (214),
% 115.92/17.75 | | | | (215), (219), (221) are inconsistent by sub-proof #156.
% 115.92/17.75 | | | |
% 115.92/17.75 | | | Case 2:
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | (222) all_36_1 = e3
% 115.92/17.75 | | | | (223) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | COMBINE_EQS: (42), (222) imply:
% 115.92/17.75 | | | | (224) all_6_1 = e3
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | REDUCE: (38), (224) imply:
% 115.92/17.75 | | | | (225) op(e3, all_6_2) = all_6_0
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | REDUCE: (102), (224) imply:
% 115.92/17.75 | | | | (226) op(e1, all_6_2) = e3
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | BETA: splitting (34) gives:
% 115.92/17.75 | | | |
% 115.92/17.75 | | | | Case 1:
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | (227) ~ (all_50_0 = e2)
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | REDUCE: (214), (227) imply:
% 115.92/17.75 | | | | | (228) $false
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | CLOSE: (228) is inconsistent.
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | Case 2:
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | (229) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | BETA: splitting (118) gives:
% 115.92/17.75 | | | | |
% 115.92/17.75 | | | | | Case 1:
% 115.92/17.75 | | | | | |
% 115.92/17.75 | | | | | | (230) ~ (all_56_14 = e2)
% 115.92/17.75 | | | | | |
% 115.92/17.75 | | | | | | REDUCE: (15), (230) imply:
% 115.92/17.75 | | | | | | (231) ~ (all_6_2 = e2)
% 115.92/17.75 | | | | | |
% 115.92/17.75 | | | | | | BETA: splitting (119) gives:
% 115.92/17.75 | | | | | |
% 115.92/17.75 | | | | | | Case 1:
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | (232) ~ (all_56_12 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (36), (232) imply:
% 115.92/17.75 | | | | | | | (233) ~ (all_10_2 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | BETA: splitting (101) gives:
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | Case 1:
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | (234) ~ (all_56_15 = e1)
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | REDUCE: (126), (234) imply:
% 115.92/17.75 | | | | | | | | (235) ~ (all_4_2 = e1)
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | REF_CLOSE: (2), (5), (13), (17), (19), (28), (30), (36), (48),
% 115.92/17.75 | | | | | | | | (53), (62), (65), (66), (67), (69), (75), (78), (88),
% 115.92/17.75 | | | | | | | | (90), (96), (100), (103), (106), (109), (110), (113),
% 115.92/17.75 | | | | | | | | (114), (126), (128), (131), (133), (141), (160),
% 115.92/17.75 | | | | | | | | (162), (163), (165), (168), (169), (171), (172),
% 115.92/17.75 | | | | | | | | (174), (180), (181), (182), (184), (192), (196),
% 115.92/17.75 | | | | | | | | (204), (208), (210), (215), (229), (231), (233),
% 115.92/17.75 | | | | | | | | (235) are inconsistent by sub-proof #155.
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | Case 2:
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | (236) all_56_15 = e1
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | COMBINE_EQS: (126), (236) imply:
% 115.92/17.75 | | | | | | | | (237) all_4_2 = e1
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | SIMP: (237) implies:
% 115.92/17.75 | | | | | | | | (238) all_4_2 = e1
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | REF_CLOSE: (6), (12), (15), (16), (19), (28), (51), (53), (55),
% 115.92/17.75 | | | | | | | | (59), (62), (69), (70), (71), (72), (75), (80), (91),
% 115.92/17.75 | | | | | | | | (95), (96), (108), (114), (120), (121), (127), (128),
% 115.92/17.75 | | | | | | | | (136), (146), (151), (162), (168), (170), (175),
% 115.92/17.75 | | | | | | | | (176), (179), (183), (185), (197), (205), (211),
% 115.92/17.75 | | | | | | | | (219), (225), (226), (231), (236), (238) are
% 115.92/17.75 | | | | | | | | inconsistent by sub-proof #343.
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | End of split
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | Case 2:
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | (239) all_56_12 = e2
% 115.92/17.75 | | | | | | | (240) ~ (all_56_10 = e0)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | COMBINE_EQS: (36), (239) imply:
% 115.92/17.75 | | | | | | | (241) all_10_2 = e2
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | SIMP: (241) implies:
% 115.92/17.75 | | | | | | | (242) all_10_2 = e2
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | COMBINE_EQS: (37), (242) imply:
% 115.92/17.75 | | | | | | | (243) all_58_0 = e2
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (47), (240) imply:
% 115.92/17.75 | | | | | | | (244) ~ (all_52_7 = e0)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (124), (242) imply:
% 115.92/17.75 | | | | | | | (245) ~ (all_52_1 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (3), (242) imply:
% 115.92/17.75 | | | | | | | (246) ~ (all_52_2 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (184), (242) imply:
% 115.92/17.75 | | | | | | | (247) ~ (all_52_3 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (1), (242) imply:
% 115.92/17.75 | | | | | | | (248) ~ (all_52_8 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (30), (242) imply:
% 115.92/17.75 | | | | | | | (249) ~ (all_52_12 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (113), (242) imply:
% 115.92/17.75 | | | | | | | (250) ~ (e3 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | SIMP: (250) implies:
% 115.92/17.75 | | | | | | | (251) ~ (e3 = e2)
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | REDUCE: (133), (242) imply:
% 115.92/17.75 | | | | | | | (252) op(e3, e2) = all_10_1
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | BETA: splitting (104) gives:
% 115.92/17.75 | | | | | | |
% 115.92/17.75 | | | | | | | Case 1:
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | (253) ~ (all_56_7 = e1)
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | REDUCE: (153), (253) imply:
% 115.92/17.75 | | | | | | | | (254) ~ (all_52_6 = e1)
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | BETA: splitting (203) gives:
% 115.92/17.75 | | | | | | | |
% 115.92/17.75 | | | | | | | | Case 1:
% 115.92/17.75 | | | | | | | | |
% 115.92/17.75 | | | | | | | | | (255) ~ (all_56_0 = e3)
% 115.92/17.75 | | | | | | | | |
% 115.92/17.75 | | | | | | | | | REDUCE: (198), (255) imply:
% 115.92/17.76 | | | | | | | | | (256) ~ (all_52_4 = e3)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | GROUND_INST: instantiating (53) with all_52_4, all_10_1, e2,
% 115.92/17.76 | | | | | | | | | e3, simplifying with (14), (252) gives:
% 115.92/17.76 | | | | | | | | | (257) all_52_4 = all_10_1
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | COMBINE_EQS: (139), (257) imply:
% 115.92/17.76 | | | | | | | | | (258) all_58_1 = all_10_1
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (155), (257) imply:
% 115.92/17.76 | | | | | | | | | (259) ~ (all_52_6 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | SIMP: (259) implies:
% 115.92/17.76 | | | | | | | | | (260) ~ (all_52_6 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (68), (257) imply:
% 115.92/17.76 | | | | | | | | | (261) ~ (all_52_7 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | SIMP: (261) implies:
% 115.92/17.76 | | | | | | | | | (262) ~ (all_52_7 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (29), (257) imply:
% 115.92/17.76 | | | | | | | | | (263) ~ (all_52_8 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | SIMP: (263) implies:
% 115.92/17.76 | | | | | | | | | (264) ~ (all_52_8 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (158), (257) imply:
% 115.92/17.76 | | | | | | | | | (265) ~ (all_52_12 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | SIMP: (265) implies:
% 115.92/17.76 | | | | | | | | | (266) ~ (all_52_12 = all_10_1)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (94), (257) imply:
% 115.92/17.76 | | | | | | | | | (267) ~ (all_10_1 = all_8_2)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | REDUCE: (256), (257) imply:
% 115.92/17.76 | | | | | | | | | (268) ~ (all_10_1 = e3)
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | BETA: splitting (84) gives:
% 115.92/17.76 | | | | | | | | |
% 115.92/17.76 | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | (269) ~ (all_56_13 = e1)
% 115.92/17.76 | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | REDUCE: (143), (269) imply:
% 115.92/17.76 | | | | | | | | | | (270) ~ (all_8_2 = e1)
% 115.92/17.76 | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | BETA: splitting (82) gives:
% 115.92/17.76 | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | (271) ~ (all_56_14 = e3)
% 115.92/17.76 | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | REDUCE: (15), (271) imply:
% 115.92/17.76 | | | | | | | | | | | (272) ~ (all_6_2 = e3)
% 115.92/17.76 | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | BETA: splitting (51) gives:
% 115.92/17.76 | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | (273) all_54_10 = e3
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | REF_CLOSE: (59), (272), (273) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | #352.
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | (274) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | BETA: splitting (274) gives:
% 115.92/17.76 | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | (275) all_54_10 = e2
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | REF_CLOSE: (59), (231), (275) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | | #438.
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | (276) ~ (all_54_10 = e2)
% 115.92/17.76 | | | | | | | | | | | | | (277) all_54_10 = e1 | all_54_10 = e0
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | BETA: splitting (277) gives:
% 115.92/17.76 | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | (278) all_54_10 = e1
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | REF_CLOSE: (59), (205), (278) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | | | #437.
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | (279) all_54_10 = e0
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | COMBINE_EQS: (59), (279) imply:
% 115.92/17.76 | | | | | | | | | | | | | | (280) all_6_2 = e0
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | SIMP: (280) implies:
% 115.92/17.76 | | | | | | | | | | | | | | (281) all_6_2 = e0
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | REDUCE: (64), (281) imply:
% 115.92/17.76 | | | | | | | | | | | | | | (282) ~ (all_52_8 = e0)
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | REDUCE: (83), (281) imply:
% 115.92/17.76 | | | | | | | | | | | | | | (283) ~ (all_52_11 = e0)
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 115.92/17.76 | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | (284) all_58_15 = e0
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | COMBINE_EQS: (106), (284) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | (285) all_4_2 = e0
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | REDUCE: (13), (285) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | (286) $false
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | (287) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 115.92/17.76 | | | | | | | | | | | | | | | e0)
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | (288) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 115.92/17.76 | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | (289) all_58_12 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (289) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | (290) all_52_3 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | SIMP: (290) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | (291) all_52_3 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (291) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | (292) all_56_9 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | REDUCE: (212), (291) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | (293) ~ (all_52_7 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | REDUCE: (172), (291) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | (294) ~ (all_4_2 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | (295) ~ (all_56_13 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | REDUCE: (143), (295) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | (296) ~ (all_8_2 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | (297) all_58_0 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (243), (251), (297) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | | | | | | | #154.
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | (298) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | (299) all_58_1 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (299) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | (300) all_10_1 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | REDUCE: (268), (300) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | (301) $false
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | (302) all_58_4 = e3 | all_58_9 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (303) all_58_4 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (303) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (304) all_52_8 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (304) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (305) ~ (all_52_11 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (306) ~ (all_52_11 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (304) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (307) ~ (all_52_12 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | SIMP: (307) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (308) ~ (all_52_12 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (304) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (309) ~ (all_10_1 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (304) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | (310) ~ (e3 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | (311) all_54_5 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (296), (311) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | #339.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | (312) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | (313) all_58_12 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (313) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | (314) e3 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (310), (314) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | (315) $false
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (315) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | (316) all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_13 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (317) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | (318) all_52_7 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | (319) all_52_7 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (319) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | (320) ~ (all_52_6 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (319) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | (321) ~ (all_8_2 = e3)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | (322) all_54_9 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (322) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | (323) all_52_6 = e3
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (320), (323) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | (324) $false
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | (325) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | (326) all_54_5 = e2
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (146), (326) are inconsistent by sub-proof
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | #338.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_54_5 = e2)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_54_5 = e1 | all_54_5 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_54_5 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (329) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_8_2 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_8_2 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (25), (33), (51), (59), (60), (71),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (84), (91), (96), (100), (106), (108),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (128), (141), (143), (168), (170), (177),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (200), (205), (231), (244), (245), (331)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #426.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_54_5 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (332) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_8_2 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (333) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (334) all_8_2 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (334) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (335) ~ (all_52_6 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (334) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_10_1 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (296), (334) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (e3 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (334) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) ~ (e2 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (e2 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (334) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) op(e2, e0) = all_8_1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_58_1 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (341) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) all_10_1 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (342) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) ~ (all_52_12 = e1)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (342) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (e3 = e1)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (342) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) ~ (e1 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_58_0 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (243), (346) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) e2 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (339), (347) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) $false
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_58_0 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (350) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_1 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (25), (31), (33), (41), (51),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (71), (82), (84), (91), (96), (100), (106),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (115), (128), (135), (141), (143), (146),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (173), (177), (197), (199), (200),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205), (244), (245), (251), (254), (317), (339),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (351) are inconsistent by sub-proof #153.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_58_4 = e0 | all_58_9 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_4 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (353) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) e3 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (310), (354) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) $false
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (355) is inconsistent.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_9 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (356) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_52_12 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (357) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) ~ (e1 = e0)
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) all_58_9 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (356), (359) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) e1 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (360) implies:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) e1 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (361) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_1 = e0
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (25), (31), (33), (41), (51),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (71), (82), (84), (91), (96), (100), (106),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (115), (128), (135), (141), (143), (146),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (170), (173), (177), (197), (199), (200),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205), (244), (245), (251), (254), (317), (339),
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345), (362) are inconsistent by sub-proof #153.
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_10 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (364) imply:
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_52_13 = e1
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (365) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) op(e2, e0) = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (190), (340), (366) are inconsistent by
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #152.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) ~ (all_58_10 = e1)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (367) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_52_13 = e1)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (19), (28), (53), (59), (62), (69),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (72), (80), (91), (95), (114), (127), (170),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205), (219), (225), (226), (231), (274), (343),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) are inconsistent by sub-proof #348.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_54_9 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (370) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_52_6 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (371) implies:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) all_52_6 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (372) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) all_58_7 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (25), (31), (33), (51), (59), (60),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (82), (84), (91), (96), (100), (106), (108),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (115), (128), (141), (143), (146), (168), (170),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177), (197), (200), (205), (231), (244), (245),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317), (369), (373) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #162.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) all_54_9 = e1 | all_54_9 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (254), (335), (374) are inconsistent by
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #159.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | (375) all_58_14 = e3 | all_58_15 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (375) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (376) all_58_14 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (306), (376) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | #218.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (377) all_58_15 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (377) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (378) all_4_2 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (378) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (379) all_56_15 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (15), (27), (44), (51), (59), (64),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (65), (75), (121), (151), (162), (169), (175),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (188), (192), (205), (231), (243), (251), (254),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (258), (268), (308), (379) are inconsistent by
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (380) all_58_9 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (59), (69), (72), (169), (205), (231),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (274), (380) are inconsistent by sub-proof #149.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | (381) ~ (all_56_9 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | REDUCE: (292), (381) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (382) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | CLOSE: (382) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | (383) all_58_13 = e0 | all_58_14 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | REF_CLOSE: (115), (141), (244), (283), (383) are inconsistent
% 115.92/17.77 | | | | | | | | | | | | | | | | by sub-proof #428.
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | (384) all_56_14 = e3
% 115.92/17.77 | | | | | | | | | | | (385) ~ (all_56_9 = e0)
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | COMBINE_EQS: (15), (384) imply:
% 115.92/17.77 | | | | | | | | | | | (386) all_6_2 = e3
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | SIMP: (386) implies:
% 115.92/17.77 | | | | | | | | | | | (387) all_6_2 = e3
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | COMBINE_EQS: (162), (387) imply:
% 115.92/17.77 | | | | | | | | | | | (388) all_58_8 = e3
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | REDUCE: (100), (385) imply:
% 115.92/17.77 | | | | | | | | | | | (389) ~ (all_52_3 = e0)
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | REDUCE: (55), (387) imply:
% 115.92/17.77 | | | | | | | | | | | (390) ~ (all_52_2 = e3)
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | REDUCE: (226), (387) imply:
% 115.92/17.77 | | | | | | | | | | | (391) op(e1, e3) = e3
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | BETA: splitting (70) gives:
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | (392) ~ (all_56_6 = e1)
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | REDUCE: (175), (392) imply:
% 115.92/17.77 | | | | | | | | | | | | (393) ~ (all_52_2 = e1)
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | BETA: splitting (200) gives:
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | (394) all_58_15 = e0
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | COMBINE_EQS: (106), (394) imply:
% 115.92/17.77 | | | | | | | | | | | | | (395) all_4_2 = e0
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | REDUCE: (13), (395) imply:
% 115.92/17.77 | | | | | | | | | | | | | (396) $false
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | CLOSE: (396) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | (397) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 115.92/17.77 | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 115.92/17.77 | | | | | | | | | | | | | e0)
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | ALPHA: (397) implies:
% 115.92/17.77 | | | | | | | | | | | | | (398) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | BETA: splitting (398) gives:
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | (399) all_58_12 = e0
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | REF_CLOSE: (177), (389), (399) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | #362.
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | (400) all_58_13 = e0 | all_58_14 = e0
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | (401) all_54_8 = e3
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | REF_CLOSE: (54), (390), (401) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | #399.
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | (402) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | BETA: splitting (402) gives:
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | (403) all_54_8 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | REF_CLOSE: (54), (246), (403) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | | #382.
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | (404) all_54_8 = e1 | all_54_8 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | BETA: splitting (404) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | (405) all_54_8 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (393), (405) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | | | #397.
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | (406) all_54_8 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (406) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (407) all_52_2 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | SIMP: (407) implies:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (408) all_52_2 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (408) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (409) all_58_6 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | REDUCE: (156), (408) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (410) ~ (all_52_1 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | REDUCE: (393), (408) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (411) ~ (e1 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | SIMP: (411) implies:
% 115.92/17.77 | | | | | | | | | | | | | | | | | (412) ~ (e1 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | (413) all_58_6 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (413) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | (414) e1 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | REDUCE: (412), (414) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | (415) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | CLOSE: (415) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | (416) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | (417) all_58_7 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (417) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | (418) all_52_6 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | REDUCE: (254), (418) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | (419) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | CLOSE: (419) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | (420) all_58_8 = e1 | all_58_11 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (421) all_58_8 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (421) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (422) e3 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (422) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (423) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | CLOSE: (423) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (424) all_58_11 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (424) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (425) all_52_14 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (425) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | (426) all_56_8 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | (427) ~ (all_56_8 = e1)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | REDUCE: (426), (427) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | (428) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | CLOSE: (428) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | (429) ~ (all_56_13 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (429) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | (430) ~ (all_8_2 = e0)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | (431) all_54_5 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (431) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | (432) all_8_2 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | SIMP: (432) implies:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | (433) all_8_2 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (433) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | (434) ~ (all_52_1 = e3)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | (435) all_54_4 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (435) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | (436) all_52_1 = e3
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (436) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | (437) $false
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (437) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | (438) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (439) all_54_4 = e2
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (245), (439) are inconsistent by sub-proof
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | #328.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | (440) all_54_4 = e1 | all_54_4 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_58_2 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (441) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_52_1 = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (442) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (443) op(e2, e3) = e1
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (79), (85), (115), (141), (159), (181),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (185), (208), (210), (244), (247), (391), (400),
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (443) are inconsistent by sub-proof #148.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_58_2 = e1)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (444) imply:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | (445) ~ (all_52_1 = e1)
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (410), (440), (445) are inconsistent by
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #147.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | (446) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (146), (270), (430), (446) are inconsistent
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #310.
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | (447) ~ (all_56_14 = e3)
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | REDUCE: (384), (447) imply:
% 115.92/17.77 | | | | | | | | | | | | (448) $false
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | | CLOSE: (448) is inconsistent.
% 115.92/17.77 | | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | (449) all_56_13 = e1
% 115.92/17.77 | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | | REF_CLOSE: (13), (15), (25), (33), (51), (59), (60), (71),
% 115.92/17.77 | | | | | | | | | | (82), (84), (91), (96), (100), (106), (108),
% 115.92/17.77 | | | | | | | | | | (115), (128), (141), (143), (168), (170), (177),
% 115.92/17.77 | | | | | | | | | | (197), (200), (205), (231), (244), (245), (449)
% 115.92/17.77 | | | | | | | | | | are inconsistent by sub-proof #146.
% 115.92/17.77 | | | | | | | | | |
% 115.92/17.77 | | | | | | | | | End of split
% 115.92/17.77 | | | | | | | | |
% 115.92/17.77 | | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | | |
% 115.92/17.77 | | | | | | | | | (450) ~ (all_56_12 = e2)
% 115.92/17.77 | | | | | | | | |
% 115.92/17.77 | | | | | | | | | REDUCE: (239), (450) imply:
% 115.92/17.77 | | | | | | | | | (451) $false
% 115.92/17.77 | | | | | | | | |
% 115.92/17.77 | | | | | | | | | CLOSE: (451) is inconsistent.
% 115.92/17.77 | | | | | | | | |
% 115.92/17.77 | | | | | | | | End of split
% 115.92/17.77 | | | | | | | |
% 115.92/17.77 | | | | | | | Case 2:
% 115.92/17.77 | | | | | | | |
% 115.92/17.77 | | | | | | | | (452) ~ (all_56_12 = e2)
% 115.92/17.77 | | | | | | | |
% 115.92/17.77 | | | | | | | | REDUCE: (239), (452) imply:
% 115.92/17.77 | | | | | | | | (453) $false
% 115.92/17.77 | | | | | | | |
% 115.92/17.77 | | | | | | | | CLOSE: (453) is inconsistent.
% 115.92/17.77 | | | | | | | |
% 115.92/17.77 | | | | | | | End of split
% 115.92/17.77 | | | | | | |
% 115.92/17.77 | | | | | | End of split
% 115.92/17.77 | | | | | |
% 115.92/17.77 | | | | | Case 2:
% 115.92/17.77 | | | | | |
% 115.92/17.77 | | | | | | (454) all_56_14 = e2
% 115.92/17.77 | | | | | |
% 115.92/17.77 | | | | | | REF_CLOSE: (7), (13), (14), (15), (16), (18), (23), (35), (37),
% 115.92/17.77 | | | | | | (40), (53), (56), (61), (65), (66), (68), (69), (71),
% 115.92/17.77 | | | | | | (76), (92), (94), (96), (108), (113), (122), (125),
% 115.92/17.77 | | | | | | (126), (128), (135), (139), (140), (142), (143), (146),
% 115.92/17.77 | | | | | | (148), (149), (152), (154), (160), (169), (170), (188),
% 115.92/17.77 | | | | | | (197), (198), (201), (204), (207), (219), (223), (225),
% 115.92/17.77 | | | | | | (226), (454) are inconsistent by sub-proof #306.
% 115.92/17.77 | | | | | |
% 115.92/17.77 | | | | | End of split
% 115.92/17.77 | | | | |
% 115.92/17.77 | | | | End of split
% 115.92/17.77 | | | |
% 115.92/17.77 | | | End of split
% 115.92/17.77 | | |
% 115.92/17.77 | | Case 2:
% 115.92/17.77 | | |
% 115.92/17.78 | | | (455) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 115.92/17.78 | | |
% 115.92/17.78 | | | BETA: splitting (34) gives:
% 115.92/17.78 | | |
% 115.92/17.78 | | | Case 1:
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | (456) ~ (all_50_0 = e2)
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | REDUCE: (214), (456) imply:
% 115.92/17.78 | | | | (457) $false
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | CLOSE: (457) is inconsistent.
% 115.92/17.78 | | | |
% 115.92/17.78 | | | Case 2:
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | (458) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | BETA: splitting (101) gives:
% 115.92/17.78 | | | |
% 115.92/17.78 | | | | Case 1:
% 115.92/17.78 | | | | |
% 115.92/17.78 | | | | | (459) ~ (all_56_15 = e1)
% 115.92/17.78 | | | | |
% 115.92/17.78 | | | | | REDUCE: (126), (459) imply:
% 115.92/17.78 | | | | | (460) ~ (all_4_2 = e1)
% 115.92/17.78 | | | | |
% 115.92/17.78 | | | | | BETA: splitting (118) gives:
% 115.92/17.78 | | | | |
% 115.92/17.78 | | | | | Case 1:
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | (461) ~ (all_56_14 = e2)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | REDUCE: (15), (461) imply:
% 115.92/17.78 | | | | | | (462) ~ (all_6_2 = e2)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | BETA: splitting (119) gives:
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | Case 1:
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | (463) ~ (all_56_12 = e2)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (36), (463) imply:
% 115.92/17.78 | | | | | | | (464) ~ (all_10_2 = e2)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REF_CLOSE: (2), (5), (13), (17), (19), (28), (30), (36), (48),
% 115.92/17.78 | | | | | | | (53), (62), (65), (66), (67), (69), (75), (78), (88),
% 115.92/17.78 | | | | | | | (90), (96), (100), (103), (106), (109), (110), (113),
% 115.92/17.78 | | | | | | | (114), (126), (128), (131), (133), (141), (160), (162),
% 115.92/17.78 | | | | | | | (163), (165), (168), (169), (171), (172), (174), (180),
% 115.92/17.78 | | | | | | | (181), (182), (184), (192), (196), (204), (208), (210),
% 115.92/17.78 | | | | | | | (215), (458), (460), (462), (464) are inconsistent by
% 115.92/17.78 | | | | | | | sub-proof #155.
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | Case 2:
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | (465) all_56_12 = e2
% 115.92/17.78 | | | | | | | (466) ~ (all_56_10 = e0)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | COMBINE_EQS: (36), (465) imply:
% 115.92/17.78 | | | | | | | (467) all_10_2 = e2
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | SIMP: (467) implies:
% 115.92/17.78 | | | | | | | (468) all_10_2 = e2
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (47), (466) imply:
% 115.92/17.78 | | | | | | | (469) ~ (all_52_7 = e0)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (124), (468) imply:
% 115.92/17.78 | | | | | | | (470) ~ (all_52_1 = e2)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (3), (468) imply:
% 115.92/17.78 | | | | | | | (471) ~ (all_52_2 = e2)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (30), (468) imply:
% 115.92/17.78 | | | | | | | (472) ~ (all_52_12 = e2)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (215), (468) imply:
% 115.92/17.78 | | | | | | | (473) op(all_10_1, e2) = e2
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (133), (468) imply:
% 115.92/17.78 | | | | | | | (474) op(e3, e2) = all_10_1
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | BETA: splitting (104) gives:
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | (475) ~ (all_56_7 = e1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (153), (475) imply:
% 115.92/17.78 | | | | | | | | (476) ~ (all_52_6 = e1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | BETA: splitting (203) gives:
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | (477) ~ (all_56_0 = e3)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (198), (477) imply:
% 115.92/17.78 | | | | | | | | | (478) ~ (all_52_4 = e3)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | GROUND_INST: instantiating (53) with all_52_4, all_10_1, e2,
% 115.92/17.78 | | | | | | | | | e3, simplifying with (14), (474) gives:
% 115.92/17.78 | | | | | | | | | (479) all_52_4 = all_10_1
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | COMBINE_EQS: (142), (479) imply:
% 115.92/17.78 | | | | | | | | | (480) all_54_1 = all_10_1
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | COMBINE_EQS: (139), (479) imply:
% 115.92/17.78 | | | | | | | | | (481) all_58_1 = all_10_1
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (155), (479) imply:
% 115.92/17.78 | | | | | | | | | (482) ~ (all_52_6 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | SIMP: (482) implies:
% 115.92/17.78 | | | | | | | | | (483) ~ (all_52_6 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (68), (479) imply:
% 115.92/17.78 | | | | | | | | | (484) ~ (all_52_7 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | SIMP: (484) implies:
% 115.92/17.78 | | | | | | | | | (485) ~ (all_52_7 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (158), (479) imply:
% 115.92/17.78 | | | | | | | | | (486) ~ (all_52_12 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | SIMP: (486) implies:
% 115.92/17.78 | | | | | | | | | (487) ~ (all_52_12 = all_10_1)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (478), (479) imply:
% 115.92/17.78 | | | | | | | | | (488) ~ (all_10_1 = e3)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | BETA: splitting (11) gives:
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | (489) ~ (all_56_6 = e1)
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | REDUCE: (175), (489) imply:
% 115.92/17.78 | | | | | | | | | | (490) ~ (all_52_2 = e1)
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | BETA: splitting (151) gives:
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | (491) all_58_6 = e1
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | REF_CLOSE: (121), (490), (491) are inconsistent by sub-proof
% 115.92/17.78 | | | | | | | | | | | #452.
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | (492) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | BETA: splitting (492) gives:
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | (493) all_58_7 = e1
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | COMBINE_EQS: (6), (493) imply:
% 115.92/17.78 | | | | | | | | | | | | (494) all_52_6 = e1
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | REDUCE: (476), (494) imply:
% 115.92/17.78 | | | | | | | | | | | | (495) $false
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | CLOSE: (495) is inconsistent.
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | (496) all_58_8 = e1 | all_58_11 = e1
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | BETA: splitting (496) gives:
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | (497) all_58_8 = e1
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | COMBINE_EQS: (162), (497) imply:
% 115.92/17.78 | | | | | | | | | | | | | (498) all_6_2 = e1
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | REDUCE: (205), (498) imply:
% 115.92/17.78 | | | | | | | | | | | | | (499) $false
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | CLOSE: (499) is inconsistent.
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | (500) all_58_11 = e1
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | COMBINE_EQS: (75), (500) imply:
% 115.92/17.78 | | | | | | | | | | | | | (501) all_52_14 = e1
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | COMBINE_EQS: (192), (501) imply:
% 115.92/17.78 | | | | | | | | | | | | | (502) all_56_8 = e1
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | REDUCE: (21), (501) imply:
% 115.92/17.78 | | | | | | | | | | | | | (503) ~ (all_52_12 = e1)
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | REDUCE: (12), (501) imply:
% 115.92/17.78 | | | | | | | | | | | | | (504) ~ (all_52_13 = e1)
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | REDUCE: (44), (501) imply:
% 115.92/17.78 | | | | | | | | | | | | | (505) ~ (all_6_2 = e1)
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | BETA: splitting (45) gives:
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | (506) ~ (all_56_8 = e1)
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | REDUCE: (502), (506) imply:
% 115.92/17.78 | | | | | | | | | | | | | | (507) $false
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | CLOSE: (507) is inconsistent.
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | (508) ~ (all_56_13 = e0)
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | REDUCE: (143), (508) imply:
% 115.92/17.78 | | | | | | | | | | | | | | (509) ~ (all_8_2 = e0)
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | (510) all_54_10 = e3
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | COMBINE_EQS: (59), (510) imply:
% 115.92/17.78 | | | | | | | | | | | | | | | (511) all_6_2 = e3
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | SIMP: (511) implies:
% 115.92/17.78 | | | | | | | | | | | | | | | (512) all_6_2 = e3
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | REDUCE: (55), (512) imply:
% 115.92/17.78 | | | | | | | | | | | | | | | (513) ~ (all_52_2 = e3)
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | REDUCE: (173), (512) imply:
% 115.92/17.78 | | | | | | | | | | | | | | | (514) ~ (all_52_6 = e3)
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | (515) all_54_8 = e3
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | REF_CLOSE: (54), (513), (515) are inconsistent by sub-proof
% 115.92/17.78 | | | | | | | | | | | | | | | | #399.
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | (516) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | (517) all_58_15 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (517) imply:
% 115.92/17.78 | | | | | | | | | | | | | | | | | (518) all_4_2 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | REDUCE: (13), (518) imply:
% 115.92/17.78 | | | | | | | | | | | | | | | | | (519) $false
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | (520) ~ (all_58_15 = e0)
% 115.92/17.78 | | | | | | | | | | | | | | | | | (521) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 115.92/17.78 | | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 115.92/17.78 | | | | | | | | | | | | | | | | | e0)
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 115.92/17.78 | | | | | | | | | | | | | | | | | (522) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | (523) all_54_8 = e2
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (471), (523) are inconsistent by sub-proof
% 115.92/17.78 | | | | | | | | | | | | | | | | | | #382.
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | (524) all_54_8 = e1 | all_54_8 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives:
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (525) all_54_8 = e1
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (490), (525) are inconsistent by sub-proof
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | #397.
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (526) all_54_8 = e0
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (18), (19), (20), (22), (23),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (25), (28), (33), (35), (40), (51), (53), (54),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (59), (71), (74), (77), (82), (84), (91), (92),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (96), (100), (106), (108), (115), (116), (125),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (128), (135), (141), (143), (148), (152), (161),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (168), (169), (170), (176), (177), (197), (199),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (200), (205), (207), (462), (469), (470), (472),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (473), (476), (480), (481), (483), (485), (487),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (488), (490), (500), (503), (504), (509), (514),
% 115.92/17.78 | | | | | | | | | | | | | | | | | | | (522), (526) are inconsistent by sub-proof #158.
% 115.92/17.78 | | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | (527) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | | REF_CLOSE: (10), (15), (27), (37), (39), (44), (53), (59),
% 115.92/17.78 | | | | | | | | | | | | | | | (86), (95), (102), (113), (167), (188), (192),
% 115.92/17.78 | | | | | | | | | | | | | | | (205), (206), (455), (462), (527) are inconsistent
% 115.92/17.78 | | | | | | | | | | | | | | | by sub-proof #259.
% 115.92/17.78 | | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | (528) all_56_6 = e1
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | COMBINE_EQS: (175), (528) imply:
% 115.92/17.78 | | | | | | | | | | (529) all_52_2 = e1
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | REDUCE: (55), (529) imply:
% 115.92/17.78 | | | | | | | | | | (530) ~ (all_6_2 = e1)
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | | REF_CLOSE: (10), (15), (27), (37), (39), (44), (51), (53),
% 115.92/17.78 | | | | | | | | | | (59), (70), (86), (95), (102), (113), (167),
% 115.92/17.78 | | | | | | | | | | (188), (192), (205), (206), (455), (462), (528)
% 115.92/17.78 | | | | | | | | | | are inconsistent by sub-proof #252.
% 115.92/17.78 | | | | | | | | | |
% 115.92/17.78 | | | | | | | | | End of split
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | (531) ~ (all_56_12 = e2)
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | REDUCE: (465), (531) imply:
% 115.92/17.78 | | | | | | | | | (532) $false
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | CLOSE: (532) is inconsistent.
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | End of split
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | Case 2:
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | (533) ~ (all_56_12 = e2)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (465), (533) imply:
% 115.92/17.78 | | | | | | | | (534) $false
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | CLOSE: (534) is inconsistent.
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | End of split
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | End of split
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | Case 2:
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | (535) all_56_14 = e2
% 115.92/17.78 | | | | | | (536) ~ (all_56_10 = e0)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | COMBINE_EQS: (15), (535) imply:
% 115.92/17.78 | | | | | | (537) all_6_2 = e2
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | SIMP: (537) implies:
% 115.92/17.78 | | | | | | (538) all_6_2 = e2
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | COMBINE_EQS: (162), (538) imply:
% 115.92/17.78 | | | | | | (539) all_58_8 = e2
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | REDUCE: (47), (536) imply:
% 115.92/17.78 | | | | | | (540) ~ (all_52_7 = e0)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | REDUCE: (173), (538) imply:
% 115.92/17.78 | | | | | | (541) ~ (all_52_6 = e2)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | REDUCE: (154), (538) imply:
% 115.92/17.78 | | | | | | (542) ~ (all_52_9 = e2)
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | REDUCE: (102), (538) imply:
% 115.92/17.78 | | | | | | (543) op(e1, e2) = all_6_1
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | BETA: splitting (46) gives:
% 115.92/17.78 | | | | | |
% 115.92/17.78 | | | | | | Case 1:
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | (544) ~ (all_56_7 = e1)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | REDUCE: (153), (544) imply:
% 115.92/17.78 | | | | | | | (545) ~ (all_52_6 = e1)
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | BETA: splitting (201) gives:
% 115.92/17.78 | | | | | | |
% 115.92/17.78 | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | (546) ~ (all_56_0 = e3)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (198), (546) imply:
% 115.92/17.78 | | | | | | | | (547) ~ (all_52_4 = e3)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | GROUND_INST: instantiating (53) with all_52_6, all_6_1, e2, e1,
% 115.92/17.78 | | | | | | | | simplifying with (149), (543) gives:
% 115.92/17.78 | | | | | | | | (548) all_52_6 = all_6_1
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | COMBINE_EQS: (77), (548) imply:
% 115.92/17.78 | | | | | | | | (549) all_54_9 = all_6_1
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | COMBINE_EQS: (6), (548) imply:
% 115.92/17.78 | | | | | | | | (550) all_58_7 = all_6_1
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (155), (548) imply:
% 115.92/17.78 | | | | | | | | (551) ~ (all_52_4 = all_6_1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (135), (548) imply:
% 115.92/17.78 | | | | | | | | (552) ~ (all_8_2 = all_6_1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | SIMP: (552) implies:
% 115.92/17.78 | | | | | | | | (553) ~ (all_8_2 = all_6_1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | REDUCE: (545), (548) imply:
% 115.92/17.78 | | | | | | | | (554) ~ (all_6_1 = e1)
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | BETA: splitting (187) gives:
% 115.92/17.78 | | | | | | | |
% 115.92/17.78 | | | | | | | | Case 1:
% 115.92/17.78 | | | | | | | | |
% 115.92/17.78 | | | | | | | | | (555) ~ (all_56_5 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | REDUCE: (170), (555) imply:
% 115.92/17.79 | | | | | | | | | (556) ~ (all_52_13 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | BETA: splitting (197) gives:
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | (557) all_58_2 = e2
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | COMBINE_EQS: (108), (557) imply:
% 115.92/17.79 | | | | | | | | | | (558) all_52_1 = e2
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | SIMP: (558) implies:
% 115.92/17.79 | | | | | | | | | | (559) all_52_1 = e2
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | REDUCE: (124), (559) imply:
% 115.92/17.79 | | | | | | | | | | (560) ~ (all_10_2 = e2)
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | SIMP: (560) implies:
% 115.92/17.79 | | | | | | | | | | (561) ~ (all_10_2 = e2)
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | BETA: splitting (196) gives:
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | (562) ~ (all_56_12 = e1)
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REDUCE: (36), (562) imply:
% 115.92/17.79 | | | | | | | | | | | (563) ~ (all_10_2 = e1)
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | BETA: splitting (163) gives:
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | (564) all_54_0 = e3
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | REF_CLOSE: (17), (113), (564) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | #451.
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | (565) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | BETA: splitting (565) gives:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | (566) all_54_0 = e2
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | REF_CLOSE: (17), (561), (566) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | #450.
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | (567) ~ (all_54_0 = e2)
% 115.92/17.79 | | | | | | | | | | | | | (568) all_54_0 = e1 | all_54_0 = e0
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | BETA: splitting (568) gives:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | (569) all_54_0 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REF_CLOSE: (17), (563), (569) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | #449.
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | (570) all_54_0 = e0
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | COMBINE_EQS: (17), (570) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (571) all_10_2 = e0
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | SIMP: (571) implies:
% 115.92/17.79 | | | | | | | | | | | | | | (572) all_10_2 = e0
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | COMBINE_EQS: (90), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (573) all_50_2 = e0
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | COMBINE_EQS: (36), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (574) all_56_12 = e0
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (184), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (575) ~ (all_52_3 = e0)
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (30), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (576) ~ (all_52_12 = e0)
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (215), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (577) op(all_10_1, e0) = e2
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (133), (572) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (578) op(e3, e0) = all_10_1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | (579) ~ (all_56_2 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | REDUCE: (69), (579) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | (580) ~ (all_52_12 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | (581) all_58_15 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (581) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | (582) all_4_2 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | REDUCE: (13), (582) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | (583) $false
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | CLOSE: (583) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | (584) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 115.92/17.79 | | | | | | | | | | | | | | | | e0)
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 115.92/17.79 | | | | | | | | | | | | | | | | (585) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | BETA: splitting (585) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | (586) all_58_12 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (575), (586) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | | | | #362.
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | (587) all_58_13 = e0 | all_58_14 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | BETA: splitting (587) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (588) all_58_13 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (540), (588) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | | | | | #430.
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (589) all_58_14 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (589) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (590) all_52_11 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | SIMP: (590) implies:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (591) all_52_11 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (591) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (592) all_56_11 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (593) ~ (all_50_1 = e1)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | REDUCE: (67), (593) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (594) ~ (all_10_1 = e1)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (28), (36), (53), (62), (75), (103),
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (106), (110), (114), (128), (169), (182), (192),
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (460), (561), (563), (565), (576), (577), (578),
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (580), (594) are inconsistent by sub-proof #169.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (595) ~ (all_56_11 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (595) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (596) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | CLOSE: (596) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (597) ~ (all_50_2 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | REDUCE: (573), (597) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (598) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | CLOSE: (598) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | (599) ~ (all_56_12 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | REDUCE: (574), (599) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | (600) $false
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | CLOSE: (600) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | (601) all_56_12 = e1
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | COMBINE_EQS: (36), (601) imply:
% 115.92/17.79 | | | | | | | | | | | (602) all_10_2 = e1
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | SIMP: (602) implies:
% 115.92/17.79 | | | | | | | | | | | (603) all_10_2 = e1
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REDUCE: (1), (603) imply:
% 115.92/17.79 | | | | | | | | | | | (604) ~ (all_52_8 = e1)
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REDUCE: (215), (603) imply:
% 115.92/17.79 | | | | | | | | | | | (605) op(all_10_1, e1) = e2
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REDUCE: (133), (603) imply:
% 115.92/17.79 | | | | | | | | | | | (606) op(e3, e1) = all_10_1
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REF_CLOSE: (5), (24), (53), (78), (88), (160), (171), (174),
% 115.92/17.79 | | | | | | | | | | | (180), (601), (603), (604), (605), (606) are
% 115.92/17.79 | | | | | | | | | | | inconsistent by sub-proof #145.
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | (607) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | REF_CLOSE: (71), (96), (128), (146), (542), (556), (607) are
% 115.92/17.79 | | | | | | | | | | inconsistent by sub-proof #401.
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | End of split
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | (608) all_56_5 = e2
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | COMBINE_EQS: (170), (608) imply:
% 115.92/17.79 | | | | | | | | | (609) all_52_13 = e2
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | REDUCE: (114), (609) imply:
% 115.92/17.79 | | | | | | | | | (610) ~ (all_52_12 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | REDUCE: (129), (609) imply:
% 115.92/17.79 | | | | | | | | | (611) ~ (all_8_2 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | REDUCE: (176), (609) imply:
% 115.92/17.79 | | | | | | | | | (612) ~ (all_4_2 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | SIMP: (612) implies:
% 115.92/17.79 | | | | | | | | | (613) ~ (all_4_2 = e2)
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | BETA: splitting (66) gives:
% 115.92/17.79 | | | | | | | | |
% 115.92/17.79 | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | (614) all_54_15 = e3
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | COMBINE_EQS: (204), (614) imply:
% 115.92/17.79 | | | | | | | | | | (615) all_4_2 = e3
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | SIMP: (615) implies:
% 115.92/17.79 | | | | | | | | | | (616) all_4_2 = e3
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | COMBINE_EQS: (126), (616) imply:
% 115.92/17.79 | | | | | | | | | | (617) all_56_15 = e3
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | REDUCE: (172), (616) imply:
% 115.92/17.79 | | | | | | | | | | (618) ~ (all_52_3 = e3)
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | REDUCE: (183), (616) imply:
% 115.92/17.79 | | | | | | | | | | (619) ~ (all_52_12 = e3)
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | BETA: splitting (11) gives:
% 115.92/17.79 | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | (620) ~ (all_56_6 = e1)
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | REDUCE: (175), (620) imply:
% 115.92/17.79 | | | | | | | | | | | (621) ~ (all_52_2 = e1)
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | BETA: splitting (151) gives:
% 115.92/17.79 | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | (622) all_58_6 = e1
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | REF_CLOSE: (121), (621), (622) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | #452.
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | (623) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | BETA: splitting (623) gives:
% 115.92/17.79 | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | (624) all_58_7 = e1
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | COMBINE_EQS: (550), (624) imply:
% 115.92/17.79 | | | | | | | | | | | | | (625) all_6_1 = e1
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | REDUCE: (554), (625) imply:
% 115.92/17.79 | | | | | | | | | | | | | (626) $false
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | CLOSE: (626) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | (627) all_58_8 = e1 | all_58_11 = e1
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | BETA: splitting (627) gives:
% 115.92/17.79 | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | (628) all_58_8 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | COMBINE_EQS: (539), (628) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (629) e2 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (60), (629) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (630) $false
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | CLOSE: (630) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | (631) all_58_11 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | COMBINE_EQS: (75), (631) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (632) all_52_14 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | SIMP: (632) implies:
% 115.92/17.79 | | | | | | | | | | | | | | (633) all_52_14 = e1
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | REDUCE: (21), (633) imply:
% 115.92/17.79 | | | | | | | | | | | | | | (634) ~ (all_52_12 = e1)
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 115.92/17.79 | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | (635) all_54_3 = e3
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | REF_CLOSE: (19), (619), (635) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | | #224.
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | (636) ~ (all_54_3 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | | (637) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | BETA: splitting (637) gives:
% 115.92/17.79 | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | (638) all_54_3 = e2
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | REF_CLOSE: (19), (610), (638) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | | | #285.
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | (639) ~ (all_54_3 = e2)
% 115.92/17.79 | | | | | | | | | | | | | | | | (640) all_54_3 = e1 | all_54_3 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | BETA: splitting (640) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | (641) all_54_3 = e1
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (634), (641) are inconsistent by sub-proof
% 115.92/17.79 | | | | | | | | | | | | | | | | | #284.
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | (642) all_54_3 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (642) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (643) all_52_12 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | SIMP: (643) implies:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (644) all_52_12 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (644) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (645) all_58_9 = e0
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | REDUCE: (158), (644) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (646) ~ (all_52_4 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | REDUCE: (619), (644) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (647) ~ (e3 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | SIMP: (647) implies:
% 115.92/17.79 | | | | | | | | | | | | | | | | | (648) ~ (e3 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (649) ~ (all_56_5 = e2)
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | REDUCE: (608), (649) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (650) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | CLOSE: (650) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (651) ~ (all_56_13 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | REDUCE: (143), (651) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | (652) ~ (all_8_2 = e0)
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (653) all_58_0 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (653) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (654) all_10_2 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (654) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (655) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | CLOSE: (655) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | (656) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (657) all_58_1 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (657) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (658) all_52_4 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (658) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (659) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | CLOSE: (659) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | (660) all_58_4 = e3 | all_58_9 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | (661) all_58_4 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (661) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | (662) all_52_8 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (662) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | (663) all_56_1 = e3
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (662) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | (664) ~ (all_10_2 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | (665) ~ (all_56_1 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (663), (665) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | (666) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (666) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | (667) ~ (all_56_13 = e1)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (667) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | (668) ~ (all_8_2 = e1)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | | (669) ~ (all_56_1 = e3)
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (663), (669) imply:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | | (670) $false
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (670) is inconsistent.
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 115.92/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | (671) ~ (all_56_12 = e1)
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (671) imply:
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | (672) ~ (all_10_2 = e1)
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | (673) all_54_0 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (113), (673) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | #451.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | (674) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (674) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_54_0 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (675) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_10_2 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (676) implies:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_10_2 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (677) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_58_0 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (677) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (679) ~ (all_52_4 = e2)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (677) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (680) op(all_10_1, e2) = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (677) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (681) op(e3, e2) = all_10_1
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_54_1 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (547), (682) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | #222.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_54_5 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (684) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_8_2 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (685) implies:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_8_2 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (686) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) ~ (all_52_1 = e3)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (686) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) ~ (all_6_1 = e3)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (688) implies:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) ~ (all_6_1 = e3)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (686) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) ~ (e3 = e2)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_54_9 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (549), (689), (691) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #230.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_58_6 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (683) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_54_1 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (679), (694) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #221.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_54_1 = e1 | all_54_1 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) all_58_1 = e1
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (696) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_52_4 = e1
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (697) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) ~ (all_6_1 = e1)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (697) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) op(e3, e2) = e1
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_58_6 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (700) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) e3 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (648), (701) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) $false
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (702) is inconsistent.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (703) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_58_7 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (550), (704) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_6_1 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (705) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ (e2 = e0)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (706) implies:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) ~ (e2 = e0)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (543), (705) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) op(e1, e2) = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e1, all_10_1, e2, e3,
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (681), (699) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_10_1 = e1
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (680), (709) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) op(e1, e2) = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e0, e2, e2, e1,
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (708), (710) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) e2 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (707), (711) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) $false
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (712) is inconsistent.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) ~ (all_58_7 = e0)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (713) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) ~ (all_6_1 = e0)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (206), (549), (554), (692), (714) are inconsistent
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #373.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) ~ (all_58_1 = e1)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (715) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) ~ (all_52_4 = e1)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (646), (695), (716) are inconsistent by
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #213.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) ~ (all_58_6 = e3)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (717) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) ~ (all_52_2 = e3)
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) all_58_0 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (678), (719) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) e3 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (720) implies:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) e3 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (721) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_58_4 = e2
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (645), (648), (660), (690), (722) are inconsistent
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #186.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (723) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_2 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (724) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_52_1 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (687), (725) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) $false
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (726) is inconsistent.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_58_6 = e3 | all_58_12 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_58_6 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (718), (728) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #318.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_58_12 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (729) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_52_3 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (618), (730) imply:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) $false
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (731) is inconsistent.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (146), (652), (668), (732) are inconsistent
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #310.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_54_0 = e1 | all_54_0 = e0
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (30), (610), (634), (637), (672),
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | | (733) are inconsistent by sub-proof #223.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | (734) all_58_9 = e3
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (645), (648), (734) are inconsistent by sub-proof
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | | #187.
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | (735) ~ (all_56_15 = e3)
% 116.10/17.80 | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | REDUCE: (617), (735) imply:
% 116.10/17.80 | | | | | | | | | | | (736) $false
% 116.10/17.80 | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | | CLOSE: (736) is inconsistent.
% 116.10/17.80 | | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | (737) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.10/17.80 | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | | REF_CLOSE: (13), (204), (460), (613), (737) are inconsistent
% 116.10/17.80 | | | | | | | | | | by sub-proof #417.
% 116.10/17.80 | | | | | | | | | |
% 116.10/17.80 | | | | | | | | | End of split
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | End of split
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | (738) ~ (all_56_14 = e2)
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | REDUCE: (535), (738) imply:
% 116.10/17.80 | | | | | | | | (739) $false
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | CLOSE: (739) is inconsistent.
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | End of split
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | Case 2:
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | (740) ~ (all_56_14 = e2)
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | REDUCE: (535), (740) imply:
% 116.10/17.80 | | | | | | | (741) $false
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | CLOSE: (741) is inconsistent.
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | End of split
% 116.10/17.80 | | | | | |
% 116.10/17.80 | | | | | End of split
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | Case 2:
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | (742) all_56_15 = e1
% 116.10/17.80 | | | | | (743) ~ (all_56_11 = e0)
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | COMBINE_EQS: (126), (742) imply:
% 116.10/17.80 | | | | | (744) all_4_2 = e1
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | SIMP: (744) implies:
% 116.10/17.80 | | | | | (745) all_4_2 = e1
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (25), (743) imply:
% 116.10/17.80 | | | | | (746) ~ (all_52_11 = e0)
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (131), (745) imply:
% 116.10/17.80 | | | | | (747) ~ (all_52_11 = e1)
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (176), (745) imply:
% 116.10/17.80 | | | | | (748) ~ (all_52_13 = e1)
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (120), (745) imply:
% 116.10/17.80 | | | | | (749) ~ (all_52_14 = e1)
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (50), (745) imply:
% 116.10/17.80 | | | | | (750) op(all_4_1, e1) = all_4_0
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | REDUCE: (161), (745) imply:
% 116.10/17.80 | | | | | (751) op(e0, e1) = all_4_1
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | BETA: splitting (122) gives:
% 116.10/17.80 | | | | |
% 116.10/17.80 | | | | | Case 1:
% 116.10/17.80 | | | | | |
% 116.10/17.80 | | | | | | (752) ~ (all_56_1 = e3)
% 116.10/17.80 | | | | | |
% 116.10/17.80 | | | | | | REDUCE: (160), (752) imply:
% 116.10/17.80 | | | | | | (753) ~ (all_52_8 = e3)
% 116.10/17.80 | | | | | |
% 116.10/17.80 | | | | | | BETA: splitting (179) gives:
% 116.10/17.80 | | | | | |
% 116.10/17.80 | | | | | | Case 1:
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | (754) ~ (all_56_4 = e2)
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | REDUCE: (168), (754) imply:
% 116.10/17.80 | | | | | | | (755) ~ (all_52_9 = e2)
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | GROUND_INST: instantiating (53) with all_52_11, all_4_1, e1, e0,
% 116.10/17.80 | | | | | | | simplifying with (144), (751) gives:
% 116.10/17.80 | | | | | | | (756) all_52_11 = all_4_1
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | COMBINE_EQS: (49), (756) imply:
% 116.10/17.80 | | | | | | | (757) all_54_14 = all_4_1
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | REDUCE: (83), (756) imply:
% 116.10/17.80 | | | | | | | (758) ~ (all_6_2 = all_4_1)
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | SIMP: (758) implies:
% 116.10/17.80 | | | | | | | (759) ~ (all_6_2 = all_4_1)
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | BETA: splitting (119) gives:
% 116.10/17.80 | | | | | | |
% 116.10/17.80 | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | (760) ~ (all_56_12 = e2)
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | REDUCE: (36), (760) imply:
% 116.10/17.80 | | | | | | | | (761) ~ (all_10_2 = e2)
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | BETA: splitting (201) gives:
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | Case 1:
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | (762) ~ (all_56_0 = e3)
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | REDUCE: (198), (762) imply:
% 116.10/17.80 | | | | | | | | | (763) ~ (all_52_4 = e3)
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | REF_CLOSE: (1), (2), (5), (17), (24), (36), (37), (53), (65),
% 116.10/17.80 | | | | | | | | | (69), (78), (113), (133), (139), (163), (169),
% 116.10/17.80 | | | | | | | | | (171), (174), (180), (188), (215), (753), (761),
% 116.10/17.80 | | | | | | | | | (763) are inconsistent by sub-proof #142.
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | (764) all_56_0 = e3
% 116.10/17.80 | | | | | | | | | (765) ~ (all_56_14 = e2)
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | COMBINE_EQS: (198), (764) imply:
% 116.10/17.80 | | | | | | | | | (766) all_52_4 = e3
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | REDUCE: (15), (765) imply:
% 116.10/17.80 | | | | | | | | | (767) ~ (all_6_2 = e2)
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | REDUCE: (195), (766) imply:
% 116.10/17.80 | | | | | | | | | (768) ~ (all_10_2 = e3)
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | | REF_CLOSE: (4), (6), (10), (12), (15), (16), (37), (39), (44),
% 116.10/17.80 | | | | | | | | | (51), (53), (55), (59), (70), (71), (75), (86),
% 116.10/17.80 | | | | | | | | | (91), (95), (96), (97), (102), (108), (113), (121),
% 116.10/17.80 | | | | | | | | | (128), (136), (146), (151), (162), (167), (170),
% 116.10/17.80 | | | | | | | | | (173), (175), (178), (185), (188), (197), (205),
% 116.10/17.80 | | | | | | | | | (206), (211), (455), (748), (749), (755), (767) are
% 116.10/17.80 | | | | | | | | | inconsistent by sub-proof #271.
% 116.10/17.80 | | | | | | | | |
% 116.10/17.80 | | | | | | | | End of split
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | Case 2:
% 116.10/17.80 | | | | | | | |
% 116.10/17.80 | | | | | | | | (769) all_56_12 = e2
% 116.10/17.81 | | | | | | | |
% 116.10/17.81 | | | | | | | | COMBINE_EQS: (36), (769) imply:
% 116.10/17.81 | | | | | | | | (770) all_10_2 = e2
% 116.10/17.81 | | | | | | | |
% 116.10/17.81 | | | | | | | | REDUCE: (124), (770) imply:
% 116.10/17.81 | | | | | | | | (771) ~ (all_52_1 = e2)
% 116.10/17.81 | | | | | | | |
% 116.10/17.81 | | | | | | | | BETA: splitting (104) gives:
% 116.10/17.81 | | | | | | | |
% 116.10/17.81 | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | (772) ~ (all_56_7 = e1)
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | REDUCE: (153), (772) imply:
% 116.10/17.81 | | | | | | | | | (773) ~ (all_52_6 = e1)
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | BETA: splitting (197) gives:
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | (774) all_58_2 = e2
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | COMBINE_EQS: (108), (774) imply:
% 116.10/17.81 | | | | | | | | | | (775) all_52_1 = e2
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | REDUCE: (771), (775) imply:
% 116.10/17.81 | | | | | | | | | | (776) $false
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | CLOSE: (776) is inconsistent.
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | (777) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | BETA: splitting (777) gives:
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | (778) all_58_3 = e2
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | COMBINE_EQS: (71), (778) imply:
% 116.10/17.81 | | | | | | | | | | | (779) all_8_2 = e2
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | REDUCE: (146), (779) imply:
% 116.10/17.81 | | | | | | | | | | | (780) $false
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | CLOSE: (780) is inconsistent.
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | (781) all_58_5 = e2 | all_58_10 = e2
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | BETA: splitting (151) gives:
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | (782) all_58_6 = e1
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | COMBINE_EQS: (121), (782) imply:
% 116.10/17.81 | | | | | | | | | | | | (783) all_52_2 = e1
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | SIMP: (783) implies:
% 116.10/17.81 | | | | | | | | | | | | (784) all_52_2 = e1
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | COMBINE_EQS: (175), (784) imply:
% 116.10/17.81 | | | | | | | | | | | | (785) all_56_6 = e1
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | REDUCE: (178), (784) imply:
% 116.10/17.81 | | | | | | | | | | | | (786) ~ (all_52_14 = e1)
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | REDUCE: (55), (784) imply:
% 116.10/17.81 | | | | | | | | | | | | (787) ~ (all_6_2 = e1)
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | BETA: splitting (70) gives:
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | (788) ~ (all_56_6 = e1)
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | REDUCE: (785), (788) imply:
% 116.10/17.81 | | | | | | | | | | | | | (789) $false
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | CLOSE: (789) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | (790) ~ (all_56_14 = e3)
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | REDUCE: (15), (790) imply:
% 116.10/17.81 | | | | | | | | | | | | | (791) ~ (all_6_2 = e3)
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | BETA: splitting (781) gives:
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | (792) all_58_5 = e2
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | COMBINE_EQS: (96), (792) imply:
% 116.10/17.81 | | | | | | | | | | | | | | (793) all_52_9 = e2
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | REDUCE: (755), (793) imply:
% 116.10/17.81 | | | | | | | | | | | | | | (794) $false
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | CLOSE: (794) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | (795) all_58_10 = e2
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | COMBINE_EQS: (128), (795) imply:
% 116.10/17.81 | | | | | | | | | | | | | | (796) all_52_13 = e2
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | COMBINE_EQS: (170), (796) imply:
% 116.10/17.81 | | | | | | | | | | | | | | (797) all_56_5 = e2
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | REDUCE: (129), (796) imply:
% 116.10/17.81 | | | | | | | | | | | | | | (798) ~ (all_8_2 = e2)
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | (799) ~ (all_56_5 = e2)
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | REDUCE: (797), (799) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | (800) $false
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | CLOSE: (800) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | (801) ~ (all_56_13 = e0)
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | REDUCE: (143), (801) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | (802) ~ (all_8_2 = e0)
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | (803) ~ (all_56_6 = e1)
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | REDUCE: (785), (803) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | (804) $false
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | CLOSE: (804) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | (805) ~ (all_56_13 = e3)
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | REDUCE: (143), (805) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | (806) ~ (all_8_2 = e3)
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | (807) all_54_10 = e3
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (791), (807) are inconsistent by sub-proof
% 116.10/17.81 | | | | | | | | | | | | | | | | | #352.
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | (808) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | (809) all_54_5 = e3
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (806), (809) are inconsistent by sub-proof
% 116.10/17.81 | | | | | | | | | | | | | | | | | | #339.
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | (810) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | (811) all_54_5 = e2
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (146), (811) are inconsistent by sub-proof
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | #338.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | (812) all_54_5 = e1 | all_54_5 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (808) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (813) all_54_10 = e2
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (813) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (814) all_6_2 = e2
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | SIMP: (814) implies:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (815) all_6_2 = e2
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | REDUCE: (759), (815) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (816) ~ (all_4_1 = e2)
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | SIMP: (816) implies:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (817) ~ (all_4_1 = e2)
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | (818) all_54_14 = e3
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (757), (818) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | (819) all_4_1 = e3
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | REDUCE: (750), (819) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | (820) op(e3, e1) = all_4_0
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (812) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | (821) all_54_5 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (821) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | (822) all_8_2 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | SIMP: (822) implies:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | (823) all_8_2 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (823) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | (824) ~ (all_52_9 = e1)
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (825) all_58_4 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (825) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (826) all_52_8 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (826) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (827) op(e3, e1) = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with e1, all_4_0, e1, e3,
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (820), (827) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (828) all_4_0 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (217), (828) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (829) $false
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (829) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | (830) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (830) gives:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | (831) all_58_5 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (831) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | (832) all_52_9 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (824), (832) imply:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | (833) $false
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (833) is inconsistent.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | (834) all_58_8 = e1 | all_58_14 = e1
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (162), (205), (747), (834) are inconsistent
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #219.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | (835) all_54_5 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (802), (835) are inconsistent by sub-proof
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | | #311.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | (836) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (746), (747), (757), (817), (836) are
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #138.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (837) all_54_10 = e1 | all_54_10 = e0
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (37), (39), (44), (53), (59), (86), (95),
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (102), (113), (167), (188), (205), (206), (455),
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | | (749), (837) are inconsistent by sub-proof #278.
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | (838) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | | REF_CLOSE: (6), (75), (162), (205), (749), (773), (838) are
% 116.10/17.81 | | | | | | | | | | | | inconsistent by sub-proof #354.
% 116.10/17.81 | | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | | |
% 116.10/17.81 | | | | | | | | | End of split
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | Case 2:
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | (839) ~ (all_56_12 = e2)
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | REDUCE: (769), (839) imply:
% 116.10/17.81 | | | | | | | | | (840) $false
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | | CLOSE: (840) is inconsistent.
% 116.10/17.81 | | | | | | | | |
% 116.10/17.81 | | | | | | | | End of split
% 116.10/17.81 | | | | | | | |
% 116.10/17.81 | | | | | | | End of split
% 116.10/17.81 | | | | | | |
% 116.10/17.81 | | | | | | Case 2:
% 116.10/17.81 | | | | | | |
% 116.10/17.81 | | | | | | | (841) ~ (all_56_15 = e1)
% 116.10/17.81 | | | | | | |
% 116.10/17.81 | | | | | | | REDUCE: (742), (841) imply:
% 116.10/17.81 | | | | | | | (842) $false
% 116.10/17.81 | | | | | | |
% 116.10/17.81 | | | | | | | CLOSE: (842) is inconsistent.
% 116.10/17.81 | | | | | | |
% 116.10/17.81 | | | | | | End of split
% 116.10/17.81 | | | | | |
% 116.10/17.81 | | | | | Case 2:
% 116.10/17.81 | | | | | |
% 116.10/17.81 | | | | | | (843) ~ (all_56_15 = e1)
% 116.10/17.81 | | | | | |
% 116.10/17.81 | | | | | | REDUCE: (742), (843) imply:
% 116.10/17.81 | | | | | | (844) $false
% 116.10/17.81 | | | | | |
% 116.10/17.81 | | | | | | CLOSE: (844) is inconsistent.
% 116.10/17.81 | | | | | |
% 116.10/17.81 | | | | | End of split
% 116.10/17.81 | | | | |
% 116.10/17.81 | | | | End of split
% 116.10/17.81 | | | |
% 116.10/17.81 | | | End of split
% 116.10/17.81 | | |
% 116.10/17.81 | | End of split
% 116.10/17.81 | |
% 116.10/17.81 | Case 2:
% 116.10/17.81 | |
% 116.10/17.81 | | (845) all_26_0 = e1
% 116.10/17.81 | | (846) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.10/17.81 | |
% 116.10/17.81 | | COMBINE_EQS: (213), (845) imply:
% 116.10/17.81 | | (847) all_4_0 = e1
% 116.10/17.81 | |
% 116.10/17.81 | | REF_CLOSE: (3), (4), (6), (7), (10), (12), (13), (14), (15), (16), (17),
% 116.10/17.81 | | (18), (19), (22), (23), (25), (27), (28), (35), (36), (37), (38),
% 116.10/17.81 | | (39), (40), (41), (42), (44), (46), (47), (50), (51), (53), (54),
% 116.10/17.81 | | (55), (56), (57), (58), (59), (61), (62), (65), (66), (68), (69),
% 116.10/17.81 | | (70), (71), (72), (74), (75), (76), (77), (79), (80), (86), (89),
% 116.10/17.81 | | (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 116.10/17.81 | | (101), (102), (105), (106), (107), (108), (112), (113), (114),
% 116.10/17.81 | | (115), (117), (118), (120), (121), (122), (123), (124), (125),
% 116.10/17.81 | | (126), (127), (128), (129), (135), (136), (137), (138), (139),
% 116.10/17.81 | | (140), (141), (142), (143), (146), (147), (148), (149), (151),
% 116.10/17.81 | | (152), (153), (154), (157), (160), (161), (162), (163), (165),
% 116.10/17.81 | | (166), (167), (168), (169), (170), (172), (173), (175), (176),
% 116.10/17.81 | | (177), (178), (179), (181), (183), (184), (185), (186), (187),
% 116.10/17.81 | | (188), (189), (192), (194), (195), (197), (198), (200), (201),
% 116.10/17.81 | | (204), (205), (206), (207), (210), (211), (846), (847) are
% 116.10/17.81 | | inconsistent by sub-proof #225.
% 116.10/17.81 | |
% 116.10/17.81 | End of split
% 116.10/17.81 |
% 116.10/17.81 End of proof
% 116.10/17.81
% 116.10/17.81 Sub-proof #138 shows that the following formulas are inconsistent:
% 116.10/17.81 ----------------------------------------------------------------
% 116.10/17.81 (1) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 116.10/17.81 (2) ~ (all_4_1 = e2)
% 116.10/17.81 (3) all_54_14 = all_52_11
% 116.10/17.81 (4) all_54_14 = all_4_1
% 116.10/17.81 (5) ~ (all_52_11 = e1)
% 116.10/17.81 (6) ~ (all_52_11 = e0)
% 116.10/17.81
% 116.10/17.81 Begin of proof
% 116.10/17.81 |
% 116.10/17.81 | BETA: splitting (1) gives:
% 116.10/17.81 |
% 116.10/17.81 | Case 1:
% 116.10/17.81 | |
% 116.10/17.81 | | (7) all_54_14 = e2
% 116.10/17.81 | |
% 116.10/17.81 | | COMBINE_EQS: (4), (7) imply:
% 116.10/17.81 | | (8) all_4_1 = e2
% 116.10/17.81 | |
% 116.10/17.81 | | SIMP: (8) implies:
% 116.10/17.81 | | (9) all_4_1 = e2
% 116.10/17.81 | |
% 116.10/17.81 | | REDUCE: (2), (9) imply:
% 116.10/17.81 | | (10) $false
% 116.10/17.81 | |
% 116.10/17.81 | | CLOSE: (10) is inconsistent.
% 116.10/17.81 | |
% 116.10/17.81 | Case 2:
% 116.10/17.81 | |
% 116.10/17.81 | | (11) all_54_14 = e1 | all_54_14 = e0
% 116.10/17.81 | |
% 116.10/17.81 | | REF_CLOSE: (3), (5), (6), (11) are inconsistent by sub-proof #139.
% 116.10/17.81 | |
% 116.10/17.81 | End of split
% 116.10/17.81 |
% 116.10/17.81 End of proof
% 116.10/17.81
% 116.10/17.81 Sub-proof #139 shows that the following formulas are inconsistent:
% 116.10/17.81 ----------------------------------------------------------------
% 116.10/17.81 (1) all_54_14 = e1 | all_54_14 = e0
% 116.10/17.81 (2) all_54_14 = all_52_11
% 116.10/17.81 (3) ~ (all_52_11 = e1)
% 116.10/17.81 (4) ~ (all_52_11 = e0)
% 116.10/17.81
% 116.10/17.81 Begin of proof
% 116.10/17.81 |
% 116.10/17.81 | BETA: splitting (1) gives:
% 116.10/17.81 |
% 116.10/17.81 | Case 1:
% 116.10/17.81 | |
% 116.10/17.81 | | (5) all_54_14 = e1
% 116.10/17.81 | |
% 116.10/17.81 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #141.
% 116.10/17.81 | |
% 116.10/17.81 | Case 2:
% 116.10/17.81 | |
% 116.10/17.81 | | (6) all_54_14 = e0
% 116.10/17.81 | |
% 116.10/17.81 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #140.
% 116.10/17.81 | |
% 116.10/17.81 | End of split
% 116.10/17.81 |
% 116.10/17.81 End of proof
% 116.10/17.81
% 116.10/17.81 Sub-proof #140 shows that the following formulas are inconsistent:
% 116.10/17.81 ----------------------------------------------------------------
% 116.10/17.81 (1) all_54_14 = all_52_11
% 116.10/17.81 (2) all_54_14 = e0
% 116.10/17.81 (3) ~ (all_52_11 = e0)
% 116.10/17.81
% 116.10/17.81 Begin of proof
% 116.10/17.81 |
% 116.10/17.81 | COMBINE_EQS: (1), (2) imply:
% 116.10/17.81 | (4) all_52_11 = e0
% 116.10/17.81 |
% 116.10/17.81 | SIMP: (4) implies:
% 116.10/17.81 | (5) all_52_11 = e0
% 116.10/17.81 |
% 116.10/17.81 | REDUCE: (3), (5) imply:
% 116.10/17.81 | (6) $false
% 116.10/17.81 |
% 116.10/17.81 | CLOSE: (6) is inconsistent.
% 116.10/17.81 |
% 116.10/17.81 End of proof
% 116.10/17.81
% 116.10/17.81 Sub-proof #141 shows that the following formulas are inconsistent:
% 116.10/17.81 ----------------------------------------------------------------
% 116.10/17.81 (1) all_54_14 = all_52_11
% 116.10/17.81 (2) all_54_14 = e1
% 116.10/17.81 (3) ~ (all_52_11 = e1)
% 116.10/17.81
% 116.10/17.81 Begin of proof
% 116.10/17.81 |
% 116.10/17.81 | COMBINE_EQS: (1), (2) imply:
% 116.10/17.81 | (4) all_52_11 = e1
% 116.10/17.81 |
% 116.10/17.81 | SIMP: (4) implies:
% 116.10/17.81 | (5) all_52_11 = e1
% 116.10/17.81 |
% 116.10/17.81 | REDUCE: (3), (5) imply:
% 116.10/17.81 | (6) $false
% 116.10/17.81 |
% 116.10/17.81 | CLOSE: (6) is inconsistent.
% 116.10/17.81 |
% 116.10/17.81 End of proof
% 116.10/17.81
% 116.10/17.81 Sub-proof #142 shows that the following formulas are inconsistent:
% 116.10/17.81 ----------------------------------------------------------------
% 116.10/17.81 (1) ~ (all_52_8 = all_10_2)
% 116.10/17.81 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.10/17.81 (3) all_54_2 = all_52_8
% 116.10/17.81 (4) all_54_0 = all_10_2
% 116.10/17.82 (5) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.82 (6) ~ (all_52_4 = e3)
% 116.10/17.82 (7) all_56_12 = all_10_2
% 116.10/17.82 (8) all_58_0 = all_10_2
% 116.10/17.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.82 (10) ~ (all_10_2 = e2)
% 116.10/17.82 (11) all_58_4 = all_52_8
% 116.10/17.82 (12) all_56_2 = all_52_12
% 116.10/17.82 (13) op(e3, e1) = all_52_8
% 116.10/17.82 (14) ~ (all_10_2 = e3)
% 116.10/17.82 (15) op(e3, all_10_2) = all_10_1
% 116.10/17.82 (16) all_58_1 = all_52_4
% 116.10/17.82 (17) ~ (all_52_8 = e3)
% 116.10/17.82 (18) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.82 (19) all_58_9 = all_52_12
% 116.10/17.82 (20) op(e2, e1) = all_52_9
% 116.10/17.82 (21) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.82 (22) ~ (all_52_8 = all_52_9)
% 116.10/17.82 (23) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.82 (24) op(all_10_1, all_10_2) = e2
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (23) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (25) all_58_0 = e3
% 116.10/17.82 | |
% 116.10/17.82 | | COMBINE_EQS: (8), (25) imply:
% 116.10/17.82 | | (26) all_10_2 = e3
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (14), (26) imply:
% 116.10/17.82 | | (27) $false
% 116.10/17.82 | |
% 116.10/17.82 | | CLOSE: (27) is inconsistent.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (28) ~ (all_58_0 = e3)
% 116.10/17.82 | | (29) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.82 | |
% 116.10/17.82 | | BETA: splitting (29) gives:
% 116.10/17.82 | |
% 116.10/17.82 | | Case 1:
% 116.10/17.82 | | |
% 116.10/17.82 | | | (30) all_58_1 = e3
% 116.10/17.82 | | |
% 116.10/17.82 | | | COMBINE_EQS: (16), (30) imply:
% 116.10/17.82 | | | (31) all_52_4 = e3
% 116.10/17.82 | | |
% 116.10/17.82 | | | REDUCE: (6), (31) imply:
% 116.10/17.82 | | | (32) $false
% 116.10/17.82 | | |
% 116.10/17.82 | | | CLOSE: (32) is inconsistent.
% 116.10/17.82 | | |
% 116.10/17.82 | | Case 2:
% 116.10/17.82 | | |
% 116.10/17.82 | | | (33) all_58_4 = e3 | all_58_9 = e3
% 116.10/17.82 | | |
% 116.10/17.82 | | | BETA: splitting (33) gives:
% 116.10/17.82 | | |
% 116.10/17.82 | | | Case 1:
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | (34) all_58_4 = e3
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | COMBINE_EQS: (11), (34) imply:
% 116.10/17.82 | | | | (35) all_52_8 = e3
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | REDUCE: (17), (35) imply:
% 116.10/17.82 | | | | (36) $false
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | CLOSE: (36) is inconsistent.
% 116.10/17.82 | | | |
% 116.10/17.82 | | | Case 2:
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | (37) all_58_9 = e3
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | COMBINE_EQS: (19), (37) imply:
% 116.10/17.82 | | | | (38) all_52_12 = e3
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | COMBINE_EQS: (12), (38) imply:
% 116.10/17.82 | | | | (39) all_56_2 = e3
% 116.10/17.82 | | | |
% 116.10/17.82 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (13), (14), (15),
% 116.10/17.82 | | | | (17), (18), (20), (21), (22), (24), (39) are inconsistent by
% 116.10/17.82 | | | | sub-proof #143.
% 116.10/17.82 | | | |
% 116.10/17.82 | | | End of split
% 116.10/17.82 | | |
% 116.10/17.82 | | End of split
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #143 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) ~ (all_52_8 = all_10_2)
% 116.10/17.82 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.10/17.82 (3) all_54_2 = all_52_8
% 116.10/17.82 (4) all_54_0 = all_10_2
% 116.10/17.82 (5) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.82 (6) all_56_12 = all_10_2
% 116.10/17.82 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.82 (8) ~ (all_10_2 = e2)
% 116.10/17.82 (9) op(e3, e1) = all_52_8
% 116.10/17.82 (10) ~ (all_10_2 = e3)
% 116.10/17.82 (11) all_56_2 = e3
% 116.10/17.82 (12) op(e3, all_10_2) = all_10_1
% 116.10/17.82 (13) ~ (all_52_8 = e3)
% 116.10/17.82 (14) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.82 (15) op(e2, e1) = all_52_9
% 116.10/17.82 (16) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.82 (17) ~ (all_52_8 = all_52_9)
% 116.10/17.82 (18) op(all_10_1, all_10_2) = e2
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (2) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (19) ~ (all_56_2 = e3)
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (11), (19) imply:
% 116.10/17.82 | | (20) $false
% 116.10/17.82 | |
% 116.10/17.82 | | CLOSE: (20) is inconsistent.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (21) ~ (all_56_12 = e0)
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (6), (21) imply:
% 116.10/17.82 | | (22) ~ (all_10_2 = e0)
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15),
% 116.10/17.82 | | (16), (17), (18), (22) are inconsistent by sub-proof #144.
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #144 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) ~ (all_52_8 = all_10_2)
% 116.10/17.82 (2) all_54_2 = all_52_8
% 116.10/17.82 (3) all_54_0 = all_10_2
% 116.10/17.82 (4) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.82 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.82 (6) ~ (all_10_2 = e2)
% 116.10/17.82 (7) op(e3, e1) = all_52_8
% 116.10/17.82 (8) ~ (all_10_2 = e3)
% 116.10/17.82 (9) op(e3, all_10_2) = all_10_1
% 116.10/17.82 (10) ~ (all_52_8 = e3)
% 116.10/17.82 (11) ~ (all_10_2 = e0)
% 116.10/17.82 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.82 (13) op(e2, e1) = all_52_9
% 116.10/17.82 (14) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.82 (15) ~ (all_52_8 = all_52_9)
% 116.10/17.82 (16) op(all_10_1, all_10_2) = e2
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (12) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (17) all_54_0 = e3
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (3), (8), (17) are inconsistent by sub-proof #451.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (18) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 116.10/17.82 | | (15), (16), (18) are inconsistent by sub-proof #164.
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #145 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) all_54_2 = all_52_8
% 116.10/17.82 (2) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.82 (3) ~ (all_52_8 = e1)
% 116.10/17.82 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.82 (5) op(e3, e1) = all_52_8
% 116.10/17.82 (6) all_10_2 = e1
% 116.10/17.82 (7) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.10/17.82 (8) op(all_10_1, e1) = e2
% 116.10/17.82 (9) all_56_12 = e1
% 116.10/17.82 (10) all_56_1 = all_52_8
% 116.10/17.82 (11) op(e2, e1) = all_52_9
% 116.10/17.82 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.82 (13) ~ (all_52_8 = all_52_9)
% 116.10/17.82 (14) op(e3, e1) = all_10_1
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (2) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (15) ~ (all_10_2 = e1)
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (6), (15) imply:
% 116.10/17.82 | | (16) $false
% 116.10/17.82 | |
% 116.10/17.82 | | CLOSE: (16) is inconsistent.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (17) ~ (all_10_1 = e0)
% 116.10/17.82 | |
% 116.10/17.82 | | BETA: splitting (7) gives:
% 116.10/17.82 | |
% 116.10/17.82 | | Case 1:
% 116.10/17.82 | | |
% 116.10/17.82 | | | (18) ~ (all_56_1 = e3)
% 116.10/17.82 | | |
% 116.10/17.82 | | | REDUCE: (10), (18) imply:
% 116.10/17.82 | | | (19) ~ (all_52_8 = e3)
% 116.10/17.82 | | |
% 116.10/17.82 | | | REF_CLOSE: (1), (3), (4), (5), (8), (11), (12), (13), (14), (17), (19) are
% 116.10/17.82 | | | inconsistent by sub-proof #165.
% 116.10/17.82 | | |
% 116.10/17.82 | | Case 2:
% 116.10/17.82 | | |
% 116.10/17.82 | | | (20) ~ (all_56_12 = e1)
% 116.10/17.82 | | |
% 116.10/17.82 | | | REDUCE: (9), (20) imply:
% 116.10/17.82 | | | (21) $false
% 116.10/17.82 | | |
% 116.10/17.82 | | | CLOSE: (21) is inconsistent.
% 116.10/17.82 | | |
% 116.10/17.82 | | End of split
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #146 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) ~ (all_52_1 = e2)
% 116.10/17.82 (2) ~ (all_4_2 = e0)
% 116.10/17.82 (3) all_56_14 = all_6_2
% 116.10/17.82 (4) all_56_11 = all_52_11
% 116.10/17.82 (5) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.10/17.82 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.82 (7) all_54_10 = all_6_2
% 116.10/17.82 (8) ~ (e2 = e1)
% 116.10/17.82 (9) all_58_3 = all_8_2
% 116.10/17.82 (10) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.10/17.82 (11) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.10/17.82 (12) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.10/17.82 (13) all_58_5 = all_52_9
% 116.10/17.82 (14) all_56_9 = all_52_3
% 116.10/17.82 (15) all_58_15 = all_4_2
% 116.10/17.82 (16) all_58_2 = all_52_1
% 116.10/17.82 (17) all_58_13 = all_52_7
% 116.10/17.82 (18) ~ (all_52_7 = e0)
% 116.10/17.82 (19) all_58_10 = all_52_13
% 116.10/17.82 (20) all_58_14 = all_52_11
% 116.10/17.82 (21) all_56_13 = all_8_2
% 116.10/17.82 (22) ~ (all_6_2 = e2)
% 116.10/17.82 (23) all_56_13 = e1
% 116.10/17.82 (24) all_56_4 = all_52_9
% 116.10/17.82 (25) all_56_5 = all_52_13
% 116.10/17.82 (26) all_58_12 = all_52_3
% 116.10/17.82 (27) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.82 (28) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.10/17.82 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.10/17.82 (29) ~ (all_6_2 = e1)
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | COMBINE_EQS: (21), (23) imply:
% 116.10/17.82 | (30) all_8_2 = e1
% 116.10/17.82 |
% 116.10/17.82 | SIMP: (30) implies:
% 116.10/17.82 | (31) all_8_2 = e1
% 116.10/17.82 |
% 116.10/17.82 | COMBINE_EQS: (9), (31) imply:
% 116.10/17.82 | (32) all_58_3 = e1
% 116.10/17.82 |
% 116.10/17.82 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 116.10/17.82 | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 116.10/17.82 | (26), (27), (28), (29), (32) are inconsistent by sub-proof #427.
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #147 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) all_54_4 = e1 | all_54_4 = e0
% 116.10/17.82 (2) all_54_4 = all_52_1
% 116.10/17.82 (3) ~ (all_52_1 = e1)
% 116.10/17.82 (4) ~ (all_52_1 = e0)
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (1) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (5) all_54_4 = e1
% 116.10/17.82 | |
% 116.10/17.82 | | COMBINE_EQS: (2), (5) imply:
% 116.10/17.82 | | (6) all_52_1 = e1
% 116.10/17.82 | |
% 116.10/17.82 | | SIMP: (6) implies:
% 116.10/17.82 | | (7) all_52_1 = e1
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (3), (7) imply:
% 116.10/17.82 | | (8) $false
% 116.10/17.82 | |
% 116.10/17.82 | | CLOSE: (8) is inconsistent.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (9) all_54_4 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #323.
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #148 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) ~ (all_52_3 = e2)
% 116.10/17.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.82 (3) op(e2, e3) = e1
% 116.10/17.82 (4) ~ (all_52_2 = all_52_3)
% 116.10/17.82 (5) op(e2, e3) = all_52_1
% 116.10/17.82 (6) all_58_13 = all_52_7
% 116.10/17.82 (7) ~ (all_52_7 = e0)
% 116.10/17.82 (8) all_58_14 = all_52_11
% 116.10/17.82 (9) ~ (all_52_1 = all_52_3)
% 116.10/17.82 (10) op(e1, e3) = e3
% 116.10/17.82 (11) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.10/17.82 (12) op(e1, e3) = all_52_2
% 116.10/17.82 (13) all_58_13 = e0 | all_58_14 = e0
% 116.10/17.82 (14) ~ (all_52_3 = all_52_11)
% 116.10/17.82 (15) all_54_12 = all_52_3
% 116.10/17.82
% 116.10/17.82 Begin of proof
% 116.10/17.82 |
% 116.10/17.82 | BETA: splitting (13) gives:
% 116.10/17.82 |
% 116.10/17.82 | Case 1:
% 116.10/17.82 | |
% 116.10/17.82 | | (16) all_58_13 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (6), (7), (16) are inconsistent by sub-proof #430.
% 116.10/17.82 | |
% 116.10/17.82 | Case 2:
% 116.10/17.82 | |
% 116.10/17.82 | | (17) all_58_14 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | COMBINE_EQS: (8), (17) imply:
% 116.10/17.82 | | (18) all_52_11 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | SIMP: (18) implies:
% 116.10/17.82 | | (19) all_52_11 = e0
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (14), (19) imply:
% 116.10/17.82 | | (20) ~ (all_52_3 = e0)
% 116.10/17.82 | |
% 116.10/17.82 | | GROUND_INST: instantiating (2) with all_52_2, e3, e3, e1, simplifying with
% 116.10/17.82 | | (10), (12) gives:
% 116.10/17.82 | | (21) all_52_2 = e3
% 116.10/17.82 | |
% 116.10/17.82 | | GROUND_INST: instantiating (2) with all_52_1, e1, e3, e2, simplifying with
% 116.10/17.82 | | (3), (5) gives:
% 116.10/17.82 | | (22) all_52_1 = e1
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (9), (22) imply:
% 116.10/17.82 | | (23) ~ (all_52_3 = e1)
% 116.10/17.82 | |
% 116.10/17.82 | | SIMP: (23) implies:
% 116.10/17.82 | | (24) ~ (all_52_3 = e1)
% 116.10/17.82 | |
% 116.10/17.82 | | REDUCE: (4), (21) imply:
% 116.10/17.82 | | (25) ~ (all_52_3 = e3)
% 116.10/17.82 | |
% 116.10/17.82 | | SIMP: (25) implies:
% 116.10/17.82 | | (26) ~ (all_52_3 = e3)
% 116.10/17.82 | |
% 116.10/17.82 | | REF_CLOSE: (1), (11), (15), (20), (24), (26) are inconsistent by sub-proof
% 116.10/17.82 | | #405.
% 116.10/17.82 | |
% 116.10/17.82 | End of split
% 116.10/17.82 |
% 116.10/17.82 End of proof
% 116.10/17.82
% 116.10/17.82 Sub-proof #149 shows that the following formulas are inconsistent:
% 116.10/17.82 ----------------------------------------------------------------
% 116.10/17.82 (1) all_56_14 = all_6_2
% 116.10/17.82 (2) all_58_9 = e3
% 116.10/17.82 (3) all_54_10 = all_6_2
% 116.10/17.82 (4) all_56_2 = all_52_12
% 116.10/17.82 (5) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 116.10/17.82 (6) ~ (all_6_2 = e2)
% 116.10/17.82 (7) all_58_9 = all_52_12
% 116.10/17.82 (8) ~ (all_6_2 = e1)
% 116.10/17.83 (9) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | COMBINE_EQS: (2), (7) imply:
% 116.10/17.83 | (10) all_52_12 = e3
% 116.10/17.83 |
% 116.10/17.83 | COMBINE_EQS: (4), (10) imply:
% 116.10/17.83 | (11) all_56_2 = e3
% 116.10/17.83 |
% 116.10/17.83 | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11) are inconsistent by sub-proof
% 116.10/17.83 | #351.
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #150 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) all_58_7 = all_52_6
% 116.10/17.83 (2) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.10/17.83 (3) all_56_14 = all_6_2
% 116.10/17.83 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.10/17.83 (5) ~ (all_52_14 = all_6_2)
% 116.10/17.83 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.83 (7) all_54_10 = all_6_2
% 116.10/17.83 (8) ~ (all_52_8 = all_6_2)
% 116.10/17.83 (9) all_58_4 = all_52_8
% 116.10/17.83 (10) all_58_11 = all_52_14
% 116.10/17.83 (11) all_58_6 = all_52_2
% 116.10/17.83 (12) ~ (all_52_12 = e3)
% 116.10/17.83 (13) all_58_0 = e2
% 116.10/17.83 (14) ~ (all_6_2 = e2)
% 116.10/17.83 (15) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.83 (16) all_58_8 = all_6_2
% 116.10/17.83 (17) all_58_9 = all_52_12
% 116.10/17.83 (18) ~ (all_10_1 = e3)
% 116.10/17.83 (19) all_56_6 = all_52_2
% 116.10/17.83 (20) all_56_15 = e3
% 116.10/17.83 (21) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.83 (22) all_56_8 = all_52_14
% 116.10/17.83 (23) ~ (all_52_6 = e1)
% 116.10/17.83 (24) ~ (e3 = e2)
% 116.10/17.83 (25) all_58_1 = all_10_1
% 116.10/17.83 (26) ~ (all_6_2 = e1)
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | BETA: splitting (2) gives:
% 116.10/17.83 |
% 116.10/17.83 | Case 1:
% 116.10/17.83 | |
% 116.10/17.83 | | (27) ~ (all_56_6 = e1)
% 116.10/17.83 | |
% 116.10/17.83 | | REDUCE: (19), (27) imply:
% 116.10/17.83 | | (28) ~ (all_52_2 = e1)
% 116.10/17.83 | |
% 116.10/17.83 | | BETA: splitting (15) gives:
% 116.10/17.83 | |
% 116.10/17.83 | | Case 1:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (29) all_58_6 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | REF_CLOSE: (11), (28), (29) are inconsistent by sub-proof #452.
% 116.10/17.83 | | |
% 116.10/17.83 | | Case 2:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (30) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 116.10/17.83 | | | (16), (17), (18), (21), (22), (23), (24), (25), (26), (30) are
% 116.10/17.83 | | | inconsistent by sub-proof #151.
% 116.10/17.83 | | |
% 116.10/17.83 | | End of split
% 116.10/17.83 | |
% 116.10/17.83 | Case 2:
% 116.10/17.83 | |
% 116.10/17.83 | | (31) ~ (all_56_15 = e3)
% 116.10/17.83 | |
% 116.10/17.83 | | REDUCE: (20), (31) imply:
% 116.10/17.83 | | (32) $false
% 116.10/17.83 | |
% 116.10/17.83 | | CLOSE: (32) is inconsistent.
% 116.10/17.83 | |
% 116.10/17.83 | End of split
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #151 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) all_58_7 = all_52_6
% 116.10/17.83 (2) all_56_14 = all_6_2
% 116.10/17.83 (3) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.10/17.83 (4) ~ (all_52_14 = all_6_2)
% 116.10/17.83 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.83 (6) all_54_10 = all_6_2
% 116.10/17.83 (7) ~ (all_52_8 = all_6_2)
% 116.10/17.83 (8) all_58_4 = all_52_8
% 116.10/17.83 (9) all_58_11 = all_52_14
% 116.10/17.83 (10) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.83 (11) ~ (all_52_12 = e3)
% 116.10/17.83 (12) all_58_0 = e2
% 116.10/17.83 (13) ~ (all_6_2 = e2)
% 116.10/17.83 (14) all_58_8 = all_6_2
% 116.10/17.83 (15) all_58_9 = all_52_12
% 116.10/17.83 (16) ~ (all_10_1 = e3)
% 116.10/17.83 (17) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.83 (18) all_56_8 = all_52_14
% 116.10/17.83 (19) ~ (all_52_6 = e1)
% 116.10/17.83 (20) ~ (e3 = e2)
% 116.10/17.83 (21) all_58_1 = all_10_1
% 116.10/17.83 (22) ~ (all_6_2 = e1)
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | BETA: splitting (10) gives:
% 116.10/17.83 |
% 116.10/17.83 | Case 1:
% 116.10/17.83 | |
% 116.10/17.83 | | (23) all_58_7 = e1
% 116.10/17.83 | |
% 116.10/17.83 | | COMBINE_EQS: (1), (23) imply:
% 116.10/17.83 | | (24) all_52_6 = e1
% 116.10/17.83 | |
% 116.10/17.83 | | REDUCE: (19), (24) imply:
% 116.10/17.83 | | (25) $false
% 116.10/17.83 | |
% 116.10/17.83 | | CLOSE: (25) is inconsistent.
% 116.10/17.83 | |
% 116.10/17.83 | Case 2:
% 116.10/17.83 | |
% 116.10/17.83 | | (26) all_58_8 = e1 | all_58_11 = e1
% 116.10/17.83 | |
% 116.10/17.83 | | BETA: splitting (26) gives:
% 116.10/17.83 | |
% 116.10/17.83 | | Case 1:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (27) all_58_8 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | COMBINE_EQS: (14), (27) imply:
% 116.10/17.83 | | | (28) all_6_2 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | REDUCE: (22), (28) imply:
% 116.10/17.83 | | | (29) $false
% 116.10/17.83 | | |
% 116.10/17.83 | | | CLOSE: (29) is inconsistent.
% 116.10/17.83 | | |
% 116.10/17.83 | | Case 2:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (30) all_58_11 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | COMBINE_EQS: (9), (30) imply:
% 116.10/17.83 | | | (31) all_52_14 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | COMBINE_EQS: (18), (31) imply:
% 116.10/17.83 | | | (32) all_56_8 = e1
% 116.10/17.83 | | |
% 116.10/17.83 | | | REDUCE: (4), (31) imply:
% 116.10/17.83 | | | (33) ~ (all_6_2 = e1)
% 116.10/17.83 | | |
% 116.10/17.83 | | | BETA: splitting (17) gives:
% 116.10/17.83 | | |
% 116.10/17.83 | | | Case 1:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | (34) all_58_0 = e3
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | REF_CLOSE: (12), (20), (34) are inconsistent by sub-proof #154.
% 116.10/17.83 | | | |
% 116.10/17.83 | | | Case 2:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | (35) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | BETA: splitting (3) gives:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | Case 1:
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | (36) ~ (all_56_8 = e1)
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | REDUCE: (32), (36) imply:
% 116.10/17.83 | | | | | (37) $false
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | CLOSE: (37) is inconsistent.
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | Case 2:
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | (38) ~ (all_56_14 = e0)
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | REDUCE: (2), (38) imply:
% 116.10/17.83 | | | | | (39) ~ (all_6_2 = e0)
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | BETA: splitting (5) gives:
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | Case 1:
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | (40) all_54_10 = e3
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | COMBINE_EQS: (6), (40) imply:
% 116.10/17.83 | | | | | | (41) all_6_2 = e3
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | SIMP: (41) implies:
% 116.10/17.83 | | | | | | (42) all_6_2 = e3
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | REDUCE: (7), (42) imply:
% 116.10/17.83 | | | | | | (43) ~ (all_52_8 = e3)
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | BETA: splitting (35) gives:
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | Case 1:
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | (44) all_58_1 = e3
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | COMBINE_EQS: (21), (44) imply:
% 116.10/17.83 | | | | | | | (45) all_10_1 = e3
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | REDUCE: (16), (45) imply:
% 116.10/17.83 | | | | | | | (46) $false
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | CLOSE: (46) is inconsistent.
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | Case 2:
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | (47) all_58_4 = e3 | all_58_9 = e3
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | | REF_CLOSE: (8), (11), (15), (43), (47) are inconsistent by
% 116.10/17.83 | | | | | | | sub-proof #184.
% 116.10/17.83 | | | | | | |
% 116.10/17.83 | | | | | | End of split
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | Case 2:
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | (48) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | | REF_CLOSE: (6), (13), (22), (39), (48) are inconsistent by sub-proof
% 116.10/17.83 | | | | | | #435.
% 116.10/17.83 | | | | | |
% 116.10/17.83 | | | | | End of split
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | End of split
% 116.10/17.83 | | | |
% 116.10/17.83 | | | End of split
% 116.10/17.83 | | |
% 116.10/17.83 | | End of split
% 116.10/17.83 | |
% 116.10/17.83 | End of split
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #152 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.83 (2) op(e2, e0) = all_8_1
% 116.10/17.83 (3) op(e2, e0) = e1
% 116.10/17.83 (4) ~ (all_8_1 = e1)
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | GROUND_INST: instantiating (1) with e1, all_8_1, e0, e2, simplifying with (2),
% 116.10/17.83 | (3) gives:
% 116.10/17.83 | (5) all_8_1 = e1
% 116.10/17.83 |
% 116.10/17.83 | REDUCE: (4), (5) imply:
% 116.10/17.83 | (6) $false
% 116.10/17.83 |
% 116.10/17.83 | CLOSE: (6) is inconsistent.
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #153 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) all_58_7 = all_52_6
% 116.10/17.83 (2) all_58_1 = e0
% 116.10/17.83 (3) ~ (all_52_1 = e2)
% 116.10/17.83 (4) ~ (all_4_2 = e0)
% 116.10/17.83 (5) all_56_14 = all_6_2
% 116.10/17.83 (6) all_56_11 = all_52_11
% 116.10/17.83 (7) ~ (e3 = e1)
% 116.10/17.83 (8) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.10/17.83 (9) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.10/17.83 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.83 (11) all_54_10 = all_6_2
% 116.10/17.83 (12) all_58_3 = all_8_2
% 116.10/17.83 (13) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.10/17.83 (14) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.10/17.83 (15) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.10/17.83 (16) all_58_5 = all_52_9
% 116.10/17.83 (17) all_56_9 = all_52_3
% 116.10/17.83 (18) all_58_15 = all_4_2
% 116.10/17.83 (19) all_58_2 = all_52_1
% 116.10/17.83 (20) all_58_13 = all_52_7
% 116.10/17.83 (21) ~ (all_52_7 = e0)
% 116.10/17.83 (22) all_58_10 = all_52_13
% 116.10/17.83 (23) ~ (all_52_6 = all_8_2)
% 116.10/17.83 (24) all_58_14 = all_52_11
% 116.10/17.83 (25) all_56_13 = all_8_2
% 116.10/17.83 (26) ~ (all_8_2 = e2)
% 116.10/17.83 (27) all_58_13 = e3
% 116.10/17.83 (28) all_56_4 = all_52_9
% 116.10/17.83 (29) all_56_5 = all_52_13
% 116.10/17.83 (30) ~ (all_52_6 = all_6_2)
% 116.10/17.83 (31) ~ (e2 = e0)
% 116.10/17.83 (32) all_58_12 = all_52_3
% 116.10/17.83 (33) ~ (all_52_6 = e1)
% 116.10/17.83 (34) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.83 (35) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.10/17.83 (36) ~ (e3 = e2)
% 116.10/17.83 (37) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.10/17.83 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.10/17.83 (38) ~ (all_6_2 = e1)
% 116.10/17.83 (39) ~ (e1 = e0)
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | BETA: splitting (9) gives:
% 116.10/17.83 |
% 116.10/17.83 | Case 1:
% 116.10/17.83 | |
% 116.10/17.83 | | (40) all_58_1 = e2
% 116.10/17.83 | |
% 116.10/17.83 | | REF_CLOSE: (2), (31), (40) are inconsistent by sub-proof #441.
% 116.10/17.83 | |
% 116.10/17.83 | Case 2:
% 116.10/17.83 | |
% 116.10/17.83 | | (41) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.10/17.83 | |
% 116.10/17.83 | | BETA: splitting (41) gives:
% 116.10/17.83 | |
% 116.10/17.83 | | Case 1:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (42) all_58_3 = e2
% 116.10/17.83 | | |
% 116.10/17.83 | | | COMBINE_EQS: (12), (42) imply:
% 116.10/17.83 | | | (43) all_8_2 = e2
% 116.10/17.83 | | |
% 116.10/17.83 | | | REDUCE: (26), (43) imply:
% 116.10/17.83 | | | (44) $false
% 116.10/17.83 | | |
% 116.10/17.83 | | | CLOSE: (44) is inconsistent.
% 116.10/17.83 | | |
% 116.10/17.83 | | Case 2:
% 116.10/17.83 | | |
% 116.10/17.83 | | | (45) all_58_7 = e2 | all_58_13 = e2
% 116.10/17.83 | | |
% 116.10/17.83 | | | BETA: splitting (45) gives:
% 116.10/17.83 | | |
% 116.10/17.83 | | | Case 1:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | (46) all_58_7 = e2
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | COMBINE_EQS: (1), (46) imply:
% 116.10/17.83 | | | | (47) all_52_6 = e2
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | REDUCE: (23), (47) imply:
% 116.10/17.83 | | | | (48) ~ (all_8_2 = e2)
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | REDUCE: (30), (47) imply:
% 116.10/17.83 | | | | (49) ~ (all_6_2 = e2)
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | SIMP: (49) implies:
% 116.10/17.83 | | | | (50) ~ (all_6_2 = e2)
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | REDUCE: (33), (47) imply:
% 116.10/17.83 | | | | (51) ~ (e2 = e1)
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | BETA: splitting (35) gives:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | Case 1:
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | (52) all_58_1 = e1
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | REF_CLOSE: (2), (39), (52) are inconsistent by sub-proof #440.
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | Case 2:
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | (53) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 116.10/17.83 | | | | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 116.10/17.83 | | | | | (26), (27), (28), (29), (32), (34), (37), (38), (46), (50),
% 116.10/17.83 | | | | | (51), (53) are inconsistent by sub-proof #162.
% 116.10/17.83 | | | | |
% 116.10/17.83 | | | | End of split
% 116.10/17.83 | | | |
% 116.10/17.83 | | | Case 2:
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | (54) all_58_13 = e2
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | COMBINE_EQS: (27), (54) imply:
% 116.10/17.83 | | | | (55) e3 = e2
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | REDUCE: (36), (55) imply:
% 116.10/17.83 | | | | (56) $false
% 116.10/17.83 | | | |
% 116.10/17.83 | | | | CLOSE: (56) is inconsistent.
% 116.10/17.83 | | | |
% 116.10/17.83 | | | End of split
% 116.10/17.83 | | |
% 116.10/17.83 | | End of split
% 116.10/17.83 | |
% 116.10/17.83 | End of split
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #154 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) all_58_0 = e3
% 116.10/17.83 (2) all_58_0 = e2
% 116.10/17.83 (3) ~ (e3 = e2)
% 116.10/17.83
% 116.10/17.83 Begin of proof
% 116.10/17.83 |
% 116.10/17.83 | COMBINE_EQS: (1), (2) imply:
% 116.10/17.83 | (4) e3 = e2
% 116.10/17.83 |
% 116.10/17.83 | SIMP: (4) implies:
% 116.10/17.83 | (5) e3 = e2
% 116.10/17.83 |
% 116.10/17.83 | REDUCE: (3), (5) imply:
% 116.10/17.83 | (6) $false
% 116.10/17.83 |
% 116.10/17.83 | CLOSE: (6) is inconsistent.
% 116.10/17.83 |
% 116.10/17.83 End of proof
% 116.10/17.83
% 116.10/17.83 Sub-proof #155 shows that the following formulas are inconsistent:
% 116.10/17.83 ----------------------------------------------------------------
% 116.10/17.83 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.10/17.83 (2) all_54_2 = all_52_8
% 116.10/17.83 (3) ~ (all_4_2 = e0)
% 116.10/17.83 (4) all_54_0 = all_10_2
% 116.10/17.83 (5) all_54_3 = all_52_12
% 116.10/17.83 (6) ~ (all_4_2 = e1)
% 116.10/17.83 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.10/17.83 (8) ~ (all_52_12 = all_10_2)
% 116.10/17.83 (9) all_56_12 = all_10_2
% 116.10/17.83 (10) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.10/17.83 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.83 (12) ~ (all_10_2 = e2)
% 116.10/17.83 (13) op(e3, e0) = all_52_12
% 116.10/17.83 (14) all_58_4 = all_52_8
% 116.10/17.83 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.10/17.83 (16) all_50_1 = all_10_1
% 116.10/17.83 (17) all_56_2 = all_52_12
% 116.10/17.83 (18) all_58_11 = all_52_14
% 116.10/17.83 (19) op(e3, e1) = all_52_8
% 116.10/17.83 (20) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.10/17.83 (21) all_50_2 = all_10_2
% 116.10/17.83 (22) all_58_5 = all_52_9
% 116.10/17.83 (23) all_56_9 = all_52_3
% 116.10/17.83 (24) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.10/17.83 (25) all_58_15 = all_4_2
% 116.10/17.83 (26) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.10/17.83 (27) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.10/17.83 (28) ~ (all_10_2 = e3)
% 116.10/17.83 (29) ~ (all_52_12 = all_52_13)
% 116.10/17.83 (30) all_56_15 = all_4_2
% 116.10/17.83 (31) all_58_10 = all_52_13
% 116.10/17.83 (32) ~ (all_52_11 = all_4_2)
% 116.10/17.83 (33) op(e3, all_10_2) = all_10_1
% 116.10/17.83 (34) all_58_14 = all_52_11
% 116.10/17.83 (35) ~ (all_6_2 = e2)
% 116.10/17.83 (36) all_56_1 = all_52_8
% 116.10/17.83 (37) all_58_8 = all_6_2
% 116.10/17.83 (38) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.83 (39) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.10/17.83 (40) all_56_4 = all_52_9
% 116.10/17.83 (41) all_58_9 = all_52_12
% 116.10/17.84 (42) op(e2, e1) = all_52_9
% 116.10/17.84 (43) ~ (all_52_3 = all_4_2)
% 116.10/17.84 (44) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.84 (45) ~ (all_52_8 = all_52_9)
% 116.10/17.84 (46) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.10/17.84 (47) op(e2, e0) = all_52_13
% 116.10/17.84 (48) ~ (all_52_3 = all_10_2)
% 116.10/17.84 (49) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.10/17.84 (50) all_56_8 = all_52_14
% 116.10/17.84 (51) op(all_10_1, all_10_2) = e2
% 116.10/17.84 (52) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.10/17.84 (53) all_54_15 = all_4_2
% 116.10/17.84 (54) ~ (all_52_3 = all_52_11)
% 116.10/17.84 (55) all_54_12 = all_52_3
% 116.10/17.84
% 116.10/17.84 Begin of proof
% 116.10/17.84 |
% 116.10/17.84 | BETA: splitting (52) gives:
% 116.10/17.84 |
% 116.10/17.84 | Case 1:
% 116.10/17.84 | |
% 116.10/17.84 | | (56) ~ (all_56_12 = e1)
% 116.10/17.84 | |
% 116.10/17.84 | | REDUCE: (9), (56) imply:
% 116.10/17.84 | | (57) ~ (all_10_2 = e1)
% 116.10/17.84 | |
% 116.10/17.84 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16), (17),
% 116.10/17.84 | | (18), (21), (24), (25), (27), (28), (29), (31), (33), (38), (41),
% 116.10/17.84 | | (47), (49), (50), (51), (57) are inconsistent by sub-proof #168.
% 116.10/17.84 | |
% 116.10/17.84 | Case 2:
% 116.10/17.84 | |
% 116.10/17.84 | | (58) all_56_12 = e1
% 116.10/17.84 | |
% 116.10/17.84 | | COMBINE_EQS: (9), (58) imply:
% 116.10/17.84 | | (59) all_10_2 = e1
% 116.10/17.84 | |
% 116.10/17.84 | | SIMP: (59) implies:
% 116.10/17.84 | | (60) all_10_2 = e1
% 116.10/17.84 | |
% 116.10/17.84 | | REDUCE: (48), (60) imply:
% 116.10/17.84 | | (61) ~ (all_52_3 = e1)
% 116.10/17.84 | |
% 116.10/17.84 | | REDUCE: (51), (60) imply:
% 116.10/17.84 | | (62) op(all_10_1, e1) = e2
% 116.10/17.84 | |
% 116.10/17.84 | | REDUCE: (33), (60) imply:
% 116.10/17.84 | | (63) op(e3, e1) = all_10_1
% 116.10/17.84 | |
% 116.10/17.84 | | BETA: splitting (20) gives:
% 116.10/17.84 | |
% 116.10/17.84 | | Case 1:
% 116.10/17.84 | | |
% 116.10/17.84 | | | (64) ~ (all_56_1 = e3)
% 116.10/17.84 | | |
% 116.10/17.84 | | | REDUCE: (36), (64) imply:
% 116.10/17.84 | | | (65) ~ (all_52_8 = e3)
% 116.10/17.84 | | |
% 116.10/17.84 | | | BETA: splitting (26) gives:
% 116.10/17.84 | | |
% 116.10/17.84 | | | Case 1:
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | (66) ~ (all_56_4 = e2)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REDUCE: (40), (66) imply:
% 116.10/17.84 | | | | (67) ~ (all_52_9 = e2)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | GROUND_INST: instantiating (11) with all_52_8, all_10_1, e1, e3,
% 116.10/17.84 | | | | simplifying with (19), (63) gives:
% 116.10/17.84 | | | | (68) all_52_8 = all_10_1
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | COMBINE_EQS: (2), (68) imply:
% 116.10/17.84 | | | | (69) all_54_2 = all_10_1
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REDUCE: (45), (68) imply:
% 116.10/17.84 | | | | (70) ~ (all_52_9 = all_10_1)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | SIMP: (70) implies:
% 116.10/17.84 | | | | (71) ~ (all_52_9 = all_10_1)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REDUCE: (65), (68) imply:
% 116.10/17.84 | | | | (72) ~ (all_10_1 = e3)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | BETA: splitting (44) gives:
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | Case 1:
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | | (73) all_54_2 = e3
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | | REF_CLOSE: (69), (72), (73) are inconsistent by sub-proof #166.
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | Case 2:
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | | (74) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | | BETA: splitting (74) gives:
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | | Case 1:
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | (75) all_54_2 = e2
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | COMBINE_EQS: (69), (75) imply:
% 116.10/17.84 | | | | | | (76) all_10_1 = e2
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | SIMP: (76) implies:
% 116.10/17.84 | | | | | | (77) all_10_1 = e2
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | REDUCE: (62), (77) imply:
% 116.10/17.84 | | | | | | (78) op(e2, e1) = e2
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | GROUND_INST: instantiating (11) with all_52_9, e2, e1, e2,
% 116.10/17.84 | | | | | | simplifying with (42), (78) gives:
% 116.10/17.84 | | | | | | (79) all_52_9 = e2
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | REDUCE: (67), (79) imply:
% 116.10/17.84 | | | | | | (80) $false
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | CLOSE: (80) is inconsistent.
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | Case 2:
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | (81) ~ (all_54_2 = e2)
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | REDUCE: (69), (81) imply:
% 116.10/17.84 | | | | | | (82) ~ (all_10_1 = e2)
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | | REF_CLOSE: (3), (6), (10), (11), (14), (15), (19), (22), (23), (30),
% 116.10/17.84 | | | | | | (32), (34), (35), (37), (39), (43), (46), (53), (54),
% 116.10/17.84 | | | | | | (55), (61), (63), (67), (82) are inconsistent by
% 116.10/17.84 | | | | | | sub-proof #403.
% 116.10/17.84 | | | | | |
% 116.10/17.84 | | | | | End of split
% 116.10/17.84 | | | | |
% 116.10/17.84 | | | | End of split
% 116.10/17.84 | | | |
% 116.10/17.84 | | | Case 2:
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | (83) ~ (all_56_12 = e1)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REDUCE: (58), (83) imply:
% 116.10/17.84 | | | | (84) $false
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | CLOSE: (84) is inconsistent.
% 116.10/17.84 | | | |
% 116.10/17.84 | | | End of split
% 116.10/17.84 | | |
% 116.10/17.84 | | Case 2:
% 116.10/17.84 | | |
% 116.10/17.84 | | | (85) ~ (all_56_12 = e1)
% 116.10/17.84 | | |
% 116.10/17.84 | | | REDUCE: (58), (85) imply:
% 116.10/17.84 | | | (86) $false
% 116.10/17.84 | | |
% 116.10/17.84 | | | CLOSE: (86) is inconsistent.
% 116.10/17.84 | | |
% 116.10/17.84 | | End of split
% 116.10/17.84 | |
% 116.10/17.84 | End of split
% 116.10/17.84 |
% 116.10/17.84 End of proof
% 116.10/17.84
% 116.10/17.84 Sub-proof #156 shows that the following formulas are inconsistent:
% 116.10/17.84 ----------------------------------------------------------------
% 116.10/17.84 (1) ~ (all_52_8 = all_10_2)
% 116.10/17.84 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.10/17.84 (3) ~ (all_52_2 = all_10_2)
% 116.10/17.84 (4) ~ (all_52_6 = all_52_14)
% 116.10/17.84 (5) all_54_2 = all_52_8
% 116.10/17.84 (6) all_58_7 = all_52_6
% 116.10/17.84 (7) ~ (all_52_13 = all_52_14)
% 116.10/17.84 (8) ~ (all_4_2 = e0)
% 116.10/17.84 (9) op(e3, e2) = all_52_4
% 116.10/17.84 (10) all_56_14 = all_6_2
% 116.10/17.84 (11) all_56_3 = all_52_1
% 116.10/17.84 (12) all_54_0 = all_10_2
% 116.10/17.84 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.10/17.84 (14) all_54_3 = all_52_12
% 116.10/17.84 (15) ~ (all_52_2 = all_52_6)
% 116.10/17.84 (16) ~ (all_52_12 = all_52_14)
% 116.10/17.84 (17) op(e0, e2) = all_52_7
% 116.10/17.84 (18) all_50_0 = e2
% 116.10/17.84 (19) ~ (all_52_7 = all_4_2)
% 116.10/17.84 (20) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.84 (21) all_56_11 = all_52_11
% 116.10/17.84 (22) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.10/17.84 (23) ~ (all_6_1 = e3)
% 116.10/17.84 (24) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.10/17.84 (25) ~ (all_52_12 = all_10_2)
% 116.10/17.84 (26) ~ (e3 = e1)
% 116.10/17.84 (27) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.10/17.84 (28) ~ (all_50_0 = e2) | ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.10/17.84 (29) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.10/17.84 (30) all_56_12 = all_10_2
% 116.10/17.84 (31) all_58_0 = all_10_2
% 116.10/17.84 (32) op(all_6_1, all_6_2) = all_6_0
% 116.10/17.84 (33) all_54_11 = all_52_14
% 116.10/17.84 (34) all_54_13 = all_52_7
% 116.10/17.84 (35) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.10/17.84 (36) ~ (all_52_14 = all_6_2)
% 116.10/17.84 (37) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 116.10/17.84 (38) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.10/17.84 (39) all_56_10 = all_52_7
% 116.10/17.84 (40) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.84 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.84 (42) all_54_8 = all_52_2
% 116.10/17.84 (43) ~ (all_52_2 = all_6_2)
% 116.10/17.84 (44) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.10/17.84 (45) all_54_10 = all_6_2
% 116.10/17.84 (46) op(e3, e0) = all_52_12
% 116.10/17.84 (47) ~ (all_52_8 = all_6_2)
% 116.10/17.84 (48) all_50_1 = all_10_1
% 116.10/17.84 (49) ~ (all_52_4 = all_52_7)
% 116.10/17.84 (50) all_56_2 = all_52_12
% 116.10/17.84 (51) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.10/17.84 (52) all_58_3 = all_8_2
% 116.10/17.84 (53) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.10/17.84 (54) all_58_11 = all_52_14
% 116.10/17.84 (55) all_54_9 = all_52_6
% 116.10/17.84 (56) op(e3, e1) = all_52_8
% 116.10/17.84 (57) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.10/17.84 (58) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.10/17.84 (59) all_50_2 = all_10_2
% 116.10/17.84 (60) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.10/17.84 (61) ~ (all_52_7 = all_8_2)
% 116.10/17.84 (62) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.10/17.84 (63) op(e1, e0) = all_52_14
% 116.10/17.84 (64) all_58_5 = all_52_9
% 116.10/17.84 (65) all_40_0 = all_6_0
% 116.10/17.84 (66) all_56_9 = all_52_3
% 116.10/17.84 (67) op(e1, all_6_2) = all_6_1
% 116.10/17.84 (68) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.10/17.84 (69) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.10/17.84 (70) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.10/17.84 (71) all_58_15 = all_4_2
% 116.10/17.84 (72) all_58_2 = all_52_1
% 116.10/17.84 (73) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.10/17.84 (74) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.10/17.84 (75) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 116.10/17.84 (76) ~ (all_10_2 = e3)
% 116.10/17.84 (77) ~ (all_52_12 = all_52_13)
% 116.10/17.84 (78) all_58_13 = all_52_7
% 116.10/17.84 (79) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.10/17.84 (80) all_40_1 = all_6_1
% 116.10/17.84 (81) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.10/17.84 (82) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.10/17.84 (83) all_58_6 = all_52_2
% 116.10/17.84 (84) ~ (all_52_1 = all_10_2)
% 116.10/17.84 (85) all_54_5 = all_8_2
% 116.10/17.84 (86) all_56_15 = all_4_2
% 116.10/17.84 (87) all_58_10 = all_52_13
% 116.10/17.84 (88) op(e3, all_10_2) = all_10_1
% 116.10/17.84 (89) ~ (all_52_6 = all_8_2)
% 116.10/17.84 (90) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.10/17.84 (91) ~ (all_6_0 = e2)
% 116.10/17.84 (92) all_58_1 = all_52_4
% 116.10/17.84 (93) all_58_14 = all_52_11
% 116.10/17.84 (94) all_54_1 = all_52_4
% 116.10/17.84 (95) all_56_13 = all_8_2
% 116.10/17.84 (96) ~ (all_8_2 = e2)
% 116.10/17.84 (97) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.10/17.84 (98) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.10/17.84 (99) op(e1, e2) = all_52_6
% 116.10/17.84 (100) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.84 (101) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.10/17.84 (102) all_56_7 = all_52_6
% 116.10/17.84 (103) ~ (all_52_4 = all_52_6)
% 116.10/17.84 (104) ~ (all_52_4 = all_52_12)
% 116.10/17.84 (105) op(e0, all_4_2) = all_4_1
% 116.10/17.84 (106) all_58_8 = all_6_2
% 116.10/17.84 (107) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.84 (108) all_40_2 = all_6_2
% 116.10/17.84 (109) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.10/17.84 (110) all_56_4 = all_52_9
% 116.10/17.84 (111) all_58_9 = all_52_12
% 116.10/17.84 (112) all_56_5 = all_52_13
% 116.10/17.84 (113) op(e2, e1) = all_52_9
% 116.10/17.84 (114) ~ (all_52_6 = all_6_2)
% 116.10/17.84 (115) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.84 (116) all_56_6 = all_52_2
% 116.10/17.84 (117) ~ (all_52_13 = all_4_2)
% 116.10/17.84 (118) all_58_12 = all_52_3
% 116.10/17.84 (119) ~ (all_52_2 = all_52_14)
% 116.10/17.84 (120) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.10/17.84 (121) ~ (all_52_8 = all_52_9)
% 116.10/17.84 (122) op(e2, e0) = all_52_13
% 116.10/17.84 (123) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.10/17.84 (124) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.84 (125) all_56_8 = all_52_14
% 116.10/17.84 (126) op(all_10_1, all_10_2) = e2
% 116.10/17.84 (127) ~ (all_52_4 = all_10_2)
% 116.10/17.84 (128) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.10/17.84 (129) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.84 (130) all_56_0 = all_52_4
% 116.10/17.84 (131) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.10/17.84 (132) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.10/17.84 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.10/17.84 (133) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.10/17.84 (134) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.10/17.84 (135) ~ (all_6_2 = e1)
% 116.10/17.84 (136) ~ (all_6_1 = e2)
% 116.10/17.84 (137) ~ (all_52_6 = all_52_7)
% 116.10/17.84
% 116.10/17.84 Begin of proof
% 116.10/17.84 |
% 116.10/17.84 | BETA: splitting (44) gives:
% 116.10/17.84 |
% 116.10/17.84 | Case 1:
% 116.10/17.84 | |
% 116.10/17.84 | | (138) ~ (all_40_0 = e3)
% 116.10/17.84 | |
% 116.10/17.84 | | REDUCE: (65), (138) imply:
% 116.10/17.84 | | (139) ~ (all_6_0 = e3)
% 116.10/17.84 | |
% 116.10/17.84 | | BETA: splitting (28) gives:
% 116.10/17.84 | |
% 116.10/17.84 | | Case 1:
% 116.10/17.84 | | |
% 116.10/17.84 | | | (140) ~ (all_50_0 = e2)
% 116.10/17.84 | | |
% 116.10/17.84 | | | REDUCE: (18), (140) imply:
% 116.10/17.84 | | | (141) $false
% 116.10/17.84 | | |
% 116.10/17.84 | | | CLOSE: (141) is inconsistent.
% 116.10/17.84 | | |
% 116.10/17.84 | | Case 2:
% 116.10/17.84 | | |
% 116.10/17.84 | | | (142) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.10/17.84 | | |
% 116.10/17.84 | | | BETA: splitting (81) gives:
% 116.10/17.84 | | |
% 116.10/17.84 | | | Case 1:
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | (143) ~ (all_56_14 = e2)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REDUCE: (10), (143) imply:
% 116.10/17.84 | | | | (144) ~ (all_6_2 = e2)
% 116.10/17.84 | | | |
% 116.10/17.84 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 116.10/17.84 | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 116.10/17.84 | | | | (23), (24), (25), (27), (29), (30), (31), (33), (34), (36),
% 116.10/17.84 | | | | (37), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 116.10/17.84 | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 116.10/17.84 | | | | (59), (60), (61), (62), (63), (64), (66), (67), (68), (69),
% 116.10/17.84 | | | | (71), (72), (73), (74), (76), (77), (78), (79), (82), (83),
% 116.10/17.84 | | | | (84), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 116.10/17.84 | | | | (95), (96), (98), (100), (101), (102), (103), (104), (105),
% 116.10/17.84 | | | | (106), (107), (109), (110), (111), (112), (113), (114),
% 116.10/17.84 | | | | (115), (116), (117), (118), (119), (120), (121), (122),
% 116.10/17.84 | | | | (123), (124), (125), (126), (129), (130), (131), (132),
% 116.10/17.84 | | | | (134), (135), (136), (137), (142), (144) are inconsistent by
% 116.10/17.84 | | | | sub-proof #157.
% 116.10/17.84 | | | |
% 116.10/17.84 | | | Case 2:
% 116.10/17.84 | | | |
% 116.10/17.85 | | | | (145) all_56_14 = e2
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | COMBINE_EQS: (10), (145) imply:
% 116.10/17.85 | | | | (146) all_6_2 = e2
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | SIMP: (146) implies:
% 116.10/17.85 | | | | (147) all_6_2 = e2
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (43), (147) imply:
% 116.10/17.85 | | | | (148) ~ (all_52_2 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (114), (147) imply:
% 116.10/17.85 | | | | (149) ~ (all_52_6 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (36), (147) imply:
% 116.10/17.85 | | | | (150) ~ (all_52_14 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (135), (147) imply:
% 116.10/17.85 | | | | (151) ~ (e2 = e1)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (32), (147) imply:
% 116.10/17.85 | | | | (152) op(all_6_1, e2) = all_6_0
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (67), (147) imply:
% 116.10/17.85 | | | | (153) op(e1, e2) = all_6_1
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REF_CLOSE: (3), (4), (6), (8), (12), (13), (15), (17), (21), (23), (26),
% 116.10/17.85 | | | | (30), (33), (34), (35), (38), (41), (42), (49), (52), (53),
% 116.10/17.85 | | | | (55), (62), (66), (68), (70), (71), (75), (78), (91), (92),
% 116.10/17.85 | | | | (93), (95), (96), (97), (99), (102), (107), (109), (116),
% 116.10/17.85 | | | | (118), (119), (125), (127), (128), (130), (131), (132),
% 116.10/17.85 | | | | (133), (137), (139), (145), (148), (149), (150), (151),
% 116.10/17.85 | | | | (152), (153) are inconsistent by sub-proof #375.
% 116.10/17.85 | | | |
% 116.10/17.85 | | | End of split
% 116.10/17.85 | | |
% 116.10/17.85 | | End of split
% 116.10/17.85 | |
% 116.10/17.85 | Case 2:
% 116.10/17.85 | |
% 116.10/17.85 | | (154) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.10/17.85 | |
% 116.10/17.85 | | BETA: splitting (28) gives:
% 116.10/17.85 | |
% 116.10/17.85 | | Case 1:
% 116.10/17.85 | | |
% 116.10/17.85 | | | (155) ~ (all_50_0 = e2)
% 116.10/17.85 | | |
% 116.10/17.85 | | | REDUCE: (18), (155) imply:
% 116.10/17.85 | | | (156) $false
% 116.10/17.85 | | |
% 116.10/17.85 | | | CLOSE: (156) is inconsistent.
% 116.10/17.85 | | |
% 116.10/17.85 | | Case 2:
% 116.10/17.85 | | |
% 116.10/17.85 | | | (157) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.10/17.85 | | |
% 116.10/17.85 | | | BETA: splitting (81) gives:
% 116.10/17.85 | | |
% 116.10/17.85 | | | Case 1:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (158) ~ (all_56_14 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (10), (158) imply:
% 116.10/17.85 | | | | (159) ~ (all_6_2 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 116.10/17.85 | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 116.10/17.85 | | | | (23), (24), (25), (27), (29), (30), (31), (33), (34), (36),
% 116.10/17.85 | | | | (37), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 116.10/17.85 | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 116.10/17.85 | | | | (59), (60), (61), (62), (63), (64), (66), (67), (68), (69),
% 116.10/17.85 | | | | (71), (72), (73), (74), (76), (77), (78), (79), (82), (83),
% 116.10/17.85 | | | | (84), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 116.10/17.85 | | | | (95), (96), (98), (100), (101), (102), (103), (104), (105),
% 116.10/17.85 | | | | (106), (107), (109), (110), (111), (112), (113), (114),
% 116.10/17.85 | | | | (115), (116), (117), (118), (119), (120), (121), (122),
% 116.10/17.85 | | | | (123), (124), (125), (126), (129), (130), (131), (132),
% 116.10/17.85 | | | | (134), (135), (136), (137), (157), (159) are inconsistent by
% 116.10/17.85 | | | | sub-proof #157.
% 116.10/17.85 | | | |
% 116.10/17.85 | | | Case 2:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (160) all_56_14 = e2
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REF_CLOSE: (10), (23), (38), (41), (53), (55), (67), (80), (99), (102),
% 116.10/17.85 | | | | (108), (114), (154), (160) are inconsistent by sub-proof
% 116.10/17.85 | | | | #372.
% 116.10/17.85 | | | |
% 116.10/17.85 | | | End of split
% 116.10/17.85 | | |
% 116.10/17.85 | | End of split
% 116.10/17.85 | |
% 116.10/17.85 | End of split
% 116.10/17.85 |
% 116.10/17.85 End of proof
% 116.10/17.85
% 116.10/17.85 Sub-proof #157 shows that the following formulas are inconsistent:
% 116.10/17.85 ----------------------------------------------------------------
% 116.10/17.85 (1) ~ (all_52_8 = all_10_2)
% 116.10/17.85 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.10/17.85 (3) ~ (all_52_2 = all_10_2)
% 116.10/17.85 (4) ~ (all_52_6 = all_52_14)
% 116.10/17.85 (5) all_54_2 = all_52_8
% 116.10/17.85 (6) all_58_7 = all_52_6
% 116.10/17.85 (7) ~ (all_52_13 = all_52_14)
% 116.10/17.85 (8) ~ (all_4_2 = e0)
% 116.10/17.85 (9) op(e3, e2) = all_52_4
% 116.10/17.85 (10) all_56_14 = all_6_2
% 116.10/17.85 (11) all_56_3 = all_52_1
% 116.10/17.85 (12) all_54_0 = all_10_2
% 116.10/17.85 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.10/17.85 (14) all_54_3 = all_52_12
% 116.10/17.85 (15) ~ (all_52_2 = all_52_6)
% 116.10/17.85 (16) ~ (all_52_12 = all_52_14)
% 116.10/17.85 (17) op(e0, e2) = all_52_7
% 116.10/17.85 (18) ~ (all_52_7 = all_4_2)
% 116.10/17.85 (19) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.10/17.85 (20) all_56_11 = all_52_11
% 116.10/17.85 (21) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.10/17.85 (22) ~ (all_6_1 = e3)
% 116.10/17.85 (23) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.10/17.85 (24) ~ (all_52_12 = all_10_2)
% 116.10/17.85 (25) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.10/17.85 (26) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.10/17.85 (27) all_56_12 = all_10_2
% 116.10/17.85 (28) all_58_0 = all_10_2
% 116.10/17.85 (29) all_54_11 = all_52_14
% 116.10/17.85 (30) all_54_13 = all_52_7
% 116.10/17.85 (31) ~ (all_52_14 = all_6_2)
% 116.10/17.85 (32) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 116.10/17.85 (33) all_56_10 = all_52_7
% 116.10/17.85 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.85 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.10/17.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.10/17.85 (36) all_54_8 = all_52_2
% 116.10/17.85 (37) ~ (all_52_2 = all_6_2)
% 116.10/17.85 (38) all_54_10 = all_6_2
% 116.10/17.85 (39) op(e3, e0) = all_52_12
% 116.10/17.85 (40) ~ (all_52_8 = all_6_2)
% 116.10/17.85 (41) all_50_1 = all_10_1
% 116.10/17.85 (42) ~ (all_52_4 = all_52_7)
% 116.10/17.85 (43) all_56_2 = all_52_12
% 116.10/17.85 (44) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.10/17.85 (45) all_58_3 = all_8_2
% 116.10/17.85 (46) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.10/17.85 (47) all_58_11 = all_52_14
% 116.10/17.85 (48) all_54_9 = all_52_6
% 116.10/17.85 (49) op(e3, e1) = all_52_8
% 116.10/17.85 (50) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.10/17.85 (51) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.10/17.85 (52) all_50_2 = all_10_2
% 116.10/17.85 (53) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.10/17.85 (54) ~ (all_52_7 = all_8_2)
% 116.10/17.85 (55) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.10/17.85 (56) op(e1, e0) = all_52_14
% 116.10/17.85 (57) all_58_5 = all_52_9
% 116.10/17.85 (58) all_56_9 = all_52_3
% 116.10/17.85 (59) op(e1, all_6_2) = all_6_1
% 116.10/17.85 (60) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.10/17.85 (61) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.10/17.85 (62) all_58_15 = all_4_2
% 116.10/17.85 (63) all_58_2 = all_52_1
% 116.10/17.85 (64) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.10/17.85 (65) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.10/17.85 (66) ~ (all_10_2 = e3)
% 116.10/17.85 (67) ~ (all_52_12 = all_52_13)
% 116.10/17.85 (68) all_58_13 = all_52_7
% 116.10/17.85 (69) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.10/17.85 (70) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.10/17.85 (71) all_58_6 = all_52_2
% 116.10/17.85 (72) ~ (all_52_1 = all_10_2)
% 116.10/17.85 (73) all_54_5 = all_8_2
% 116.10/17.85 (74) all_56_15 = all_4_2
% 116.10/17.85 (75) all_58_10 = all_52_13
% 116.10/17.85 (76) op(e3, all_10_2) = all_10_1
% 116.10/17.85 (77) ~ (all_52_6 = all_8_2)
% 116.10/17.85 (78) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.10/17.85 (79) all_58_1 = all_52_4
% 116.10/17.85 (80) all_58_14 = all_52_11
% 116.10/17.85 (81) all_54_1 = all_52_4
% 116.10/17.85 (82) all_56_13 = all_8_2
% 116.10/17.85 (83) ~ (all_8_2 = e2)
% 116.10/17.85 (84) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.10/17.85 (85) ~ (all_6_2 = e2)
% 116.10/17.85 (86) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.10/17.85 (87) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.10/17.85 (88) all_56_7 = all_52_6
% 116.10/17.85 (89) ~ (all_52_4 = all_52_6)
% 116.10/17.85 (90) ~ (all_52_4 = all_52_12)
% 116.10/17.85 (91) op(e0, all_4_2) = all_4_1
% 116.10/17.85 (92) all_58_8 = all_6_2
% 116.10/17.85 (93) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.85 (94) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.10/17.85 (95) all_56_4 = all_52_9
% 116.10/17.85 (96) all_58_9 = all_52_12
% 116.10/17.85 (97) all_56_5 = all_52_13
% 116.10/17.85 (98) op(e2, e1) = all_52_9
% 116.10/17.85 (99) ~ (all_52_6 = all_6_2)
% 116.10/17.85 (100) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.10/17.85 (101) all_56_6 = all_52_2
% 116.10/17.85 (102) ~ (all_52_13 = all_4_2)
% 116.10/17.85 (103) all_58_12 = all_52_3
% 116.10/17.85 (104) ~ (all_52_2 = all_52_14)
% 116.10/17.85 (105) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.10/17.85 (106) ~ (all_52_8 = all_52_9)
% 116.10/17.85 (107) op(e2, e0) = all_52_13
% 116.10/17.85 (108) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.10/17.85 (109) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.10/17.85 (110) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.10/17.85 (111) all_56_8 = all_52_14
% 116.10/17.85 (112) op(all_10_1, all_10_2) = e2
% 116.10/17.85 (113) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.85 (114) all_56_0 = all_52_4
% 116.10/17.85 (115) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.10/17.85 (116) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.10/17.85 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.10/17.85 (117) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.10/17.85 (118) ~ (all_6_2 = e1)
% 116.10/17.85 (119) ~ (all_6_1 = e2)
% 116.10/17.85 (120) ~ (all_52_6 = all_52_7)
% 116.10/17.85
% 116.10/17.85 Begin of proof
% 116.10/17.85 |
% 116.10/17.85 | BETA: splitting (70) gives:
% 116.10/17.85 |
% 116.10/17.85 | Case 1:
% 116.10/17.85 | |
% 116.10/17.85 | | (121) ~ (all_56_12 = e2)
% 116.10/17.85 | |
% 116.10/17.85 | | REDUCE: (27), (121) imply:
% 116.10/17.85 | | (122) ~ (all_10_2 = e2)
% 116.10/17.85 | |
% 116.10/17.85 | | BETA: splitting (109) gives:
% 116.10/17.85 | |
% 116.10/17.85 | | Case 1:
% 116.10/17.85 | | |
% 116.10/17.85 | | | (123) ~ (all_56_5 = e2)
% 116.10/17.85 | | |
% 116.10/17.85 | | | REDUCE: (97), (123) imply:
% 116.10/17.85 | | | (124) ~ (all_52_13 = e2)
% 116.10/17.85 | | |
% 116.10/17.85 | | | BETA: splitting (25) gives:
% 116.10/17.85 | | |
% 116.10/17.85 | | | Case 1:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (125) ~ (all_56_4 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REDUCE: (95), (125) imply:
% 116.10/17.85 | | | | (126) ~ (all_52_9 = e2)
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | BETA: splitting (113) gives:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | Case 1:
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | (127) all_58_2 = e2
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | COMBINE_EQS: (63), (127) imply:
% 116.10/17.85 | | | | | (128) all_52_1 = e2
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | COMBINE_EQS: (11), (128) imply:
% 116.10/17.85 | | | | | (129) all_56_3 = e2
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | REF_CLOSE: (10), (21), (22), (28), (29), (31), (34), (35), (38), (56),
% 116.10/17.85 | | | | | (59), (66), (78), (85), (94), (110), (111), (118), (119),
% 116.10/17.85 | | | | | (129) are inconsistent by sub-proof #199.
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | Case 2:
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | (130) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | REF_CLOSE: (45), (57), (75), (83), (124), (126), (130) are
% 116.10/17.85 | | | | | inconsistent by sub-proof #401.
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | End of split
% 116.10/17.85 | | | |
% 116.10/17.85 | | | Case 2:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (131) all_56_4 = e2
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REF_CLOSE: (2), (12), (14), (23), (24), (27), (35), (39), (41), (43),
% 116.10/17.85 | | | | (47), (52), (60), (62), (64), (65), (66), (67), (74), (75),
% 116.10/17.85 | | | | (76), (93), (96), (105), (107), (108), (111), (112), (122),
% 116.10/17.85 | | | | (131) are inconsistent by sub-proof #167.
% 116.10/17.85 | | | |
% 116.10/17.85 | | | End of split
% 116.10/17.85 | | |
% 116.10/17.85 | | Case 2:
% 116.10/17.85 | | |
% 116.10/17.85 | | | (132) all_56_5 = e2
% 116.10/17.85 | | | (133) ~ (all_56_12 = e0)
% 116.10/17.85 | | |
% 116.10/17.85 | | | COMBINE_EQS: (97), (132) imply:
% 116.10/17.85 | | | (134) all_52_13 = e2
% 116.10/17.85 | | |
% 116.10/17.85 | | | REDUCE: (27), (133) imply:
% 116.10/17.85 | | | (135) ~ (all_10_2 = e0)
% 116.10/17.85 | | |
% 116.10/17.85 | | | BETA: splitting (93) gives:
% 116.10/17.85 | | |
% 116.10/17.85 | | | Case 1:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (136) all_54_0 = e3
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | REF_CLOSE: (12), (66), (136) are inconsistent by sub-proof #451.
% 116.10/17.85 | | | |
% 116.10/17.85 | | | Case 2:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | (137) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | BETA: splitting (53) gives:
% 116.10/17.85 | | | |
% 116.10/17.85 | | | | Case 1:
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | (138) ~ (all_56_5 = e2)
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | REDUCE: (132), (138) imply:
% 116.10/17.85 | | | | | (139) $false
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | CLOSE: (139) is inconsistent.
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | Case 2:
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | (140) ~ (all_56_14 = e0)
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | REDUCE: (10), (140) imply:
% 116.10/17.85 | | | | | (141) ~ (all_6_2 = e0)
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | BETA: splitting (34) gives:
% 116.10/17.85 | | | | |
% 116.10/17.85 | | | | | Case 1:
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | (142) all_54_10 = e3
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | COMBINE_EQS: (38), (142) imply:
% 116.10/17.85 | | | | | | (143) all_6_2 = e3
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | SIMP: (143) implies:
% 116.10/17.85 | | | | | | (144) all_6_2 = e3
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | REDUCE: (40), (144) imply:
% 116.10/17.85 | | | | | | (145) ~ (all_52_8 = e3)
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | REF_CLOSE: (1), (5), (12), (19), (35), (49), (76), (98), (100),
% 116.10/17.85 | | | | | | (106), (112), (122), (135), (137), (145) are inconsistent
% 116.10/17.85 | | | | | | by sub-proof #164.
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | Case 2:
% 116.10/17.85 | | | | | |
% 116.10/17.85 | | | | | | (146) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.10/17.85 | | | | | |
% 116.10/17.86 | | | | | | REF_CLOSE: (38), (85), (118), (141), (146) are inconsistent by
% 116.10/17.86 | | | | | | sub-proof #435.
% 116.10/17.86 | | | | | |
% 116.10/17.86 | | | | | End of split
% 116.10/17.86 | | | | |
% 116.26/17.86 | | | | End of split
% 116.26/17.86 | | | |
% 116.26/17.86 | | | End of split
% 116.26/17.86 | | |
% 116.26/17.86 | | End of split
% 116.26/17.86 | |
% 116.26/17.86 | Case 2:
% 116.26/17.86 | |
% 116.26/17.86 | | (147) all_56_12 = e2
% 116.26/17.86 | | (148) ~ (all_56_10 = e0)
% 116.26/17.86 | |
% 116.26/17.86 | | COMBINE_EQS: (27), (147) imply:
% 116.26/17.86 | | (149) all_10_2 = e2
% 116.26/17.86 | |
% 116.26/17.86 | | SIMP: (149) implies:
% 116.26/17.86 | | (150) all_10_2 = e2
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (33), (148) imply:
% 116.26/17.86 | | (151) ~ (all_52_7 = e0)
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (72), (150) imply:
% 116.26/17.86 | | (152) ~ (all_52_1 = e2)
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (3), (150) imply:
% 116.26/17.86 | | (153) ~ (all_52_2 = e2)
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (24), (150) imply:
% 116.26/17.86 | | (154) ~ (all_52_12 = e2)
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (112), (150) imply:
% 116.26/17.86 | | (155) op(all_10_1, e2) = e2
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (76), (150) imply:
% 116.26/17.86 | | (156) op(e3, e2) = all_10_1
% 116.26/17.86 | |
% 116.26/17.86 | | BETA: splitting (117) gives:
% 116.26/17.86 | |
% 116.26/17.86 | | Case 1:
% 116.26/17.86 | | |
% 116.26/17.86 | | | (157) ~ (all_56_0 = e3)
% 116.26/17.86 | | |
% 116.26/17.86 | | | REDUCE: (114), (157) imply:
% 116.26/17.86 | | | (158) ~ (all_52_4 = e3)
% 116.26/17.86 | | |
% 116.26/17.86 | | | BETA: splitting (61) gives:
% 116.26/17.86 | | |
% 116.26/17.86 | | | Case 1:
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | (159) ~ (all_56_7 = e1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (88), (159) imply:
% 116.26/17.86 | | | | (160) ~ (all_52_6 = e1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | GROUND_INST: instantiating (35) with all_52_4, all_10_1, e2, e3,
% 116.26/17.86 | | | | simplifying with (9), (156) gives:
% 116.26/17.86 | | | | (161) all_52_4 = all_10_1
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | COMBINE_EQS: (81), (161) imply:
% 116.26/17.86 | | | | (162) all_54_1 = all_10_1
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | COMBINE_EQS: (79), (161) imply:
% 116.26/17.86 | | | | (163) all_58_1 = all_10_1
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (89), (161) imply:
% 116.26/17.86 | | | | (164) ~ (all_52_6 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | SIMP: (164) implies:
% 116.26/17.86 | | | | (165) ~ (all_52_6 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (42), (161) imply:
% 116.26/17.86 | | | | (166) ~ (all_52_7 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | SIMP: (166) implies:
% 116.26/17.86 | | | | (167) ~ (all_52_7 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (90), (161) imply:
% 116.26/17.86 | | | | (168) ~ (all_52_12 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | SIMP: (168) implies:
% 116.26/17.86 | | | | (169) ~ (all_52_12 = all_10_1)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (158), (161) imply:
% 116.26/17.86 | | | | (170) ~ (all_10_1 = e3)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | BETA: splitting (32) gives:
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | Case 1:
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | (171) ~ (all_56_8 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (111), (171) imply:
% 116.26/17.86 | | | | | (172) ~ (all_52_14 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | BETA: splitting (86) gives:
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | Case 1:
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | (173) all_58_6 = e1
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | COMBINE_EQS: (71), (173) imply:
% 116.26/17.86 | | | | | | (174) all_52_2 = e1
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | REF_CLOSE: (10), (21), (22), (28), (29), (31), (34), (35), (38),
% 116.26/17.86 | | | | | | (44), (56), (59), (66), (85), (94), (101), (110), (111),
% 116.26/17.86 | | | | | | (118), (119), (174) are inconsistent by sub-proof #163.
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | Case 2:
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | (175) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | REF_CLOSE: (6), (47), (92), (118), (160), (172), (175) are
% 116.26/17.86 | | | | | | inconsistent by sub-proof #354.
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | End of split
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | Case 2:
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | (176) all_56_8 = e1
% 116.26/17.86 | | | | | (177) ~ (all_56_13 = e0)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | COMBINE_EQS: (111), (176) imply:
% 116.26/17.86 | | | | | (178) all_52_14 = e1
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | COMBINE_EQS: (47), (178) imply:
% 116.26/17.86 | | | | | (179) all_58_11 = e1
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (82), (177) imply:
% 116.26/17.86 | | | | | (180) ~ (all_8_2 = e0)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (104), (178) imply:
% 116.26/17.86 | | | | | (181) ~ (all_52_2 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (16), (178) imply:
% 116.26/17.86 | | | | | (182) ~ (all_52_12 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (7), (178) imply:
% 116.26/17.86 | | | | | (183) ~ (all_52_13 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | REDUCE: (31), (178) imply:
% 116.26/17.86 | | | | | (184) ~ (all_6_2 = e1)
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | BETA: splitting (21) gives:
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | | Case 1:
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | (185) ~ (all_56_8 = e1)
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | REDUCE: (176), (185) imply:
% 116.26/17.86 | | | | | | (186) $false
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | CLOSE: (186) is inconsistent.
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | Case 2:
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | (187) ~ (all_56_14 = e0)
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | REDUCE: (10), (187) imply:
% 116.26/17.86 | | | | | | (188) ~ (all_6_2 = e0)
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | BETA: splitting (34) gives:
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | | Case 1:
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | (189) all_54_10 = e3
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | COMBINE_EQS: (38), (189) imply:
% 116.26/17.86 | | | | | | | (190) all_6_2 = e3
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | SIMP: (190) implies:
% 116.26/17.86 | | | | | | | (191) all_6_2 = e3
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | REDUCE: (37), (191) imply:
% 116.26/17.86 | | | | | | | (192) ~ (all_52_2 = e3)
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | REDUCE: (99), (191) imply:
% 116.26/17.86 | | | | | | | (193) ~ (all_52_6 = e3)
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | BETA: splitting (116) gives:
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | Case 1:
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | (194) all_58_15 = e0
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | COMBINE_EQS: (62), (194) imply:
% 116.26/17.86 | | | | | | | | (195) all_4_2 = e0
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | REDUCE: (8), (195) imply:
% 116.26/17.86 | | | | | | | | (196) $false
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | CLOSE: (196) is inconsistent.
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | Case 2:
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | (197) ~ (all_58_15 = e0)
% 116.26/17.86 | | | | | | | | (198) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.86 | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | ALPHA: (198) implies:
% 116.26/17.86 | | | | | | | | (199) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | BETA: splitting (55) gives:
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | | Case 1:
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | | (200) all_54_8 = e3
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | | REF_CLOSE: (36), (192), (200) are inconsistent by sub-proof
% 116.26/17.86 | | | | | | | | | #399.
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | Case 2:
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | | (201) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | | BETA: splitting (201) gives:
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | | Case 1:
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | (202) all_54_8 = e2
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | REF_CLOSE: (36), (153), (202) are inconsistent by sub-proof
% 116.26/17.86 | | | | | | | | | | #382.
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | Case 2:
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | (203) all_54_8 = e1 | all_54_8 = e0
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | BETA: splitting (203) gives:
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | Case 1:
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | | (204) all_54_8 = e1
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | | COMBINE_EQS: (36), (204) imply:
% 116.26/17.86 | | | | | | | | | | | (205) all_52_2 = e1
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | | REF_CLOSE: (10), (21), (22), (28), (29), (31), (34), (35),
% 116.26/17.86 | | | | | | | | | | | (38), (44), (56), (59), (66), (85), (94), (101),
% 116.26/17.86 | | | | | | | | | | | (110), (111), (118), (119), (205) are inconsistent
% 116.26/17.86 | | | | | | | | | | | by sub-proof #163.
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | Case 2:
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | | (206) all_54_8 = e0
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (13), (14), (15), (17), (18),
% 116.26/17.86 | | | | | | | | | | | (20), (23), (25), (26), (30), (34), (35), (36),
% 116.26/17.86 | | | | | | | | | | | (38), (45), (46), (48), (50), (51), (53), (54),
% 116.26/17.86 | | | | | | | | | | | (57), (58), (62), (63), (68), (69), (73), (75),
% 116.26/17.86 | | | | | | | | | | | (77), (80), (82), (84), (85), (87), (91), (95),
% 116.26/17.86 | | | | | | | | | | | (96), (97), (102), (103), (113), (115), (116),
% 116.26/17.86 | | | | | | | | | | | (118), (120), (151), (152), (154), (155), (160),
% 116.26/17.86 | | | | | | | | | | | (162), (163), (165), (167), (169), (170), (179),
% 116.26/17.86 | | | | | | | | | | | (180), (181), (182), (183), (193), (199), (206)
% 116.26/17.86 | | | | | | | | | | | are inconsistent by sub-proof #158.
% 116.26/17.86 | | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | | End of split
% 116.26/17.86 | | | | | | | | | |
% 116.26/17.86 | | | | | | | | | End of split
% 116.26/17.86 | | | | | | | | |
% 116.26/17.86 | | | | | | | | End of split
% 116.26/17.86 | | | | | | | |
% 116.26/17.86 | | | | | | | End of split
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | Case 2:
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | (207) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | | REF_CLOSE: (38), (85), (118), (188), (207) are inconsistent by
% 116.26/17.86 | | | | | | | sub-proof #435.
% 116.26/17.86 | | | | | | |
% 116.26/17.86 | | | | | | End of split
% 116.26/17.86 | | | | | |
% 116.26/17.86 | | | | | End of split
% 116.26/17.86 | | | | |
% 116.26/17.86 | | | | End of split
% 116.26/17.86 | | | |
% 116.26/17.86 | | | Case 2:
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | (208) ~ (all_56_12 = e2)
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | REDUCE: (147), (208) imply:
% 116.26/17.86 | | | | (209) $false
% 116.26/17.86 | | | |
% 116.26/17.86 | | | | CLOSE: (209) is inconsistent.
% 116.26/17.86 | | | |
% 116.26/17.86 | | | End of split
% 116.26/17.86 | | |
% 116.26/17.86 | | Case 2:
% 116.26/17.86 | | |
% 116.26/17.86 | | | (210) ~ (all_56_12 = e2)
% 116.26/17.86 | | |
% 116.26/17.86 | | | REDUCE: (147), (210) imply:
% 116.26/17.86 | | | (211) $false
% 116.26/17.86 | | |
% 116.26/17.86 | | | CLOSE: (211) is inconsistent.
% 116.26/17.86 | | |
% 116.26/17.86 | | End of split
% 116.26/17.86 | |
% 116.26/17.86 | End of split
% 116.26/17.86 |
% 116.26/17.86 End of proof
% 116.26/17.86
% 116.26/17.86 Sub-proof #158 shows that the following formulas are inconsistent:
% 116.26/17.86 ----------------------------------------------------------------
% 116.26/17.86 (1) all_58_7 = all_52_6
% 116.26/17.86 (2) ~ (all_52_1 = e2)
% 116.26/17.86 (3) ~ (all_4_2 = e0)
% 116.26/17.86 (4) all_56_14 = all_6_2
% 116.26/17.86 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.86 (6) all_54_3 = all_52_12
% 116.26/17.86 (7) ~ (all_52_2 = all_52_6)
% 116.26/17.86 (8) op(e0, e2) = all_52_7
% 116.26/17.86 (9) ~ (all_52_6 = all_10_1)
% 116.26/17.86 (10) ~ (all_52_7 = all_4_2)
% 116.26/17.86 (11) all_56_11 = all_52_11
% 116.26/17.86 (12) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.86 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.86 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.86 (15) op(all_10_1, e2) = e2
% 116.26/17.86 (16) all_54_13 = all_52_7
% 116.26/17.86 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.86 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.86 (19) all_54_8 = all_52_2
% 116.26/17.86 (20) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 116.26/17.86 (21) all_54_10 = all_6_2
% 116.26/17.86 (22) ~ (all_52_12 = e1)
% 116.26/17.86 (23) all_58_3 = all_8_2
% 116.26/17.86 (24) ~ (all_52_12 = all_10_1)
% 116.26/17.86 (25) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.86 (26) all_54_9 = all_52_6
% 116.26/17.86 (27) all_58_11 = e1
% 116.26/17.86 (28) ~ (all_8_2 = e0)
% 116.26/17.86 (29) ~ (all_52_6 = e3)
% 116.26/17.86 (30) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.86 (31) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.86 (32) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.86 (33) ~ (all_52_7 = all_8_2)
% 116.26/17.86 (34) all_58_5 = all_52_9
% 116.26/17.86 (35) ~ (all_52_7 = all_10_1)
% 116.26/17.86 (36) all_56_9 = all_52_3
% 116.26/17.86 (37) all_58_15 = all_4_2
% 116.26/17.86 (38) all_58_2 = all_52_1
% 116.26/17.86 (39) all_58_13 = all_52_7
% 116.26/17.86 (40) ~ (all_52_7 = e0)
% 116.26/17.86 (41) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/17.86 (42) ~ (all_52_2 = e1)
% 116.26/17.86 (43) ~ (all_52_13 = e1)
% 116.26/17.86 (44) all_54_5 = all_8_2
% 116.26/17.86 (45) all_58_10 = all_52_13
% 116.26/17.86 (46) ~ (all_52_6 = all_8_2)
% 116.26/17.86 (47) all_58_14 = all_52_11
% 116.26/17.86 (48) ~ (all_52_12 = e2)
% 116.26/17.86 (49) all_56_13 = all_8_2
% 116.26/17.86 (50) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.26/17.86 (51) all_54_1 = all_10_1
% 116.26/17.86 (52) ~ (all_6_2 = e2)
% 116.26/17.86 (53) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.86 (54) op(e0, all_4_2) = all_4_1
% 116.26/17.86 (55) all_56_4 = all_52_9
% 116.26/17.86 (56) all_58_9 = all_52_12
% 116.26/17.86 (57) all_56_5 = all_52_13
% 116.26/17.86 (58) ~ (all_10_1 = e3)
% 116.26/17.86 (59) all_54_8 = e0
% 116.26/17.86 (60) ~ (all_52_13 = all_4_2)
% 116.26/17.86 (61) all_58_12 = all_52_3
% 116.26/17.86 (62) ~ (all_52_6 = e1)
% 116.26/17.86 (63) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.86 (64) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.86 (65) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.86 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.86 (66) all_58_1 = all_10_1
% 116.26/17.86 (67) ~ (all_6_2 = e1)
% 116.26/17.86 (68) ~ (all_52_6 = all_52_7)
% 116.26/17.86
% 116.26/17.86 Begin of proof
% 116.26/17.86 |
% 116.26/17.86 | COMBINE_EQS: (19), (59) imply:
% 116.26/17.86 | (69) all_52_2 = e0
% 116.26/17.86 |
% 116.26/17.86 | SIMP: (69) implies:
% 116.26/17.86 | (70) all_52_2 = e0
% 116.26/17.86 |
% 116.26/17.86 | REDUCE: (7), (70) imply:
% 116.26/17.86 | (71) ~ (all_52_6 = e0)
% 116.26/17.86 |
% 116.26/17.86 | SIMP: (71) implies:
% 116.26/17.86 | (72) ~ (all_52_6 = e0)
% 116.26/17.86 |
% 116.26/17.86 | REDUCE: (42), (70) imply:
% 116.26/17.86 | (73) ~ (e1 = e0)
% 116.26/17.86 |
% 116.26/17.86 | SIMP: (73) implies:
% 116.26/17.86 | (74) ~ (e1 = e0)
% 116.26/17.86 |
% 116.26/17.86 | BETA: splitting (25) gives:
% 116.26/17.86 |
% 116.26/17.86 | Case 1:
% 116.26/17.86 | |
% 116.26/17.86 | | (75) all_54_9 = e3
% 116.26/17.86 | |
% 116.26/17.86 | | COMBINE_EQS: (26), (75) imply:
% 116.26/17.86 | | (76) all_52_6 = e3
% 116.26/17.86 | |
% 116.26/17.86 | | SIMP: (76) implies:
% 116.26/17.86 | | (77) all_52_6 = e3
% 116.26/17.86 | |
% 116.26/17.86 | | REDUCE: (29), (77) imply:
% 116.26/17.86 | | (78) $false
% 116.26/17.86 | |
% 116.26/17.86 | | CLOSE: (78) is inconsistent.
% 116.26/17.86 | |
% 116.26/17.86 | Case 2:
% 116.26/17.86 | |
% 116.26/17.86 | | (79) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.86 | |
% 116.26/17.86 | | BETA: splitting (79) gives:
% 116.26/17.86 | |
% 116.26/17.86 | | Case 1:
% 116.26/17.86 | | |
% 116.26/17.86 | | | (80) all_54_9 = e2
% 116.26/17.86 | | |
% 116.26/17.86 | | | COMBINE_EQS: (26), (80) imply:
% 116.26/17.87 | | | (81) all_52_6 = e2
% 116.26/17.87 | | |
% 116.26/17.87 | | | SIMP: (81) implies:
% 116.26/17.87 | | | (82) all_52_6 = e2
% 116.26/17.87 | | |
% 116.26/17.87 | | | COMBINE_EQS: (1), (82) imply:
% 116.26/17.87 | | | (83) all_58_7 = e2
% 116.26/17.87 | | |
% 116.26/17.87 | | | REDUCE: (68), (82) imply:
% 116.26/17.87 | | | (84) ~ (all_52_7 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | SIMP: (84) implies:
% 116.26/17.87 | | | (85) ~ (all_52_7 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | REDUCE: (9), (82) imply:
% 116.26/17.87 | | | (86) ~ (all_10_1 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | SIMP: (86) implies:
% 116.26/17.87 | | | (87) ~ (all_10_1 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | REDUCE: (46), (82) imply:
% 116.26/17.87 | | | (88) ~ (all_8_2 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | SIMP: (88) implies:
% 116.26/17.87 | | | (89) ~ (all_8_2 = e2)
% 116.26/17.87 | | |
% 116.26/17.87 | | | REDUCE: (62), (82) imply:
% 116.26/17.87 | | | (90) ~ (e2 = e1)
% 116.26/17.87 | | |
% 116.26/17.87 | | | BETA: splitting (50) gives:
% 116.26/17.87 | | |
% 116.26/17.87 | | | Case 1:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | (91) all_58_1 = e0
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | COMBINE_EQS: (66), (91) imply:
% 116.26/17.87 | | | | (92) all_10_1 = e0
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REDUCE: (24), (92) imply:
% 116.26/17.87 | | | | (93) ~ (all_52_12 = e0)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REDUCE: (87), (92) imply:
% 116.26/17.87 | | | | (94) ~ (e2 = e0)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | SIMP: (94) implies:
% 116.26/17.87 | | | | (95) ~ (e2 = e0)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REDUCE: (15), (92) imply:
% 116.26/17.87 | | | | (96) op(e0, e2) = e2
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | BETA: splitting (12) gives:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | Case 1:
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | (97) all_54_3 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | COMBINE_EQS: (6), (97) imply:
% 116.26/17.87 | | | | | (98) all_52_12 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | SIMP: (98) implies:
% 116.26/17.87 | | | | | (99) all_52_12 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | COMBINE_EQS: (56), (99) imply:
% 116.26/17.87 | | | | | (100) all_58_9 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REDUCE: (48), (99) imply:
% 116.26/17.87 | | | | | (101) ~ (e3 = e2)
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REDUCE: (22), (99) imply:
% 116.26/17.87 | | | | | (102) ~ (e3 = e1)
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REDUCE: (93), (99) imply:
% 116.26/17.87 | | | | | (103) ~ (e3 = e0)
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (13), (16), (17), (18),
% 116.26/17.87 | | | | | (20), (21), (23), (27), (30), (31), (32), (34), (36), (37),
% 116.26/17.87 | | | | | (38), (39), (40), (41), (43), (45), (47), (49), (52), (54),
% 116.26/17.87 | | | | | (55), (57), (60), (61), (63), (64), (65), (67), (74), (83),
% 116.26/17.87 | | | | | (89), (90), (91), (95), (96), (100), (101), (102), (103)
% 116.26/17.87 | | | | | are inconsistent by sub-proof #161.
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | Case 2:
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | (104) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REF_CLOSE: (6), (22), (48), (93), (104) are inconsistent by sub-proof
% 116.26/17.87 | | | | | #283.
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | End of split
% 116.26/17.87 | | | |
% 116.26/17.87 | | | Case 2:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | (105) ~ (all_58_1 = e0)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REDUCE: (66), (105) imply:
% 116.26/17.87 | | | | (106) ~ (all_10_1 = e0)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REF_CLOSE: (2), (3), (4), (5), (11), (13), (14), (16), (17), (21), (23),
% 116.26/17.87 | | | | (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 116.26/17.87 | | | | (39), (40), (44), (45), (47), (49), (51), (52), (53), (55),
% 116.26/17.87 | | | | (57), (58), (61), (63), (65), (67), (85), (87), (89), (90),
% 116.26/17.87 | | | | (106) are inconsistent by sub-proof #160.
% 116.26/17.87 | | | |
% 116.26/17.87 | | | End of split
% 116.26/17.87 | | |
% 116.26/17.87 | | Case 2:
% 116.26/17.87 | | |
% 116.26/17.87 | | | (107) all_54_9 = e1 | all_54_9 = e0
% 116.26/17.87 | | |
% 116.26/17.87 | | | REF_CLOSE: (26), (62), (72), (107) are inconsistent by sub-proof #159.
% 116.26/17.87 | | |
% 116.26/17.87 | | End of split
% 116.26/17.87 | |
% 116.26/17.87 | End of split
% 116.26/17.87 |
% 116.26/17.87 End of proof
% 116.26/17.87
% 116.26/17.87 Sub-proof #159 shows that the following formulas are inconsistent:
% 116.26/17.87 ----------------------------------------------------------------
% 116.26/17.87 (1) all_54_9 = e1 | all_54_9 = e0
% 116.26/17.87 (2) all_54_9 = all_52_6
% 116.26/17.87 (3) ~ (all_52_6 = e1)
% 116.26/17.87 (4) ~ (all_52_6 = e0)
% 116.26/17.87
% 116.26/17.87 Begin of proof
% 116.26/17.87 |
% 116.26/17.87 | BETA: splitting (1) gives:
% 116.26/17.87 |
% 116.26/17.87 | Case 1:
% 116.26/17.87 | |
% 116.26/17.87 | | (5) all_54_9 = e1
% 116.26/17.87 | |
% 116.26/17.87 | | COMBINE_EQS: (2), (5) imply:
% 116.26/17.87 | | (6) all_52_6 = e1
% 116.26/17.87 | |
% 116.26/17.87 | | REDUCE: (3), (6) imply:
% 116.26/17.87 | | (7) $false
% 116.26/17.87 | |
% 116.26/17.87 | | CLOSE: (7) is inconsistent.
% 116.26/17.87 | |
% 116.26/17.87 | Case 2:
% 116.26/17.87 | |
% 116.26/17.87 | | (8) all_54_9 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | COMBINE_EQS: (2), (8) imply:
% 116.26/17.87 | | (9) all_52_6 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | REDUCE: (4), (9) imply:
% 116.26/17.87 | | (10) $false
% 116.26/17.87 | |
% 116.26/17.87 | | CLOSE: (10) is inconsistent.
% 116.26/17.87 | |
% 116.26/17.87 | End of split
% 116.26/17.87 |
% 116.26/17.87 End of proof
% 116.26/17.87
% 116.26/17.87 Sub-proof #160 shows that the following formulas are inconsistent:
% 116.26/17.87 ----------------------------------------------------------------
% 116.26/17.87 (1) ~ (all_52_1 = e2)
% 116.26/17.87 (2) ~ (all_4_2 = e0)
% 116.26/17.87 (3) all_56_14 = all_6_2
% 116.26/17.87 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.87 (5) all_56_11 = all_52_11
% 116.26/17.87 (6) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.87 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.87 (8) all_54_13 = all_52_7
% 116.26/17.87 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.87 (10) all_54_10 = all_6_2
% 116.26/17.87 (11) ~ (e2 = e1)
% 116.26/17.87 (12) all_58_3 = all_8_2
% 116.26/17.87 (13) ~ (all_8_2 = e0)
% 116.26/17.87 (14) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.87 (15) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.87 (16) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.87 (17) ~ (all_52_7 = all_8_2)
% 116.26/17.87 (18) all_58_5 = all_52_9
% 116.26/17.87 (19) ~ (all_52_7 = all_10_1)
% 116.26/17.87 (20) all_56_9 = all_52_3
% 116.26/17.87 (21) all_58_15 = all_4_2
% 116.26/17.87 (22) all_58_2 = all_52_1
% 116.26/17.87 (23) all_58_13 = all_52_7
% 116.26/17.87 (24) ~ (all_52_7 = e0)
% 116.26/17.87 (25) all_54_5 = all_8_2
% 116.26/17.87 (26) all_58_10 = all_52_13
% 116.26/17.87 (27) ~ (all_52_7 = e2)
% 116.26/17.87 (28) ~ (all_10_1 = e2)
% 116.26/17.87 (29) all_58_14 = all_52_11
% 116.26/17.87 (30) all_56_13 = all_8_2
% 116.26/17.87 (31) ~ (all_8_2 = e2)
% 116.26/17.87 (32) all_54_1 = all_10_1
% 116.26/17.87 (33) ~ (all_6_2 = e2)
% 116.26/17.87 (34) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.87 (35) ~ (all_10_1 = e0)
% 116.26/17.87 (36) all_56_4 = all_52_9
% 116.26/17.87 (37) all_56_5 = all_52_13
% 116.26/17.87 (38) ~ (all_10_1 = e3)
% 116.26/17.87 (39) all_58_12 = all_52_3
% 116.26/17.87 (40) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.87 (41) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.87 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.87 (42) ~ (all_6_2 = e1)
% 116.26/17.87
% 116.26/17.87 Begin of proof
% 116.26/17.87 |
% 116.26/17.87 | BETA: splitting (34) gives:
% 116.26/17.87 |
% 116.26/17.87 | Case 1:
% 116.26/17.87 | |
% 116.26/17.87 | | (43) all_54_1 = e3
% 116.26/17.87 | |
% 116.26/17.87 | | REF_CLOSE: (32), (38), (43) are inconsistent by sub-proof #443.
% 116.26/17.87 | |
% 116.26/17.87 | Case 2:
% 116.26/17.87 | |
% 116.26/17.87 | | (44) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | BETA: splitting (44) gives:
% 116.26/17.87 | |
% 116.26/17.87 | | Case 1:
% 116.26/17.87 | | |
% 116.26/17.87 | | | (45) all_54_1 = e2
% 116.26/17.87 | | |
% 116.26/17.87 | | | REF_CLOSE: (28), (32), (45) are inconsistent by sub-proof #442.
% 116.26/17.87 | | |
% 116.26/17.87 | | Case 2:
% 116.26/17.87 | | |
% 116.26/17.87 | | | (46) all_54_1 = e1 | all_54_1 = e0
% 116.26/17.87 | | |
% 116.26/17.87 | | | BETA: splitting (15) gives:
% 116.26/17.87 | | |
% 116.26/17.87 | | | Case 1:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | (47) ~ (all_56_13 = e1)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REDUCE: (30), (47) imply:
% 116.26/17.87 | | | | (48) ~ (all_8_2 = e1)
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | BETA: splitting (7) gives:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | Case 1:
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | (49) all_54_5 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | COMBINE_EQS: (25), (49) imply:
% 116.26/17.87 | | | | | (50) all_8_2 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | SIMP: (50) implies:
% 116.26/17.87 | | | | | (51) all_8_2 = e3
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REDUCE: (17), (51) imply:
% 116.26/17.87 | | | | | (52) ~ (all_52_7 = e3)
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | BETA: splitting (4) gives:
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | Case 1:
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | | (53) all_54_13 = e3
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | | REF_CLOSE: (8), (52), (53) are inconsistent by sub-proof #336.
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | Case 2:
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | | (54) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | | BETA: splitting (54) gives:
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | | Case 1:
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | | (55) all_54_13 = e2
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | | REF_CLOSE: (8), (27), (55) are inconsistent by sub-proof #181.
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | Case 2:
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | | (56) all_54_13 = e1 | all_54_13 = e0
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | | BETA: splitting (56) gives:
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | | Case 1:
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | (57) all_54_13 = e1
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | COMBINE_EQS: (8), (57) imply:
% 116.26/17.87 | | | | | | | | (58) all_52_7 = e1
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | SIMP: (58) implies:
% 116.26/17.87 | | | | | | | | (59) all_52_7 = e1
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | REDUCE: (19), (59) imply:
% 116.26/17.87 | | | | | | | | (60) ~ (all_10_1 = e1)
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | SIMP: (60) implies:
% 116.26/17.87 | | | | | | | | (61) ~ (all_10_1 = e1)
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | BETA: splitting (46) gives:
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | Case 1:
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | (62) all_54_1 = e1
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | COMBINE_EQS: (32), (62) imply:
% 116.26/17.87 | | | | | | | | | (63) all_10_1 = e1
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | REDUCE: (61), (63) imply:
% 116.26/17.87 | | | | | | | | | (64) $false
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | CLOSE: (64) is inconsistent.
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | Case 2:
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | (65) all_54_1 = e0
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | COMBINE_EQS: (32), (65) imply:
% 116.26/17.87 | | | | | | | | | (66) all_10_1 = e0
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | REDUCE: (35), (66) imply:
% 116.26/17.87 | | | | | | | | | (67) $false
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | | CLOSE: (67) is inconsistent.
% 116.26/17.87 | | | | | | | | |
% 116.26/17.87 | | | | | | | | End of split
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | Case 2:
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | (68) all_54_13 = e0
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | | REF_CLOSE: (8), (24), (68) are inconsistent by sub-proof #334.
% 116.26/17.87 | | | | | | | |
% 116.26/17.87 | | | | | | | End of split
% 116.26/17.87 | | | | | | |
% 116.26/17.87 | | | | | | End of split
% 116.26/17.87 | | | | | |
% 116.26/17.87 | | | | | End of split
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | Case 2:
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | (69) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | | REF_CLOSE: (13), (25), (31), (48), (69) are inconsistent by sub-proof
% 116.26/17.87 | | | | | #310.
% 116.26/17.87 | | | | |
% 116.26/17.87 | | | | End of split
% 116.26/17.87 | | | |
% 116.26/17.87 | | | Case 2:
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | (70) all_56_13 = e1
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | COMBINE_EQS: (30), (70) imply:
% 116.26/17.87 | | | | (71) all_8_2 = e1
% 116.26/17.87 | | | |
% 116.26/17.87 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (14), (15),
% 116.26/17.87 | | | | (16), (18), (20), (21), (22), (23), (24), (26), (29), (30),
% 116.26/17.87 | | | | (33), (36), (37), (39), (40), (41), (42), (71) are
% 116.26/17.87 | | | | inconsistent by sub-proof #426.
% 116.26/17.87 | | | |
% 116.26/17.87 | | | End of split
% 116.26/17.87 | | |
% 116.26/17.87 | | End of split
% 116.26/17.87 | |
% 116.26/17.87 | End of split
% 116.26/17.87 |
% 116.26/17.87 End of proof
% 116.26/17.87
% 116.26/17.87 Sub-proof #161 shows that the following formulas are inconsistent:
% 116.26/17.87 ----------------------------------------------------------------
% 116.26/17.87 (1) all_58_1 = e0
% 116.26/17.87 (2) ~ (all_52_1 = e2)
% 116.26/17.87 (3) all_56_14 = all_6_2
% 116.26/17.87 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.87 (5) op(e0, e2) = all_52_7
% 116.26/17.87 (6) ~ (all_52_7 = all_4_2)
% 116.26/17.87 (7) all_56_11 = all_52_11
% 116.26/17.87 (8) all_58_9 = e3
% 116.26/17.87 (9) ~ (e3 = e1)
% 116.26/17.87 (10) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.87 (11) all_54_13 = all_52_7
% 116.26/17.87 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.87 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.87 (14) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 116.26/17.87 (15) all_54_10 = all_6_2
% 116.26/17.87 (16) ~ (e2 = e1)
% 116.26/17.87 (17) op(e0, e2) = e2
% 116.26/17.87 (18) all_58_7 = e2
% 116.26/17.87 (19) all_58_3 = all_8_2
% 116.26/17.87 (20) all_58_11 = e1
% 116.26/17.87 (21) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.87 (22) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.87 (23) ~ (e3 = e0)
% 116.26/17.87 (24) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.87 (25) all_58_5 = all_52_9
% 116.26/17.87 (26) all_56_9 = all_52_3
% 116.26/17.87 (27) all_58_15 = all_4_2
% 116.26/17.87 (28) all_58_2 = all_52_1
% 116.26/17.87 (29) all_58_13 = all_52_7
% 116.26/17.87 (30) ~ (all_52_7 = e0)
% 116.26/17.87 (31) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/17.87 (32) ~ (all_52_13 = e1)
% 116.26/17.87 (33) all_58_10 = all_52_13
% 116.26/17.87 (34) all_58_14 = all_52_11
% 116.26/17.87 (35) all_56_13 = all_8_2
% 116.26/17.87 (36) ~ (all_8_2 = e2)
% 116.26/17.87 (37) ~ (all_6_2 = e2)
% 116.26/17.87 (38) op(e0, all_4_2) = all_4_1
% 116.26/17.87 (39) all_56_4 = all_52_9
% 116.26/17.87 (40) all_56_5 = all_52_13
% 116.26/17.87 (41) ~ (all_52_13 = all_4_2)
% 116.26/17.87 (42) ~ (e2 = e0)
% 116.26/17.87 (43) all_58_12 = all_52_3
% 116.26/17.87 (44) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.87 (45) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.87 (46) ~ (e3 = e2)
% 116.26/17.87 (47) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.87 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.87 (48) ~ (all_6_2 = e1)
% 116.26/17.87 (49) ~ (e1 = e0)
% 116.26/17.87
% 116.26/17.87 Begin of proof
% 116.26/17.87 |
% 116.26/17.87 | BETA: splitting (14) gives:
% 116.26/17.87 |
% 116.26/17.87 | Case 1:
% 116.26/17.87 | |
% 116.26/17.87 | | (50) all_58_9 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | COMBINE_EQS: (8), (50) imply:
% 116.26/17.87 | | (51) e3 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | REDUCE: (23), (51) imply:
% 116.26/17.87 | | (52) $false
% 116.26/17.87 | |
% 116.26/17.87 | | CLOSE: (52) is inconsistent.
% 116.26/17.87 | |
% 116.26/17.87 | Case 2:
% 116.26/17.87 | |
% 116.26/17.87 | | (53) all_58_10 = e0 | all_58_11 = e0
% 116.26/17.87 | |
% 116.26/17.87 | | BETA: splitting (53) gives:
% 116.26/17.87 | |
% 116.26/17.87 | | Case 1:
% 116.26/17.87 | | |
% 116.26/17.87 | | | (54) all_58_10 = e0
% 116.26/17.87 | | |
% 116.26/17.87 | | | COMBINE_EQS: (33), (54) imply:
% 116.26/17.87 | | | (55) all_52_13 = e0
% 116.26/17.87 | | |
% 116.26/17.88 | | | REDUCE: (41), (55) imply:
% 116.26/17.88 | | | (56) ~ (all_4_2 = e0)
% 116.26/17.88 | | |
% 116.26/17.88 | | | SIMP: (56) implies:
% 116.26/17.88 | | | (57) ~ (all_4_2 = e0)
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (32), (55) imply:
% 116.26/17.88 | | | (58) ~ (e1 = e0)
% 116.26/17.88 | | |
% 116.26/17.88 | | | BETA: splitting (31) gives:
% 116.26/17.88 | | |
% 116.26/17.88 | | | Case 1:
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | (59) all_58_9 = e2
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | COMBINE_EQS: (8), (59) imply:
% 116.26/17.88 | | | | (60) e3 = e2
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | REDUCE: (46), (60) imply:
% 116.26/17.88 | | | | (61) $false
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | CLOSE: (61) is inconsistent.
% 116.26/17.88 | | | |
% 116.26/17.88 | | | Case 2:
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | (62) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | BETA: splitting (4) gives:
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | Case 1:
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | (63) all_54_13 = e3
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | COMBINE_EQS: (11), (63) imply:
% 116.26/17.88 | | | | | (64) all_52_7 = e3
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | SIMP: (64) implies:
% 116.26/17.88 | | | | | (65) all_52_7 = e3
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | COMBINE_EQS: (29), (65) imply:
% 116.26/17.88 | | | | | (66) all_58_13 = e3
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | BETA: splitting (45) gives:
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | Case 1:
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | (67) all_58_1 = e1
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | REF_CLOSE: (1), (49), (67) are inconsistent by sub-proof #440.
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | Case 2:
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | (68) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | REF_CLOSE: (2), (3), (7), (9), (10), (12), (15), (16), (18), (19),
% 116.26/17.88 | | | | | | (21), (22), (24), (25), (26), (27), (28), (29), (30),
% 116.26/17.88 | | | | | | (33), (34), (35), (36), (37), (39), (40), (43), (44),
% 116.26/17.88 | | | | | | (47), (48), (57), (66), (68) are inconsistent by
% 116.26/17.88 | | | | | | sub-proof #162.
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | End of split
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | Case 2:
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | (69) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | BETA: splitting (62) gives:
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | | Case 1:
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | (70) all_58_10 = e2
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | COMBINE_EQS: (54), (70) imply:
% 116.26/17.88 | | | | | | (71) e2 = e0
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | SIMP: (71) implies:
% 116.26/17.88 | | | | | | (72) e2 = e0
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | REDUCE: (42), (72) imply:
% 116.26/17.88 | | | | | | (73) $false
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | CLOSE: (73) is inconsistent.
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | Case 2:
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | (74) all_58_11 = e2 | all_58_15 = e2
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | BETA: splitting (74) gives:
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | | Case 1:
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | (75) all_58_11 = e2
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | COMBINE_EQS: (20), (75) imply:
% 116.26/17.88 | | | | | | | (76) e2 = e1
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | SIMP: (76) implies:
% 116.26/17.88 | | | | | | | (77) e2 = e1
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | REDUCE: (16), (77) imply:
% 116.26/17.88 | | | | | | | (78) $false
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | CLOSE: (78) is inconsistent.
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | Case 2:
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | (79) all_58_15 = e2
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | COMBINE_EQS: (27), (79) imply:
% 116.26/17.88 | | | | | | | (80) all_4_2 = e2
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | REDUCE: (6), (80) imply:
% 116.26/17.88 | | | | | | | (81) ~ (all_52_7 = e2)
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | REDUCE: (38), (80) imply:
% 116.26/17.88 | | | | | | | (82) op(e0, e2) = all_4_1
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | | REF_CLOSE: (5), (11), (13), (17), (30), (69), (81), (82) are
% 116.26/17.88 | | | | | | | inconsistent by sub-proof #180.
% 116.26/17.88 | | | | | | |
% 116.26/17.88 | | | | | | End of split
% 116.26/17.88 | | | | | |
% 116.26/17.88 | | | | | End of split
% 116.26/17.88 | | | | |
% 116.26/17.88 | | | | End of split
% 116.26/17.88 | | | |
% 116.26/17.88 | | | End of split
% 116.26/17.88 | | |
% 116.26/17.88 | | Case 2:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (83) all_58_11 = e0
% 116.26/17.88 | | |
% 116.26/17.88 | | | COMBINE_EQS: (20), (83) imply:
% 116.26/17.88 | | | (84) e1 = e0
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (49), (84) imply:
% 116.26/17.88 | | | (85) $false
% 116.26/17.88 | | |
% 116.26/17.88 | | | CLOSE: (85) is inconsistent.
% 116.26/17.88 | | |
% 116.26/17.88 | | End of split
% 116.26/17.88 | |
% 116.26/17.88 | End of split
% 116.26/17.88 |
% 116.26/17.88 End of proof
% 116.26/17.88
% 116.26/17.88 Sub-proof #162 shows that the following formulas are inconsistent:
% 116.26/17.88 ----------------------------------------------------------------
% 116.26/17.88 (1) ~ (all_52_1 = e2)
% 116.26/17.88 (2) ~ (all_4_2 = e0)
% 116.26/17.88 (3) all_56_14 = all_6_2
% 116.26/17.88 (4) all_56_11 = all_52_11
% 116.26/17.88 (5) ~ (e3 = e1)
% 116.26/17.88 (6) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.88 (7) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.88 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.88 (9) all_54_10 = all_6_2
% 116.26/17.88 (10) ~ (e2 = e1)
% 116.26/17.88 (11) all_58_7 = e2
% 116.26/17.88 (12) all_58_3 = all_8_2
% 116.26/17.88 (13) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.88 (14) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.88 (15) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.88 (16) all_58_5 = all_52_9
% 116.26/17.88 (17) all_56_9 = all_52_3
% 116.26/17.88 (18) all_58_15 = all_4_2
% 116.26/17.88 (19) all_58_2 = all_52_1
% 116.26/17.88 (20) all_58_13 = all_52_7
% 116.26/17.88 (21) ~ (all_52_7 = e0)
% 116.26/17.88 (22) all_58_10 = all_52_13
% 116.26/17.88 (23) all_58_14 = all_52_11
% 116.26/17.88 (24) all_56_13 = all_8_2
% 116.26/17.88 (25) ~ (all_8_2 = e2)
% 116.26/17.88 (26) ~ (all_6_2 = e2)
% 116.26/17.88 (27) all_58_13 = e3
% 116.26/17.88 (28) all_56_4 = all_52_9
% 116.26/17.88 (29) all_56_5 = all_52_13
% 116.26/17.88 (30) all_58_12 = all_52_3
% 116.26/17.88 (31) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.88 (32) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.88 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.88 (33) ~ (all_6_2 = e1)
% 116.26/17.88
% 116.26/17.88 Begin of proof
% 116.26/17.88 |
% 116.26/17.88 | BETA: splitting (7) gives:
% 116.26/17.88 |
% 116.26/17.88 | Case 1:
% 116.26/17.88 | |
% 116.26/17.88 | | (34) all_58_3 = e1
% 116.26/17.88 | |
% 116.26/17.88 | | COMBINE_EQS: (12), (34) imply:
% 116.26/17.88 | | (35) all_8_2 = e1
% 116.26/17.88 | |
% 116.26/17.88 | | COMBINE_EQS: (24), (35) imply:
% 116.26/17.88 | | (36) all_56_13 = e1
% 116.26/17.88 | |
% 116.26/17.88 | | REDUCE: (25), (35) imply:
% 116.26/17.88 | | (37) ~ (e2 = e1)
% 116.26/17.88 | |
% 116.26/17.88 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (13), (14), (15), (16),
% 116.26/17.88 | | (17), (18), (19), (20), (21), (22), (23), (26), (28), (29), (30),
% 116.26/17.88 | | (31), (32), (33), (34), (36) are inconsistent by sub-proof #427.
% 116.26/17.88 | |
% 116.26/17.88 | Case 2:
% 116.26/17.88 | |
% 116.26/17.88 | | (38) all_58_7 = e1 | all_58_13 = e1
% 116.26/17.88 | |
% 116.26/17.88 | | BETA: splitting (38) gives:
% 116.26/17.88 | |
% 116.26/17.88 | | Case 1:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (39) all_58_7 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | COMBINE_EQS: (11), (39) imply:
% 116.26/17.88 | | | (40) e2 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (10), (40) imply:
% 116.26/17.88 | | | (41) $false
% 116.26/17.88 | | |
% 116.26/17.88 | | | CLOSE: (41) is inconsistent.
% 116.26/17.88 | | |
% 116.26/17.88 | | Case 2:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (42) all_58_13 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | COMBINE_EQS: (27), (42) imply:
% 116.26/17.88 | | | (43) e3 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (5), (43) imply:
% 116.26/17.88 | | | (44) $false
% 116.26/17.88 | | |
% 116.26/17.88 | | | CLOSE: (44) is inconsistent.
% 116.26/17.88 | | |
% 116.26/17.88 | | End of split
% 116.26/17.88 | |
% 116.26/17.88 | End of split
% 116.26/17.88 |
% 116.26/17.88 End of proof
% 116.26/17.88
% 116.26/17.88 Sub-proof #163 shows that the following formulas are inconsistent:
% 116.26/17.88 ----------------------------------------------------------------
% 116.26/17.88 (1) all_56_14 = all_6_2
% 116.26/17.88 (2) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/17.88 (3) ~ (all_6_1 = e3)
% 116.26/17.88 (4) all_58_0 = all_10_2
% 116.26/17.88 (5) all_54_11 = all_52_14
% 116.26/17.88 (6) ~ (all_52_14 = all_6_2)
% 116.26/17.88 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.88 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.88 (9) all_54_10 = all_6_2
% 116.26/17.88 (10) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/17.88 (11) op(e1, e0) = all_52_14
% 116.26/17.88 (12) all_52_2 = e1
% 116.26/17.88 (13) op(e1, all_6_2) = all_6_1
% 116.26/17.88 (14) ~ (all_10_2 = e3)
% 116.26/17.88 (15) ~ (all_6_2 = e2)
% 116.26/17.88 (16) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/17.88 (17) all_56_6 = all_52_2
% 116.26/17.88 (18) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/17.88 (19) all_56_8 = all_52_14
% 116.26/17.88 (20) ~ (all_6_2 = e1)
% 116.26/17.88 (21) ~ (all_6_1 = e2)
% 116.26/17.88
% 116.26/17.88 Begin of proof
% 116.26/17.88 |
% 116.26/17.88 | SIMP: (12) implies:
% 116.26/17.88 | (22) all_52_2 = e1
% 116.26/17.88 |
% 116.26/17.88 | COMBINE_EQS: (17), (22) imply:
% 116.26/17.88 | (23) all_56_6 = e1
% 116.26/17.88 |
% 116.26/17.88 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 116.26/17.88 | (14), (15), (16), (18), (19), (20), (21), (23) are inconsistent by
% 116.26/17.88 | sub-proof #394.
% 116.26/17.88 |
% 116.26/17.88 End of proof
% 116.26/17.88
% 116.26/17.88 Sub-proof #164 shows that the following formulas are inconsistent:
% 116.26/17.88 ----------------------------------------------------------------
% 116.26/17.88 (1) ~ (all_52_8 = all_10_2)
% 116.26/17.88 (2) all_54_2 = all_52_8
% 116.26/17.88 (3) all_54_0 = all_10_2
% 116.26/17.88 (4) ~ (all_10_1 = e0) | ~ (all_10_2 = e1)
% 116.26/17.88 (5) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.88 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.88 (7) ~ (all_10_2 = e2)
% 116.26/17.88 (8) op(e3, e1) = all_52_8
% 116.26/17.88 (9) op(e3, all_10_2) = all_10_1
% 116.26/17.88 (10) ~ (all_52_8 = e3)
% 116.26/17.88 (11) ~ (all_10_2 = e0)
% 116.26/17.88 (12) op(e2, e1) = all_52_9
% 116.26/17.88 (13) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.88 (14) ~ (all_52_8 = all_52_9)
% 116.26/17.88 (15) op(all_10_1, all_10_2) = e2
% 116.26/17.88
% 116.26/17.88 Begin of proof
% 116.26/17.88 |
% 116.26/17.88 | BETA: splitting (5) gives:
% 116.26/17.88 |
% 116.26/17.88 | Case 1:
% 116.26/17.88 | |
% 116.26/17.88 | | (16) all_54_0 = e2
% 116.26/17.88 | |
% 116.26/17.88 | | REF_CLOSE: (3), (7), (16) are inconsistent by sub-proof #450.
% 116.26/17.88 | |
% 116.26/17.88 | Case 2:
% 116.26/17.88 | |
% 116.26/17.88 | | (17) all_54_0 = e1 | all_54_0 = e0
% 116.26/17.88 | |
% 116.26/17.88 | | BETA: splitting (17) gives:
% 116.26/17.88 | |
% 116.26/17.88 | | Case 1:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (18) all_54_0 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | COMBINE_EQS: (3), (18) imply:
% 116.26/17.88 | | | (19) all_10_2 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | SIMP: (19) implies:
% 116.26/17.88 | | | (20) all_10_2 = e1
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (1), (20) imply:
% 116.26/17.88 | | | (21) ~ (all_52_8 = e1)
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (15), (20) imply:
% 116.26/17.88 | | | (22) op(all_10_1, e1) = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (9), (20) imply:
% 116.26/17.88 | | | (23) op(e3, e1) = all_10_1
% 116.26/17.88 | | |
% 116.26/17.88 | | | BETA: splitting (4) gives:
% 116.26/17.88 | | |
% 116.26/17.88 | | | Case 1:
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | (24) ~ (all_10_2 = e1)
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | REF_CLOSE: (3), (11), (17), (24) are inconsistent by sub-proof #423.
% 116.26/17.88 | | | |
% 116.26/17.88 | | | Case 2:
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | (25) ~ (all_10_1 = e0)
% 116.26/17.88 | | | |
% 116.26/17.88 | | | | REF_CLOSE: (2), (6), (8), (10), (12), (13), (14), (21), (22), (23), (25)
% 116.26/17.88 | | | | are inconsistent by sub-proof #165.
% 116.26/17.88 | | | |
% 116.26/17.88 | | | End of split
% 116.26/17.88 | | |
% 116.26/17.88 | | Case 2:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (26) all_54_0 = e0
% 116.26/17.88 | | |
% 116.26/17.88 | | | REF_CLOSE: (3), (11), (26) are inconsistent by sub-proof #424.
% 116.26/17.88 | | |
% 116.26/17.88 | | End of split
% 116.26/17.88 | |
% 116.26/17.88 | End of split
% 116.26/17.88 |
% 116.26/17.88 End of proof
% 116.26/17.88
% 116.26/17.88 Sub-proof #165 shows that the following formulas are inconsistent:
% 116.26/17.88 ----------------------------------------------------------------
% 116.26/17.88 (1) all_54_2 = all_52_8
% 116.26/17.88 (2) ~ (all_52_8 = e1)
% 116.26/17.88 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.88 (4) op(e3, e1) = all_52_8
% 116.26/17.88 (5) op(all_10_1, e1) = e2
% 116.26/17.88 (6) ~ (all_52_8 = e3)
% 116.26/17.88 (7) ~ (all_10_1 = e0)
% 116.26/17.88 (8) op(e2, e1) = all_52_9
% 116.26/17.88 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.88 (10) ~ (all_52_8 = all_52_9)
% 116.26/17.88 (11) op(e3, e1) = all_10_1
% 116.26/17.88
% 116.26/17.88 Begin of proof
% 116.26/17.88 |
% 116.26/17.88 | GROUND_INST: instantiating (3) with all_52_8, all_10_1, e1, e3, simplifying
% 116.26/17.88 | with (4), (11) gives:
% 116.26/17.88 | (12) all_52_8 = all_10_1
% 116.26/17.88 |
% 116.26/17.88 | COMBINE_EQS: (1), (12) imply:
% 116.26/17.88 | (13) all_54_2 = all_10_1
% 116.26/17.88 |
% 116.26/17.88 | REDUCE: (10), (12) imply:
% 116.26/17.88 | (14) ~ (all_52_9 = all_10_1)
% 116.26/17.88 |
% 116.26/17.88 | SIMP: (14) implies:
% 116.26/17.88 | (15) ~ (all_52_9 = all_10_1)
% 116.26/17.88 |
% 116.26/17.88 | REDUCE: (6), (12) imply:
% 116.26/17.88 | (16) ~ (all_10_1 = e3)
% 116.26/17.88 |
% 116.26/17.88 | REDUCE: (2), (12) imply:
% 116.26/17.88 | (17) ~ (all_10_1 = e1)
% 116.26/17.88 |
% 116.26/17.88 | BETA: splitting (9) gives:
% 116.26/17.88 |
% 116.26/17.88 | Case 1:
% 116.26/17.88 | |
% 116.26/17.88 | | (18) all_54_2 = e3
% 116.26/17.88 | |
% 116.26/17.88 | | REF_CLOSE: (13), (16), (18) are inconsistent by sub-proof #166.
% 116.26/17.88 | |
% 116.26/17.88 | Case 2:
% 116.26/17.88 | |
% 116.26/17.88 | | (19) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.88 | |
% 116.26/17.88 | | BETA: splitting (19) gives:
% 116.26/17.88 | |
% 116.26/17.88 | | Case 1:
% 116.26/17.88 | | |
% 116.26/17.88 | | | (20) all_54_2 = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | COMBINE_EQS: (13), (20) imply:
% 116.26/17.88 | | | (21) all_10_1 = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | SIMP: (21) implies:
% 116.26/17.88 | | | (22) all_10_1 = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (15), (22) imply:
% 116.26/17.88 | | | (23) ~ (all_52_9 = e2)
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (5), (22) imply:
% 116.26/17.88 | | | (24) op(e2, e1) = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | GROUND_INST: instantiating (3) with all_52_9, e2, e1, e2, simplifying with
% 116.26/17.88 | | | (8), (24) gives:
% 116.26/17.88 | | | (25) all_52_9 = e2
% 116.26/17.88 | | |
% 116.26/17.88 | | | REDUCE: (23), (25) imply:
% 116.26/17.89 | | | (26) $false
% 116.26/17.89 | | |
% 116.26/17.89 | | | CLOSE: (26) is inconsistent.
% 116.26/17.89 | | |
% 116.26/17.89 | | Case 2:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (27) all_54_2 = e1 | all_54_2 = e0
% 116.26/17.89 | | |
% 116.26/17.89 | | | BETA: splitting (27) gives:
% 116.26/17.89 | | |
% 116.26/17.89 | | | Case 1:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (28) all_54_2 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (13), (28) imply:
% 116.26/17.89 | | | | (29) all_10_1 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | SIMP: (29) implies:
% 116.26/17.89 | | | | (30) all_10_1 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (17), (30) imply:
% 116.26/17.89 | | | | (31) $false
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | CLOSE: (31) is inconsistent.
% 116.26/17.89 | | | |
% 116.26/17.89 | | | Case 2:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (32) all_54_2 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (13), (32) imply:
% 116.26/17.89 | | | | (33) all_10_1 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | SIMP: (33) implies:
% 116.26/17.89 | | | | (34) all_10_1 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (7), (34) imply:
% 116.26/17.89 | | | | (35) $false
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | CLOSE: (35) is inconsistent.
% 116.26/17.89 | | | |
% 116.26/17.89 | | | End of split
% 116.26/17.89 | | |
% 116.26/17.89 | | End of split
% 116.26/17.89 | |
% 116.26/17.89 | End of split
% 116.26/17.89 |
% 116.26/17.89 End of proof
% 116.26/17.89
% 116.26/17.89 Sub-proof #166 shows that the following formulas are inconsistent:
% 116.26/17.89 ----------------------------------------------------------------
% 116.26/17.89 (1) all_54_2 = all_10_1
% 116.26/17.89 (2) all_54_2 = e3
% 116.26/17.89 (3) ~ (all_10_1 = e3)
% 116.26/17.89
% 116.26/17.89 Begin of proof
% 116.26/17.89 |
% 116.26/17.89 | COMBINE_EQS: (1), (2) imply:
% 116.26/17.89 | (4) all_10_1 = e3
% 116.26/17.89 |
% 116.26/17.89 | SIMP: (4) implies:
% 116.26/17.89 | (5) all_10_1 = e3
% 116.26/17.89 |
% 116.26/17.89 | REDUCE: (3), (5) imply:
% 116.26/17.89 | (6) $false
% 116.26/17.89 |
% 116.26/17.89 | CLOSE: (6) is inconsistent.
% 116.26/17.89 |
% 116.26/17.89 End of proof
% 116.26/17.89
% 116.26/17.89 Sub-proof #167 shows that the following formulas are inconsistent:
% 116.26/17.89 ----------------------------------------------------------------
% 116.26/17.89 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/17.89 (2) all_54_0 = all_10_2
% 116.26/17.89 (3) all_54_3 = all_52_12
% 116.26/17.89 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.89 (5) ~ (all_52_12 = all_10_2)
% 116.26/17.89 (6) all_56_12 = all_10_2
% 116.26/17.89 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.89 (8) ~ (all_10_2 = e2)
% 116.26/17.89 (9) op(e3, e0) = all_52_12
% 116.26/17.89 (10) all_50_1 = all_10_1
% 116.26/17.89 (11) all_56_2 = all_52_12
% 116.26/17.89 (12) all_58_11 = all_52_14
% 116.26/17.89 (13) all_50_2 = all_10_2
% 116.26/17.89 (14) all_56_4 = e2
% 116.26/17.89 (15) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.89 (16) all_58_15 = all_4_2
% 116.26/17.89 (17) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/17.89 (18) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.26/17.89 (19) ~ (all_10_2 = e3)
% 116.26/17.89 (20) ~ (all_52_12 = all_52_13)
% 116.26/17.89 (21) all_56_15 = all_4_2
% 116.26/17.89 (22) all_58_10 = all_52_13
% 116.26/17.89 (23) op(e3, all_10_2) = all_10_1
% 116.26/17.89 (24) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.89 (25) all_58_9 = all_52_12
% 116.26/17.89 (26) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.26/17.89 (27) op(e2, e0) = all_52_13
% 116.26/17.89 (28) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.26/17.89 (29) all_56_8 = all_52_14
% 116.26/17.89 (30) op(all_10_1, all_10_2) = e2
% 116.26/17.89
% 116.26/17.89 Begin of proof
% 116.26/17.89 |
% 116.26/17.89 | BETA: splitting (17) gives:
% 116.26/17.89 |
% 116.26/17.89 | Case 1:
% 116.26/17.89 | |
% 116.26/17.89 | | (31) ~ (all_56_4 = e2)
% 116.26/17.89 | |
% 116.26/17.89 | | REDUCE: (14), (31) imply:
% 116.26/17.89 | | (32) $false
% 116.26/17.89 | |
% 116.26/17.89 | | CLOSE: (32) is inconsistent.
% 116.26/17.89 | |
% 116.26/17.89 | Case 2:
% 116.26/17.89 | |
% 116.26/17.89 | | (33) ~ (all_56_12 = e1)
% 116.26/17.89 | |
% 116.26/17.89 | | REDUCE: (6), (33) imply:
% 116.26/17.89 | | (34) ~ (all_10_2 = e1)
% 116.26/17.89 | |
% 116.26/17.89 | | BETA: splitting (26) gives:
% 116.26/17.89 | |
% 116.26/17.89 | | Case 1:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (35) ~ (all_56_4 = e2)
% 116.26/17.89 | | |
% 116.26/17.89 | | | REDUCE: (14), (35) imply:
% 116.26/17.89 | | | (36) $false
% 116.26/17.89 | | |
% 116.26/17.89 | | | CLOSE: (36) is inconsistent.
% 116.26/17.89 | | |
% 116.26/17.89 | | Case 2:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (37) ~ (all_56_15 = e1)
% 116.26/17.89 | | |
% 116.26/17.89 | | | REDUCE: (21), (37) imply:
% 116.26/17.89 | | | (38) ~ (all_4_2 = e1)
% 116.26/17.89 | | |
% 116.26/17.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 116.26/17.89 | | | (13), (15), (16), (18), (19), (20), (22), (23), (24), (25),
% 116.26/17.89 | | | (27), (28), (29), (30), (34), (38) are inconsistent by
% 116.26/17.89 | | | sub-proof #168.
% 116.26/17.89 | | |
% 116.26/17.89 | | End of split
% 116.26/17.89 | |
% 116.26/17.89 | End of split
% 116.26/17.89 |
% 116.26/17.89 End of proof
% 116.26/17.89
% 116.26/17.89 Sub-proof #168 shows that the following formulas are inconsistent:
% 116.26/17.89 ----------------------------------------------------------------
% 116.26/17.89 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/17.89 (2) all_54_0 = all_10_2
% 116.26/17.89 (3) all_54_3 = all_52_12
% 116.26/17.89 (4) ~ (all_4_2 = e1)
% 116.26/17.89 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.89 (6) ~ (all_52_12 = all_10_2)
% 116.26/17.89 (7) all_56_12 = all_10_2
% 116.26/17.89 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.89 (9) ~ (all_10_2 = e2)
% 116.26/17.89 (10) op(e3, e0) = all_52_12
% 116.26/17.89 (11) all_50_1 = all_10_1
% 116.26/17.89 (12) all_56_2 = all_52_12
% 116.26/17.89 (13) all_58_11 = all_52_14
% 116.26/17.89 (14) ~ (all_10_2 = e1)
% 116.26/17.89 (15) all_50_2 = all_10_2
% 116.26/17.89 (16) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.89 (17) all_58_15 = all_4_2
% 116.26/17.89 (18) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.26/17.89 (19) ~ (all_10_2 = e3)
% 116.26/17.89 (20) ~ (all_52_12 = all_52_13)
% 116.26/17.89 (21) all_58_10 = all_52_13
% 116.26/17.89 (22) op(e3, all_10_2) = all_10_1
% 116.26/17.89 (23) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.89 (24) all_58_9 = all_52_12
% 116.26/17.89 (25) op(e2, e0) = all_52_13
% 116.26/17.89 (26) ~ (all_50_1 = e1) | ~ (all_50_2 = e0)
% 116.26/17.89 (27) all_56_8 = all_52_14
% 116.26/17.89 (28) op(all_10_1, all_10_2) = e2
% 116.26/17.89
% 116.26/17.89 Begin of proof
% 116.26/17.89 |
% 116.26/17.89 | BETA: splitting (23) gives:
% 116.26/17.89 |
% 116.26/17.89 | Case 1:
% 116.26/17.89 | |
% 116.26/17.89 | | (29) all_54_0 = e3
% 116.26/17.89 | |
% 116.26/17.89 | | REF_CLOSE: (2), (19), (29) are inconsistent by sub-proof #451.
% 116.26/17.89 | |
% 116.26/17.89 | Case 2:
% 116.26/17.89 | |
% 116.26/17.89 | | (30) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.89 | |
% 116.26/17.89 | | BETA: splitting (30) gives:
% 116.26/17.89 | |
% 116.26/17.89 | | Case 1:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (31) all_54_0 = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | REF_CLOSE: (2), (9), (31) are inconsistent by sub-proof #450.
% 116.26/17.89 | | |
% 116.26/17.89 | | Case 2:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (32) ~ (all_54_0 = e2)
% 116.26/17.89 | | | (33) all_54_0 = e1 | all_54_0 = e0
% 116.26/17.89 | | |
% 116.26/17.89 | | | BETA: splitting (33) gives:
% 116.26/17.89 | | |
% 116.26/17.89 | | | Case 1:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (34) all_54_0 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REF_CLOSE: (2), (14), (34) are inconsistent by sub-proof #449.
% 116.26/17.89 | | | |
% 116.26/17.89 | | | Case 2:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (35) all_54_0 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (2), (35) imply:
% 116.26/17.89 | | | | (36) all_10_2 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | SIMP: (36) implies:
% 116.26/17.89 | | | | (37) all_10_2 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (15), (37) imply:
% 116.26/17.89 | | | | (38) all_50_2 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (7), (37) imply:
% 116.26/17.89 | | | | (39) all_56_12 = e0
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (6), (37) imply:
% 116.26/17.89 | | | | (40) ~ (all_52_12 = e0)
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (28), (37) imply:
% 116.26/17.89 | | | | (41) op(all_10_1, e0) = e2
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (22), (37) imply:
% 116.26/17.89 | | | | (42) op(e3, e0) = all_10_1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | BETA: splitting (26) gives:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | Case 1:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | (43) ~ (all_50_1 = e1)
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | REDUCE: (11), (43) imply:
% 116.26/17.89 | | | | | (44) ~ (all_10_1 = e1)
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | BETA: splitting (1) gives:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | Case 1:
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | (45) ~ (all_56_2 = e3)
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | REDUCE: (12), (45) imply:
% 116.26/17.89 | | | | | | (46) ~ (all_52_12 = e3)
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (13), (14),
% 116.26/17.89 | | | | | | (16), (17), (18), (20), (21), (24), (25), (27), (30),
% 116.26/17.89 | | | | | | (40), (41), (42), (44), (46) are inconsistent by
% 116.26/17.89 | | | | | | sub-proof #169.
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | Case 2:
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | (47) ~ (all_56_12 = e0)
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | REDUCE: (39), (47) imply:
% 116.26/17.89 | | | | | | (48) $false
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | CLOSE: (48) is inconsistent.
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | End of split
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | Case 2:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | (49) ~ (all_50_2 = e0)
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | REDUCE: (38), (49) imply:
% 116.26/17.89 | | | | | (50) $false
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | CLOSE: (50) is inconsistent.
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | End of split
% 116.26/17.89 | | | |
% 116.26/17.89 | | | End of split
% 116.26/17.89 | | |
% 116.26/17.89 | | End of split
% 116.26/17.89 | |
% 116.26/17.89 | End of split
% 116.26/17.89 |
% 116.26/17.89 End of proof
% 116.26/17.89
% 116.26/17.89 Sub-proof #169 shows that the following formulas are inconsistent:
% 116.26/17.89 ----------------------------------------------------------------
% 116.26/17.89 (1) all_54_0 = all_10_2
% 116.26/17.89 (2) all_54_3 = all_52_12
% 116.26/17.89 (3) ~ (all_4_2 = e1)
% 116.26/17.89 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.89 (5) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.89 (6) all_56_12 = all_10_2
% 116.26/17.89 (7) op(e3, e0) = all_10_1
% 116.26/17.89 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.89 (9) ~ (all_10_2 = e2)
% 116.26/17.89 (10) op(e3, e0) = all_52_12
% 116.26/17.89 (11) ~ (all_52_12 = e0)
% 116.26/17.89 (12) all_58_11 = all_52_14
% 116.26/17.89 (13) ~ (all_10_2 = e1)
% 116.26/17.89 (14) op(all_10_1, e0) = e2
% 116.26/17.89 (15) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.89 (16) all_58_15 = all_4_2
% 116.26/17.89 (17) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.26/17.89 (18) ~ (all_52_12 = all_52_13)
% 116.26/17.89 (19) ~ (all_52_12 = e3)
% 116.26/17.89 (20) all_58_10 = all_52_13
% 116.26/17.89 (21) all_58_9 = all_52_12
% 116.26/17.89 (22) op(e2, e0) = all_52_13
% 116.26/17.89 (23) all_56_8 = all_52_14
% 116.26/17.89 (24) ~ (all_10_1 = e1)
% 116.26/17.89
% 116.26/17.89 Begin of proof
% 116.26/17.89 |
% 116.26/17.89 | GROUND_INST: instantiating (8) with all_52_12, all_10_1, e0, e3, simplifying
% 116.26/17.89 | with (7), (10) gives:
% 116.26/17.89 | (25) all_52_12 = all_10_1
% 116.26/17.89 |
% 116.26/17.89 | COMBINE_EQS: (2), (25) imply:
% 116.26/17.89 | (26) all_54_3 = all_10_1
% 116.26/17.89 |
% 116.26/17.89 | COMBINE_EQS: (21), (25) imply:
% 116.26/17.89 | (27) all_58_9 = all_10_1
% 116.26/17.89 |
% 116.26/17.89 | REDUCE: (18), (25) imply:
% 116.26/17.89 | (28) ~ (all_52_13 = all_10_1)
% 116.26/17.89 |
% 116.26/17.89 | SIMP: (28) implies:
% 116.26/17.89 | (29) ~ (all_52_13 = all_10_1)
% 116.26/17.89 |
% 116.26/17.89 | REDUCE: (19), (25) imply:
% 116.26/17.89 | (30) ~ (all_10_1 = e3)
% 116.26/17.89 |
% 116.26/17.89 | REDUCE: (11), (25) imply:
% 116.26/17.89 | (31) ~ (all_10_1 = e0)
% 116.26/17.89 |
% 116.26/17.89 | BETA: splitting (4) gives:
% 116.26/17.89 |
% 116.26/17.89 | Case 1:
% 116.26/17.89 | |
% 116.26/17.89 | | (32) all_54_3 = e3
% 116.26/17.89 | |
% 116.26/17.89 | | REF_CLOSE: (26), (30), (32) are inconsistent by sub-proof #215.
% 116.26/17.89 | |
% 116.26/17.89 | Case 2:
% 116.26/17.89 | |
% 116.26/17.89 | | (33) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.89 | |
% 116.26/17.89 | | BETA: splitting (33) gives:
% 116.26/17.89 | |
% 116.26/17.89 | | Case 1:
% 116.26/17.89 | | |
% 116.26/17.89 | | | (34) all_54_3 = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | COMBINE_EQS: (26), (34) imply:
% 116.26/17.89 | | | (35) all_10_1 = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | SIMP: (35) implies:
% 116.26/17.89 | | | (36) all_10_1 = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | COMBINE_EQS: (27), (36) imply:
% 116.26/17.89 | | | (37) all_58_9 = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | REDUCE: (29), (36) imply:
% 116.26/17.89 | | | (38) ~ (all_52_13 = e2)
% 116.26/17.89 | | |
% 116.26/17.89 | | | REDUCE: (24), (36) imply:
% 116.26/17.89 | | | (39) ~ (e2 = e1)
% 116.26/17.89 | | |
% 116.26/17.89 | | | REDUCE: (14), (36) imply:
% 116.26/17.89 | | | (40) op(e2, e0) = e2
% 116.26/17.89 | | |
% 116.26/17.89 | | | BETA: splitting (17) gives:
% 116.26/17.89 | | |
% 116.26/17.89 | | | Case 1:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (41) all_58_9 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | COMBINE_EQS: (37), (41) imply:
% 116.26/17.89 | | | | (42) e2 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | REDUCE: (39), (42) imply:
% 116.26/17.89 | | | | (43) $false
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | CLOSE: (43) is inconsistent.
% 116.26/17.89 | | | |
% 116.26/17.89 | | | Case 2:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | (44) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | BETA: splitting (44) gives:
% 116.26/17.89 | | | |
% 116.26/17.89 | | | | Case 1:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | (45) all_58_10 = e1
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | COMBINE_EQS: (20), (45) imply:
% 116.26/17.89 | | | | | (46) all_52_13 = e1
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | REDUCE: (38), (46) imply:
% 116.26/17.89 | | | | | (47) ~ (e2 = e1)
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | REDUCE: (22), (46) imply:
% 116.26/17.89 | | | | | (48) op(e2, e0) = e1
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | REF_CLOSE: (8), (39), (40), (48) are inconsistent by sub-proof #170.
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | Case 2:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | (49) all_58_11 = e1 | all_58_15 = e1
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | BETA: splitting (49) gives:
% 116.26/17.89 | | | | |
% 116.26/17.89 | | | | | Case 1:
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | (50) all_58_11 = e1
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | COMBINE_EQS: (12), (50) imply:
% 116.26/17.89 | | | | | | (51) all_52_14 = e1
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | COMBINE_EQS: (23), (51) imply:
% 116.26/17.89 | | | | | | (52) all_56_8 = e1
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | REF_CLOSE: (1), (5), (6), (9), (13), (15), (52) are inconsistent by
% 116.26/17.89 | | | | | | sub-proof #385.
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | Case 2:
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | (53) all_58_15 = e1
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | COMBINE_EQS: (16), (53) imply:
% 116.26/17.89 | | | | | | (54) all_4_2 = e1
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | REDUCE: (3), (54) imply:
% 116.26/17.89 | | | | | | (55) $false
% 116.26/17.89 | | | | | |
% 116.26/17.89 | | | | | | CLOSE: (55) is inconsistent.
% 116.26/17.90 | | | | | |
% 116.26/17.90 | | | | | End of split
% 116.26/17.90 | | | | |
% 116.26/17.90 | | | | End of split
% 116.26/17.90 | | | |
% 116.26/17.90 | | | End of split
% 116.26/17.90 | | |
% 116.26/17.90 | | Case 2:
% 116.26/17.90 | | |
% 116.26/17.90 | | | (56) all_54_3 = e1 | all_54_3 = e0
% 116.26/17.90 | | |
% 116.26/17.90 | | | REF_CLOSE: (24), (26), (31), (56) are inconsistent by sub-proof #448.
% 116.26/17.90 | | |
% 116.26/17.90 | | End of split
% 116.26/17.90 | |
% 116.26/17.90 | End of split
% 116.26/17.90 |
% 116.26/17.90 End of proof
% 116.26/17.90
% 116.26/17.90 Sub-proof #170 shows that the following formulas are inconsistent:
% 116.26/17.90 ----------------------------------------------------------------
% 116.26/17.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.90 (2) op(e2, e0) = e2
% 116.26/17.90 (3) op(e2, e0) = e1
% 116.26/17.90 (4) ~ (e2 = e1)
% 116.26/17.90
% 116.26/17.90 Begin of proof
% 116.26/17.90 |
% 116.26/17.90 | GROUND_INST: instantiating (1) with e1, e2, e0, e2, simplifying with (2), (3)
% 116.26/17.90 | gives:
% 116.26/17.90 | (5) e2 = e1
% 116.26/17.90 |
% 116.26/17.90 | REDUCE: (4), (5) imply:
% 116.26/17.90 | (6) $false
% 116.26/17.90 |
% 116.26/17.90 | CLOSE: (6) is inconsistent.
% 116.26/17.90 |
% 116.26/17.90 End of proof
% 116.26/17.90
% 116.26/17.90 Sub-proof #171 shows that the following formulas are inconsistent:
% 116.26/17.90 ----------------------------------------------------------------
% 116.26/17.90 (1) ~ (all_52_8 = all_10_2)
% 116.26/17.90 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/17.90 (3) ~ (all_52_2 = all_10_2)
% 116.26/17.90 (4) ~ (all_52_6 = all_52_14)
% 116.26/17.90 (5) all_54_2 = all_52_8
% 116.26/17.90 (6) all_58_7 = all_52_6
% 116.26/17.90 (7) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 116.26/17.90 (8) ~ (all_52_8 = all_52_11)
% 116.26/17.90 (9) ~ (all_52_9 = all_8_2)
% 116.26/17.90 (10) all_28_1 = all_6_1
% 116.26/17.90 (11) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.26/17.90 (12) ~ (all_52_13 = all_52_14)
% 116.26/17.90 (13) ~ (all_4_2 = e0)
% 116.26/17.90 (14) op(e3, e2) = all_52_4
% 116.26/17.90 (15) all_56_14 = all_6_2
% 116.26/17.90 (16) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.26/17.90 (17) all_56_3 = all_52_1
% 116.26/17.90 (18) all_38_1 = all_10_1
% 116.26/17.90 (19) all_54_0 = all_10_2
% 116.26/17.90 (20) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.90 (21) all_54_3 = all_52_12
% 116.26/17.90 (22) ~ (all_52_2 = all_52_6)
% 116.26/17.90 (23) op(e0, e2) = all_52_7
% 116.26/17.90 (24) ~ (all_52_7 = all_4_2)
% 116.26/17.90 (25) all_56_11 = all_52_11
% 116.26/17.90 (26) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 116.26/17.90 (27) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/17.90 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.90 (29) ~ (all_52_12 = all_10_2)
% 116.26/17.90 (30) ~ (all_14_1 = e3) | ~ (all_14_2 = e0)
% 116.26/17.90 (31) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.90 (32) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.90 (33) all_56_12 = all_10_2
% 116.26/17.90 (34) all_58_0 = all_10_2
% 116.26/17.90 (35) op(all_6_1, all_6_2) = all_6_0
% 116.26/17.90 (36) all_42_2 = all_8_2
% 116.26/17.90 (37) all_54_11 = all_52_14
% 116.26/17.90 (38) all_54_13 = all_52_7
% 116.26/17.90 (39) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.26/17.90 (40) ~ (all_52_14 = all_6_2)
% 116.26/17.90 (41) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 116.26/17.90 (42) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.26/17.90 (43) all_56_10 = all_52_7
% 116.26/17.90 (44) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.26/17.90 (45) all_54_14 = all_52_11
% 116.26/17.90 (46) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.90 (47) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 116.26/17.90 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.90 (49) all_54_8 = all_52_2
% 116.26/17.90 (50) ~ (all_52_2 = all_6_2)
% 116.26/17.90 (51) all_32_2 = all_10_2
% 116.26/17.90 (52) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.26/17.90 (53) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 116.26/17.90 (54) all_54_10 = all_6_2
% 116.26/17.90 (55) op(e3, e0) = all_52_12
% 116.26/17.90 (56) all_38_0 = all_10_0
% 116.26/17.90 (57) ~ (all_52_8 = all_6_2)
% 116.26/17.90 (58) all_58_4 = all_52_8
% 116.26/17.90 (59) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/17.90 (60) ~ (all_52_4 = all_52_7)
% 116.26/17.90 (61) all_56_2 = all_52_12
% 116.26/17.90 (62) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/17.90 (63) all_58_3 = all_8_2
% 116.26/17.90 (64) all_54_6 = all_52_9
% 116.26/17.90 (65) ~ (all_10_0 = e2)
% 116.26/17.90 (66) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.90 (67) all_58_11 = all_52_14
% 116.26/17.90 (68) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.26/17.90 (69) all_54_9 = all_52_6
% 116.26/17.90 (70) op(e3, e1) = all_52_8
% 116.26/17.90 (71) ~ (all_52_2 = all_52_3)
% 116.26/17.90 (72) all_14_2 = all_8_2
% 116.26/17.90 (73) op(all_10_1, all_10_2) = all_10_0
% 116.26/17.90 (74) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.90 (75) ~ (all_52_11 = all_6_2)
% 116.26/17.90 (76) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.90 (77) op(e2, e3) = all_52_1
% 116.26/17.90 (78) all_28_2 = all_6_2
% 116.26/17.90 (79) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.26/17.90 (80) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.26/17.90 (81) ~ (e3 = e0)
% 116.26/17.90 (82) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.90 (83) ~ (all_52_7 = all_8_2)
% 116.26/17.90 (84) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/17.90 (85) ~ (all_52_4 = all_8_2)
% 116.26/17.90 (86) op(e1, e0) = all_52_14
% 116.26/17.90 (87) all_58_5 = all_52_9
% 116.26/17.90 (88) ~ (all_52_9 = all_52_13)
% 116.26/17.90 (89) all_56_9 = all_52_3
% 116.26/17.90 (90) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.26/17.90 (91) op(e1, all_6_2) = all_6_1
% 116.26/17.90 (92) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.90 (93) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.26/17.90 (94) all_32_0 = all_10_0
% 116.26/17.90 (95) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.26/17.90 (96) all_58_15 = all_4_2
% 116.26/17.90 (97) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.26/17.90 (98) all_58_2 = all_52_1
% 116.26/17.90 (99) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/17.90 (100) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.26/17.90 (101) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 116.26/17.90 (102) ~ (all_10_2 = e3)
% 116.26/17.90 (103) all_58_13 = all_52_7
% 116.26/17.90 (104) all_32_1 = all_10_1
% 116.26/17.90 (105) all_28_0 = e2
% 116.26/17.90 (106) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.26/17.90 (107) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.26/17.90 (108) ~ (all_52_14 = all_4_2)
% 116.26/17.90 (109) all_58_6 = all_52_2
% 116.26/17.90 (110) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.26/17.90 (111) ~ (all_52_1 = all_10_2)
% 116.26/17.90 (112) all_54_5 = all_8_2
% 116.26/17.90 (113) all_56_15 = all_4_2
% 116.26/17.90 (114) all_58_10 = all_52_13
% 116.26/17.90 (115) ~ (all_52_13 = all_8_2)
% 116.26/17.90 (116) op(e2, all_8_2) = all_8_1
% 116.26/17.90 (117) ~ (all_52_11 = all_4_2)
% 116.26/17.90 (118) op(e3, all_10_2) = all_10_1
% 116.26/17.90 (119) ~ (all_52_6 = all_8_2)
% 116.26/17.90 (120) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.26/17.90 (121) all_28_0 = all_6_0
% 116.26/17.90 (122) ~ (all_42_0 = e1) | ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 116.26/17.90 (123) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 116.26/17.90 (124) all_38_2 = all_10_2
% 116.26/17.90 (125) all_14_1 = all_8_1
% 116.26/17.90 (126) all_58_1 = all_52_4
% 116.26/17.90 (127) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.26/17.90 (128) ~ (all_52_9 = all_52_11)
% 116.26/17.90 (129) all_58_14 = all_52_11
% 116.26/17.90 (130) all_54_1 = all_52_4
% 116.26/17.90 (131) all_56_13 = all_8_2
% 116.26/17.90 (132) op(e0, e1) = all_52_11
% 116.26/17.90 (133) ~ (all_52_1 = all_8_2)
% 116.26/17.90 (134) ~ (all_8_2 = e2)
% 116.26/17.90 (135) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.26/17.90 (136) ~ (all_52_7 = all_52_11)
% 116.26/17.90 (137) op(e1, e2) = all_52_6
% 116.26/17.90 (138) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/17.90 (139) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.90 (140) all_56_7 = all_52_6
% 116.26/17.90 (141) ~ (all_52_9 = all_6_2)
% 116.26/17.90 (142) ~ (all_52_4 = all_52_6)
% 116.26/17.90 (143) ~ (all_52_1 = all_52_2)
% 116.26/17.90 (144) all_56_1 = all_52_8
% 116.26/17.90 (145) op(e0, all_4_2) = all_4_1
% 116.26/17.90 (146) all_58_8 = all_6_2
% 116.26/17.90 (147) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.90 (148) ~ (all_10_0 = e1)
% 116.26/17.90 (149) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/17.90 (150) all_56_4 = all_52_9
% 116.26/17.90 (151) all_58_9 = all_52_12
% 116.26/17.90 (152) all_56_5 = all_52_13
% 116.26/17.90 (153) op(e2, e1) = all_52_9
% 116.26/17.90 (154) ~ (all_52_6 = all_6_2)
% 116.26/17.90 (155) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.90 (156) all_56_6 = all_52_2
% 116.26/17.90 (157) ~ (all_52_13 = all_4_2)
% 116.26/17.90 (158) ~ (e2 = e0)
% 116.26/17.90 (159) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.26/17.90 (160) all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 116.26/17.90 (161) all_58_12 = all_52_3
% 116.26/17.90 (162) ~ (all_52_2 = all_52_14)
% 116.26/17.90 (163) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.26/17.90 (164) ~ (all_52_8 = all_52_9)
% 116.26/17.90 (165) op(e2, e0) = all_52_13
% 116.26/17.90 (166) ~ (all_52_12 = all_4_2)
% 116.26/17.90 (167) ~ (all_52_3 = all_10_2)
% 116.26/17.90 (168) op(e1, e3) = all_52_2
% 116.26/17.90 (169) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.26/17.90 (170) all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 116.26/17.90 (171) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.26/17.90 (172) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/17.90 (173) all_42_0 = e1
% 116.26/17.90 (174) ~ (all_52_8 = all_52_12)
% 116.26/17.90 (175) all_56_8 = all_52_14
% 116.26/17.90 (176) ~ (all_52_4 = all_10_2)
% 116.26/17.90 (177) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/17.90 (178) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.90 (179) all_56_0 = all_52_4
% 116.26/17.90 (180) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.90 (181) ~ (e3 = e2)
% 116.26/17.90 (182) all_42_1 = all_8_1
% 116.26/17.90 (183) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.90 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.90 (184) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.26/17.90 (185) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/17.90 (186) all_54_15 = all_4_2
% 116.26/17.90 (187) ~ (all_6_2 = e1)
% 116.26/17.90 (188) ~ (all_6_1 = e2)
% 116.26/17.90 (189) ~ (all_52_6 = all_52_7)
% 116.26/17.90 (190) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 116.26/17.90 (191) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.26/17.90
% 116.26/17.90 Begin of proof
% 116.26/17.90 |
% 116.26/17.90 | COMBINE_EQS: (105), (121) imply:
% 116.26/17.90 | (192) all_6_0 = e2
% 116.26/17.90 |
% 116.26/17.90 | REDUCE: (35), (192) imply:
% 116.26/17.90 | (193) op(all_6_1, all_6_2) = e2
% 116.26/17.90 |
% 116.26/17.90 | BETA: splitting (7) gives:
% 116.26/17.90 |
% 116.26/17.90 | Case 1:
% 116.26/17.90 | |
% 116.26/17.90 | | (194) ~ (all_32_1 = e1)
% 116.26/17.90 | |
% 116.26/17.90 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 116.26/17.90 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 116.26/17.90 | | (25), (26), (27), (28), (29), (31), (32), (33), (34), (37), (38),
% 116.26/17.90 | | (39), (40), (41), (42), (43), (45), (46), (48), (49), (50), (52),
% 116.26/17.90 | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 116.26/17.90 | | (64), (65), (67), (68), (70), (71), (73), (74), (75), (76), (78),
% 116.26/17.90 | | (79), (80), (82), (84), (85), (86), (87), (88), (89), (90), (91),
% 116.26/17.90 | | (92), (93), (95), (96), (97), (98), (99), (100), (101), (102),
% 116.26/17.90 | | (103), (104), (106), (107), (108), (109), (111), (112), (113),
% 116.26/17.90 | | (114), (115), (117), (118), (119), (120), (123), (124), (126),
% 116.26/17.90 | | (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 116.26/17.90 | | (137), (138), (139), (140), (141), (142), (143), (144), (145),
% 116.26/17.90 | | (146), (147), (148), (149), (150), (151), (152), (153), (154),
% 116.26/17.90 | | (155), (156), (157), (158), (159), (161), (162), (163), (164),
% 116.26/17.90 | | (165), (166), (167), (168), (169), (172), (174), (175), (176),
% 116.26/17.90 | | (177), (178), (179), (180), (181), (183), (184), (185), (186),
% 116.26/17.90 | | (187), (188), (189), (190), (191), (193), (194) are inconsistent
% 116.26/17.90 | | by sub-proof #254.
% 116.26/17.90 | |
% 116.26/17.90 | Case 2:
% 116.26/17.90 | |
% 116.26/17.90 | | (195) all_32_1 = e1
% 116.26/17.90 | | (196) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 116.26/17.90 | |
% 116.26/17.90 | | COMBINE_EQS: (104), (195) imply:
% 116.26/17.90 | | (197) all_10_1 = e1
% 116.26/17.90 | |
% 116.26/17.90 | | REDUCE: (73), (197) imply:
% 116.26/17.90 | | (198) op(e1, all_10_2) = all_10_0
% 116.26/17.90 | |
% 116.26/17.90 | | REDUCE: (118), (197) imply:
% 116.26/17.90 | | (199) op(e3, all_10_2) = e1
% 116.26/17.90 | |
% 116.26/17.90 | | BETA: splitting (122) gives:
% 116.26/17.90 | |
% 116.26/17.90 | | Case 1:
% 116.26/17.90 | | |
% 116.26/17.90 | | | (200) ~ (all_42_0 = e1)
% 116.26/17.90 | | |
% 116.26/17.90 | | | REDUCE: (173), (200) imply:
% 116.26/17.90 | | | (201) $false
% 116.26/17.90 | | |
% 116.26/17.90 | | | CLOSE: (201) is inconsistent.
% 116.26/17.90 | | |
% 116.26/17.90 | | Case 2:
% 116.26/17.90 | | |
% 116.26/17.90 | | | (202) ~ (all_42_1 = e0) | ~ (all_42_2 = e3)
% 116.26/17.90 | | |
% 116.26/17.90 | | | BETA: splitting (106) gives:
% 116.26/17.90 | | |
% 116.26/17.90 | | | Case 1:
% 116.26/17.90 | | | |
% 116.26/17.90 | | | | (203) ~ (all_56_14 = e2)
% 116.26/17.90 | | | |
% 116.26/17.90 | | | | REDUCE: (15), (203) imply:
% 116.26/17.90 | | | | (204) ~ (all_6_2 = e2)
% 116.26/17.90 | | | |
% 116.26/17.91 | | | | REF_CLOSE: (1), (2), (3), (6), (9), (10), (11), (13), (14), (15), (16),
% 116.26/17.91 | | | | (17), (19), (22), (24), (27), (31), (32), (33), (34), (37),
% 116.26/17.91 | | | | (39), (40), (44), (46), (48), (49), (50), (51), (54), (57),
% 116.26/17.91 | | | | (58), (59), (61), (62), (63), (65), (66), (69), (70), (75),
% 116.26/17.91 | | | | (78), (83), (84), (85), (86), (87), (91), (93), (94), (96),
% 116.26/17.91 | | | | (98), (99), (101), (102), (103), (107), (112), (113), (114),
% 116.26/17.91 | | | | (120), (126), (129), (131), (134), (136), (137), (140),
% 116.26/17.91 | | | | (141), (146), (147), (149), (150), (151), (152), (154),
% 116.26/17.91 | | | | (156), (161), (163), (167), (168), (171), (172), (175),
% 116.26/17.91 | | | | (176), (178), (183), (186), (187), (188), (189), (196),
% 116.26/17.91 | | | | (198), (199), (204) are inconsistent by sub-proof #249.
% 116.26/17.91 | | | |
% 116.26/17.91 | | | Case 2:
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | (205) all_56_14 = e2
% 116.26/17.91 | | | | (206) ~ (all_56_10 = e0)
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | COMBINE_EQS: (15), (205) imply:
% 116.26/17.91 | | | | (207) all_6_2 = e2
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | SIMP: (207) implies:
% 116.26/17.91 | | | | (208) all_6_2 = e2
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (43), (206) imply:
% 116.26/17.91 | | | | (209) ~ (all_52_7 = e0)
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (57), (208) imply:
% 116.26/17.91 | | | | (210) ~ (all_52_8 = e2)
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (141), (208) imply:
% 116.26/17.91 | | | | (211) ~ (all_52_9 = e2)
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (75), (208) imply:
% 116.26/17.91 | | | | (212) ~ (all_52_11 = e2)
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (193), (208) imply:
% 116.26/17.91 | | | | (213) op(all_6_1, e2) = e2
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | REDUCE: (91), (208) imply:
% 116.26/17.91 | | | | (214) op(e1, e2) = all_6_1
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | BETA: splitting (184) gives:
% 116.26/17.91 | | | |
% 116.26/17.91 | | | | Case 1:
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | (215) ~ (all_56_0 = e3)
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | REDUCE: (179), (215) imply:
% 116.26/17.91 | | | | | (216) ~ (all_52_4 = e3)
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | GROUND_INST: instantiating (48) with all_52_6, all_6_1, e2, e1,
% 116.26/17.91 | | | | | simplifying with (137), (214) gives:
% 116.26/17.91 | | | | | (217) all_52_6 = all_6_1
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | COMBINE_EQS: (6), (217) imply:
% 116.26/17.91 | | | | | (218) all_58_7 = all_6_1
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | REDUCE: (189), (217) imply:
% 116.26/17.91 | | | | | (219) ~ (all_52_7 = all_6_1)
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | SIMP: (219) implies:
% 116.26/17.91 | | | | | (220) ~ (all_52_7 = all_6_1)
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | BETA: splitting (101) gives:
% 116.26/17.91 | | | | |
% 116.26/17.91 | | | | | Case 1:
% 116.26/17.91 | | | | | |
% 116.26/17.91 | | | | | | (221) ~ (all_56_13 = e3)
% 116.26/17.91 | | | | | |
% 116.26/17.91 | | | | | | REDUCE: (131), (221) imply:
% 116.26/17.91 | | | | | | (222) ~ (all_8_2 = e3)
% 116.26/17.91 | | | | | |
% 116.26/17.91 | | | | | | BETA: splitting (171) gives:
% 116.26/17.91 | | | | | |
% 116.26/17.91 | | | | | | Case 1:
% 116.26/17.91 | | | | | | |
% 116.26/17.91 | | | | | | | (223) ~ (all_56_5 = e2)
% 116.26/17.91 | | | | | | |
% 116.26/17.91 | | | | | | | REDUCE: (152), (223) imply:
% 116.26/17.91 | | | | | | | (224) ~ (all_52_13 = e2)
% 116.26/17.91 | | | | | | |
% 116.26/17.91 | | | | | | | BETA: splitting (178) gives:
% 116.26/17.91 | | | | | | |
% 116.26/17.91 | | | | | | | Case 1:
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | (225) all_58_2 = e2
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | COMBINE_EQS: (98), (225) imply:
% 116.26/17.91 | | | | | | | | (226) all_52_1 = e2
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | REDUCE: (111), (226) imply:
% 116.26/17.91 | | | | | | | | (227) ~ (all_10_2 = e2)
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | SIMP: (227) implies:
% 116.26/17.91 | | | | | | | | (228) ~ (all_10_2 = e2)
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | REDUCE: (133), (226) imply:
% 116.26/17.91 | | | | | | | | (229) ~ (all_8_2 = e2)
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | BETA: splitting (110) gives:
% 116.26/17.91 | | | | | | | |
% 116.26/17.91 | | | | | | | | Case 1:
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | (230) ~ (all_56_1 = e3)
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | REDUCE: (144), (230) imply:
% 116.26/17.91 | | | | | | | | | (231) ~ (all_52_8 = e3)
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | REF_CLOSE: (1), (2), (19), (29), (33), (34), (48), (58), (61),
% 116.26/17.91 | | | | | | | | | (70), (102), (126), (147), (151), (172), (199),
% 116.26/17.91 | | | | | | | | | (216), (228), (231) are inconsistent by sub-proof
% 116.26/17.91 | | | | | | | | | #244.
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | Case 2:
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | (232) all_56_1 = e3
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | COMBINE_EQS: (144), (232) imply:
% 116.26/17.91 | | | | | | | | | (233) all_52_8 = e3
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | REDUCE: (164), (233) imply:
% 116.26/17.91 | | | | | | | | | (234) ~ (all_52_9 = e3)
% 116.26/17.91 | | | | | | | | |
% 116.26/17.91 | | | | | | | | | SIMP: (234) implies:
% 116.26/17.94 | | | | | | | | | (235) ~ (all_52_9 = e3)
% 116.26/17.94 | | | | | | | | |
% 116.26/17.94 | | | | | | | | | BETA: splitting (47) gives:
% 116.26/17.94 | | | | | | | | |
% 116.26/17.94 | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | (236) ~ (all_56_1 = e3)
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | REDUCE: (232), (236) imply:
% 116.26/17.94 | | | | | | | | | | (237) $false
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | CLOSE: (237) is inconsistent.
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | Case 2:
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | (238) ~ (all_56_13 = e1)
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | REDUCE: (131), (238) imply:
% 116.26/17.94 | | | | | | | | | | (239) ~ (all_8_2 = e1)
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | BETA: splitting (160) gives:
% 116.26/17.94 | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | (240) all_58_2 = e3
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | COMBINE_EQS: (225), (240) imply:
% 116.26/17.94 | | | | | | | | | | | (241) e3 = e2
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | REDUCE: (181), (241) imply:
% 116.26/17.94 | | | | | | | | | | | (242) $false
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | Case 2:
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | (243) all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | BETA: splitting (243) gives:
% 116.26/17.94 | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | (244) all_58_3 = e3
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | COMBINE_EQS: (63), (244) imply:
% 116.26/17.94 | | | | | | | | | | | | (245) all_8_2 = e3
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | REDUCE: (222), (245) imply:
% 116.26/17.94 | | | | | | | | | | | | (246) $false
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | Case 2:
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | (247) all_58_5 = e3 | all_58_10 = e3
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | BETA: splitting (247) gives:
% 116.26/17.94 | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | (248) all_58_5 = e3
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | REF_CLOSE: (87), (235), (248) are inconsistent by sub-proof
% 116.26/17.94 | | | | | | | | | | | | | #175.
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | Case 2:
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | (249) all_58_10 = e3
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | COMBINE_EQS: (114), (249) imply:
% 116.26/17.94 | | | | | | | | | | | | | (250) all_52_13 = e3
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | SIMP: (250) implies:
% 116.26/17.94 | | | | | | | | | | | | | (251) all_52_13 = e3
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | REDUCE: (115), (251) imply:
% 116.26/17.94 | | | | | | | | | | | | | (252) ~ (all_8_2 = e3)
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | REDUCE: (165), (251) imply:
% 116.26/17.94 | | | | | | | | | | | | | (253) op(e2, e0) = e3
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 116.26/17.94 | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | (254) all_54_5 = e3
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | REF_CLOSE: (112), (222), (254) are inconsistent by sub-proof
% 116.26/17.94 | | | | | | | | | | | | | | #339.
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | Case 2:
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | (255) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 116.26/17.94 | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | Case 1:
% 116.26/17.94 | | | | | | | | | | | | | | |
% 116.26/17.94 | | | | | | | | | | | | | | | (256) all_54_5 = e2
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | REF_CLOSE: (112), (134), (256) are inconsistent by sub-proof
% 116.26/17.95 | | | | | | | | | | | | | | | #338.
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | (257) all_54_5 = e1 | all_54_5 = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | (258) all_58_2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (258) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | (259) e2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | SIMP: (259) implies:
% 116.26/17.95 | | | | | | | | | | | | | | | | (260) e2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | REDUCE: (158), (260) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | (261) $false
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | (262) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | (263) all_58_3 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (263) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | (264) all_8_2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (264) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | (265) all_14_2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | REDUCE: (116), (264) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | (266) op(e2, e0) = all_8_1
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | (267) ~ (all_14_1 = e3)
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | REDUCE: (125), (267) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | | (268) ~ (all_8_1 = e3)
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (253), (266), (268) are inconsistent by
% 116.26/17.95 | | | | | | | | | | | | | | | | | | sub-proof #247.
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | (269) ~ (all_14_2 = e0)
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | REDUCE: (265), (269) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | | (270) $false
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | (271) ~ (all_58_3 = e0)
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | REDUCE: (63), (271) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | | | (272) ~ (all_8_2 = e0)
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (239), (257), (272) are inconsistent by
% 116.26/17.95 | | | | | | | | | | | | | | | | | sub-proof #174.
% 116.26/17.95 | | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | End of split
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | (273) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | REF_CLOSE: (63), (87), (114), (134), (211), (224), (273) are
% 116.26/17.95 | | | | | | | | inconsistent by sub-proof #401.
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | End of split
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | Case 2:
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | (274) all_56_5 = e2
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | COMBINE_EQS: (152), (274) imply:
% 116.26/17.95 | | | | | | | (275) all_52_13 = e2
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | REDUCE: (115), (275) imply:
% 116.26/17.95 | | | | | | | (276) ~ (all_8_2 = e2)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | REDUCE: (157), (275) imply:
% 116.26/17.95 | | | | | | | (277) ~ (all_4_2 = e2)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | SIMP: (277) implies:
% 116.26/17.95 | | | | | | | (278) ~ (all_4_2 = e2)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | BETA: splitting (68) gives:
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | (279) ~ (all_56_5 = e2)
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | REDUCE: (274), (279) imply:
% 116.26/17.95 | | | | | | | | (280) $false
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | CLOSE: (280) is inconsistent.
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | (281) ~ (all_56_13 = e0)
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | REDUCE: (131), (281) imply:
% 116.26/17.95 | | | | | | | | (282) ~ (all_8_2 = e0)
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | REF_CLOSE: (13), (14), (25), (32), (39), (48), (60), (63), (76),
% 116.26/17.95 | | | | | | | | (96), (97), (103), (112), (126), (129), (131), (134),
% 116.26/17.95 | | | | | | | | (135), (158), (181), (183), (209), (212), (213),
% 116.26/17.95 | | | | | | | | (216), (218), (220), (222), (278), (282) are
% 116.26/17.95 | | | | | | | | inconsistent by sub-proof #261.
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | End of split
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | End of split
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | Case 2:
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | (283) all_56_13 = e3
% 116.26/17.95 | | | | | | (284) ~ (all_56_9 = e0)
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | COMBINE_EQS: (131), (283) imply:
% 116.26/17.95 | | | | | | (285) all_8_2 = e3
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | SIMP: (285) implies:
% 116.26/17.95 | | | | | | (286) all_8_2 = e3
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | COMBINE_EQS: (36), (286) imply:
% 116.26/17.95 | | | | | | (287) all_42_2 = e3
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | COMBINE_EQS: (63), (286) imply:
% 116.26/17.95 | | | | | | (288) all_58_3 = e3
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | REDUCE: (89), (284) imply:
% 116.26/17.95 | | | | | | (289) ~ (all_52_3 = e0)
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | REDUCE: (116), (286) imply:
% 116.26/17.95 | | | | | | (290) op(e2, e3) = all_8_1
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | BETA: splitting (26) gives:
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | | Case 1:
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | (291) ~ (all_56_3 = e2)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | REDUCE: (17), (291) imply:
% 116.26/17.95 | | | | | | | (292) ~ (all_52_1 = e2)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | BETA: splitting (183) gives:
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | (293) all_58_15 = e0
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | COMBINE_EQS: (96), (293) imply:
% 116.26/17.95 | | | | | | | | (294) all_4_2 = e0
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | REDUCE: (13), (294) imply:
% 116.26/17.95 | | | | | | | | (295) $false
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | CLOSE: (295) is inconsistent.
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | (296) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.95 | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | ALPHA: (296) implies:
% 116.26/17.95 | | | | | | | | (297) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | BETA: splitting (297) gives:
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | (298) all_58_12 = e0
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | COMBINE_EQS: (161), (298) imply:
% 116.26/17.95 | | | | | | | | | (299) all_52_3 = e0
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | REDUCE: (289), (299) imply:
% 116.26/17.95 | | | | | | | | | (300) $false
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | CLOSE: (300) is inconsistent.
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | (301) all_58_13 = e0 | all_58_14 = e0
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | BETA: splitting (301) gives:
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | (302) all_58_13 = e0
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | REF_CLOSE: (103), (209), (302) are inconsistent by sub-proof
% 116.26/17.95 | | | | | | | | | | #430.
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | (303) all_58_14 = e0
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | COMBINE_EQS: (129), (303) imply:
% 116.26/17.95 | | | | | | | | | | (304) all_52_11 = e0
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | SIMP: (304) implies:
% 116.26/17.95 | | | | | | | | | | (305) all_52_11 = e0
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | REDUCE: (128), (305) imply:
% 116.26/17.95 | | | | | | | | | | (306) ~ (all_52_9 = e0)
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | REDUCE: (212), (305) imply:
% 116.26/17.95 | | | | | | | | | | (307) ~ (e2 = e0)
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | BETA: splitting (178) gives:
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | (308) all_58_2 = e2
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | COMBINE_EQS: (98), (308) imply:
% 116.26/17.95 | | | | | | | | | | | (309) all_52_1 = e2
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | REDUCE: (292), (309) imply:
% 116.26/17.95 | | | | | | | | | | | (310) $false
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | CLOSE: (310) is inconsistent.
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | (311) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | BETA: splitting (311) gives:
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | (312) all_58_3 = e2
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | COMBINE_EQS: (288), (312) imply:
% 116.26/17.95 | | | | | | | | | | | | (313) e3 = e2
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | REDUCE: (181), (313) imply:
% 116.26/17.95 | | | | | | | | | | | | (314) $false
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | CLOSE: (314) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | (315) all_58_5 = e2 | all_58_10 = e2
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | BETA: splitting (315) gives:
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | (316) all_58_5 = e2
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | COMBINE_EQS: (87), (316) imply:
% 116.26/17.95 | | | | | | | | | | | | | (317) all_52_9 = e2
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | REDUCE: (211), (317) imply:
% 116.26/17.95 | | | | | | | | | | | | | (318) $false
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | CLOSE: (318) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | (319) all_58_10 = e2
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | COMBINE_EQS: (114), (319) imply:
% 116.26/17.95 | | | | | | | | | | | | | (320) all_52_13 = e2
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | BETA: splitting (202) gives:
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | (321) ~ (all_42_2 = e3)
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | REDUCE: (287), (321) imply:
% 116.26/17.95 | | | | | | | | | | | | | | (322) $false
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | (323) ~ (all_42_1 = e0)
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | REDUCE: (182), (323) imply:
% 116.26/17.95 | | | | | | | | | | | | | | (324) ~ (all_8_1 = e0)
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | Case 1:
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | (325) all_58_2 = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | COMBINE_EQS: (98), (325) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | (326) all_52_1 = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | REDUCE: (77), (326) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | (327) op(e2, e3) = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | GROUND_INST: instantiating (48) with e0, all_8_1, e3, e2,
% 116.26/17.95 | | | | | | | | | | | | | | | simplifying with (290), (327) gives:
% 116.26/17.95 | | | | | | | | | | | | | | | (328) all_8_1 = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | REDUCE: (324), (328) imply:
% 116.26/17.95 | | | | | | | | | | | | | | | (329) $false
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | CLOSE: (329) is inconsistent.
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | Case 2:
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | (330) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | | REF_CLOSE: (81), (87), (158), (288), (306), (319), (330) are
% 116.26/17.95 | | | | | | | | | | | | | | | inconsistent by sub-proof #172.
% 116.26/17.95 | | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | | |
% 116.26/17.95 | | | | | | | | | End of split
% 116.26/17.95 | | | | | | | | |
% 116.26/17.95 | | | | | | | | End of split
% 116.26/17.95 | | | | | | | |
% 116.26/17.95 | | | | | | | End of split
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | Case 2:
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | (331) ~ (all_56_13 = e3)
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | REDUCE: (283), (331) imply:
% 116.26/17.95 | | | | | | | (332) $false
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | | CLOSE: (332) is inconsistent.
% 116.26/17.95 | | | | | | |
% 116.26/17.95 | | | | | | End of split
% 116.26/17.95 | | | | | |
% 116.26/17.95 | | | | | End of split
% 116.26/17.95 | | | | |
% 116.26/17.95 | | | | Case 2:
% 116.26/17.95 | | | | |
% 116.26/17.95 | | | | | (333) ~ (all_56_14 = e2)
% 116.26/17.95 | | | | |
% 116.26/17.95 | | | | | REDUCE: (205), (333) imply:
% 116.26/17.95 | | | | | (334) $false
% 116.26/17.95 | | | | |
% 116.26/17.95 | | | | | CLOSE: (334) is inconsistent.
% 116.26/17.95 | | | | |
% 116.26/17.95 | | | | End of split
% 116.26/17.95 | | | |
% 116.26/17.95 | | | End of split
% 116.26/17.95 | | |
% 116.26/17.95 | | End of split
% 116.26/17.96 | |
% 116.26/17.96 | End of split
% 116.26/17.96 |
% 116.26/17.96 End of proof
% 116.26/17.96
% 116.26/17.96 Sub-proof #172 shows that the following formulas are inconsistent:
% 116.26/17.96 ----------------------------------------------------------------
% 116.26/17.96 (1) all_58_10 = e2
% 116.26/17.96 (2) ~ (all_52_9 = e0)
% 116.26/17.96 (3) ~ (e3 = e0)
% 116.26/17.96 (4) all_58_5 = all_52_9
% 116.26/17.96 (5) all_58_3 = e3
% 116.26/17.96 (6) all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 116.26/17.96 (7) ~ (e2 = e0)
% 116.26/17.96
% 116.26/17.96 Begin of proof
% 116.26/17.96 |
% 116.26/17.96 | BETA: splitting (6) gives:
% 116.26/17.96 |
% 116.26/17.96 | Case 1:
% 116.26/17.96 | |
% 116.26/17.96 | | (8) all_58_3 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | COMBINE_EQS: (5), (8) imply:
% 116.26/17.96 | | (9) e3 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | REDUCE: (3), (9) imply:
% 116.26/17.96 | | (10) $false
% 116.26/17.96 | |
% 116.26/17.96 | | CLOSE: (10) is inconsistent.
% 116.26/17.96 | |
% 116.26/17.96 | Case 2:
% 116.26/17.96 | |
% 116.26/17.96 | | (11) all_58_5 = e0 | all_58_10 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | REF_CLOSE: (1), (2), (4), (7), (11) are inconsistent by sub-proof #173.
% 116.26/17.96 | |
% 116.26/17.96 | End of split
% 116.26/17.96 |
% 116.26/17.96 End of proof
% 116.26/17.96
% 116.26/17.96 Sub-proof #173 shows that the following formulas are inconsistent:
% 116.26/17.96 ----------------------------------------------------------------
% 116.26/17.96 (1) all_58_10 = e2
% 116.26/17.96 (2) ~ (all_52_9 = e0)
% 116.26/17.96 (3) all_58_5 = all_52_9
% 116.26/17.96 (4) all_58_5 = e0 | all_58_10 = e0
% 116.26/17.96 (5) ~ (e2 = e0)
% 116.26/17.96
% 116.26/17.96 Begin of proof
% 116.26/17.96 |
% 116.26/17.96 | BETA: splitting (4) gives:
% 116.26/17.96 |
% 116.26/17.96 | Case 1:
% 116.26/17.96 | |
% 116.26/17.96 | | (6) all_58_5 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | COMBINE_EQS: (3), (6) imply:
% 116.26/17.96 | | (7) all_52_9 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | REDUCE: (2), (7) imply:
% 116.26/17.96 | | (8) $false
% 116.26/17.96 | |
% 116.26/17.96 | | CLOSE: (8) is inconsistent.
% 116.26/17.96 | |
% 116.26/17.96 | Case 2:
% 116.26/17.96 | |
% 116.26/17.96 | | (9) all_58_10 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | COMBINE_EQS: (1), (9) imply:
% 116.26/17.96 | | (10) e2 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | REDUCE: (5), (10) imply:
% 116.26/17.96 | | (11) $false
% 116.26/17.96 | |
% 116.26/17.96 | | CLOSE: (11) is inconsistent.
% 116.26/17.96 | |
% 116.26/17.96 | End of split
% 116.26/17.96 |
% 116.26/17.96 End of proof
% 116.26/17.96
% 116.26/17.96 Sub-proof #174 shows that the following formulas are inconsistent:
% 116.26/17.96 ----------------------------------------------------------------
% 116.26/17.96 (1) all_54_5 = e1 | all_54_5 = e0
% 116.26/17.96 (2) all_54_5 = all_8_2
% 116.26/17.96 (3) ~ (all_8_2 = e1)
% 116.26/17.96 (4) ~ (all_8_2 = e0)
% 116.26/17.96
% 116.26/17.96 Begin of proof
% 116.26/17.96 |
% 116.26/17.96 | BETA: splitting (1) gives:
% 116.26/17.96 |
% 116.26/17.96 | Case 1:
% 116.26/17.96 | |
% 116.26/17.96 | | (5) all_54_5 = e1
% 116.26/17.96 | |
% 116.26/17.96 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #337.
% 116.26/17.96 | |
% 116.26/17.96 | Case 2:
% 116.26/17.96 | |
% 116.26/17.96 | | (6) all_54_5 = e0
% 116.26/17.96 | |
% 116.26/17.96 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #311.
% 116.26/17.96 | |
% 116.26/17.96 | End of split
% 116.26/17.96 |
% 116.26/17.96 End of proof
% 116.26/17.96
% 116.26/17.96 Sub-proof #175 shows that the following formulas are inconsistent:
% 116.26/17.96 ----------------------------------------------------------------
% 116.26/17.96 (1) all_58_5 = all_52_9
% 116.26/17.96 (2) all_58_5 = e3
% 116.26/17.96 (3) ~ (all_52_9 = e3)
% 116.26/17.96
% 116.26/17.96 Begin of proof
% 116.26/17.96 |
% 116.26/17.96 | COMBINE_EQS: (1), (2) imply:
% 116.26/17.96 | (4) all_52_9 = e3
% 116.26/17.96 |
% 116.26/17.96 | SIMP: (4) implies:
% 116.26/17.96 | (5) all_52_9 = e3
% 116.26/17.96 |
% 116.26/17.96 | REDUCE: (3), (5) imply:
% 116.26/17.96 | (6) $false
% 116.26/17.96 |
% 116.26/17.96 | CLOSE: (6) is inconsistent.
% 116.26/17.96 |
% 116.26/17.96 End of proof
% 116.26/17.96
% 116.26/17.96 Sub-proof #176 shows that the following formulas are inconsistent:
% 116.26/17.96 ----------------------------------------------------------------
% 116.26/17.96 (1) ~ (all_52_8 = all_10_2)
% 116.26/17.96 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/17.96 (3) ~ (all_52_2 = all_10_2)
% 116.26/17.96 (4) ~ (all_52_6 = all_52_14)
% 116.26/17.96 (5) all_54_2 = all_52_8
% 116.26/17.96 (6) all_58_7 = all_52_6
% 116.26/17.96 (7) all_36_2 = all_6_2
% 116.26/17.96 (8) ~ (all_52_8 = all_52_11)
% 116.26/17.96 (9) ~ (all_52_9 = all_8_2)
% 116.26/17.96 (10) all_28_1 = all_6_1
% 116.26/17.96 (11) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.26/17.96 (12) ~ (all_52_13 = all_52_14)
% 116.26/17.96 (13) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.26/17.96 (14) ~ (all_4_2 = e0)
% 116.26/17.96 (15) op(e3, e2) = all_52_4
% 116.26/17.96 (16) all_56_14 = all_6_2
% 116.26/17.96 (17) all_56_3 = all_52_1
% 116.26/17.96 (18) all_54_0 = all_10_2
% 116.26/17.96 (19) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.96 (20) all_54_3 = all_52_12
% 116.26/17.96 (21) ~ (all_52_2 = all_52_6)
% 116.26/17.96 (22) ~ (all_52_12 = all_52_14)
% 116.26/17.96 (23) op(e0, e2) = all_52_7
% 116.26/17.96 (24) ~ (all_52_7 = all_4_2)
% 116.26/17.96 (25) all_56_11 = all_52_11
% 116.26/17.96 (26) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 116.26/17.96 (27) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/17.96 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.96 (29) ~ (all_52_4 = all_52_8)
% 116.26/17.96 (30) ~ (all_52_12 = all_10_2)
% 116.26/17.96 (31) ~ (e3 = e1)
% 116.26/17.96 (32) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.26/17.96 (33) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.26/17.96 (34) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.96 (35) all_56_12 = all_10_2
% 116.26/17.96 (36) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 116.26/17.96 (37) all_58_0 = all_10_2
% 116.26/17.96 (38) op(all_6_1, all_6_2) = all_6_0
% 116.26/17.96 (39) all_54_11 = all_52_14
% 116.26/17.96 (40) all_54_13 = all_52_7
% 116.26/17.96 (41) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.26/17.96 (42) all_36_1 = all_6_1
% 116.26/17.96 (43) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.26/17.96 (44) ~ (all_52_14 = all_6_2)
% 116.26/17.96 (45) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.26/17.96 (46) all_56_10 = all_52_7
% 116.26/17.96 (47) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.26/17.96 (48) op(all_4_1, all_4_2) = all_4_0
% 116.26/17.96 (49) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.96 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.96 (51) all_54_8 = all_52_2
% 116.26/17.96 (52) ~ (all_52_2 = all_6_2)
% 116.26/17.96 (53) ~ (all_52_1 = all_52_9)
% 116.26/17.96 (54) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.26/17.96 (55) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.26/17.96 (56) all_44_2 = all_4_2
% 116.26/17.96 (57) all_54_10 = all_6_2
% 116.26/17.96 (58) all_36_0 = all_6_0
% 116.26/17.96 (59) op(e3, e0) = all_52_12
% 116.26/17.96 (60) ~ (all_52_8 = all_6_2)
% 116.26/17.96 (61) all_58_4 = all_52_8
% 116.26/17.96 (62) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/17.96 (63) ~ (all_52_4 = all_52_7)
% 116.26/17.96 (64) all_56_2 = all_52_12
% 116.26/17.96 (65) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/17.96 (66) all_58_3 = all_8_2
% 116.26/17.96 (67) all_54_6 = all_52_9
% 116.26/17.97 (68) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 116.26/17.97 (69) ~ (all_10_0 = e2)
% 116.26/17.97 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.97 (71) all_58_11 = all_52_14
% 116.26/17.97 (72) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.26/17.97 (73) all_54_9 = all_52_6
% 116.26/17.97 (74) ~ (all_52_2 = all_52_3)
% 116.26/17.97 (75) all_54_7 = all_52_13
% 116.26/17.97 (76) all_16_1 = all_10_1
% 116.26/17.97 (77) op(all_10_1, all_10_2) = all_10_0
% 116.26/17.97 (78) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/17.97 (79) ~ (all_52_11 = all_6_2)
% 116.26/17.97 (80) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.97 (81) op(e2, e3) = all_52_1
% 116.26/17.97 (82) all_24_0 = all_10_0
% 116.26/17.97 (83) all_28_2 = all_6_2
% 116.26/17.97 (84) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.26/17.97 (85) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.26/17.97 (86) all_44_0 = all_4_0
% 116.26/17.97 (87) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.26/17.97 (88) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/17.97 (89) ~ (all_52_7 = all_8_2)
% 116.26/17.97 (90) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/17.97 (91) ~ (all_52_4 = all_8_2)
% 116.26/17.97 (92) op(e1, e0) = all_52_14
% 116.26/17.97 (93) all_58_5 = all_52_9
% 116.26/17.97 (94) ~ (all_52_9 = all_52_13)
% 116.26/17.97 (95) all_40_0 = all_6_0
% 116.26/17.97 (96) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.26/17.97 (97) ~ (all_4_0 = e3)
% 116.26/17.97 (98) all_56_9 = all_52_3
% 116.26/17.97 (99) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.26/17.97 (100) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/17.97 (101) op(e1, all_6_2) = all_6_1
% 116.26/17.97 (102) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.97 (103) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.26/17.97 (104) all_58_15 = all_4_2
% 116.26/17.97 (105) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.26/17.97 (106) all_58_2 = all_52_1
% 116.26/17.97 (107) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/17.97 (108) ~ (all_52_1 = all_52_13)
% 116.26/17.97 (109) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 116.26/17.97 (110) op(e0, e3) = all_52_3
% 116.26/17.97 (111) ~ (all_10_2 = e3)
% 116.26/17.97 (112) ~ (all_52_12 = all_52_13)
% 116.26/17.97 (113) all_58_13 = all_52_7
% 116.26/17.97 (114) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/17.97 (115) all_40_1 = all_6_1
% 116.26/17.97 (116) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.26/17.97 (117) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.26/17.97 (118) ~ (all_52_14 = all_4_2)
% 116.26/17.97 (119) all_58_6 = all_52_2
% 116.26/17.97 (120) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.26/17.97 (121) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.26/17.97 (122) ~ (all_52_1 = all_10_2)
% 116.26/17.97 (123) all_54_5 = all_8_2
% 116.26/17.97 (124) all_56_15 = all_4_2
% 116.26/17.97 (125) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 116.26/17.97 (126) all_58_10 = all_52_13
% 116.26/17.97 (127) ~ (all_52_13 = all_8_2)
% 116.26/17.97 (128) ~ (all_52_11 = all_4_2)
% 116.26/17.97 (129) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 116.26/17.97 (130) all_16_0 = all_10_0
% 116.26/17.97 (131) op(e3, all_10_2) = all_10_1
% 116.26/17.97 (132) ~ (all_52_6 = all_8_2)
% 116.26/17.97 (133) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.26/17.97 (134) all_28_0 = all_6_0
% 116.26/17.97 (135) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 116.26/17.97 (136) all_58_1 = all_52_4
% 116.26/17.97 (137) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.26/17.97 (138) all_58_14 = all_52_11
% 116.26/17.97 (139) all_54_1 = all_52_4
% 116.26/17.97 (140) all_56_13 = all_8_2
% 116.26/17.97 (141) ~ (all_52_1 = all_8_2)
% 116.26/17.97 (142) ~ (all_8_2 = e2)
% 116.26/17.97 (143) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.26/17.97 (144) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.26/17.97 (145) op(e1, e2) = all_52_6
% 116.26/17.97 (146) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/17.97 (147) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.97 (148) all_56_7 = all_52_6
% 116.26/17.97 (149) ~ (all_52_9 = all_6_2)
% 116.26/17.97 (150) ~ (all_52_4 = all_52_6)
% 116.26/17.97 (151) all_26_2 = all_4_2
% 116.26/17.97 (152) ~ (all_52_4 = all_52_12)
% 116.26/17.97 (153) all_56_1 = all_52_8
% 116.26/17.97 (154) op(e0, all_4_2) = all_4_1
% 116.26/17.97 (155) all_58_8 = all_6_2
% 116.26/17.97 (156) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.97 (157) all_16_2 = all_10_2
% 116.26/17.97 (158) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.26/17.97 (159) all_40_2 = all_6_2
% 116.26/17.97 (160) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/17.97 (161) all_56_4 = all_52_9
% 116.26/17.97 (162) all_58_9 = all_52_12
% 116.26/17.97 (163) all_56_5 = all_52_13
% 116.26/17.97 (164) ~ (all_52_3 = all_4_2)
% 116.26/17.97 (165) ~ (all_52_6 = all_6_2)
% 116.26/17.97 (166) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.97 (167) all_56_6 = all_52_2
% 116.26/17.97 (168) ~ (all_52_13 = all_4_2)
% 116.26/17.97 (169) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.26/17.97 (170) all_58_12 = all_52_3
% 116.26/17.97 (171) ~ (all_52_2 = all_52_14)
% 116.26/17.97 (172) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.26/17.97 (173) ~ (all_52_8 = all_52_9)
% 116.26/17.97 (174) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.26/17.97 (175) ~ (all_52_12 = all_4_2)
% 116.26/17.97 (176) ~ (all_52_3 = all_10_2)
% 116.26/17.97 (177) all_24_1 = all_10_1
% 116.26/17.97 (178) op(e1, e3) = all_52_2
% 116.26/17.97 (179) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.26/17.97 (180) all_24_2 = all_10_2
% 116.26/17.97 (181) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.26/17.97 (182) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/17.97 (183) all_44_1 = all_4_1
% 116.26/17.97 (184) ~ (all_52_8 = all_52_12)
% 116.26/17.97 (185) all_56_8 = all_52_14
% 116.26/17.97 (186) all_16_0 = e1
% 116.26/17.97 (187) ~ (all_26_0 = e1) | ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.26/17.97 (188) all_26_1 = all_4_1
% 116.26/17.97 (189) ~ (all_24_0 = e1) | ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/17.97 (190) ~ (all_52_4 = all_10_2)
% 116.26/17.97 (191) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.26/17.97 (192) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/17.97 (193) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.97 (194) all_56_0 = all_52_4
% 116.26/17.97 (195) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.26/17.97 (196) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.97 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.97 (197) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.26/17.97 (198) all_54_4 = all_52_1
% 116.26/17.97 (199) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/17.97 (200) all_54_15 = all_4_2
% 116.26/17.97 (201) ~ (all_6_2 = e1)
% 116.26/17.97 (202) ~ (all_6_1 = e2)
% 116.26/17.97 (203) ~ (all_52_6 = all_52_7)
% 116.26/17.97 (204) ~ (all_52_3 = all_52_11)
% 116.26/17.97 (205) all_54_12 = all_52_3
% 116.26/17.97 (206) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.26/17.97 (207) all_26_0 = all_4_0
% 116.26/17.97
% 116.26/17.97 Begin of proof
% 116.26/17.97 |
% 116.26/17.97 | COMBINE_EQS: (130), (186) imply:
% 116.26/17.97 | (208) all_10_0 = e1
% 116.26/17.97 |
% 116.26/17.97 | COMBINE_EQS: (82), (208) imply:
% 116.26/17.97 | (209) all_24_0 = e1
% 116.26/17.97 |
% 116.26/17.97 | REDUCE: (69), (208) imply:
% 116.26/17.97 | (210) ~ (e2 = e1)
% 116.26/17.97 |
% 116.26/17.97 | SIMP: (210) implies:
% 116.26/17.97 | (211) ~ (e2 = e1)
% 116.26/17.97 |
% 116.26/17.97 | REDUCE: (77), (208) imply:
% 116.26/17.97 | (212) op(all_10_1, all_10_2) = e1
% 116.26/17.97 |
% 116.26/17.97 | BETA: splitting (189) gives:
% 116.26/17.97 |
% 116.26/17.97 | Case 1:
% 116.26/17.97 | |
% 116.26/17.97 | | (213) ~ (all_24_0 = e1)
% 116.26/17.97 | |
% 116.26/17.97 | | REDUCE: (209), (213) imply:
% 116.26/17.97 | | (214) $false
% 116.26/17.97 | |
% 116.26/17.97 | | CLOSE: (214) is inconsistent.
% 116.26/17.97 | |
% 116.26/17.97 | Case 2:
% 116.26/17.97 | |
% 116.26/17.97 | | (215) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/17.97 | |
% 116.26/17.97 | | BETA: splitting (187) gives:
% 116.26/17.97 | |
% 116.26/17.97 | | Case 1:
% 116.26/17.97 | | |
% 116.26/17.97 | | | (216) ~ (all_26_0 = e1)
% 116.26/17.97 | | |
% 116.26/17.97 | | | REDUCE: (207), (216) imply:
% 116.26/17.97 | | | (217) ~ (all_4_0 = e1)
% 116.26/17.97 | | |
% 116.26/17.97 | | | BETA: splitting (121) gives:
% 116.26/17.97 | | |
% 116.26/17.97 | | | Case 1:
% 116.26/17.97 | | | |
% 116.26/17.97 | | | | (218) ~ (all_28_0 = e2)
% 116.26/17.97 | | | |
% 116.26/17.97 | | | | REDUCE: (134), (218) imply:
% 116.26/17.97 | | | | (219) ~ (all_6_0 = e2)
% 116.26/17.97 | | | |
% 116.26/17.97 | | | | BETA: splitting (135) gives:
% 116.26/17.97 | | | |
% 116.26/17.97 | | | | Case 1:
% 116.26/17.97 | | | | |
% 116.26/17.97 | | | | | (220) ~ (all_36_1 = e3)
% 116.26/17.97 | | | | |
% 116.26/17.97 | | | | | REDUCE: (42), (220) imply:
% 116.26/17.97 | | | | | (221) ~ (all_6_1 = e3)
% 116.26/17.97 | | | | |
% 116.26/17.97 | | | | | BETA: splitting (55) gives:
% 116.26/17.97 | | | | |
% 116.26/17.97 | | | | | Case 1:
% 116.26/17.97 | | | | | |
% 116.26/17.97 | | | | | | (222) ~ (all_40_0 = e3)
% 116.26/17.97 | | | | | |
% 116.26/17.97 | | | | | | REDUCE: (95), (222) imply:
% 116.26/17.97 | | | | | | (223) ~ (all_6_0 = e3)
% 116.26/17.97 | | | | | |
% 116.26/17.97 | | | | | | BETA: splitting (116) gives:
% 116.26/17.97 | | | | | |
% 116.26/17.97 | | | | | | Case 1:
% 116.26/17.97 | | | | | | |
% 116.26/17.97 | | | | | | | (224) ~ (all_56_14 = e2)
% 116.26/17.97 | | | | | | |
% 116.26/17.97 | | | | | | | REDUCE: (16), (224) imply:
% 116.26/17.97 | | | | | | | (225) ~ (all_6_2 = e2)
% 116.26/17.97 | | | | | | |
% 116.26/17.97 | | | | | | | REF_CLOSE: (1), (4), (5), (6), (11), (12), (13), (14), (15), (16),
% 116.26/17.97 | | | | | | | (17), (18), (19), (20), (24), (25), (27), (28), (29),
% 116.26/17.97 | | | | | | | (30), (31), (32), (34), (35), (36), (37), (39), (40),
% 116.26/17.97 | | | | | | | (43), (44), (46), (48), (49), (50), (51), (52), (53),
% 116.26/17.97 | | | | | | | (54), (57), (59), (60), (61), (62), (63), (65), (66),
% 116.26/17.97 | | | | | | | (71), (76), (78), (81), (87), (88), (89), (90), (91),
% 116.26/17.97 | | | | | | | (92), (93), (97), (98), (100), (101), (102), (104),
% 116.26/17.98 | | | | | | | (106), (107), (110), (111), (113), (117), (118), (119),
% 116.26/17.98 | | | | | | | (122), (123), (124), (126), (131), (132), (133), (136),
% 116.26/17.98 | | | | | | | (138), (139), (141), (142), (145), (146), (147), (148),
% 116.26/17.98 | | | | | | | (149), (150), (152), (154), (155), (156), (157), (158),
% 116.26/17.98 | | | | | | | (160), (161), (162), (163), (164), (165), (166), (167),
% 116.26/17.98 | | | | | | | (170), (171), (172), (173), (174), (175), (176), (177),
% 116.26/17.98 | | | | | | | (178), (179), (180), (181), (182), (184), (185), (190),
% 116.26/17.98 | | | | | | | (191), (192), (193), (194), (196), (198), (199), (200),
% 116.26/17.98 | | | | | | | (201), (202), (203), (205), (212), (215), (217), (221),
% 116.26/17.98 | | | | | | | (225) are inconsistent by sub-proof #194.
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | Case 2:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | (226) all_56_14 = e2
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | REF_CLOSE: (3), (4), (6), (14), (16), (18), (19), (21), (23),
% 116.26/17.98 | | | | | | | (25), (31), (35), (38), (39), (40), (41), (44), (45),
% 116.26/17.98 | | | | | | | (50), (51), (52), (63), (66), (70), (73), (90), (98),
% 116.26/17.98 | | | | | | | (101), (102), (103), (104), (109), (113), (136), (138),
% 116.26/17.98 | | | | | | | (140), (142), (143), (145), (148), (156), (160), (165),
% 116.26/17.98 | | | | | | | (167), (170), (171), (185), (190), (192), (194), (195),
% 116.26/17.98 | | | | | | | (196), (197), (201), (203), (219), (221), (223), (226)
% 116.26/17.98 | | | | | | | are inconsistent by sub-proof #374.
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | End of split
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | Case 2:
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | (227) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | BETA: splitting (116) gives:
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | Case 1:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | (228) ~ (all_56_14 = e2)
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | REDUCE: (16), (228) imply:
% 116.26/17.98 | | | | | | | (229) ~ (all_6_2 = e2)
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | REF_CLOSE: (1), (4), (5), (6), (11), (12), (13), (14), (15), (16),
% 116.26/17.98 | | | | | | | (17), (18), (19), (20), (24), (25), (27), (28), (29),
% 116.26/17.98 | | | | | | | (30), (31), (32), (34), (35), (36), (37), (39), (40),
% 116.26/17.98 | | | | | | | (43), (44), (46), (48), (49), (50), (51), (52), (53),
% 116.26/17.98 | | | | | | | (54), (57), (59), (60), (61), (62), (63), (65), (66),
% 116.26/17.98 | | | | | | | (71), (76), (78), (81), (87), (88), (89), (90), (91),
% 116.26/17.98 | | | | | | | (92), (93), (97), (98), (100), (101), (102), (104),
% 116.26/17.98 | | | | | | | (106), (107), (110), (111), (113), (117), (118), (119),
% 116.26/17.98 | | | | | | | (122), (123), (124), (126), (131), (132), (133), (136),
% 116.26/17.98 | | | | | | | (138), (139), (141), (142), (145), (146), (147), (148),
% 116.26/17.98 | | | | | | | (149), (150), (152), (154), (155), (156), (157), (158),
% 116.26/17.98 | | | | | | | (160), (161), (162), (163), (164), (165), (166), (167),
% 116.26/17.98 | | | | | | | (170), (171), (172), (173), (174), (175), (176), (177),
% 116.26/17.98 | | | | | | | (178), (179), (180), (181), (182), (184), (185), (190),
% 116.26/17.98 | | | | | | | (191), (192), (193), (194), (196), (198), (199), (200),
% 116.26/17.98 | | | | | | | (201), (202), (203), (205), (212), (215), (217), (221),
% 116.26/17.98 | | | | | | | (229) are inconsistent by sub-proof #194.
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | Case 2:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | (230) all_56_14 = e2
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | REF_CLOSE: (16), (45), (50), (70), (73), (101), (115), (145),
% 116.26/17.98 | | | | | | | (148), (159), (165), (221), (227), (230) are
% 116.26/17.98 | | | | | | | inconsistent by sub-proof #372.
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | End of split
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | End of split
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | Case 2:
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | (231) all_36_1 = e3
% 116.26/17.98 | | | | | (232) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | COMBINE_EQS: (42), (231) imply:
% 116.26/17.98 | | | | | (233) all_6_1 = e3
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | SIMP: (233) implies:
% 116.26/17.98 | | | | | (234) all_6_1 = e3
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REDUCE: (202), (234) imply:
% 116.26/17.98 | | | | | (235) ~ (e3 = e2)
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REDUCE: (38), (234) imply:
% 116.26/17.98 | | | | | (236) op(e3, all_6_2) = all_6_0
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REDUCE: (101), (234) imply:
% 116.26/17.98 | | | | | (237) op(e1, all_6_2) = e3
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (12), (14), (15), (16), (17),
% 116.26/17.98 | | | | | (18), (19), (20), (21), (22), (24), (25), (26), (27), (28),
% 116.26/17.98 | | | | | (29), (30), (31), (34), (35), (36), (37), (39), (40), (44),
% 116.26/17.98 | | | | | (45), (46), (47), (49), (50), (51), (52), (53), (54), (57),
% 116.26/17.98 | | | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 116.26/17.98 | | | | | (68), (71), (72), (74), (75), (76), (78), (84), (87), (88),
% 116.26/17.98 | | | | | (89), (90), (91), (92), (93), (94), (98), (99), (100),
% 116.26/17.98 | | | | | (101), (102), (104), (106), (107), (108), (111), (112),
% 116.26/17.98 | | | | | (113), (114), (116), (117), (118), (119), (120), (123),
% 116.26/17.98 | | | | | (124), (125), (126), (127), (128), (129), (131), (132),
% 116.26/17.98 | | | | | (133), (136), (137), (138), (139), (140), (141), (142),
% 116.26/17.98 | | | | | (144), (145), (146), (147), (148), (149), (150), (152),
% 116.26/17.98 | | | | | (153), (155), (156), (157), (158), (160), (161), (162),
% 116.26/17.98 | | | | | (163), (164), (165), (167), (168), (169), (170), (171),
% 116.26/17.98 | | | | | (172), (174), (175), (176), (177), (178), (179), (180),
% 116.26/17.98 | | | | | (181), (182), (185), (190), (192), (193), (194), (196),
% 116.26/17.98 | | | | | (197), (199), (200), (201), (202), (203), (204), (205),
% 116.26/17.98 | | | | | (206), (211), (212), (215), (219), (232), (235), (236),
% 116.26/17.98 | | | | | (237) are inconsistent by sub-proof #182.
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | End of split
% 116.26/17.98 | | | |
% 116.26/17.98 | | | Case 2:
% 116.26/17.98 | | | |
% 116.26/17.98 | | | | (238) all_28_0 = e2
% 116.26/17.98 | | | | (239) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.26/17.98 | | | |
% 116.26/17.98 | | | | COMBINE_EQS: (134), (238) imply:
% 116.26/17.98 | | | | (240) all_6_0 = e2
% 116.26/17.98 | | | |
% 116.26/17.98 | | | | REDUCE: (38), (240) imply:
% 116.26/17.98 | | | | (241) op(all_6_1, all_6_2) = e2
% 116.26/17.98 | | | |
% 116.26/17.98 | | | | BETA: splitting (116) gives:
% 116.26/17.98 | | | |
% 116.26/17.98 | | | | Case 1:
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | (242) ~ (all_56_14 = e2)
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REDUCE: (16), (242) imply:
% 116.26/17.98 | | | | | (243) ~ (all_6_2 = e2)
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | BETA: splitting (117) gives:
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | Case 1:
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | (244) ~ (all_56_12 = e2)
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | REDUCE: (35), (244) imply:
% 116.26/17.98 | | | | | | (245) ~ (all_10_2 = e2)
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | BETA: splitting (156) gives:
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | Case 1:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | (246) all_54_0 = e3
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | REF_CLOSE: (18), (111), (246) are inconsistent by sub-proof #451.
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | Case 2:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | (247) ~ (all_54_0 = e3)
% 116.26/17.98 | | | | | | | (248) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | BETA: splitting (248) gives:
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | | (249) all_54_0 = e2
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | | REF_CLOSE: (18), (245), (249) are inconsistent by sub-proof
% 116.26/17.98 | | | | | | | | #450.
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | | (250) ~ (all_54_0 = e2)
% 116.26/17.98 | | | | | | | | (251) all_54_0 = e1 | all_54_0 = e0
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | | BETA: splitting (251) gives:
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | (252) all_54_0 = e1
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | COMBINE_EQS: (18), (252) imply:
% 116.26/17.98 | | | | | | | | | (253) all_10_2 = e1
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | SIMP: (253) implies:
% 116.26/17.98 | | | | | | | | | (254) all_10_2 = e1
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | COMBINE_EQS: (35), (254) imply:
% 116.26/17.98 | | | | | | | | | (255) all_56_12 = e1
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | BETA: splitting (192) gives:
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | (256) ~ (all_56_12 = e1)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | REDUCE: (255), (256) imply:
% 116.26/17.98 | | | | | | | | | | (257) $false
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | CLOSE: (257) is inconsistent.
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | (258) ~ (all_56_11 = e0)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | REDUCE: (25), (258) imply:
% 116.26/17.98 | | | | | | | | | | (259) ~ (all_52_11 = e0)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | BETA: splitting (49) gives:
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | (260) all_54_10 = e3
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | COMBINE_EQS: (57), (260) imply:
% 116.26/17.98 | | | | | | | | | | | (261) all_6_2 = e3
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | COMBINE_EQS: (16), (261) imply:
% 116.26/17.98 | | | | | | | | | | | (262) all_56_14 = e3
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | REDUCE: (52), (261) imply:
% 116.26/17.98 | | | | | | | | | | | (263) ~ (all_52_2 = e3)
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | REDUCE: (101), (261) imply:
% 116.26/17.98 | | | | | | | | | | | (264) op(e1, e3) = all_6_1
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | BETA: splitting (78) gives:
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | (265) ~ (all_56_14 = e3)
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | REDUCE: (262), (265) imply:
% 116.26/17.98 | | | | | | | | | | | | (266) $false
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | CLOSE: (266) is inconsistent.
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | (267) ~ (all_56_9 = e0)
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | REDUCE: (98), (267) imply:
% 116.26/17.98 | | | | | | | | | | | | (268) ~ (all_52_3 = e0)
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | BETA: splitting (196) gives:
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | (269) all_58_15 = e0
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | COMBINE_EQS: (104), (269) imply:
% 116.26/17.98 | | | | | | | | | | | | | (270) all_4_2 = e0
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | REDUCE: (14), (270) imply:
% 116.26/17.98 | | | | | | | | | | | | | (271) $false
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | CLOSE: (271) is inconsistent.
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | (272) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 116.26/17.98 | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 116.26/17.98 | | | | | | | | | | | | | e0)
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | ALPHA: (272) implies:
% 116.26/17.98 | | | | | | | | | | | | | (273) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | BETA: splitting (273) gives:
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | (274) all_58_12 = e0
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | COMBINE_EQS: (170), (274) imply:
% 116.26/17.98 | | | | | | | | | | | | | | (275) all_52_3 = e0
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | REDUCE: (268), (275) imply:
% 116.26/17.98 | | | | | | | | | | | | | | (276) $false
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | CLOSE: (276) is inconsistent.
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | (277) all_58_13 = e0 | all_58_14 = e0
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | (278) all_58_13 = e0
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | COMBINE_EQS: (113), (278) imply:
% 116.26/17.98 | | | | | | | | | | | | | | | (279) all_52_7 = e0
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | REDUCE: (24), (279) imply:
% 116.26/17.98 | | | | | | | | | | | | | | | (280) ~ (all_4_2 = e0)
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with all_52_2, all_6_1, e3, e1,
% 116.26/17.98 | | | | | | | | | | | | | | | simplifying with (178), (264) gives:
% 116.26/17.98 | | | | | | | | | | | | | | | (281) all_52_2 = all_6_1
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | REDUCE: (263), (281) imply:
% 116.26/17.98 | | | | | | | | | | | | | | | (282) ~ (all_6_1 = e3)
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (11), (12), (13), (14), (15),
% 116.26/17.98 | | | | | | | | | | | | | | | (16), (17), (18), (19), (20), (24), (25), (27),
% 116.26/17.98 | | | | | | | | | | | | | | | (28), (29), (30), (31), (32), (34), (35), (36),
% 116.26/17.98 | | | | | | | | | | | | | | | (37), (39), (40), (43), (44), (46), (48), (49),
% 116.26/17.98 | | | | | | | | | | | | | | | (50), (51), (52), (53), (54), (57), (59), (60),
% 116.26/17.98 | | | | | | | | | | | | | | | (61), (62), (63), (65), (66), (71), (76), (78),
% 116.26/17.98 | | | | | | | | | | | | | | | (81), (87), (88), (89), (90), (91), (92), (93),
% 116.26/17.98 | | | | | | | | | | | | | | | (97), (98), (100), (101), (102), (104), (106),
% 116.26/17.98 | | | | | | | | | | | | | | | (107), (110), (111), (113), (117), (118), (119),
% 116.26/17.98 | | | | | | | | | | | | | | | (122), (123), (124), (126), (131), (132), (133),
% 116.26/17.98 | | | | | | | | | | | | | | | (136), (138), (139), (141), (142), (145), (146),
% 116.26/17.98 | | | | | | | | | | | | | | | (147), (148), (149), (150), (152), (154), (155),
% 116.26/17.98 | | | | | | | | | | | | | | | (156), (157), (158), (160), (161), (162), (163),
% 116.26/17.98 | | | | | | | | | | | | | | | (164), (165), (166), (167), (170), (171), (172),
% 116.26/17.98 | | | | | | | | | | | | | | | (173), (174), (175), (176), (177), (178), (179),
% 116.26/17.98 | | | | | | | | | | | | | | | (180), (181), (182), (184), (185), (190), (191),
% 116.26/17.98 | | | | | | | | | | | | | | | (192), (193), (194), (196), (198), (199), (200),
% 116.26/17.98 | | | | | | | | | | | | | | | (201), (202), (203), (205), (212), (215), (217),
% 116.26/17.98 | | | | | | | | | | | | | | | (243), (282) are inconsistent by sub-proof #194.
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | (283) all_58_14 = e0
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | COMBINE_EQS: (138), (283) imply:
% 116.26/17.98 | | | | | | | | | | | | | | | (284) all_52_11 = e0
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | REDUCE: (259), (284) imply:
% 116.26/17.98 | | | | | | | | | | | | | | | (285) $false
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 116.26/17.98 | | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | (286) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | | REF_CLOSE: (10), (16), (27), (37), (39), (44), (50), (57),
% 116.26/17.98 | | | | | | | | | | | (83), (92), (101), (111), (160), (182), (185),
% 116.26/17.98 | | | | | | | | | | | (201), (202), (239), (243), (286) are inconsistent
% 116.26/17.98 | | | | | | | | | | | by sub-proof #259.
% 116.26/17.98 | | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | (287) all_54_0 = e0
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | COMBINE_EQS: (18), (287) imply:
% 116.26/17.98 | | | | | | | | | (288) all_10_2 = e0
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | SIMP: (288) implies:
% 116.26/17.98 | | | | | | | | | (289) all_10_2 = e0
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | COMBINE_EQS: (35), (289) imply:
% 116.26/17.98 | | | | | | | | | (290) all_56_12 = e0
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | BETA: splitting (181) gives:
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | | Case 1:
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | (291) ~ (all_56_5 = e2)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | REDUCE: (163), (291) imply:
% 116.26/17.98 | | | | | | | | | | (292) ~ (all_52_13 = e2)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (9), (10), (14), (16), (17), (18),
% 116.26/17.98 | | | | | | | | | | (27), (33), (34), (35), (37), (39), (44), (49),
% 116.26/17.98 | | | | | | | | | | (50), (51), (52), (57), (60), (61), (64), (65),
% 116.26/17.98 | | | | | | | | | | (66), (79), (83), (89), (90), (91), (92), (93),
% 116.26/17.98 | | | | | | | | | | (101), (104), (106), (107), (109), (111), (113),
% 116.26/17.98 | | | | | | | | | | (123), (126), (133), (136), (138), (140), (142),
% 116.26/17.98 | | | | | | | | | | (149), (156), (160), (161), (162), (167), (170),
% 116.26/17.98 | | | | | | | | | | (176), (178), (182), (185), (193), (196), (201),
% 116.26/17.98 | | | | | | | | | | (202), (239), (243), (245), (292) are inconsistent
% 116.26/17.98 | | | | | | | | | | by sub-proof #250.
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | Case 2:
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | (293) ~ (all_56_12 = e0)
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | REDUCE: (290), (293) imply:
% 116.26/17.98 | | | | | | | | | | (294) $false
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | | CLOSE: (294) is inconsistent.
% 116.26/17.98 | | | | | | | | | |
% 116.26/17.98 | | | | | | | | | End of split
% 116.26/17.98 | | | | | | | | |
% 116.26/17.98 | | | | | | | | End of split
% 116.26/17.98 | | | | | | | |
% 116.26/17.98 | | | | | | | End of split
% 116.26/17.98 | | | | | | |
% 116.26/17.98 | | | | | | End of split
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | Case 2:
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | (295) all_56_12 = e2
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | | REF_CLOSE: (15), (35), (50), (131), (139), (145), (147), (150),
% 116.26/17.98 | | | | | | (177), (180), (190), (194), (199), (212), (215), (295)
% 116.26/17.98 | | | | | | are inconsistent by sub-proof #195.
% 116.26/17.98 | | | | | |
% 116.26/17.98 | | | | | End of split
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | Case 2:
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | (296) all_56_14 = e2
% 116.26/17.98 | | | | | (297) ~ (all_56_10 = e0)
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (14), (15), (16), (18),
% 116.26/17.98 | | | | | (19), (20), (21), (23), (24), (25), (28), (30), (34), (35),
% 116.26/17.98 | | | | | (40), (45), (46), (50), (51), (52), (59), (60), (62), (64),
% 116.26/17.98 | | | | | (66), (70), (71), (72), (73), (74), (76), (80), (85), (90),
% 116.26/17.98 | | | | | (92), (93), (98), (100), (101), (102), (103), (104), (106),
% 116.26/17.98 | | | | | (111), (113), (118), (119), (122), (123), (124), (126),
% 116.26/17.98 | | | | | (129), (131), (138), (139), (140), (142), (145), (146),
% 116.26/17.98 | | | | | (147), (148), (149), (150), (153), (154), (155), (156),
% 116.26/17.98 | | | | | (157), (158), (163), (164), (165), (166), (167), (170),
% 116.26/17.98 | | | | | (176), (177), (180), (185), (190), (192), (193), (194),
% 116.26/17.98 | | | | | (196), (197), (200), (201), (203), (212), (215), (241),
% 116.26/17.98 | | | | | (296), (297) are inconsistent by sub-proof #177.
% 116.26/17.98 | | | | |
% 116.26/17.98 | | | | End of split
% 116.26/17.98 | | | |
% 116.26/17.98 | | | End of split
% 116.26/17.98 | | |
% 116.26/17.98 | | Case 2:
% 116.26/17.98 | | |
% 116.26/17.98 | | | (298) all_26_0 = e1
% 116.26/17.99 | | | (299) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.26/17.99 | | |
% 116.26/17.99 | | | COMBINE_EQS: (207), (298) imply:
% 116.26/17.99 | | | (300) all_4_0 = e1
% 116.26/17.99 | | |
% 116.26/17.99 | | | REF_CLOSE: (3), (4), (6), (7), (10), (12), (14), (15), (16), (17), (18),
% 116.26/17.99 | | | (19), (20), (23), (24), (25), (27), (28), (34), (35), (37),
% 116.26/17.99 | | | (38), (39), (40), (41), (42), (44), (45), (46), (48), (49),
% 116.26/17.99 | | | (50), (51), (52), (54), (55), (56), (57), (58), (59), (61),
% 116.26/17.99 | | | (62), (63), (64), (65), (66), (68), (70), (71), (72), (73),
% 116.26/17.99 | | | (74), (75), (83), (86), (88), (89), (90), (91), (92), (93),
% 116.26/17.99 | | | (94), (95), (96), (98), (99), (101), (103), (104), (105),
% 116.26/17.99 | | | (106), (110), (111), (112), (113), (115), (116), (118), (119),
% 116.26/17.99 | | | (120), (121), (122), (123), (124), (125), (126), (127), (132),
% 116.26/17.99 | | | (133), (134), (135), (136), (137), (138), (139), (140), (142),
% 116.26/17.99 | | | (143), (144), (145), (146), (147), (148), (149), (151), (153),
% 116.26/17.99 | | | (154), (155), (156), (158), (159), (160), (161), (162), (163),
% 116.26/17.99 | | | (164), (165), (167), (168), (170), (171), (172), (174), (175),
% 116.26/17.99 | | | (176), (178), (179), (181), (182), (183), (185), (188), (190),
% 116.26/17.99 | | | (193), (194), (196), (197), (200), (201), (202), (203), (205),
% 116.26/17.99 | | | (206), (299), (300) are inconsistent by sub-proof #225.
% 116.26/17.99 | | |
% 116.26/17.99 | | End of split
% 116.26/17.99 | |
% 116.26/17.99 | End of split
% 116.26/17.99 |
% 116.26/17.99 End of proof
% 116.26/17.99
% 116.26/17.99 Sub-proof #177 shows that the following formulas are inconsistent:
% 116.26/17.99 ----------------------------------------------------------------
% 116.26/17.99 (1) ~ (all_52_8 = all_10_2)
% 116.26/17.99 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/17.99 (3) ~ (all_52_2 = all_10_2)
% 116.26/17.99 (4) ~ (all_52_6 = all_52_14)
% 116.26/17.99 (5) all_54_2 = all_52_8
% 116.26/17.99 (6) all_58_7 = all_52_6
% 116.26/17.99 (7) ~ (all_52_8 = all_52_11)
% 116.26/17.99 (8) ~ (all_4_2 = e0)
% 116.26/17.99 (9) op(e3, e2) = all_52_4
% 116.26/17.99 (10) all_56_14 = all_6_2
% 116.26/17.99 (11) all_54_0 = all_10_2
% 116.26/17.99 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.99 (13) all_54_3 = all_52_12
% 116.26/17.99 (14) ~ (all_52_2 = all_52_6)
% 116.26/17.99 (15) op(e0, e2) = all_52_7
% 116.26/17.99 (16) ~ (all_52_7 = all_4_2)
% 116.26/17.99 (17) all_56_11 = all_52_11
% 116.26/17.99 (18) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/17.99 (19) ~ (all_52_12 = all_10_2)
% 116.26/17.99 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/17.99 (21) all_56_12 = all_10_2
% 116.26/17.99 (22) all_56_14 = e2
% 116.26/17.99 (23) all_54_13 = all_52_7
% 116.26/17.99 (24) op(all_10_1, all_10_2) = e1
% 116.26/17.99 (25) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.26/17.99 (26) all_56_10 = all_52_7
% 116.26/17.99 (27) op(all_6_1, all_6_2) = e2
% 116.26/17.99 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/17.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/17.99 (29) all_54_8 = all_52_2
% 116.26/17.99 (30) ~ (all_52_2 = all_6_2)
% 116.26/17.99 (31) op(e3, e0) = all_52_12
% 116.26/17.99 (32) ~ (all_52_8 = all_6_2)
% 116.26/17.99 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/17.99 (34) all_56_2 = all_52_12
% 116.26/17.99 (35) all_58_3 = all_8_2
% 116.26/17.99 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.99 (37) all_58_11 = all_52_14
% 116.26/17.99 (38) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.26/17.99 (39) all_54_9 = all_52_6
% 116.26/17.99 (40) ~ (all_52_2 = all_52_3)
% 116.26/17.99 (41) all_16_1 = all_10_1
% 116.26/17.99 (42) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.26/17.99 (43) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.26/17.99 (44) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/17.99 (45) op(e1, e0) = all_52_14
% 116.26/17.99 (46) ~ (all_56_10 = e0)
% 116.26/17.99 (47) all_58_5 = all_52_9
% 116.26/17.99 (48) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/17.99 (49) all_56_9 = all_52_3
% 116.26/17.99 (50) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/17.99 (51) op(e1, all_6_2) = all_6_1
% 116.26/17.99 (52) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/17.99 (53) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.26/17.99 (54) all_58_15 = all_4_2
% 116.26/17.99 (55) all_58_2 = all_52_1
% 116.26/17.99 (56) ~ (all_10_2 = e3)
% 116.26/17.99 (57) all_58_13 = all_52_7
% 116.26/17.99 (58) ~ (all_52_14 = all_4_2)
% 116.26/17.99 (59) all_58_6 = all_52_2
% 116.26/17.99 (60) ~ (all_52_1 = all_10_2)
% 116.26/17.99 (61) all_54_5 = all_8_2
% 116.26/17.99 (62) all_56_15 = all_4_2
% 116.26/17.99 (63) all_58_10 = all_52_13
% 116.26/17.99 (64) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 116.26/17.99 (65) op(e3, all_10_2) = all_10_1
% 116.26/17.99 (66) all_58_14 = all_52_11
% 116.26/17.99 (67) all_54_1 = all_52_4
% 116.26/17.99 (68) all_56_13 = all_8_2
% 116.26/17.99 (69) ~ (all_8_2 = e2)
% 116.26/17.99 (70) op(e1, e2) = all_52_6
% 116.26/17.99 (71) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/17.99 (72) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/17.99 (73) all_56_7 = all_52_6
% 116.26/17.99 (74) ~ (all_52_9 = all_6_2)
% 116.26/17.99 (75) ~ (all_52_4 = all_52_6)
% 116.26/17.99 (76) all_56_1 = all_52_8
% 116.26/17.99 (77) op(e0, all_4_2) = all_4_1
% 116.26/17.99 (78) all_58_8 = all_6_2
% 116.26/17.99 (79) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/17.99 (80) all_16_2 = all_10_2
% 116.26/17.99 (81) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.26/17.99 (82) all_56_5 = all_52_13
% 116.26/17.99 (83) ~ (all_52_3 = all_4_2)
% 116.26/17.99 (84) ~ (all_52_6 = all_6_2)
% 116.26/17.99 (85) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.99 (86) all_56_6 = all_52_2
% 116.26/17.99 (87) all_58_12 = all_52_3
% 116.26/17.99 (88) ~ (all_52_3 = all_10_2)
% 116.26/17.99 (89) all_24_1 = all_10_1
% 116.26/17.99 (90) all_24_2 = all_10_2
% 116.26/17.99 (91) all_56_8 = all_52_14
% 116.26/17.99 (92) ~ (all_52_4 = all_10_2)
% 116.26/17.99 (93) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/17.99 (94) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/17.99 (95) all_56_0 = all_52_4
% 116.26/17.99 (96) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.99 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/17.99 (97) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.26/17.99 (98) all_54_15 = all_4_2
% 116.26/17.99 (99) ~ (all_6_2 = e1)
% 116.26/17.99 (100) ~ (all_52_6 = all_52_7)
% 116.26/17.99
% 116.26/17.99 Begin of proof
% 116.26/17.99 |
% 116.26/17.99 | COMBINE_EQS: (10), (22) imply:
% 116.26/17.99 | (101) all_6_2 = e2
% 116.26/17.99 |
% 116.26/17.99 | SIMP: (101) implies:
% 116.26/17.99 | (102) all_6_2 = e2
% 116.26/17.99 |
% 116.26/17.99 | COMBINE_EQS: (78), (102) imply:
% 116.26/17.99 | (103) all_58_8 = e2
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (26), (46) imply:
% 116.26/17.99 | (104) ~ (all_52_7 = e0)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (30), (102) imply:
% 116.26/17.99 | (105) ~ (all_52_2 = e2)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (84), (102) imply:
% 116.26/17.99 | (106) ~ (all_52_6 = e2)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (32), (102) imply:
% 116.26/17.99 | (107) ~ (all_52_8 = e2)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (74), (102) imply:
% 116.26/17.99 | (108) ~ (all_52_9 = e2)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (99), (102) imply:
% 116.26/17.99 | (109) ~ (e2 = e1)
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (27), (102) imply:
% 116.26/17.99 | (110) op(all_6_1, e2) = e2
% 116.26/17.99 |
% 116.26/17.99 | REDUCE: (51), (102) imply:
% 116.26/17.99 | (111) op(e1, e2) = all_6_1
% 116.26/17.99 |
% 116.26/17.99 | BETA: splitting (25) gives:
% 116.26/17.99 |
% 116.26/17.99 | Case 1:
% 116.26/17.99 | |
% 116.26/17.99 | | (112) ~ (all_56_7 = e1)
% 116.26/17.99 | |
% 116.26/17.99 | | REDUCE: (73), (112) imply:
% 116.26/17.99 | | (113) ~ (all_52_6 = e1)
% 116.26/17.99 | |
% 116.26/17.99 | | BETA: splitting (97) gives:
% 116.26/17.99 | |
% 116.26/17.99 | | Case 1:
% 116.26/17.99 | | |
% 116.26/17.99 | | | (114) ~ (all_56_0 = e3)
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (95), (114) imply:
% 116.26/17.99 | | | (115) ~ (all_52_4 = e3)
% 116.26/17.99 | | |
% 116.26/17.99 | | | GROUND_INST: instantiating (28) with all_52_6, all_6_1, e2, e1,
% 116.26/17.99 | | | simplifying with (70), (111) gives:
% 116.26/17.99 | | | (116) all_52_6 = all_6_1
% 116.26/17.99 | | |
% 116.26/17.99 | | | COMBINE_EQS: (39), (116) imply:
% 116.26/17.99 | | | (117) all_54_9 = all_6_1
% 116.26/17.99 | | |
% 116.26/17.99 | | | COMBINE_EQS: (6), (116) imply:
% 116.26/17.99 | | | (118) all_58_7 = all_6_1
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (14), (116) imply:
% 116.26/17.99 | | | (119) ~ (all_52_2 = all_6_1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (100), (116) imply:
% 116.26/17.99 | | | (120) ~ (all_52_7 = all_6_1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | SIMP: (120) implies:
% 116.26/17.99 | | | (121) ~ (all_52_7 = all_6_1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (4), (116) imply:
% 116.26/17.99 | | | (122) ~ (all_52_14 = all_6_1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | SIMP: (122) implies:
% 116.26/17.99 | | | (123) ~ (all_52_14 = all_6_1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (106), (116) imply:
% 116.26/17.99 | | | (124) ~ (all_6_1 = e2)
% 116.26/17.99 | | |
% 116.26/17.99 | | | REDUCE: (113), (116) imply:
% 116.26/17.99 | | | (125) ~ (all_6_1 = e1)
% 116.26/17.99 | | |
% 116.26/17.99 | | | BETA: splitting (53) gives:
% 116.26/17.99 | | |
% 116.26/17.99 | | | Case 1:
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | (126) ~ (all_56_6 = e1)
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | REDUCE: (86), (126) imply:
% 116.26/17.99 | | | | (127) ~ (all_52_2 = e1)
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | BETA: splitting (71) gives:
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | Case 1:
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | | (128) all_58_6 = e1
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | | REF_CLOSE: (59), (127), (128) are inconsistent by sub-proof #452.
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | Case 2:
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | | (129) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | | BETA: splitting (129) gives:
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | | Case 1:
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | (130) all_58_7 = e1
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | COMBINE_EQS: (118), (130) imply:
% 116.26/17.99 | | | | | | (131) all_6_1 = e1
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | REDUCE: (125), (131) imply:
% 116.26/17.99 | | | | | | (132) $false
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | CLOSE: (132) is inconsistent.
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | Case 2:
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | (133) all_58_8 = e1 | all_58_11 = e1
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | BETA: splitting (133) gives:
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | | Case 1:
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | (134) all_58_8 = e1
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | COMBINE_EQS: (103), (134) imply:
% 116.26/17.99 | | | | | | | (135) e2 = e1
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | REDUCE: (109), (135) imply:
% 116.26/17.99 | | | | | | | (136) $false
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | CLOSE: (136) is inconsistent.
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | Case 2:
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | (137) all_58_11 = e1
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | COMBINE_EQS: (37), (137) imply:
% 116.26/17.99 | | | | | | | (138) all_52_14 = e1
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | COMBINE_EQS: (91), (138) imply:
% 116.26/17.99 | | | | | | | (139) all_56_8 = e1
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | REDUCE: (123), (138) imply:
% 116.26/17.99 | | | | | | | (140) ~ (all_6_1 = e1)
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | REDUCE: (58), (138) imply:
% 116.26/17.99 | | | | | | | (141) ~ (all_4_2 = e1)
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | SIMP: (141) implies:
% 116.26/17.99 | | | | | | | (142) ~ (all_4_2 = e1)
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | BETA: splitting (52) gives:
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | (143) ~ (all_56_8 = e1)
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | REDUCE: (139), (143) imply:
% 116.26/17.99 | | | | | | | | (144) $false
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | CLOSE: (144) is inconsistent.
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | (145) ~ (all_56_12 = e0)
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | REDUCE: (21), (145) imply:
% 116.26/17.99 | | | | | | | | (146) ~ (all_10_2 = e0)
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | BETA: splitting (93) gives:
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | (147) ~ (all_56_12 = e1)
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | REDUCE: (21), (147) imply:
% 116.26/17.99 | | | | | | | | | (148) ~ (all_10_2 = e1)
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | REF_CLOSE: (9), (11), (24), (28), (48), (56), (65), (67),
% 116.26/17.99 | | | | | | | | | (70), (72), (75), (79), (89), (90), (92), (115),
% 116.26/17.99 | | | | | | | | | (146), (148) are inconsistent by sub-proof #183.
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | (149) all_56_12 = e1
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | COMBINE_EQS: (21), (149) imply:
% 116.26/17.99 | | | | | | | | | (150) all_10_2 = e1
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | REDUCE: (1), (150) imply:
% 116.26/17.99 | | | | | | | | | (151) ~ (all_52_8 = e1)
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | BETA: splitting (96) gives:
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | (152) all_58_15 = e0
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | COMBINE_EQS: (54), (152) imply:
% 116.26/17.99 | | | | | | | | | | (153) all_4_2 = e0
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | REDUCE: (8), (153) imply:
% 116.26/17.99 | | | | | | | | | | (154) $false
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | CLOSE: (154) is inconsistent.
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | (155) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/17.99 | | | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | ALPHA: (155) implies:
% 116.26/17.99 | | | | | | | | | | (156) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | BETA: splitting (43) gives:
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | (157) ~ (all_56_1 = e3)
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | REDUCE: (76), (157) imply:
% 116.26/17.99 | | | | | | | | | | | (158) ~ (all_52_8 = e3)
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | BETA: splitting (156) gives:
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | (159) all_58_12 = e0
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | COMBINE_EQS: (87), (159) imply:
% 116.26/17.99 | | | | | | | | | | | | (160) all_52_3 = e0
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | SIMP: (160) implies:
% 116.26/17.99 | | | | | | | | | | | | (161) all_52_3 = e0
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | COMBINE_EQS: (49), (161) imply:
% 116.26/17.99 | | | | | | | | | | | | (162) all_56_9 = e0
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | REDUCE: (40), (161) imply:
% 116.26/17.99 | | | | | | | | | | | | (163) ~ (all_52_2 = e0)
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | REDUCE: (83), (161) imply:
% 116.26/17.99 | | | | | | | | | | | | (164) ~ (all_4_2 = e0)
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | BETA: splitting (81) gives:
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | (165) ~ (all_56_15 = e3)
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | REDUCE: (62), (165) imply:
% 116.26/17.99 | | | | | | | | | | | | | (166) ~ (all_4_2 = e3)
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | BETA: splitting (44) gives:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | (167) all_54_8 = e3
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | COMBINE_EQS: (29), (167) imply:
% 116.26/17.99 | | | | | | | | | | | | | | (168) all_52_2 = e3
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | SIMP: (168) implies:
% 116.26/17.99 | | | | | | | | | | | | | | (169) all_52_2 = e3
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | COMBINE_EQS: (59), (169) imply:
% 116.26/17.99 | | | | | | | | | | | | | | (170) all_58_6 = e3
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | REDUCE: (119), (169) imply:
% 116.26/17.99 | | | | | | | | | | | | | | (171) ~ (all_6_1 = e3)
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | SIMP: (171) implies:
% 116.26/17.99 | | | | | | | | | | | | | | (172) ~ (all_6_1 = e3)
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | REDUCE: (163), (169) imply:
% 116.26/17.99 | | | | | | | | | | | | | | (173) ~ (e3 = e0)
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | (174) all_54_9 = e3
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | REF_CLOSE: (117), (172), (174) are inconsistent by sub-proof
% 116.26/17.99 | | | | | | | | | | | | | | | #230.
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | (175) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | (176) all_54_15 = e3
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | REF_CLOSE: (98), (166), (176) are inconsistent by sub-proof
% 116.26/17.99 | | | | | | | | | | | | | | | | #312.
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | (177) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | (178) all_58_6 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (178) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | (179) e3 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 116.26/17.99 | | | | | | | | | | | | | | | | | (180) e3 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | REDUCE: (173), (180) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | (181) $false
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | (182) all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (183) all_54_15 = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (183) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (184) all_4_2 = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | SIMP: (184) implies:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (185) all_4_2 = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | REDUCE: (16), (185) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (186) ~ (all_52_7 = e2)
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | REDUCE: (77), (185) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (187) op(e0, e2) = all_4_1
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (188) all_54_13 = e3
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (188) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (189) all_52_7 = e3
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (190) all_52_7 = e3
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | REDUCE: (186), (190) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (191) ~ (e3 = e2)
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | REDUCE: (15), (190) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (192) op(e0, e2) = e3
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (193) all_58_7 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (193) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (194) all_6_1 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (194) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (195) op(e0, e2) = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with e2, e3, e2, e0,
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | simplifying with (192), (195) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (196) e3 = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (196) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (197) $false
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (198) ~ (all_58_7 = e0)
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (198) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (199) ~ (all_6_1 = e0)
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (124), (125), (175), (199) are inconsistent
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | by sub-proof #373.
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | (200) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (201) all_58_7 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (201) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (202) all_6_1 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (202) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (203) op(e0, e2) = e2
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (28), (104), (186), (187), (200),
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (203) are inconsistent by sub-proof #180.
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (204) ~ (all_58_7 = e0)
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (204) imply:
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | (205) ~ (all_6_1 = e0)
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (124), (125), (175), (205) are inconsistent
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | | by sub-proof #373.
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | (206) all_54_15 = e1 | all_54_15 = e0
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (98), (142), (206) are inconsistent by
% 116.26/17.99 | | | | | | | | | | | | | | | | | | sub-proof #418.
% 116.26/17.99 | | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | (207) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | REF_CLOSE: (29), (105), (127), (163), (207) are inconsistent
% 116.26/17.99 | | | | | | | | | | | | | | by sub-proof #381.
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | (208) ~ (all_56_9 = e0)
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | REDUCE: (162), (208) imply:
% 116.26/17.99 | | | | | | | | | | | | | (209) $false
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | (210) all_58_13 = e0 | all_58_14 = e0
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | BETA: splitting (210) gives:
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | (211) all_58_13 = e0
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | REF_CLOSE: (57), (104), (211) are inconsistent by sub-proof
% 116.26/17.99 | | | | | | | | | | | | | #430.
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | (212) all_58_14 = e0
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | COMBINE_EQS: (66), (212) imply:
% 116.26/17.99 | | | | | | | | | | | | | (213) all_52_11 = e0
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | SIMP: (213) implies:
% 116.26/17.99 | | | | | | | | | | | | | (214) all_52_11 = e0
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | REDUCE: (7), (214) imply:
% 116.26/17.99 | | | | | | | | | | | | | (215) ~ (all_52_8 = e0)
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | Case 1:
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | (216) all_54_2 = e3
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (216) are inconsistent by sub-proof
% 116.26/17.99 | | | | | | | | | | | | | | #179.
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | (217) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | | REF_CLOSE: (5), (107), (151), (215), (217) are inconsistent
% 116.26/17.99 | | | | | | | | | | | | | | by sub-proof #209.
% 116.26/17.99 | | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | Case 2:
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | (218) ~ (all_56_12 = e1)
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | REDUCE: (149), (218) imply:
% 116.26/17.99 | | | | | | | | | | | (219) $false
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 116.26/17.99 | | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | | |
% 116.26/17.99 | | | | | | | | | End of split
% 116.26/17.99 | | | | | | | | |
% 116.26/17.99 | | | | | | | | End of split
% 116.26/17.99 | | | | | | | |
% 116.26/17.99 | | | | | | | End of split
% 116.26/17.99 | | | | | | |
% 116.26/17.99 | | | | | | End of split
% 116.26/17.99 | | | | | |
% 116.26/17.99 | | | | | End of split
% 116.26/17.99 | | | | |
% 116.26/17.99 | | | | End of split
% 116.26/17.99 | | | |
% 116.26/17.99 | | | Case 2:
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | (220) all_56_6 = e1
% 116.26/17.99 | | | | (221) ~ (all_56_13 = e3)
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | COMBINE_EQS: (86), (220) imply:
% 116.26/17.99 | | | | (222) all_52_2 = e1
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | REDUCE: (68), (221) imply:
% 116.26/17.99 | | | | (223) ~ (all_8_2 = e3)
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | REDUCE: (3), (222) imply:
% 116.26/17.99 | | | | (224) ~ (all_10_2 = e1)
% 116.26/17.99 | | | |
% 116.26/17.99 | | | | SIMP: (224) implies:
% 116.26/18.00 | | | | (225) ~ (all_10_2 = e1)
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | BETA: splitting (42) gives:
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | Case 1:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | (226) ~ (all_56_13 = e1)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | REDUCE: (68), (226) imply:
% 116.26/18.00 | | | | | (227) ~ (all_8_2 = e1)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | BETA: splitting (20) gives:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | Case 1:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | (228) all_54_5 = e3
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | REF_CLOSE: (61), (223), (228) are inconsistent by sub-proof #339.
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | Case 2:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | (229) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | BETA: splitting (229) gives:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | Case 1:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | (230) all_54_5 = e2
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | REF_CLOSE: (61), (69), (230) are inconsistent by sub-proof #338.
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | Case 2:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | (231) ~ (all_54_5 = e2)
% 116.26/18.00 | | | | | | | (232) all_54_5 = e1 | all_54_5 = e0
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | BETA: splitting (232) gives:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | Case 1:
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | (233) all_54_5 = e1
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | REF_CLOSE: (61), (227), (233) are inconsistent by sub-proof
% 116.26/18.00 | | | | | | | | #337.
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | Case 2:
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | (234) all_54_5 = e0
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | COMBINE_EQS: (61), (234) imply:
% 116.26/18.00 | | | | | | | | (235) all_8_2 = e0
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | SIMP: (235) implies:
% 116.26/18.00 | | | | | | | | (236) all_8_2 = e0
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | COMBINE_EQS: (68), (236) imply:
% 116.26/18.00 | | | | | | | | (237) all_56_13 = e0
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | BETA: splitting (38) gives:
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | | Case 1:
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | | (238) ~ (all_56_5 = e2)
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | | REF_CLOSE: (2), (11), (13), (18), (19), (21), (24), (28),
% 116.26/18.00 | | | | | | | | | (31), (34), (35), (41), (45), (47), (50), (52),
% 116.26/18.00 | | | | | | | | | (55), (56), (60), (63), (65), (69), (79), (80),
% 116.26/18.00 | | | | | | | | | (82), (91), (94), (108), (225), (238) are
% 116.26/18.00 | | | | | | | | | inconsistent by sub-proof #178.
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | Case 2:
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | | (239) ~ (all_56_13 = e0)
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | | REDUCE: (237), (239) imply:
% 116.26/18.00 | | | | | | | | | (240) $false
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | | CLOSE: (240) is inconsistent.
% 116.26/18.00 | | | | | | | | |
% 116.26/18.00 | | | | | | | | End of split
% 116.26/18.00 | | | | | | | |
% 116.26/18.00 | | | | | | | End of split
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | End of split
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | End of split
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | Case 2:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | (241) ~ (all_56_11 = e0)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | REDUCE: (17), (241) imply:
% 116.26/18.00 | | | | | (242) ~ (all_52_11 = e0)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | BETA: splitting (96) gives:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | Case 1:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | (243) all_58_15 = e0
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | COMBINE_EQS: (54), (243) imply:
% 116.26/18.00 | | | | | | (244) all_4_2 = e0
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | REDUCE: (8), (244) imply:
% 116.26/18.00 | | | | | | (245) $false
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | CLOSE: (245) is inconsistent.
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | Case 2:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | (246) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/18.00 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | ALPHA: (246) implies:
% 116.26/18.00 | | | | | | (247) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | BETA: splitting (247) gives:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | Case 1:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | (248) all_58_12 = e0
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | COMBINE_EQS: (87), (248) imply:
% 116.26/18.00 | | | | | | | (249) all_52_3 = e0
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | SIMP: (249) implies:
% 116.26/18.00 | | | | | | | (250) all_52_3 = e0
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | REDUCE: (88), (250) imply:
% 116.26/18.00 | | | | | | | (251) ~ (all_10_2 = e0)
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | SIMP: (251) implies:
% 116.26/18.00 | | | | | | | (252) ~ (all_10_2 = e0)
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | REF_CLOSE: (9), (11), (24), (28), (48), (56), (65), (67), (70),
% 116.26/18.00 | | | | | | | (72), (75), (79), (89), (90), (92), (115), (225), (252)
% 116.26/18.00 | | | | | | | are inconsistent by sub-proof #183.
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | Case 2:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | (253) all_58_13 = e0 | all_58_14 = e0
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | REF_CLOSE: (57), (66), (104), (242), (253) are inconsistent by
% 116.26/18.00 | | | | | | | sub-proof #428.
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | End of split
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | End of split
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | End of split
% 116.26/18.00 | | | |
% 116.26/18.00 | | | End of split
% 116.26/18.00 | | |
% 116.26/18.00 | | Case 2:
% 116.26/18.00 | | |
% 116.26/18.00 | | | (254) ~ (all_56_14 = e2)
% 116.26/18.00 | | |
% 116.26/18.00 | | | REDUCE: (22), (254) imply:
% 116.26/18.00 | | | (255) $false
% 116.26/18.00 | | |
% 116.26/18.00 | | | CLOSE: (255) is inconsistent.
% 116.26/18.00 | | |
% 116.26/18.00 | | End of split
% 116.26/18.00 | |
% 116.26/18.00 | Case 2:
% 116.26/18.00 | |
% 116.26/18.00 | | (256) ~ (all_56_14 = e2)
% 116.26/18.00 | |
% 116.26/18.00 | | REDUCE: (22), (256) imply:
% 116.26/18.00 | | (257) $false
% 116.26/18.00 | |
% 116.26/18.00 | | CLOSE: (257) is inconsistent.
% 116.26/18.00 | |
% 116.26/18.00 | End of split
% 116.26/18.00 |
% 116.26/18.00 End of proof
% 116.26/18.00
% 116.26/18.00 Sub-proof #178 shows that the following formulas are inconsistent:
% 116.26/18.00 ----------------------------------------------------------------
% 116.26/18.00 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.00 (2) ~ (all_52_9 = e2)
% 116.26/18.00 (3) all_54_0 = all_10_2
% 116.26/18.00 (4) all_54_3 = all_52_12
% 116.26/18.00 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.00 (6) ~ (all_52_12 = all_10_2)
% 116.26/18.00 (7) all_56_12 = all_10_2
% 116.26/18.00 (8) op(all_10_1, all_10_2) = e1
% 116.26/18.00 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.00 (10) op(e3, e0) = all_52_12
% 116.26/18.00 (11) all_56_2 = all_52_12
% 116.26/18.00 (12) all_58_3 = all_8_2
% 116.26/18.00 (13) all_16_1 = all_10_1
% 116.26/18.00 (14) ~ (all_10_2 = e1)
% 116.26/18.00 (15) op(e1, e0) = all_52_14
% 116.26/18.00 (16) all_58_5 = all_52_9
% 116.26/18.00 (17) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.00 (18) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.00 (19) all_58_2 = all_52_1
% 116.26/18.00 (20) ~ (all_10_2 = e3)
% 116.26/18.00 (21) ~ (all_52_1 = all_10_2)
% 116.26/18.00 (22) all_58_10 = all_52_13
% 116.26/18.00 (23) op(e3, all_10_2) = all_10_1
% 116.26/18.00 (24) ~ (all_56_5 = e2)
% 116.26/18.00 (25) ~ (all_8_2 = e2)
% 116.26/18.00 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.00 (27) all_16_2 = all_10_2
% 116.26/18.00 (28) all_56_5 = all_52_13
% 116.26/18.00 (29) all_56_8 = all_52_14
% 116.26/18.00 (30) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.00
% 116.26/18.00 Begin of proof
% 116.26/18.00 |
% 116.26/18.00 | REDUCE: (24), (28) imply:
% 116.26/18.00 | (31) ~ (all_52_13 = e2)
% 116.26/18.00 |
% 116.26/18.00 | BETA: splitting (30) gives:
% 116.26/18.00 |
% 116.26/18.00 | Case 1:
% 116.26/18.00 | |
% 116.26/18.00 | | (32) all_58_2 = e2
% 116.26/18.00 | |
% 116.26/18.00 | | COMBINE_EQS: (19), (32) imply:
% 116.26/18.00 | | (33) all_52_1 = e2
% 116.26/18.00 | |
% 116.26/18.00 | | REDUCE: (21), (33) imply:
% 116.26/18.00 | | (34) ~ (all_10_2 = e2)
% 116.26/18.00 | |
% 116.26/18.00 | | SIMP: (34) implies:
% 116.26/18.00 | | (35) ~ (all_10_2 = e2)
% 116.26/18.00 | |
% 116.26/18.00 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 116.26/18.00 | | (15), (17), (18), (20), (23), (26), (27), (29), (35) are
% 116.26/18.00 | | inconsistent by sub-proof #193.
% 116.26/18.00 | |
% 116.26/18.00 | Case 2:
% 116.26/18.00 | |
% 116.26/18.00 | | (36) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.00 | |
% 116.26/18.00 | | REF_CLOSE: (2), (12), (16), (22), (25), (31), (36) are inconsistent by
% 116.26/18.00 | | sub-proof #401.
% 116.26/18.00 | |
% 116.26/18.00 | End of split
% 116.26/18.00 |
% 116.26/18.00 End of proof
% 116.26/18.00
% 116.26/18.00 Sub-proof #179 shows that the following formulas are inconsistent:
% 116.26/18.00 ----------------------------------------------------------------
% 116.26/18.00 (1) all_54_2 = all_52_8
% 116.26/18.00 (2) all_54_2 = e3
% 116.26/18.00 (3) ~ (all_52_8 = e3)
% 116.26/18.00
% 116.26/18.00 Begin of proof
% 116.26/18.00 |
% 116.26/18.00 | COMBINE_EQS: (1), (2) imply:
% 116.26/18.00 | (4) all_52_8 = e3
% 116.26/18.00 |
% 116.26/18.00 | SIMP: (4) implies:
% 116.26/18.00 | (5) all_52_8 = e3
% 116.26/18.00 |
% 116.26/18.00 | REDUCE: (3), (5) imply:
% 116.26/18.00 | (6) $false
% 116.26/18.00 |
% 116.26/18.00 | CLOSE: (6) is inconsistent.
% 116.26/18.00 |
% 116.26/18.00 End of proof
% 116.26/18.00
% 116.26/18.00 Sub-proof #180 shows that the following formulas are inconsistent:
% 116.26/18.00 ----------------------------------------------------------------
% 116.26/18.00 (1) op(e0, e2) = all_4_1
% 116.26/18.00 (2) op(e0, e2) = all_52_7
% 116.26/18.00 (3) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/18.00 (4) all_54_13 = all_52_7
% 116.26/18.00 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.00 (6) op(e0, e2) = e2
% 116.26/18.00 (7) ~ (all_52_7 = e0)
% 116.26/18.00 (8) ~ (all_52_7 = e2)
% 116.26/18.00
% 116.26/18.00 Begin of proof
% 116.26/18.00 |
% 116.26/18.00 | BETA: splitting (3) gives:
% 116.26/18.00 |
% 116.26/18.00 | Case 1:
% 116.26/18.00 | |
% 116.26/18.00 | | (9) all_54_13 = e2
% 116.26/18.00 | |
% 116.26/18.00 | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #181.
% 116.26/18.00 | |
% 116.26/18.00 | Case 2:
% 116.26/18.00 | |
% 116.26/18.00 | | (10) ~ (all_54_13 = e2)
% 116.26/18.00 | | (11) all_54_13 = e1 | all_54_13 = e0
% 116.26/18.00 | |
% 116.26/18.00 | | BETA: splitting (11) gives:
% 116.26/18.00 | |
% 116.26/18.00 | | Case 1:
% 116.26/18.00 | | |
% 116.26/18.00 | | | (12) all_54_13 = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | COMBINE_EQS: (4), (12) imply:
% 116.26/18.00 | | | (13) all_52_7 = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | SIMP: (13) implies:
% 116.26/18.00 | | | (14) all_52_7 = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | REDUCE: (8), (14) imply:
% 116.26/18.00 | | | (15) ~ (e2 = e1)
% 116.26/18.00 | | |
% 116.26/18.00 | | | SIMP: (15) implies:
% 116.26/18.00 | | | (16) ~ (e2 = e1)
% 116.26/18.00 | | |
% 116.26/18.00 | | | REDUCE: (2), (14) imply:
% 116.26/18.00 | | | (17) op(e0, e2) = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | GROUND_INST: instantiating (5) with e2, all_4_1, e2, e0, simplifying with
% 116.26/18.00 | | | (1), (6) gives:
% 116.26/18.00 | | | (18) all_4_1 = e2
% 116.26/18.00 | | |
% 116.26/18.00 | | | GROUND_INST: instantiating (5) with e1, all_4_1, e2, e0, simplifying with
% 116.26/18.00 | | | (1), (17) gives:
% 116.26/18.00 | | | (19) all_4_1 = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | COMBINE_EQS: (18), (19) imply:
% 116.26/18.00 | | | (20) e2 = e1
% 116.26/18.00 | | |
% 116.26/18.00 | | | REDUCE: (16), (20) imply:
% 116.26/18.00 | | | (21) $false
% 116.26/18.00 | | |
% 116.26/18.00 | | | CLOSE: (21) is inconsistent.
% 116.26/18.00 | | |
% 116.26/18.00 | | Case 2:
% 116.26/18.00 | | |
% 116.26/18.00 | | | (22) all_54_13 = e0
% 116.26/18.00 | | |
% 116.26/18.00 | | | REF_CLOSE: (4), (7), (22) are inconsistent by sub-proof #334.
% 116.26/18.00 | | |
% 116.26/18.00 | | End of split
% 116.26/18.00 | |
% 116.26/18.00 | End of split
% 116.26/18.00 |
% 116.26/18.00 End of proof
% 116.26/18.00
% 116.26/18.00 Sub-proof #181 shows that the following formulas are inconsistent:
% 116.26/18.00 ----------------------------------------------------------------
% 116.26/18.00 (1) all_54_13 = all_52_7
% 116.26/18.00 (2) all_54_13 = e2
% 116.26/18.00 (3) ~ (all_52_7 = e2)
% 116.26/18.00
% 116.26/18.00 Begin of proof
% 116.26/18.00 |
% 116.26/18.00 | COMBINE_EQS: (1), (2) imply:
% 116.26/18.00 | (4) all_52_7 = e2
% 116.26/18.00 |
% 116.26/18.00 | SIMP: (4) implies:
% 116.26/18.00 | (5) all_52_7 = e2
% 116.26/18.00 |
% 116.26/18.00 | REDUCE: (3), (5) imply:
% 116.26/18.00 | (6) $false
% 116.26/18.00 |
% 116.26/18.00 | CLOSE: (6) is inconsistent.
% 116.26/18.00 |
% 116.26/18.00 End of proof
% 116.26/18.00
% 116.26/18.00 Sub-proof #182 shows that the following formulas are inconsistent:
% 116.26/18.00 ----------------------------------------------------------------
% 116.26/18.00 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.00 (2) ~ (all_52_2 = all_10_2)
% 116.26/18.00 (3) ~ (all_52_6 = all_52_14)
% 116.26/18.00 (4) all_58_7 = all_52_6
% 116.26/18.00 (5) all_36_2 = all_6_2
% 116.26/18.00 (6) ~ (all_52_9 = all_8_2)
% 116.26/18.00 (7) ~ (all_52_13 = all_52_14)
% 116.26/18.00 (8) ~ (all_4_2 = e0)
% 116.26/18.00 (9) op(e3, e2) = all_52_4
% 116.26/18.00 (10) all_56_14 = all_6_2
% 116.26/18.00 (11) all_56_3 = all_52_1
% 116.26/18.00 (12) all_54_0 = all_10_2
% 116.26/18.00 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/18.00 (14) all_54_3 = all_52_12
% 116.26/18.00 (15) ~ (all_52_2 = all_52_6)
% 116.26/18.00 (16) ~ (all_52_12 = all_52_14)
% 116.26/18.00 (17) ~ (all_52_7 = all_4_2)
% 116.26/18.00 (18) all_56_11 = all_52_11
% 116.26/18.00 (19) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 116.26/18.00 (20) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/18.00 (21) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.00 (22) ~ (all_52_4 = all_52_8)
% 116.26/18.00 (23) ~ (all_52_12 = all_10_2)
% 116.26/18.00 (24) ~ (e3 = e1)
% 116.26/18.00 (25) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/18.00 (26) all_56_12 = all_10_2
% 116.26/18.00 (27) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 116.26/18.00 (28) all_58_0 = all_10_2
% 116.26/18.00 (29) all_54_11 = all_52_14
% 116.26/18.00 (30) all_54_13 = all_52_7
% 116.26/18.00 (31) op(all_10_1, all_10_2) = e1
% 116.26/18.00 (32) ~ (all_52_14 = all_6_2)
% 116.26/18.00 (33) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.26/18.00 (34) all_56_10 = all_52_7
% 116.26/18.00 (35) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.26/18.00 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.00 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.00 (38) all_54_8 = all_52_2
% 116.26/18.00 (39) ~ (all_52_2 = all_6_2)
% 116.26/18.00 (40) ~ (all_52_1 = all_52_9)
% 116.26/18.00 (41) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.26/18.00 (42) all_54_10 = all_6_2
% 116.26/18.00 (43) ~ (e2 = e1)
% 116.26/18.00 (44) all_36_0 = all_6_0
% 116.26/18.00 (45) op(e3, e0) = all_52_12
% 116.26/18.00 (46) ~ (all_52_8 = all_6_2)
% 116.26/18.00 (47) all_58_4 = all_52_8
% 116.26/18.00 (48) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/18.00 (49) ~ (all_52_4 = all_52_7)
% 116.26/18.00 (50) all_56_2 = all_52_12
% 116.26/18.00 (51) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/18.00 (52) all_58_3 = all_8_2
% 116.26/18.00 (53) all_54_6 = all_52_9
% 116.26/18.00 (54) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 116.26/18.00 (55) all_58_11 = all_52_14
% 116.26/18.00 (56) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.26/18.00 (57) op(e3, all_6_2) = all_6_0
% 116.26/18.00 (58) ~ (all_52_2 = all_52_3)
% 116.26/18.00 (59) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 116.26/18.00 (60) all_54_7 = all_52_13
% 116.26/18.00 (61) all_16_1 = all_10_1
% 116.26/18.00 (62) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/18.00 (63) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.26/18.00 (64) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.26/18.00 (65) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/18.00 (66) ~ (all_52_7 = all_8_2)
% 116.26/18.00 (67) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/18.00 (68) ~ (all_52_4 = all_8_2)
% 116.26/18.00 (69) op(e1, e0) = all_52_14
% 116.26/18.00 (70) all_58_5 = all_52_9
% 116.26/18.00 (71) ~ (all_52_9 = all_52_13)
% 116.26/18.00 (72) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.00 (73) all_56_9 = all_52_3
% 116.26/18.00 (74) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.26/18.00 (75) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.00 (76) op(e1, all_6_2) = all_6_1
% 116.26/18.00 (77) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.00 (78) all_58_15 = all_4_2
% 116.26/18.00 (79) all_58_2 = all_52_1
% 116.26/18.00 (80) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/18.00 (81) ~ (all_52_1 = all_52_13)
% 116.26/18.00 (82) ~ (all_10_2 = e3)
% 116.26/18.00 (83) ~ (all_52_12 = all_52_13)
% 116.26/18.00 (84) all_58_13 = all_52_7
% 116.26/18.00 (85) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/18.00 (86) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.26/18.00 (87) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.26/18.00 (88) ~ (all_52_14 = all_4_2)
% 116.26/18.00 (89) all_58_6 = all_52_2
% 116.26/18.00 (90) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.26/18.00 (91) all_54_5 = all_8_2
% 116.26/18.00 (92) all_56_15 = all_4_2
% 116.26/18.00 (93) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 116.26/18.00 (94) all_58_10 = all_52_13
% 116.26/18.00 (95) ~ (all_52_13 = all_8_2)
% 116.26/18.00 (96) ~ (all_52_11 = all_4_2)
% 116.26/18.00 (97) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 116.26/18.00 (98) op(e3, all_10_2) = all_10_1
% 116.26/18.00 (99) ~ (all_52_6 = all_8_2)
% 116.26/18.00 (100) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.26/18.00 (101) ~ (all_6_0 = e2)
% 116.26/18.00 (102) all_58_1 = all_52_4
% 116.26/18.00 (103) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.26/18.00 (104) all_58_14 = all_52_11
% 116.26/18.00 (105) all_54_1 = all_52_4
% 116.26/18.00 (106) all_56_13 = all_8_2
% 116.26/18.00 (107) ~ (all_52_1 = all_8_2)
% 116.26/18.00 (108) op(e1, all_6_2) = e3
% 116.26/18.00 (109) ~ (all_8_2 = e2)
% 116.26/18.00 (110) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.26/18.00 (111) op(e1, e2) = all_52_6
% 116.26/18.00 (112) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.00 (113) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.00 (114) all_56_7 = all_52_6
% 116.26/18.00 (115) ~ (all_52_9 = all_6_2)
% 116.26/18.00 (116) ~ (all_52_4 = all_52_6)
% 116.26/18.00 (117) ~ (all_52_4 = all_52_12)
% 116.26/18.00 (118) all_56_1 = all_52_8
% 116.26/18.00 (119) all_58_8 = all_6_2
% 116.26/18.00 (120) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.00 (121) all_16_2 = all_10_2
% 116.26/18.00 (122) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.26/18.00 (123) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/18.00 (124) all_56_4 = all_52_9
% 116.26/18.00 (125) all_58_9 = all_52_12
% 116.26/18.00 (126) all_56_5 = all_52_13
% 116.26/18.00 (127) ~ (all_52_3 = all_4_2)
% 116.26/18.00 (128) ~ (all_52_6 = all_6_2)
% 116.26/18.00 (129) all_56_6 = all_52_2
% 116.26/18.00 (130) ~ (all_52_13 = all_4_2)
% 116.26/18.00 (131) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.26/18.00 (132) all_58_12 = all_52_3
% 116.26/18.00 (133) ~ (all_52_2 = all_52_14)
% 116.26/18.00 (134) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.26/18.00 (135) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.26/18.00 (136) ~ (all_52_12 = all_4_2)
% 116.26/18.00 (137) ~ (all_52_3 = all_10_2)
% 116.26/18.00 (138) all_24_1 = all_10_1
% 116.26/18.00 (139) op(e1, e3) = all_52_2
% 116.26/18.00 (140) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.26/18.00 (141) all_24_2 = all_10_2
% 116.26/18.00 (142) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.26/18.00 (143) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/18.00 (144) all_56_8 = all_52_14
% 116.26/18.00 (145) ~ (all_52_4 = all_10_2)
% 116.26/18.00 (146) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/18.00 (147) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.00 (148) all_56_0 = all_52_4
% 116.26/18.00 (149) ~ (e3 = e2)
% 116.26/18.00 (150) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/18.00 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/18.00 (151) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.26/18.00 (152) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/18.00 (153) all_54_15 = all_4_2
% 116.26/18.00 (154) ~ (all_6_2 = e1)
% 116.26/18.00 (155) ~ (all_6_1 = e2)
% 116.26/18.00 (156) ~ (all_52_6 = all_52_7)
% 116.26/18.00 (157) ~ (all_52_3 = all_52_11)
% 116.26/18.00 (158) all_54_12 = all_52_3
% 116.26/18.00 (159) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.26/18.00
% 116.26/18.00 Begin of proof
% 116.26/18.00 |
% 116.26/18.00 | BETA: splitting (74) gives:
% 116.26/18.00 |
% 116.26/18.00 | Case 1:
% 116.26/18.00 | |
% 116.26/18.00 | | (160) ~ (all_56_15 = e1)
% 116.26/18.00 | |
% 116.26/18.00 | | REDUCE: (92), (160) imply:
% 116.26/18.00 | | (161) ~ (all_4_2 = e1)
% 116.26/18.00 | |
% 116.26/18.00 | | BETA: splitting (86) gives:
% 116.26/18.00 | |
% 116.26/18.00 | | Case 1:
% 116.26/18.00 | | |
% 116.26/18.00 | | | (162) ~ (all_56_14 = e2)
% 116.26/18.00 | | |
% 116.26/18.00 | | | REDUCE: (10), (162) imply:
% 116.26/18.00 | | | (163) ~ (all_6_2 = e2)
% 116.26/18.00 | | |
% 116.26/18.00 | | | BETA: splitting (87) gives:
% 116.26/18.00 | | |
% 116.26/18.00 | | | Case 1:
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | (164) ~ (all_56_12 = e2)
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | REDUCE: (26), (164) imply:
% 116.26/18.00 | | | | (165) ~ (all_10_2 = e2)
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | BETA: splitting (142) gives:
% 116.26/18.00 | | | |
% 116.26/18.00 | | | | Case 1:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | (166) ~ (all_56_5 = e2)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | REDUCE: (126), (166) imply:
% 116.26/18.00 | | | | | (167) ~ (all_52_13 = e2)
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | BETA: splitting (122) gives:
% 116.26/18.00 | | | | |
% 116.26/18.00 | | | | | Case 1:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | (168) ~ (all_56_15 = e3)
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | REDUCE: (92), (168) imply:
% 116.26/18.00 | | | | | | (169) ~ (all_4_2 = e3)
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | BETA: splitting (27) gives:
% 116.26/18.00 | | | | | |
% 116.26/18.00 | | | | | | Case 1:
% 116.26/18.00 | | | | | | |
% 116.26/18.00 | | | | | | | (170) ~ (all_56_7 = e1)
% 116.26/18.00 | | | | | | |
% 116.26/18.01 | | | | | | | REF_CLOSE: (1), (2), (4), (8), (10), (12), (14), (18), (20), (21),
% 116.26/18.01 | | | | | | | (23), (24), (26), (31), (34), (36), (37), (42), (45),
% 116.26/18.01 | | | | | | | (48), (50), (51), (55), (61), (62), (69), (73), (75),
% 116.26/18.01 | | | | | | | (77), (78), (82), (84), (88), (89), (92), (98), (104),
% 116.26/18.01 | | | | | | | (112), (114), (119), (120), (121), (129), (132), (140),
% 116.26/18.01 | | | | | | | (144), (146), (150), (153), (154), (163), (165), (169),
% 116.26/18.01 | | | | | | | (170) are inconsistent by sub-proof #191.
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | Case 2:
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | (171) all_56_7 = e1
% 116.26/18.01 | | | | | | | (172) ~ (all_56_15 = e2)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | COMBINE_EQS: (114), (171) imply:
% 116.26/18.01 | | | | | | | (173) all_52_6 = e1
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (92), (172) imply:
% 116.26/18.01 | | | | | | | (174) ~ (all_4_2 = e2)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (128), (173) imply:
% 116.26/18.01 | | | | | | | (175) ~ (all_6_2 = e1)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (14), (21), (36), (37),
% 116.26/18.01 | | | | | | | (39), (42), (45), (48), (50), (51), (52), (54), (55),
% 116.26/18.01 | | | | | | | (57), (60), (65), (69), (70), (79), (83), (88), (89),
% 116.26/18.01 | | | | | | | (92), (93), (94), (100), (101), (108), (109), (112),
% 116.26/18.01 | | | | | | | (119), (124), (126), (129), (130), (134), (136), (139),
% 116.26/18.01 | | | | | | | (147), (153), (154), (159), (163), (169), (174) are
% 116.26/18.01 | | | | | | | inconsistent by sub-proof #342.
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | End of split
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | Case 2:
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | (176) all_56_15 = e3
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | COMBINE_EQS: (92), (176) imply:
% 116.26/18.01 | | | | | | (177) all_4_2 = e3
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | BETA: splitting (41) gives:
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | Case 1:
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | (178) ~ (all_56_3 = e2)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (11), (178) imply:
% 116.26/18.01 | | | | | | | (179) ~ (all_52_1 = e2)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REF_CLOSE: (1), (12), (14), (21), (23), (26), (31), (37), (45),
% 116.26/18.01 | | | | | | | (50), (52), (61), (69), (70), (75), (77), (79), (80),
% 116.26/18.01 | | | | | | | (82), (94), (98), (109), (120), (121), (124), (144),
% 116.26/18.01 | | | | | | | (147), (165), (167), (179) are inconsistent by
% 116.26/18.01 | | | | | | | sub-proof #189.
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | Case 2:
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | (180) ~ (all_56_15 = e3)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (176), (180) imply:
% 116.26/18.01 | | | | | | | (181) $false
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | CLOSE: (181) is inconsistent.
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | End of split
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | End of split
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | Case 2:
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | (182) all_56_5 = e2
% 116.26/18.01 | | | | | (183) ~ (all_56_12 = e0)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | COMBINE_EQS: (126), (182) imply:
% 116.26/18.01 | | | | | (184) all_52_13 = e2
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | COMBINE_EQS: (94), (184) imply:
% 116.26/18.01 | | | | | (185) all_58_10 = e2
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (26), (183) imply:
% 116.26/18.01 | | | | | (186) ~ (all_10_2 = e0)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (71), (184) imply:
% 116.26/18.01 | | | | | (187) ~ (all_52_9 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (83), (184) imply:
% 116.26/18.01 | | | | | (188) ~ (all_52_12 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (7), (184) imply:
% 116.26/18.01 | | | | | (189) ~ (all_52_14 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | SIMP: (189) implies:
% 116.26/18.01 | | | | | (190) ~ (all_52_14 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (95), (184) imply:
% 116.26/18.01 | | | | | (191) ~ (all_8_2 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | REDUCE: (130), (184) imply:
% 116.26/18.01 | | | | | (192) ~ (all_4_2 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | SIMP: (192) implies:
% 116.26/18.01 | | | | | (193) ~ (all_4_2 = e2)
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | BETA: splitting (65) gives:
% 116.26/18.01 | | | | |
% 116.26/18.01 | | | | | Case 1:
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | (194) ~ (all_56_5 = e2)
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | REDUCE: (182), (194) imply:
% 116.26/18.01 | | | | | | (195) $false
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | CLOSE: (195) is inconsistent.
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | Case 2:
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | (196) ~ (all_56_14 = e0)
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | REDUCE: (10), (196) imply:
% 116.26/18.01 | | | | | | (197) ~ (all_6_2 = e0)
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | BETA: splitting (48) gives:
% 116.26/18.01 | | | | | |
% 116.26/18.01 | | | | | | Case 1:
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | (198) all_54_15 = e3
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | COMBINE_EQS: (153), (198) imply:
% 116.26/18.01 | | | | | | | (199) all_4_2 = e3
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | COMBINE_EQS: (92), (199) imply:
% 116.26/18.01 | | | | | | | (200) all_56_15 = e3
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | COMBINE_EQS: (78), (199) imply:
% 116.26/18.01 | | | | | | | (201) all_58_15 = e3
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (127), (199) imply:
% 116.26/18.01 | | | | | | | (202) ~ (all_52_3 = e3)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | REDUCE: (136), (199) imply:
% 116.26/18.01 | | | | | | | (203) ~ (all_52_12 = e3)
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | BETA: splitting (122) gives:
% 116.26/18.01 | | | | | | |
% 116.26/18.01 | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | (204) ~ (all_56_15 = e3)
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | REDUCE: (200), (204) imply:
% 116.26/18.01 | | | | | | | | (205) $false
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | CLOSE: (205) is inconsistent.
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | (206) ~ (all_56_9 = e0)
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | REDUCE: (73), (206) imply:
% 116.26/18.01 | | | | | | | | (207) ~ (all_52_3 = e0)
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | BETA: splitting (36) gives:
% 116.26/18.01 | | | | | | | |
% 116.26/18.01 | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | (208) all_54_10 = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | COMBINE_EQS: (42), (208) imply:
% 116.26/18.01 | | | | | | | | | (209) all_6_2 = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | SIMP: (209) implies:
% 116.26/18.01 | | | | | | | | | (210) all_6_2 = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | COMBINE_EQS: (10), (210) imply:
% 116.26/18.01 | | | | | | | | | (211) all_56_14 = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | COMBINE_EQS: (119), (210) imply:
% 116.26/18.01 | | | | | | | | | (212) all_58_8 = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | REDUCE: (39), (210) imply:
% 116.26/18.01 | | | | | | | | | (213) ~ (all_52_2 = e3)
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | REDUCE: (46), (210) imply:
% 116.26/18.01 | | | | | | | | | (214) ~ (all_52_8 = e3)
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | REDUCE: (115), (210) imply:
% 116.26/18.01 | | | | | | | | | (215) ~ (all_52_9 = e3)
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | REDUCE: (32), (210) imply:
% 116.26/18.01 | | | | | | | | | (216) ~ (all_52_14 = e3)
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | REDUCE: (108), (210) imply:
% 116.26/18.01 | | | | | | | | | (217) op(e1, e3) = e3
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | BETA: splitting (120) gives:
% 116.26/18.01 | | | | | | | | |
% 116.26/18.01 | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | (218) all_54_0 = e3
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | REF_CLOSE: (12), (82), (218) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | #451.
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | (219) ~ (all_54_0 = e3)
% 116.26/18.01 | | | | | | | | | | (220) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | BETA: splitting (220) gives:
% 116.26/18.01 | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | (221) all_54_0 = e2
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | REF_CLOSE: (12), (165), (221) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | #450.
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | (222) ~ (all_54_0 = e2)
% 116.26/18.01 | | | | | | | | | | | (223) all_54_0 = e1 | all_54_0 = e0
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | BETA: splitting (56) gives:
% 116.26/18.01 | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | (224) ~ (all_56_5 = e2)
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | REDUCE: (182), (224) imply:
% 116.26/18.01 | | | | | | | | | | | | (225) $false
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | (226) ~ (all_56_13 = e0)
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | REDUCE: (106), (226) imply:
% 116.26/18.01 | | | | | | | | | | | | (227) ~ (all_8_2 = e0)
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | BETA: splitting (223) gives:
% 116.26/18.01 | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | (228) all_54_0 = e1
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | COMBINE_EQS: (12), (228) imply:
% 116.26/18.01 | | | | | | | | | | | | | (229) all_10_2 = e1
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | SIMP: (229) implies:
% 116.26/18.01 | | | | | | | | | | | | | (230) all_10_2 = e1
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | COMBINE_EQS: (28), (230) imply:
% 116.26/18.01 | | | | | | | | | | | | | (231) all_58_0 = e1
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | REDUCE: (137), (230) imply:
% 116.26/18.01 | | | | | | | | | | | | | (232) ~ (all_52_3 = e1)
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | REDUCE: (23), (230) imply:
% 116.26/18.01 | | | | | | | | | | | | | (233) ~ (all_52_12 = e1)
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | REDUCE: (82), (230) imply:
% 116.26/18.01 | | | | | | | | | | | | | (234) ~ (e3 = e1)
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | BETA: splitting (21) gives:
% 116.26/18.01 | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | (235) all_54_3 = e3
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | REF_CLOSE: (14), (203), (235) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | #224.
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | (236) ~ (all_54_3 = e3)
% 116.26/18.01 | | | | | | | | | | | | | | (237) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 116.26/18.01 | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | (238) all_54_3 = e2
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | REF_CLOSE: (14), (188), (238) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | #285.
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | (239) all_54_3 = e1 | all_54_3 = e0
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 116.26/18.01 | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | (240) all_54_12 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (240) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | (241) all_52_3 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | REDUCE: (202), (241) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | (242) $false
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | (243) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | (244) all_54_3 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (233), (244) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | #284.
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | (245) all_54_3 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (245) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (246) all_52_12 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | SIMP: (246) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (247) all_52_12 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (247) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (248) all_58_9 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | REDUCE: (16), (247) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (249) ~ (all_52_14 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | SIMP: (249) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (250) ~ (all_52_14 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | REDUCE: (203), (247) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (251) ~ (e3 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | SIMP: (251) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | (252) ~ (e3 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | (253) all_54_11 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (216), (253) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | #388.
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | (254) ~ (all_54_11 = e3)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | (255) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | (256) all_54_11 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (190), (256) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | #387.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | (257) ~ (all_54_11 = e2)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | (258) all_54_11 = e1 | all_54_11 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | (259) all_58_0 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (55), (64), (125), (149), (185), (201),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | (203), (216), (231), (259) are inconsistent by
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | sub-proof #200.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | (260) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | (261) all_54_12 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (261) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | (262) all_52_3 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | (263) all_52_3 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (263) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | (264) ~ (all_52_2 = e2)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | (265) all_54_8 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (213), (265) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | #399.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | (266) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | (267) all_58_6 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (267) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | (268) all_52_2 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (268) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | (269) $false
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | (270) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (271) all_58_4 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (271) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (272) all_52_8 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (272) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (273) ~ (all_52_4 = e2)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (272) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | (274) ~ (e3 = e2)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_54_11 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (275) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_52_14 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (276) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_52_14 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (277) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (278) ~ (all_52_2 = e1)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (277) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_52_6 = e1)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_58_1 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (280) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_52_4 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (281) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (282) ~ (all_8_2 = e3)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_8_2 = e3)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_54_5 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (283), (284) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | #339.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_54_5 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (109), (286) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #338.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_54_5 = e1 | all_54_5 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_7 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (288) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_52_6 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_54_8 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (264), (290) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #382.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_54_8 = e1 | all_54_8 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_6 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (292) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_52_2 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (293) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_52_2 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (294) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) op(e1, e3) = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_54_5 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (296) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_8_2 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (297) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_8_2 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (298) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) ~ (all_52_9 = e1)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (298) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) ~ (e2 = e1)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_54_6 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (215), (301) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #268.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_4 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (303) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e2 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (304) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e2 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (305) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_58_7 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (42), (43), (55), (119), (154), (163),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (197), (270), (306) are inconsistent by
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #274.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_54_6 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (308) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_52_9 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_52_9 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (310) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_56_4 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (14), (21), (23), (26), (31), (37),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (50), (61), (69), (75), (77), (80), (82),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (120), (121), (144), (165), (311) are
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #190.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_54_6 = e1 | all_54_6 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_54_6 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (299), (313) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #188.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_54_6 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (314) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_52_9 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_52_9 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (316) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_58_5 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (299), (316) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) ~ (e1 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) ~ (e1 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_58_5 = e1
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (317), (320) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) e1 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (319), (321) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) $false
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (322) is inconsistent.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with e0, e3, e3, e1,
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (217), (295) gives:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) e3 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (323) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) all_56_14 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (12), (14), (20), (21), (23), (26),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (37), (45), (50), (55), (61), (69), (75),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (77), (82), (89), (98), (112), (119), (120),
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (144), (154), (165), (279), (324) are
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) all_54_5 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (227), (325) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #311.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_58_6 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (326) imply:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) ~ (all_52_2 = e0)
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (278), (291), (327) are inconsistent by
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #396.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) all_58_8 = e2 | all_58_11 = e2
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (149), (190), (212), (328) are inconsistent
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #345.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | (329) all_58_4 = e3 | all_58_9 = e3
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (248), (252), (271), (329) are inconsistent
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #186.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | (330) all_54_11 = e0
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (250), (330) are inconsistent by sub-proof
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | | #384.
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | | (331) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (48), (70), (73), (92), (96), (104), (119),
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | | (122), (127), (135), (153), (157), (158), (161),
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | | (163), (187), (232), (331) are inconsistent by
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #404.
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | (332) all_54_12 = e1 | all_54_12 = e0
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (207), (232), (332) are inconsistent by
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | | sub-proof #185.
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | (333) all_54_0 = e0
% 116.26/18.02 | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | | REF_CLOSE: (12), (186), (333) are inconsistent by sub-proof
% 116.26/18.02 | | | | | | | | | | | | | #424.
% 116.26/18.02 | | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | (334) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | REF_CLOSE: (10), (42), (65), (154), (163), (182), (334) are
% 116.26/18.02 | | | | | | | | | inconsistent by sub-proof #434.
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | End of split
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | End of split
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | Case 2:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (335) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | REF_CLOSE: (8), (153), (161), (193), (335) are inconsistent by
% 116.26/18.02 | | | | | | | sub-proof #417.
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | End of split
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | End of split
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | End of split
% 116.26/18.02 | | | |
% 116.26/18.02 | | | Case 2:
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | (336) all_56_12 = e2
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | REF_CLOSE: (9), (26), (31), (37), (72), (98), (105), (111), (113),
% 116.26/18.02 | | | | (116), (138), (141), (145), (148), (152), (336) are
% 116.26/18.02 | | | | inconsistent by sub-proof #195.
% 116.26/18.02 | | | |
% 116.26/18.02 | | | End of split
% 116.26/18.02 | | |
% 116.26/18.02 | | Case 2:
% 116.26/18.02 | | |
% 116.26/18.02 | | | (337) all_56_14 = e2
% 116.26/18.02 | | |
% 116.26/18.02 | | | REF_CLOSE: (5), (8), (9), (10), (11), (13), (17), (25), (28), (30), (37),
% 116.26/18.02 | | | (41), (44), (47), (48), (49), (50), (52), (56), (57), (59),
% 116.26/18.02 | | | (66), (68), (70), (79), (82), (90), (91), (92), (94), (99),
% 116.26/18.02 | | | (101), (102), (103), (105), (106), (108), (109), (110), (111),
% 116.26/18.02 | | | (113), (115), (118), (125), (126), (143), (147), (148), (151),
% 116.26/18.02 | | | (153), (156), (337) are inconsistent by sub-proof #306.
% 116.26/18.02 | | |
% 116.26/18.02 | | End of split
% 116.26/18.02 | |
% 116.26/18.02 | Case 2:
% 116.26/18.02 | |
% 116.26/18.02 | | (338) all_56_15 = e1
% 116.26/18.02 | |
% 116.26/18.02 | | COMBINE_EQS: (92), (338) imply:
% 116.26/18.02 | | (339) all_4_2 = e1
% 116.26/18.02 | |
% 116.26/18.02 | | SIMP: (339) implies:
% 116.26/18.02 | | (340) all_4_2 = e1
% 116.26/18.02 | |
% 116.26/18.02 | | COMBINE_EQS: (78), (340) imply:
% 116.26/18.02 | | (341) all_58_15 = e1
% 116.26/18.02 | |
% 116.26/18.02 | | REDUCE: (136), (340) imply:
% 116.26/18.02 | | (342) ~ (all_52_12 = e1)
% 116.26/18.02 | |
% 116.26/18.02 | | REDUCE: (130), (340) imply:
% 116.26/18.02 | | (343) ~ (all_52_13 = e1)
% 116.26/18.02 | |
% 116.26/18.02 | | REDUCE: (88), (340) imply:
% 116.26/18.02 | | (344) ~ (all_52_14 = e1)
% 116.26/18.02 | |
% 116.26/18.02 | | BETA: splitting (90) gives:
% 116.26/18.02 | |
% 116.26/18.02 | | Case 1:
% 116.26/18.02 | | |
% 116.26/18.02 | | | (345) ~ (all_56_1 = e3)
% 116.26/18.02 | | |
% 116.26/18.02 | | | REDUCE: (118), (345) imply:
% 116.26/18.02 | | | (346) ~ (all_52_8 = e3)
% 116.26/18.02 | | |
% 116.26/18.02 | | | BETA: splitting (134) gives:
% 116.26/18.02 | | |
% 116.26/18.02 | | | Case 1:
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | (347) ~ (all_56_4 = e2)
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | REDUCE: (124), (347) imply:
% 116.26/18.02 | | | | (348) ~ (all_52_9 = e2)
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | BETA: splitting (1) gives:
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | Case 1:
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | (349) ~ (all_56_2 = e3)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | REDUCE: (50), (349) imply:
% 116.26/18.02 | | | | | (350) ~ (all_52_12 = e3)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | BETA: splitting (143) gives:
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | Case 1:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | (351) all_58_0 = e3
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | COMBINE_EQS: (28), (351) imply:
% 116.26/18.02 | | | | | | (352) all_10_2 = e3
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | REDUCE: (82), (352) imply:
% 116.26/18.02 | | | | | | (353) $false
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | CLOSE: (353) is inconsistent.
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | Case 2:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | (354) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | BETA: splitting (354) gives:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | Case 1:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (355) all_58_1 = e3
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | COMBINE_EQS: (102), (355) imply:
% 116.26/18.02 | | | | | | | (356) all_52_4 = e3
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | COMBINE_EQS: (148), (356) imply:
% 116.26/18.02 | | | | | | | (357) all_56_0 = e3
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | BETA: splitting (151) gives:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (358) ~ (all_56_0 = e3)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REDUCE: (357), (358) imply:
% 116.26/18.02 | | | | | | | | (359) $false
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | CLOSE: (359) is inconsistent.
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (360) ~ (all_56_14 = e2)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REDUCE: (10), (360) imply:
% 116.26/18.02 | | | | | | | | (361) ~ (all_6_2 = e2)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REF_CLOSE: (4), (7), (10), (11), (14), (21), (36), (37), (39),
% 116.26/18.02 | | | | | | | | (42), (45), (50), (51), (52), (54), (55), (57), (60),
% 116.26/18.02 | | | | | | | | (65), (69), (70), (79), (83), (89), (93), (94),
% 116.26/18.02 | | | | | | | | (100), (101), (108), (109), (112), (119), (124),
% 116.26/18.02 | | | | | | | | (126), (129), (134), (139), (147), (154), (159),
% 116.26/18.02 | | | | | | | | (338), (342), (343), (344), (361) are inconsistent by
% 116.26/18.02 | | | | | | | | sub-proof #344.
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | End of split
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | Case 2:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (362) all_58_4 = e3 | all_58_9 = e3
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | REF_CLOSE: (47), (125), (346), (350), (362) are inconsistent by
% 116.26/18.02 | | | | | | | sub-proof #184.
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | End of split
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | End of split
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | Case 2:
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | (363) all_56_2 = e3
% 116.26/18.02 | | | | | (364) ~ (all_56_12 = e0)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | COMBINE_EQS: (50), (363) imply:
% 116.26/18.02 | | | | | (365) all_52_12 = e3
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | COMBINE_EQS: (125), (365) imply:
% 116.26/18.02 | | | | | (366) all_58_9 = e3
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | REDUCE: (26), (364) imply:
% 116.26/18.02 | | | | | (367) ~ (all_10_2 = e0)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | REDUCE: (117), (365) imply:
% 116.26/18.02 | | | | | (368) ~ (all_52_4 = e3)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | REDUCE: (23), (365) imply:
% 116.26/18.02 | | | | | (369) ~ (all_10_2 = e3)
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | BETA: splitting (19) gives:
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | | Case 1:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | (370) ~ (all_56_3 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | REDUCE: (11), (370) imply:
% 116.26/18.02 | | | | | | (371) ~ (all_52_1 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | BETA: splitting (147) gives:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | Case 1:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (372) all_58_2 = e2
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | REF_CLOSE: (79), (371), (372) are inconsistent by sub-proof #335.
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | Case 2:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (373) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | BETA: splitting (51) gives:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (374) ~ (all_56_6 = e1)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REDUCE: (129), (374) imply:
% 116.26/18.02 | | | | | | | | (375) ~ (all_52_2 = e1)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | BETA: splitting (112) gives:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | (376) all_58_6 = e1
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | REF_CLOSE: (89), (375), (376) are inconsistent by sub-proof
% 116.26/18.02 | | | | | | | | | #452.
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | (377) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | BETA: splitting (377) gives:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | (378) all_58_7 = e1
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | COMBINE_EQS: (4), (378) imply:
% 116.26/18.02 | | | | | | | | | | (379) all_52_6 = e1
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | COMBINE_EQS: (114), (379) imply:
% 116.26/18.02 | | | | | | | | | | (380) all_56_7 = e1
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | REDUCE: (128), (379) imply:
% 116.26/18.02 | | | | | | | | | | (381) ~ (all_6_2 = e1)
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | BETA: splitting (33) gives:
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | (382) ~ (all_56_7 = e1)
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | REDUCE: (380), (382) imply:
% 116.26/18.02 | | | | | | | | | | | (383) $false
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | CLOSE: (383) is inconsistent.
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | (384) ~ (all_56_14 = e2)
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | REDUCE: (10), (384) imply:
% 116.26/18.02 | | | | | | | | | | | (385) ~ (all_6_2 = e2)
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | | REF_CLOSE: (7), (10), (36), (37), (39), (42), (52), (55),
% 116.26/18.02 | | | | | | | | | | | (65), (70), (71), (76), (89), (94), (109), (119),
% 116.26/18.02 | | | | | | | | | | | (126), (139), (154), (155), (159), (343), (348),
% 116.26/18.02 | | | | | | | | | | | (373), (378), (385) are inconsistent by sub-proof
% 116.26/18.02 | | | | | | | | | | | #272.
% 116.26/18.02 | | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | (386) all_58_8 = e1 | all_58_11 = e1
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | | REF_CLOSE: (55), (119), (154), (344), (386) are inconsistent
% 116.26/18.02 | | | | | | | | | | by sub-proof #445.
% 116.26/18.02 | | | | | | | | | |
% 116.26/18.02 | | | | | | | | | End of split
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | End of split
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (387) all_56_6 = e1
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | COMBINE_EQS: (129), (387) imply:
% 116.26/18.02 | | | | | | | | (388) all_52_2 = e1
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REDUCE: (2), (388) imply:
% 116.26/18.02 | | | | | | | | (389) ~ (all_10_2 = e1)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | SIMP: (389) implies:
% 116.26/18.02 | | | | | | | | (390) ~ (all_10_2 = e1)
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REF_CLOSE: (9), (12), (31), (37), (72), (82), (98), (105),
% 116.26/18.02 | | | | | | | | (111), (113), (116), (120), (138), (141), (145),
% 116.26/18.02 | | | | | | | | (367), (368), (390) are inconsistent by sub-proof
% 116.26/18.02 | | | | | | | | #183.
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | End of split
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | End of split
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | Case 2:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | (391) all_56_3 = e2
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | COMBINE_EQS: (11), (391) imply:
% 116.26/18.02 | | | | | | (392) all_52_1 = e2
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | REDUCE: (40), (392) imply:
% 116.26/18.02 | | | | | | (393) ~ (all_52_9 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | REDUCE: (81), (392) imply:
% 116.26/18.02 | | | | | | (394) ~ (all_52_13 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | SIMP: (394) implies:
% 116.26/18.02 | | | | | | (395) ~ (all_52_13 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | REDUCE: (107), (392) imply:
% 116.26/18.02 | | | | | | (396) ~ (all_8_2 = e2)
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | BETA: splitting (85) gives:
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | | Case 1:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (397) all_58_9 = e2
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | COMBINE_EQS: (366), (397) imply:
% 116.26/18.02 | | | | | | | (398) e3 = e2
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | REDUCE: (149), (398) imply:
% 116.26/18.02 | | | | | | | (399) $false
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | CLOSE: (399) is inconsistent.
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | Case 2:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | (400) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | BETA: splitting (400) gives:
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (401) all_58_10 = e2
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | COMBINE_EQS: (94), (401) imply:
% 116.26/18.02 | | | | | | | | (402) all_52_13 = e2
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | REDUCE: (395), (402) imply:
% 116.26/18.02 | | | | | | | | (403) $false
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | CLOSE: (403) is inconsistent.
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | (404) all_58_11 = e2 | all_58_15 = e2
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | BETA: splitting (404) gives:
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | | Case 1:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | (405) all_58_11 = e2
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | COMBINE_EQS: (55), (405) imply:
% 116.26/18.02 | | | | | | | | | (406) all_52_14 = e2
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | SIMP: (406) implies:
% 116.26/18.02 | | | | | | | | | (407) all_52_14 = e2
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | REDUCE: (32), (407) imply:
% 116.26/18.02 | | | | | | | | | (408) ~ (all_6_2 = e2)
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | SIMP: (408) implies:
% 116.26/18.02 | | | | | | | | | (409) ~ (all_6_2 = e2)
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | REF_CLOSE: (7), (10), (11), (14), (21), (36), (37), (42),
% 116.26/18.02 | | | | | | | | | (45), (50), (52), (54), (57), (60), (65), (69),
% 116.26/18.02 | | | | | | | | | (70), (79), (83), (93), (94), (100), (101), (108),
% 116.26/18.02 | | | | | | | | | (109), (126), (147), (154), (342), (343), (348),
% 116.26/18.02 | | | | | | | | | (395), (409) are inconsistent by sub-proof #347.
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | Case 2:
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | (410) all_58_15 = e2
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | COMBINE_EQS: (341), (410) imply:
% 116.26/18.02 | | | | | | | | | (411) e2 = e1
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | SIMP: (411) implies:
% 116.26/18.02 | | | | | | | | | (412) e2 = e1
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | REDUCE: (43), (412) imply:
% 116.26/18.02 | | | | | | | | | (413) $false
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | | CLOSE: (413) is inconsistent.
% 116.26/18.02 | | | | | | | | |
% 116.26/18.02 | | | | | | | | End of split
% 116.26/18.02 | | | | | | | |
% 116.26/18.02 | | | | | | | End of split
% 116.26/18.02 | | | | | | |
% 116.26/18.02 | | | | | | End of split
% 116.26/18.02 | | | | | |
% 116.26/18.02 | | | | | End of split
% 116.26/18.02 | | | | |
% 116.26/18.02 | | | | End of split
% 116.26/18.02 | | | |
% 116.26/18.02 | | | Case 2:
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | (414) ~ (all_56_15 = e1)
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | REDUCE: (338), (414) imply:
% 116.26/18.02 | | | | (415) $false
% 116.26/18.02 | | | |
% 116.26/18.02 | | | | CLOSE: (415) is inconsistent.
% 116.26/18.02 | | | |
% 116.26/18.02 | | | End of split
% 116.26/18.02 | | |
% 116.26/18.02 | | Case 2:
% 116.26/18.02 | | |
% 116.26/18.02 | | | (416) ~ (all_56_15 = e1)
% 116.26/18.02 | | |
% 116.26/18.02 | | | REDUCE: (338), (416) imply:
% 116.26/18.02 | | | (417) $false
% 116.26/18.02 | | |
% 116.26/18.02 | | | CLOSE: (417) is inconsistent.
% 116.26/18.02 | | |
% 116.26/18.02 | | End of split
% 116.26/18.02 | |
% 116.26/18.02 | End of split
% 116.26/18.02 |
% 116.26/18.02 End of proof
% 116.26/18.02
% 116.26/18.02 Sub-proof #183 shows that the following formulas are inconsistent:
% 116.26/18.02 ----------------------------------------------------------------
% 116.26/18.02 (1) op(e3, e2) = all_52_4
% 116.26/18.02 (2) all_54_0 = all_10_2
% 116.26/18.02 (3) ~ (all_52_4 = e3)
% 116.26/18.02 (4) op(all_10_1, all_10_2) = e1
% 116.26/18.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.02 (6) ~ (all_10_2 = e1)
% 116.26/18.02 (7) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.02 (8) ~ (all_10_2 = e3)
% 116.26/18.03 (9) op(e3, all_10_2) = all_10_1
% 116.26/18.03 (10) all_54_1 = all_52_4
% 116.26/18.03 (11) op(e1, e2) = all_52_6
% 116.26/18.03 (12) ~ (all_10_2 = e0)
% 116.26/18.03 (13) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.03 (14) ~ (all_52_4 = all_52_6)
% 116.26/18.03 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 (16) all_24_1 = all_10_1
% 116.26/18.03 (17) all_24_2 = all_10_2
% 116.26/18.03 (18) ~ (all_52_4 = all_10_2)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (15) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (19) all_54_0 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (2), (8), (19) are inconsistent by sub-proof #451.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (20) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 | |
% 116.26/18.03 | | BETA: splitting (20) gives:
% 116.26/18.03 | |
% 116.26/18.03 | | Case 1:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (21) all_54_0 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | COMBINE_EQS: (2), (21) imply:
% 116.26/18.03 | | | (22) all_10_2 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | SIMP: (22) implies:
% 116.26/18.03 | | | (23) all_10_2 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | COMBINE_EQS: (17), (23) imply:
% 116.26/18.03 | | | (24) all_24_2 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | REDUCE: (18), (23) imply:
% 116.26/18.03 | | | (25) ~ (all_52_4 = e2)
% 116.26/18.03 | | |
% 116.26/18.03 | | | REDUCE: (4), (23) imply:
% 116.26/18.03 | | | (26) op(all_10_1, e2) = e1
% 116.26/18.03 | | |
% 116.26/18.03 | | | REDUCE: (9), (23) imply:
% 116.26/18.03 | | | (27) op(e3, e2) = all_10_1
% 116.26/18.03 | | |
% 116.26/18.03 | | | REF_CLOSE: (1), (3), (5), (7), (10), (11), (13), (14), (16), (24), (25),
% 116.26/18.03 | | | (26), (27) are inconsistent by sub-proof #197.
% 116.26/18.03 | | |
% 116.26/18.03 | | Case 2:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (28) all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 | | |
% 116.26/18.03 | | | REF_CLOSE: (2), (6), (12), (28) are inconsistent by sub-proof #423.
% 116.26/18.03 | | |
% 116.26/18.03 | | End of split
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #184 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) all_58_4 = all_52_8
% 116.26/18.03 (2) ~ (all_52_12 = e3)
% 116.26/18.03 (3) all_58_4 = e3 | all_58_9 = e3
% 116.26/18.03 (4) ~ (all_52_8 = e3)
% 116.26/18.03 (5) all_58_9 = all_52_12
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (3) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (6) all_58_4 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #331.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (7) all_58_9 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #330.
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #185 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) all_54_12 = e1 | all_54_12 = e0
% 116.26/18.03 (2) all_54_12 = all_52_3
% 116.26/18.03 (3) ~ (all_52_3 = e1)
% 116.26/18.03 (4) ~ (all_52_3 = e0)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (1) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (5) all_54_12 = e1
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #408.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (6) all_54_12 = e0
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #407.
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #186 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) all_58_4 = e2
% 116.26/18.03 (2) all_58_9 = e0
% 116.26/18.03 (3) ~ (e3 = e0)
% 116.26/18.03 (4) all_58_4 = e3 | all_58_9 = e3
% 116.26/18.03 (5) ~ (e3 = e2)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (4) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (6) all_58_4 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | COMBINE_EQS: (1), (6) imply:
% 116.26/18.03 | | (7) e3 = e2
% 116.26/18.03 | |
% 116.26/18.03 | | SIMP: (7) implies:
% 116.26/18.03 | | (8) e3 = e2
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (5), (8) imply:
% 116.26/18.03 | | (9) $false
% 116.26/18.03 | |
% 116.26/18.03 | | CLOSE: (9) is inconsistent.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (10) all_58_9 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #187.
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #187 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) all_58_9 = e3
% 116.26/18.03 (2) all_58_9 = e0
% 116.26/18.03 (3) ~ (e3 = e0)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | COMBINE_EQS: (1), (2) imply:
% 116.26/18.03 | (4) e3 = e0
% 116.26/18.03 |
% 116.26/18.03 | SIMP: (4) implies:
% 116.26/18.03 | (5) e3 = e0
% 116.26/18.03 |
% 116.26/18.03 | REDUCE: (3), (5) imply:
% 116.26/18.03 | (6) $false
% 116.26/18.03 |
% 116.26/18.03 | CLOSE: (6) is inconsistent.
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #188 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) all_54_6 = all_52_9
% 116.26/18.03 (2) all_54_6 = e1
% 116.26/18.03 (3) ~ (all_52_9 = e1)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | COMBINE_EQS: (1), (2) imply:
% 116.26/18.03 | (4) all_52_9 = e1
% 116.26/18.03 |
% 116.26/18.03 | SIMP: (4) implies:
% 116.26/18.03 | (5) all_52_9 = e1
% 116.26/18.03 |
% 116.26/18.03 | REDUCE: (3), (5) imply:
% 116.26/18.03 | (6) $false
% 116.26/18.03 |
% 116.26/18.03 | CLOSE: (6) is inconsistent.
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #189 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.03 (2) ~ (all_52_1 = e2)
% 116.26/18.03 (3) all_54_0 = all_10_2
% 116.26/18.03 (4) all_54_3 = all_52_12
% 116.26/18.03 (5) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.03 (6) ~ (all_52_12 = all_10_2)
% 116.26/18.03 (7) all_56_12 = all_10_2
% 116.26/18.03 (8) op(all_10_1, all_10_2) = e1
% 116.26/18.03 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.03 (10) ~ (all_10_2 = e2)
% 116.26/18.03 (11) op(e3, e0) = all_52_12
% 116.26/18.03 (12) all_56_2 = all_52_12
% 116.26/18.03 (13) all_58_3 = all_8_2
% 116.26/18.03 (14) all_16_1 = all_10_1
% 116.26/18.03 (15) op(e1, e0) = all_52_14
% 116.26/18.03 (16) all_58_5 = all_52_9
% 116.26/18.03 (17) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.03 (18) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.03 (19) all_58_2 = all_52_1
% 116.26/18.03 (20) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/18.03 (21) ~ (all_10_2 = e3)
% 116.26/18.03 (22) ~ (all_52_13 = e2)
% 116.26/18.03 (23) all_58_10 = all_52_13
% 116.26/18.03 (24) op(e3, all_10_2) = all_10_1
% 116.26/18.03 (25) ~ (all_8_2 = e2)
% 116.26/18.03 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 (27) all_16_2 = all_10_2
% 116.26/18.03 (28) all_56_4 = all_52_9
% 116.26/18.03 (29) all_56_8 = all_52_14
% 116.26/18.03 (30) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (30) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (31) all_58_2 = e2
% 116.26/18.03 | |
% 116.26/18.03 | | COMBINE_EQS: (19), (31) imply:
% 116.26/18.03 | | (32) all_52_1 = e2
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (2), (32) imply:
% 116.26/18.03 | | (33) $false
% 116.26/18.03 | |
% 116.26/18.03 | | CLOSE: (33) is inconsistent.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (34) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.03 | |
% 116.26/18.03 | | BETA: splitting (34) gives:
% 116.26/18.03 | |
% 116.26/18.03 | | Case 1:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (35) all_58_3 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | COMBINE_EQS: (13), (35) imply:
% 116.26/18.03 | | | (36) all_8_2 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | REDUCE: (25), (36) imply:
% 116.26/18.03 | | | (37) $false
% 116.26/18.03 | | |
% 116.26/18.03 | | | CLOSE: (37) is inconsistent.
% 116.26/18.03 | | |
% 116.26/18.03 | | Case 2:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (38) all_58_5 = e2 | all_58_10 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | BETA: splitting (38) gives:
% 116.26/18.03 | | |
% 116.26/18.03 | | | Case 1:
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | (39) all_58_5 = e2
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | COMBINE_EQS: (16), (39) imply:
% 116.26/18.03 | | | | (40) all_52_9 = e2
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | COMBINE_EQS: (28), (40) imply:
% 116.26/18.03 | | | | (41) all_56_4 = e2
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 116.26/18.03 | | | | (14), (15), (17), (18), (20), (21), (24), (26), (27), (29),
% 116.26/18.03 | | | | (41) are inconsistent by sub-proof #190.
% 116.26/18.03 | | | |
% 116.26/18.03 | | | Case 2:
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | (42) all_58_10 = e2
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | COMBINE_EQS: (23), (42) imply:
% 116.26/18.03 | | | | (43) all_52_13 = e2
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | REDUCE: (22), (43) imply:
% 116.26/18.03 | | | | (44) $false
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | CLOSE: (44) is inconsistent.
% 116.26/18.03 | | | |
% 116.26/18.03 | | | End of split
% 116.26/18.03 | | |
% 116.26/18.03 | | End of split
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #190 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.03 (2) all_54_0 = all_10_2
% 116.26/18.03 (3) all_54_3 = all_52_12
% 116.26/18.03 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.03 (5) ~ (all_52_12 = all_10_2)
% 116.26/18.03 (6) all_56_12 = all_10_2
% 116.26/18.03 (7) op(all_10_1, all_10_2) = e1
% 116.26/18.03 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.03 (9) ~ (all_10_2 = e2)
% 116.26/18.03 (10) op(e3, e0) = all_52_12
% 116.26/18.03 (11) all_56_2 = all_52_12
% 116.26/18.03 (12) all_16_1 = all_10_1
% 116.26/18.03 (13) op(e1, e0) = all_52_14
% 116.26/18.03 (14) all_56_4 = e2
% 116.26/18.03 (15) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.03 (16) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.03 (17) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/18.03 (18) ~ (all_10_2 = e3)
% 116.26/18.03 (19) op(e3, all_10_2) = all_10_1
% 116.26/18.03 (20) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 (21) all_16_2 = all_10_2
% 116.26/18.03 (22) all_56_8 = all_52_14
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (17) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (23) ~ (all_56_4 = e2)
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (14), (23) imply:
% 116.26/18.03 | | (24) $false
% 116.26/18.03 | |
% 116.26/18.03 | | CLOSE: (24) is inconsistent.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (25) ~ (all_56_12 = e1)
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (6), (25) imply:
% 116.26/18.03 | | (26) ~ (all_10_2 = e1)
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 116.26/18.03 | | (13), (15), (16), (18), (19), (20), (21), (22), (26) are
% 116.26/18.03 | | inconsistent by sub-proof #193.
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #191 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.03 (2) ~ (all_52_2 = all_10_2)
% 116.26/18.03 (3) all_58_7 = all_52_6
% 116.26/18.03 (4) ~ (all_4_2 = e0)
% 116.26/18.03 (5) all_56_14 = all_6_2
% 116.26/18.03 (6) all_54_0 = all_10_2
% 116.26/18.03 (7) all_54_3 = all_52_12
% 116.26/18.03 (8) all_56_11 = all_52_11
% 116.26/18.03 (9) ~ (all_56_7 = e1)
% 116.26/18.03 (10) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/18.03 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.03 (12) ~ (all_52_12 = all_10_2)
% 116.26/18.03 (13) ~ (e3 = e1)
% 116.26/18.03 (14) all_56_12 = all_10_2
% 116.26/18.03 (15) op(all_10_1, all_10_2) = e1
% 116.26/18.03 (16) all_56_10 = all_52_7
% 116.26/18.03 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.03 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.03 (19) ~ (all_10_2 = e2)
% 116.26/18.03 (20) all_54_10 = all_6_2
% 116.26/18.03 (21) op(e3, e0) = all_52_12
% 116.26/18.03 (22) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/18.03 (23) all_56_2 = all_52_12
% 116.26/18.03 (24) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/18.03 (25) all_58_11 = all_52_14
% 116.26/18.03 (26) all_16_1 = all_10_1
% 116.26/18.03 (27) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/18.03 (28) ~ (all_4_2 = e3)
% 116.26/18.03 (29) op(e1, e0) = all_52_14
% 116.26/18.03 (30) all_56_9 = all_52_3
% 116.26/18.03 (31) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.03 (32) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.03 (33) all_58_15 = all_4_2
% 116.26/18.03 (34) ~ (all_10_2 = e3)
% 116.26/18.03 (35) all_58_13 = all_52_7
% 116.26/18.03 (36) ~ (all_52_14 = all_4_2)
% 116.26/18.03 (37) all_58_6 = all_52_2
% 116.26/18.03 (38) all_56_15 = all_4_2
% 116.26/18.03 (39) op(e3, all_10_2) = all_10_1
% 116.26/18.03 (40) all_58_14 = all_52_11
% 116.26/18.03 (41) ~ (all_6_2 = e2)
% 116.26/18.03 (42) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.03 (43) all_56_7 = all_52_6
% 116.26/18.03 (44) all_58_8 = all_6_2
% 116.26/18.03 (45) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 (46) all_16_2 = all_10_2
% 116.26/18.03 (47) all_56_6 = all_52_2
% 116.26/18.03 (48) all_58_12 = all_52_3
% 116.26/18.03 (49) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.26/18.03 (50) all_56_8 = all_52_14
% 116.26/18.03 (51) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/18.03 (52) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/18.03 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/18.03 (53) all_54_15 = all_4_2
% 116.26/18.03 (54) ~ (all_6_2 = e1)
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | REDUCE: (9), (43) imply:
% 116.26/18.03 | (55) ~ (all_52_6 = e1)
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (17) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (56) all_54_10 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | COMBINE_EQS: (20), (56) imply:
% 116.26/18.03 | | (57) all_6_2 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | SIMP: (57) implies:
% 116.26/18.03 | | (58) all_6_2 = e3
% 116.26/18.03 | |
% 116.26/18.03 | | REF_CLOSE: (3), (4), (5), (6), (8), (13), (14), (16), (19), (22), (24),
% 116.26/18.03 | | (25), (27), (28), (30), (32), (33), (34), (35), (36), (37), (38),
% 116.26/18.03 | | (40), (42), (44), (45), (47), (48), (49), (50), (51), (52), (53),
% 116.26/18.03 | | (55), (58) are inconsistent by sub-proof #357.
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (59) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.03 | |
% 116.26/18.03 | | BETA: splitting (59) gives:
% 116.26/18.03 | |
% 116.26/18.03 | | Case 1:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (60) all_54_10 = e2
% 116.26/18.03 | | |
% 116.26/18.03 | | | REF_CLOSE: (20), (41), (60) are inconsistent by sub-proof #438.
% 116.26/18.03 | | |
% 116.26/18.03 | | Case 2:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (61) all_54_10 = e1 | all_54_10 = e0
% 116.26/18.03 | | |
% 116.26/18.03 | | | BETA: splitting (61) gives:
% 116.26/18.03 | | |
% 116.26/18.03 | | | Case 1:
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | (62) all_54_10 = e1
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | REF_CLOSE: (20), (54), (62) are inconsistent by sub-proof #437.
% 116.26/18.03 | | | |
% 116.26/18.03 | | | Case 2:
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | (63) all_54_10 = e0
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | COMBINE_EQS: (20), (63) imply:
% 116.26/18.03 | | | | (64) all_6_2 = e0
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | SIMP: (64) implies:
% 116.26/18.03 | | | | (65) all_6_2 = e0
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | COMBINE_EQS: (5), (65) imply:
% 116.26/18.03 | | | | (66) all_56_14 = e0
% 116.26/18.03 | | | |
% 116.26/18.03 | | | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (11), (12), (14), (15), (18),
% 116.26/18.03 | | | | (19), (21), (23), (25), (26), (29), (31), (32), (34), (37),
% 116.26/18.03 | | | | (39), (42), (44), (45), (46), (50), (54), (55), (66) are
% 116.26/18.03 | | | | inconsistent by sub-proof #192.
% 116.26/18.03 | | | |
% 116.26/18.03 | | | End of split
% 116.26/18.03 | | |
% 116.26/18.03 | | End of split
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #192 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.03 (2) ~ (all_52_2 = all_10_2)
% 116.26/18.03 (3) all_58_7 = all_52_6
% 116.26/18.03 (4) all_54_0 = all_10_2
% 116.26/18.03 (5) all_54_3 = all_52_12
% 116.26/18.03 (6) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/18.03 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.03 (8) ~ (all_52_12 = all_10_2)
% 116.26/18.03 (9) all_56_12 = all_10_2
% 116.26/18.03 (10) op(all_10_1, all_10_2) = e1
% 116.26/18.03 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.03 (12) ~ (all_10_2 = e2)
% 116.26/18.03 (13) op(e3, e0) = all_52_12
% 116.26/18.03 (14) all_56_2 = all_52_12
% 116.26/18.03 (15) all_58_11 = all_52_14
% 116.26/18.03 (16) all_16_1 = all_10_1
% 116.26/18.03 (17) op(e1, e0) = all_52_14
% 116.26/18.03 (18) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.03 (19) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.03 (20) ~ (all_10_2 = e3)
% 116.26/18.03 (21) all_58_6 = all_52_2
% 116.26/18.03 (22) op(e3, all_10_2) = all_10_1
% 116.26/18.03 (23) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.03 (24) all_58_8 = all_6_2
% 116.26/18.03 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.03 (26) all_16_2 = all_10_2
% 116.26/18.03 (27) all_56_8 = all_52_14
% 116.26/18.03 (28) ~ (all_52_6 = e1)
% 116.26/18.03 (29) ~ (all_6_2 = e1)
% 116.26/18.03 (30) all_56_14 = e0
% 116.26/18.03
% 116.26/18.03 Begin of proof
% 116.26/18.03 |
% 116.26/18.03 | BETA: splitting (6) gives:
% 116.26/18.03 |
% 116.26/18.03 | Case 1:
% 116.26/18.03 | |
% 116.26/18.03 | | (31) ~ (all_56_8 = e1)
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (27), (31) imply:
% 116.26/18.03 | | (32) ~ (all_52_14 = e1)
% 116.26/18.03 | |
% 116.26/18.03 | | BETA: splitting (23) gives:
% 116.26/18.03 | |
% 116.26/18.03 | | Case 1:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (33) all_58_6 = e1
% 116.26/18.03 | | |
% 116.26/18.03 | | | COMBINE_EQS: (21), (33) imply:
% 116.26/18.03 | | | (34) all_52_2 = e1
% 116.26/18.03 | | |
% 116.26/18.03 | | | SIMP: (34) implies:
% 116.26/18.03 | | | (35) all_52_2 = e1
% 116.26/18.03 | | |
% 116.26/18.03 | | | REDUCE: (2), (35) imply:
% 116.26/18.03 | | | (36) ~ (all_10_2 = e1)
% 116.26/18.03 | | |
% 116.26/18.03 | | | SIMP: (36) implies:
% 116.26/18.03 | | | (37) ~ (all_10_2 = e1)
% 116.26/18.03 | | |
% 116.26/18.03 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 116.26/18.03 | | | (16), (17), (18), (19), (20), (22), (25), (26), (27), (37) are
% 116.26/18.03 | | | inconsistent by sub-proof #193.
% 116.26/18.03 | | |
% 116.26/18.03 | | Case 2:
% 116.26/18.03 | | |
% 116.26/18.03 | | | (38) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.03 | | |
% 116.26/18.03 | | | REF_CLOSE: (3), (15), (24), (28), (29), (32), (38) are inconsistent by
% 116.26/18.03 | | | sub-proof #354.
% 116.26/18.03 | | |
% 116.26/18.03 | | End of split
% 116.26/18.03 | |
% 116.26/18.03 | Case 2:
% 116.26/18.03 | |
% 116.26/18.03 | | (39) ~ (all_56_14 = e0)
% 116.26/18.03 | |
% 116.26/18.03 | | REDUCE: (30), (39) imply:
% 116.26/18.03 | | (40) $false
% 116.26/18.03 | |
% 116.26/18.03 | | CLOSE: (40) is inconsistent.
% 116.26/18.03 | |
% 116.26/18.03 | End of split
% 116.26/18.03 |
% 116.26/18.03 End of proof
% 116.26/18.03
% 116.26/18.03 Sub-proof #193 shows that the following formulas are inconsistent:
% 116.26/18.03 ----------------------------------------------------------------
% 116.26/18.03 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.26/18.04 (2) all_54_0 = all_10_2
% 116.26/18.04 (3) all_54_3 = all_52_12
% 116.26/18.04 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.04 (5) ~ (all_52_12 = all_10_2)
% 116.26/18.04 (6) all_56_12 = all_10_2
% 116.26/18.04 (7) op(all_10_1, all_10_2) = e1
% 116.26/18.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.04 (9) ~ (all_10_2 = e2)
% 116.26/18.04 (10) op(e3, e0) = all_52_12
% 116.26/18.04 (11) all_56_2 = all_52_12
% 116.26/18.04 (12) all_16_1 = all_10_1
% 116.26/18.04 (13) ~ (all_10_2 = e1)
% 116.26/18.04 (14) op(e1, e0) = all_52_14
% 116.26/18.04 (15) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.04 (16) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.04 (17) ~ (all_10_2 = e3)
% 116.26/18.04 (18) op(e3, all_10_2) = all_10_1
% 116.26/18.04 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.04 (20) all_16_2 = all_10_2
% 116.26/18.04 (21) all_56_8 = all_52_14
% 116.26/18.04
% 116.26/18.04 Begin of proof
% 116.26/18.04 |
% 116.26/18.04 | BETA: splitting (19) gives:
% 116.26/18.04 |
% 116.26/18.04 | Case 1:
% 116.26/18.04 | |
% 116.26/18.04 | | (22) all_54_0 = e3
% 116.26/18.04 | |
% 116.26/18.04 | | REF_CLOSE: (2), (17), (22) are inconsistent by sub-proof #451.
% 116.26/18.04 | |
% 116.26/18.04 | Case 2:
% 116.26/18.04 | |
% 116.26/18.04 | | (23) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.04 | |
% 116.26/18.04 | | BETA: splitting (23) gives:
% 116.26/18.04 | |
% 116.26/18.04 | | Case 1:
% 116.26/18.04 | | |
% 116.26/18.04 | | | (24) all_54_0 = e2
% 116.26/18.04 | | |
% 116.26/18.04 | | | REF_CLOSE: (2), (9), (24) are inconsistent by sub-proof #450.
% 116.26/18.04 | | |
% 116.26/18.04 | | Case 2:
% 116.26/18.04 | | |
% 116.26/18.04 | | | (25) ~ (all_54_0 = e2)
% 116.26/18.04 | | | (26) all_54_0 = e1 | all_54_0 = e0
% 116.26/18.04 | | |
% 116.26/18.04 | | | BETA: splitting (26) gives:
% 116.26/18.04 | | |
% 116.26/18.04 | | | Case 1:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | (27) all_54_0 = e1
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REF_CLOSE: (2), (13), (27) are inconsistent by sub-proof #449.
% 116.26/18.04 | | | |
% 116.26/18.04 | | | Case 2:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | (28) all_54_0 = e0
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | COMBINE_EQS: (2), (28) imply:
% 116.26/18.04 | | | | (29) all_10_2 = e0
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | SIMP: (29) implies:
% 116.26/18.04 | | | | (30) all_10_2 = e0
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | COMBINE_EQS: (20), (30) imply:
% 116.26/18.04 | | | | (31) all_16_2 = e0
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | COMBINE_EQS: (6), (30) imply:
% 116.26/18.04 | | | | (32) all_56_12 = e0
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (5), (30) imply:
% 116.26/18.04 | | | | (33) ~ (all_52_12 = e0)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (7), (30) imply:
% 116.26/18.04 | | | | (34) op(all_10_1, e0) = e1
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (18), (30) imply:
% 116.26/18.04 | | | | (35) op(e3, e0) = all_10_1
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | BETA: splitting (15) gives:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | Case 1:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (36) ~ (all_16_1 = e2)
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REDUCE: (12), (36) imply:
% 116.26/18.04 | | | | | (37) ~ (all_10_1 = e2)
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | BETA: splitting (1) gives:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | Case 1:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | (38) ~ (all_56_2 = e3)
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | REDUCE: (11), (38) imply:
% 116.26/18.04 | | | | | | (39) ~ (all_52_12 = e3)
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | GROUND_INST: instantiating (8) with all_52_12, all_10_1, e0, e3,
% 116.26/18.04 | | | | | | simplifying with (10), (35) gives:
% 116.26/18.04 | | | | | | (40) all_52_12 = all_10_1
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | COMBINE_EQS: (3), (40) imply:
% 116.26/18.04 | | | | | | (41) all_54_3 = all_10_1
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | REDUCE: (39), (40) imply:
% 116.26/18.04 | | | | | | (42) ~ (all_10_1 = e3)
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | REDUCE: (33), (40) imply:
% 116.26/18.04 | | | | | | (43) ~ (all_10_1 = e0)
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | BETA: splitting (4) gives:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | Case 1:
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | (44) all_54_3 = e3
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | REF_CLOSE: (41), (42), (44) are inconsistent by sub-proof #215.
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | Case 2:
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | (45) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | BETA: splitting (45) gives:
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | Case 1:
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | | (46) all_54_3 = e2
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | | REF_CLOSE: (37), (41), (46) are inconsistent by sub-proof #214.
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | Case 2:
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | | (47) all_54_3 = e1 | all_54_3 = e0
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | | BETA: splitting (47) gives:
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | | Case 1:
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | (48) all_54_3 = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | COMBINE_EQS: (41), (48) imply:
% 116.26/18.04 | | | | | | | | | (49) all_10_1 = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | SIMP: (49) implies:
% 116.26/18.04 | | | | | | | | | (50) all_10_1 = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | REDUCE: (34), (50) imply:
% 116.26/18.04 | | | | | | | | | (51) op(e1, e0) = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | GROUND_INST: instantiating (8) with all_52_14, e1, e0, e1,
% 116.26/18.04 | | | | | | | | | simplifying with (14), (51) gives:
% 116.26/18.04 | | | | | | | | | (52) all_52_14 = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | COMBINE_EQS: (21), (52) imply:
% 116.26/18.04 | | | | | | | | | (53) all_56_8 = e1
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | REF_CLOSE: (2), (6), (9), (13), (16), (23), (53) are
% 116.26/18.04 | | | | | | | | | inconsistent by sub-proof #385.
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | Case 2:
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | (54) all_54_3 = e0
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | | REF_CLOSE: (41), (43), (54) are inconsistent by sub-proof
% 116.26/18.04 | | | | | | | | | #207.
% 116.26/18.04 | | | | | | | | |
% 116.26/18.04 | | | | | | | | End of split
% 116.26/18.04 | | | | | | | |
% 116.26/18.04 | | | | | | | End of split
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | End of split
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | Case 2:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | (55) ~ (all_56_12 = e0)
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | REDUCE: (32), (55) imply:
% 116.26/18.04 | | | | | | (56) $false
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | CLOSE: (56) is inconsistent.
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | End of split
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | Case 2:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (57) ~ (all_16_2 = e0)
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REDUCE: (31), (57) imply:
% 116.26/18.04 | | | | | (58) $false
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | CLOSE: (58) is inconsistent.
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | End of split
% 116.26/18.04 | | | |
% 116.26/18.04 | | | End of split
% 116.26/18.04 | | |
% 116.26/18.04 | | End of split
% 116.26/18.04 | |
% 116.26/18.04 | End of split
% 116.26/18.04 |
% 116.26/18.04 End of proof
% 116.26/18.04
% 116.26/18.04 Sub-proof #194 shows that the following formulas are inconsistent:
% 116.26/18.04 ----------------------------------------------------------------
% 116.26/18.04 (1) ~ (all_52_8 = all_10_2)
% 116.26/18.04 (2) ~ (all_52_6 = all_52_14)
% 116.26/18.04 (3) all_54_2 = all_52_8
% 116.26/18.04 (4) all_58_7 = all_52_6
% 116.26/18.04 (5) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.26/18.04 (6) ~ (all_52_13 = all_52_14)
% 116.26/18.04 (7) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.26/18.04 (8) ~ (all_4_2 = e0)
% 116.26/18.04 (9) op(e3, e2) = all_52_4
% 116.26/18.04 (10) all_56_14 = all_6_2
% 116.26/18.04 (11) all_56_3 = all_52_1
% 116.26/18.04 (12) all_54_0 = all_10_2
% 116.26/18.04 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.26/18.04 (14) all_54_3 = all_52_12
% 116.26/18.04 (15) ~ (all_52_7 = all_4_2)
% 116.26/18.04 (16) all_56_11 = all_52_11
% 116.26/18.04 (17) ~ (all_4_0 = e1)
% 116.26/18.04 (18) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/18.04 (19) ~ (all_6_1 = e3)
% 116.26/18.04 (20) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.26/18.04 (21) ~ (all_52_4 = all_52_8)
% 116.26/18.04 (22) ~ (all_52_12 = all_10_2)
% 116.26/18.04 (23) ~ (e3 = e1)
% 116.26/18.04 (24) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.26/18.04 (25) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.26/18.04 (26) all_56_12 = all_10_2
% 116.26/18.04 (27) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 116.26/18.04 (28) all_58_0 = all_10_2
% 116.26/18.04 (29) all_54_11 = all_52_14
% 116.26/18.04 (30) all_54_13 = all_52_7
% 116.26/18.04 (31) op(all_10_1, all_10_2) = e1
% 116.26/18.04 (32) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.26/18.04 (33) ~ (all_52_14 = all_6_2)
% 116.26/18.04 (34) all_56_10 = all_52_7
% 116.26/18.04 (35) op(all_4_1, all_4_2) = all_4_0
% 116.26/18.04 (36) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.04 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.04 (38) all_54_8 = all_52_2
% 116.26/18.04 (39) ~ (all_52_2 = all_6_2)
% 116.26/18.04 (40) ~ (all_52_1 = all_52_9)
% 116.26/18.04 (41) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.26/18.04 (42) all_54_10 = all_6_2
% 116.26/18.04 (43) op(e3, e0) = all_52_12
% 116.26/18.04 (44) ~ (all_52_8 = all_6_2)
% 116.26/18.04 (45) all_58_4 = all_52_8
% 116.26/18.04 (46) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/18.04 (47) ~ (all_52_4 = all_52_7)
% 116.26/18.04 (48) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.26/18.04 (49) all_58_3 = all_8_2
% 116.26/18.04 (50) all_58_11 = all_52_14
% 116.26/18.04 (51) all_16_1 = all_10_1
% 116.26/18.04 (52) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.26/18.04 (53) op(e2, e3) = all_52_1
% 116.26/18.04 (54) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.26/18.04 (55) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.26/18.04 (56) ~ (all_52_7 = all_8_2)
% 116.26/18.04 (57) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.26/18.04 (58) ~ (all_52_4 = all_8_2)
% 116.26/18.04 (59) op(e1, e0) = all_52_14
% 116.26/18.04 (60) all_58_5 = all_52_9
% 116.26/18.04 (61) ~ (all_4_0 = e3)
% 116.26/18.04 (62) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.04 (63) all_56_9 = all_52_3
% 116.26/18.04 (64) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.26/18.04 (65) op(e1, all_6_2) = all_6_1
% 116.26/18.04 (66) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.26/18.04 (67) all_58_15 = all_4_2
% 116.26/18.04 (68) all_58_2 = all_52_1
% 116.26/18.04 (69) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.26/18.04 (70) op(e0, e3) = all_52_3
% 116.26/18.04 (71) ~ (all_10_2 = e3)
% 116.26/18.04 (72) all_58_13 = all_52_7
% 116.26/18.04 (73) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.26/18.04 (74) ~ (all_52_14 = all_4_2)
% 116.26/18.04 (75) all_58_6 = all_52_2
% 116.26/18.04 (76) ~ (all_52_1 = all_10_2)
% 116.26/18.04 (77) all_54_5 = all_8_2
% 116.26/18.04 (78) all_56_15 = all_4_2
% 116.26/18.04 (79) all_58_10 = all_52_13
% 116.26/18.04 (80) op(e3, all_10_2) = all_10_1
% 116.26/18.04 (81) ~ (all_52_6 = all_8_2)
% 116.26/18.04 (82) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.26/18.04 (83) all_58_1 = all_52_4
% 116.26/18.04 (84) all_58_14 = all_52_11
% 116.26/18.04 (85) all_54_1 = all_52_4
% 116.26/18.04 (86) ~ (all_52_1 = all_8_2)
% 116.26/18.04 (87) ~ (all_8_2 = e2)
% 116.26/18.04 (88) ~ (all_6_2 = e2)
% 116.26/18.04 (89) op(e1, e2) = all_52_6
% 116.26/18.04 (90) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.26/18.04 (91) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.04 (92) all_56_7 = all_52_6
% 116.26/18.04 (93) ~ (all_52_9 = all_6_2)
% 116.26/18.04 (94) ~ (all_52_4 = all_52_6)
% 116.26/18.04 (95) ~ (all_52_4 = all_52_12)
% 116.26/18.04 (96) op(e0, all_4_2) = all_4_1
% 116.26/18.04 (97) all_58_8 = all_6_2
% 116.26/18.04 (98) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.04 (99) all_16_2 = all_10_2
% 116.26/18.04 (100) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.26/18.04 (101) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/18.04 (102) all_56_4 = all_52_9
% 116.26/18.04 (103) all_58_9 = all_52_12
% 116.26/18.04 (104) all_56_5 = all_52_13
% 116.26/18.04 (105) ~ (all_52_3 = all_4_2)
% 116.26/18.04 (106) ~ (all_52_6 = all_6_2)
% 116.26/18.04 (107) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.26/18.04 (108) all_56_6 = all_52_2
% 116.26/18.04 (109) all_58_12 = all_52_3
% 116.26/18.04 (110) ~ (all_52_2 = all_52_14)
% 116.26/18.04 (111) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.26/18.04 (112) ~ (all_52_8 = all_52_9)
% 116.26/18.04 (113) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.26/18.04 (114) ~ (all_52_12 = all_4_2)
% 116.26/18.04 (115) ~ (all_52_3 = all_10_2)
% 116.26/18.04 (116) all_24_1 = all_10_1
% 116.26/18.04 (117) op(e1, e3) = all_52_2
% 116.26/18.04 (118) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.26/18.04 (119) all_24_2 = all_10_2
% 116.26/18.04 (120) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.26/18.04 (121) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/18.04 (122) ~ (all_52_8 = all_52_12)
% 116.26/18.04 (123) all_56_8 = all_52_14
% 116.26/18.04 (124) ~ (all_52_4 = all_10_2)
% 116.26/18.04 (125) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.26/18.04 (126) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.26/18.04 (127) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.04 (128) all_56_0 = all_52_4
% 116.26/18.04 (129) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.26/18.04 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.26/18.04 (130) all_54_4 = all_52_1
% 116.26/18.04 (131) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/18.04 (132) all_54_15 = all_4_2
% 116.26/18.04 (133) ~ (all_6_2 = e1)
% 116.26/18.04 (134) ~ (all_6_1 = e2)
% 116.26/18.04 (135) ~ (all_52_6 = all_52_7)
% 116.26/18.04 (136) all_54_12 = all_52_3
% 116.26/18.04
% 116.26/18.04 Begin of proof
% 116.26/18.04 |
% 116.26/18.04 | BETA: splitting (73) gives:
% 116.26/18.04 |
% 116.26/18.04 | Case 1:
% 116.26/18.04 | |
% 116.26/18.04 | | (137) ~ (all_56_12 = e2)
% 116.26/18.04 | |
% 116.26/18.04 | | REDUCE: (26), (137) imply:
% 116.26/18.04 | | (138) ~ (all_10_2 = e2)
% 116.26/18.04 | |
% 116.26/18.04 | | BETA: splitting (100) gives:
% 116.26/18.04 | |
% 116.26/18.04 | | Case 1:
% 116.26/18.04 | | |
% 116.26/18.04 | | | (139) ~ (all_56_15 = e3)
% 116.26/18.04 | | |
% 116.26/18.04 | | | REDUCE: (78), (139) imply:
% 116.26/18.04 | | | (140) ~ (all_4_2 = e3)
% 116.26/18.04 | | |
% 116.26/18.04 | | | BETA: splitting (27) gives:
% 116.26/18.04 | | |
% 116.26/18.04 | | | Case 1:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | (141) ~ (all_56_7 = e1)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (92), (141) imply:
% 116.26/18.04 | | | | (142) ~ (all_52_6 = e1)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | BETA: splitting (52) gives:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | Case 1:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (143) ~ (all_56_14 = e3)
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REDUCE: (10), (143) imply:
% 116.26/18.04 | | | | | (144) ~ (all_6_2 = e3)
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REF_CLOSE: (10), (18), (19), (28), (29), (33), (36), (37), (42), (59),
% 116.26/18.04 | | | | | (65), (71), (88), (101), (121), (123), (133), (134), (144)
% 116.26/18.04 | | | | | are inconsistent by sub-proof #413.
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | Case 2:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (145) all_56_14 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | COMBINE_EQS: (10), (145) imply:
% 116.26/18.04 | | | | | (146) all_6_2 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | SIMP: (146) implies:
% 116.26/18.04 | | | | | (147) all_6_2 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | COMBINE_EQS: (97), (147) imply:
% 116.26/18.04 | | | | | (148) all_58_8 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REF_CLOSE: (4), (8), (12), (16), (23), (26), (34), (46), (48), (50),
% 116.26/18.04 | | | | | (52), (63), (66), (67), (71), (72), (74), (75), (78), (84),
% 116.26/18.04 | | | | | (90), (98), (108), (109), (118), (123), (126), (129),
% 116.26/18.04 | | | | | (132), (138), (140), (142), (145), (148) are inconsistent
% 116.26/18.04 | | | | | by sub-proof #358.
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | End of split
% 116.26/18.04 | | | |
% 116.26/18.04 | | | Case 2:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | (149) all_56_7 = e1
% 116.26/18.04 | | | | (150) ~ (all_56_15 = e2)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | COMBINE_EQS: (92), (149) imply:
% 116.26/18.04 | | | | (151) all_52_6 = e1
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (78), (150) imply:
% 116.26/18.04 | | | | (152) ~ (all_4_2 = e2)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (2), (151) imply:
% 116.26/18.04 | | | | (153) ~ (all_52_14 = e1)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | SIMP: (153) implies:
% 116.26/18.04 | | | | (154) ~ (all_52_14 = e1)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | REDUCE: (106), (151) imply:
% 116.26/18.04 | | | | (155) ~ (all_6_2 = e1)
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | BETA: splitting (46) gives:
% 116.26/18.04 | | | |
% 116.26/18.04 | | | | Case 1:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (156) all_54_15 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | COMBINE_EQS: (132), (156) imply:
% 116.26/18.04 | | | | | (157) all_4_2 = e3
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | REDUCE: (140), (157) imply:
% 116.26/18.04 | | | | | (158) $false
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | CLOSE: (158) is inconsistent.
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | Case 2:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | (159) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | BETA: splitting (159) gives:
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | | Case 1:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | (160) all_54_15 = e2
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | COMBINE_EQS: (132), (160) imply:
% 116.26/18.04 | | | | | | (161) all_4_2 = e2
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | REDUCE: (152), (161) imply:
% 116.26/18.04 | | | | | | (162) $false
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | CLOSE: (162) is inconsistent.
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | Case 2:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | (163) all_54_15 = e1 | all_54_15 = e0
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | BETA: splitting (163) gives:
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | | Case 1:
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | (164) all_54_15 = e1
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | COMBINE_EQS: (132), (164) imply:
% 116.26/18.04 | | | | | | | (165) all_4_2 = e1
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | COMBINE_EQS: (78), (165) imply:
% 116.26/18.04 | | | | | | | (166) all_56_15 = e1
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | REF_CLOSE: (6), (10), (11), (18), (19), (28), (29), (33), (36),
% 116.26/18.04 | | | | | | | (37), (38), (39), (42), (48), (49), (55), (57), (59),
% 116.26/18.04 | | | | | | | (60), (65), (68), (71), (79), (82), (87), (88), (101),
% 116.26/18.04 | | | | | | | (102), (104), (108), (110), (111), (117), (121), (123),
% 116.26/18.04 | | | | | | | (127), (133), (134), (154), (166) are inconsistent by
% 116.26/18.04 | | | | | | | sub-proof #393.
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | Case 2:
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | (167) all_54_15 = e0
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | COMBINE_EQS: (132), (167) imply:
% 116.26/18.04 | | | | | | | (168) all_4_2 = e0
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | REDUCE: (8), (168) imply:
% 116.26/18.04 | | | | | | | (169) $false
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | | CLOSE: (169) is inconsistent.
% 116.26/18.04 | | | | | | |
% 116.26/18.04 | | | | | | End of split
% 116.26/18.04 | | | | | |
% 116.26/18.04 | | | | | End of split
% 116.26/18.04 | | | | |
% 116.26/18.04 | | | | End of split
% 116.26/18.04 | | | |
% 116.26/18.04 | | | End of split
% 116.26/18.04 | | |
% 116.26/18.04 | | Case 2:
% 116.26/18.04 | | |
% 116.26/18.04 | | | (170) all_56_15 = e3
% 116.26/18.04 | | | (171) ~ (all_56_9 = e0)
% 116.26/18.04 | | |
% 116.26/18.04 | | | COMBINE_EQS: (78), (170) imply:
% 116.26/18.05 | | | (172) all_4_2 = e3
% 116.26/18.05 | | |
% 116.26/18.05 | | | SIMP: (172) implies:
% 116.26/18.05 | | | (173) all_4_2 = e3
% 116.26/18.05 | | |
% 116.26/18.05 | | | COMBINE_EQS: (67), (173) imply:
% 116.26/18.05 | | | (174) all_58_15 = e3
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (63), (171) imply:
% 116.26/18.05 | | | (175) ~ (all_52_3 = e0)
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (105), (173) imply:
% 116.26/18.05 | | | (176) ~ (all_52_3 = e3)
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (15), (173) imply:
% 116.26/18.05 | | | (177) ~ (all_52_7 = e3)
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (114), (173) imply:
% 116.26/18.05 | | | (178) ~ (all_52_12 = e3)
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (35), (173) imply:
% 116.26/18.05 | | | (179) op(all_4_1, e3) = all_4_0
% 116.26/18.05 | | |
% 116.26/18.05 | | | REDUCE: (96), (173) imply:
% 116.26/18.05 | | | (180) op(e0, e3) = all_4_1
% 116.26/18.05 | | |
% 116.26/18.05 | | | BETA: splitting (5) gives:
% 116.26/18.05 | | |
% 116.26/18.05 | | | Case 1:
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | (181) ~ (all_56_6 = e1)
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | REDUCE: (108), (181) imply:
% 116.26/18.05 | | | | (182) ~ (all_52_2 = e1)
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | BETA: splitting (41) gives:
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | Case 1:
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | (183) ~ (all_56_3 = e2)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | REDUCE: (11), (183) imply:
% 116.26/18.05 | | | | | (184) ~ (all_52_1 = e2)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | GROUND_INST: instantiating (37) with all_52_3, all_4_1, e3, e0,
% 116.26/18.05 | | | | | simplifying with (70), (180) gives:
% 116.26/18.05 | | | | | (185) all_52_3 = all_4_1
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | COMBINE_EQS: (136), (185) imply:
% 116.26/18.05 | | | | | (186) all_54_12 = all_4_1
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | COMBINE_EQS: (109), (185) imply:
% 116.26/18.05 | | | | | (187) all_58_12 = all_4_1
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | REDUCE: (115), (185) imply:
% 116.26/18.05 | | | | | (188) ~ (all_10_2 = all_4_1)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | SIMP: (188) implies:
% 116.26/18.05 | | | | | (189) ~ (all_10_2 = all_4_1)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | REDUCE: (176), (185) imply:
% 116.26/18.05 | | | | | (190) ~ (all_4_1 = e3)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | REDUCE: (175), (185) imply:
% 116.26/18.05 | | | | | (191) ~ (all_4_1 = e0)
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | BETA: splitting (120) gives:
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | Case 1:
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | (192) ~ (all_56_5 = e2)
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | REDUCE: (104), (192) imply:
% 116.26/18.05 | | | | | | (193) ~ (all_52_13 = e2)
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | BETA: splitting (127) gives:
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | Case 1:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | (194) all_58_2 = e2
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | REF_CLOSE: (68), (184), (194) are inconsistent by sub-proof #335.
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | Case 2:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | (195) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | BETA: splitting (195) gives:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | (196) all_58_3 = e2
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | COMBINE_EQS: (49), (196) imply:
% 116.26/18.05 | | | | | | | | (197) all_8_2 = e2
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | REDUCE: (87), (197) imply:
% 116.26/18.05 | | | | | | | | (198) $false
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | CLOSE: (198) is inconsistent.
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | (199) all_58_5 = e2 | all_58_10 = e2
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | BETA: splitting (199) gives:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | (200) all_58_5 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | COMBINE_EQS: (60), (200) imply:
% 116.26/18.05 | | | | | | | | | (201) all_52_9 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | SIMP: (201) implies:
% 116.26/18.05 | | | | | | | | | (202) all_52_9 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | COMBINE_EQS: (102), (202) imply:
% 116.26/18.05 | | | | | | | | | (203) all_56_4 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REDUCE: (112), (202) imply:
% 116.26/18.05 | | | | | | | | | (204) ~ (all_52_8 = e2)
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REDUCE: (93), (202) imply:
% 116.26/18.05 | | | | | | | | | (205) ~ (all_6_2 = e2)
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | BETA: splitting (69) gives:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | (206) ~ (all_56_4 = e2)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REDUCE: (203), (206) imply:
% 116.26/18.05 | | | | | | | | | | (207) $false
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | CLOSE: (207) is inconsistent.
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | (208) ~ (all_56_12 = e1)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REDUCE: (26), (208) imply:
% 116.26/18.05 | | | | | | | | | | (209) ~ (all_10_2 = e1)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (10), (12), (13), (14), (17),
% 116.26/18.05 | | | | | | | | | | (18), (19), (20), (21), (22), (24), (25), (26),
% 116.26/18.05 | | | | | | | | | | (28), (29), (30), (32), (33), (36), (37), (42),
% 116.26/18.05 | | | | | | | | | | (43), (44), (45), (47), (50), (51), (53), (56),
% 116.26/18.05 | | | | | | | | | | (58), (59), (64), (65), (66), (68), (71), (73),
% 116.26/18.05 | | | | | | | | | | (75), (76), (77), (80), (81), (83), (85), (86),
% 116.26/18.05 | | | | | | | | | | (88), (90), (91), (95), (97), (98), (99), (101),
% 116.26/18.05 | | | | | | | | | | (103), (107), (121), (122), (123), (124), (125),
% 116.26/18.05 | | | | | | | | | | (128), (130), (131), (133), (134), (135), (177),
% 116.26/18.05 | | | | | | | | | | (178), (179), (182), (184), (187), (190), (204),
% 116.26/18.05 | | | | | | | | | | (209) are inconsistent by sub-proof #203.
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | End of split
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | (210) all_58_10 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | COMBINE_EQS: (79), (210) imply:
% 116.26/18.05 | | | | | | | | | (211) all_52_13 = e2
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REDUCE: (193), (211) imply:
% 116.26/18.05 | | | | | | | | | (212) $false
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | CLOSE: (212) is inconsistent.
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | End of split
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | End of split
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | End of split
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | Case 2:
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | (213) all_56_5 = e2
% 116.26/18.05 | | | | | | (214) ~ (all_56_12 = e0)
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | COMBINE_EQS: (104), (213) imply:
% 116.26/18.05 | | | | | | (215) all_52_13 = e2
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | COMBINE_EQS: (79), (215) imply:
% 116.26/18.05 | | | | | | (216) all_58_10 = e2
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | REDUCE: (26), (214) imply:
% 116.26/18.05 | | | | | | (217) ~ (all_10_2 = e0)
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | BETA: splitting (98) gives:
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | | Case 1:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | (218) all_54_0 = e3
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | REF_CLOSE: (12), (71), (218) are inconsistent by sub-proof #451.
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | Case 2:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | (219) ~ (all_54_0 = e3)
% 116.26/18.05 | | | | | | | (220) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | BETA: splitting (220) gives:
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | (221) all_54_0 = e2
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | REF_CLOSE: (1), (10), (12), (18), (19), (26), (28), (29), (33),
% 116.26/18.05 | | | | | | | | (36), (37), (42), (44), (45), (59), (65), (71), (83),
% 116.26/18.05 | | | | | | | | (88), (101), (103), (121), (123), (128), (131),
% 116.26/18.05 | | | | | | | | (133), (134), (178), (221) are inconsistent by
% 116.26/18.05 | | | | | | | | sub-proof #202.
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | (222) all_54_0 = e1 | all_54_0 = e0
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | BETA: splitting (36) gives:
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | (223) all_54_10 = e3
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | COMBINE_EQS: (42), (223) imply:
% 116.26/18.05 | | | | | | | | | (224) all_6_2 = e3
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REDUCE: (39), (224) imply:
% 116.26/18.05 | | | | | | | | | (225) ~ (all_52_2 = e3)
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REDUCE: (33), (224) imply:
% 116.26/18.05 | | | | | | | | | (226) ~ (all_52_14 = e3)
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | BETA: splitting (222) gives:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | (227) all_54_0 = e1
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | COMBINE_EQS: (12), (227) imply:
% 116.26/18.05 | | | | | | | | | | (228) all_10_2 = e1
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | SIMP: (228) implies:
% 116.26/18.05 | | | | | | | | | | (229) all_10_2 = e1
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | COMBINE_EQS: (28), (229) imply:
% 116.26/18.05 | | | | | | | | | | (230) all_58_0 = e1
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REDUCE: (189), (229) imply:
% 116.26/18.05 | | | | | | | | | | (231) ~ (all_4_1 = e1)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | SIMP: (231) implies:
% 116.26/18.05 | | | | | | | | | | (232) ~ (all_4_1 = e1)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REDUCE: (71), (229) imply:
% 116.26/18.05 | | | | | | | | | | (233) ~ (e3 = e1)
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | BETA: splitting (113) gives:
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | (234) all_54_12 = e3
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | REF_CLOSE: (186), (190), (234) are inconsistent by sub-proof
% 116.26/18.05 | | | | | | | | | | | #239.
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | (235) ~ (all_54_12 = e3)
% 116.26/18.05 | | | | | | | | | | | (236) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | BETA: splitting (236) gives:
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | (237) all_54_12 = e2
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | COMBINE_EQS: (186), (237) imply:
% 116.26/18.05 | | | | | | | | | | | | (238) all_4_1 = e2
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | SIMP: (238) implies:
% 116.26/18.05 | | | | | | | | | | | | (239) all_4_1 = e2
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | REDUCE: (190), (239) imply:
% 116.26/18.05 | | | | | | | | | | | | (240) ~ (e3 = e2)
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | SIMP: (240) implies:
% 116.26/18.05 | | | | | | | | | | | | (241) ~ (e3 = e2)
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | REDUCE: (179), (239) imply:
% 116.26/18.05 | | | | | | | | | | | | (242) op(e2, e3) = all_4_0
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | BETA: splitting (24) gives:
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | Case 1:
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | | (243) all_58_0 = e3
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | | REF_CLOSE: (23), (50), (54), (103), (174), (178), (216),
% 116.26/18.05 | | | | | | | | | | | | | (226), (230), (241), (243) are inconsistent by
% 116.26/18.05 | | | | | | | | | | | | | sub-proof #200.
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | | (244) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | | REF_CLOSE: (37), (53), (61), (68), (75), (187), (190), (225),
% 116.26/18.05 | | | | | | | | | | | | | (242), (244) are inconsistent by sub-proof #317.
% 116.26/18.05 | | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | End of split
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | (245) all_54_12 = e1 | all_54_12 = e0
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | | REF_CLOSE: (186), (191), (232), (245) are inconsistent by
% 116.26/18.05 | | | | | | | | | | | | sub-proof #315.
% 116.26/18.05 | | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | | End of split
% 116.26/18.05 | | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | End of split
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | (246) all_54_0 = e0
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | | REF_CLOSE: (12), (217), (246) are inconsistent by sub-proof
% 116.26/18.05 | | | | | | | | | | #424.
% 116.26/18.05 | | | | | | | | | |
% 116.26/18.05 | | | | | | | | | End of split
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | Case 2:
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | (247) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | | REF_CLOSE: (10), (18), (19), (28), (29), (33), (37), (42),
% 116.26/18.05 | | | | | | | | | (59), (65), (71), (88), (101), (121), (123), (133),
% 116.26/18.05 | | | | | | | | | (134), (247) are inconsistent by sub-proof #414.
% 116.26/18.05 | | | | | | | | |
% 116.26/18.05 | | | | | | | | End of split
% 116.26/18.05 | | | | | | | |
% 116.26/18.05 | | | | | | | End of split
% 116.26/18.05 | | | | | | |
% 116.26/18.05 | | | | | | End of split
% 116.26/18.05 | | | | | |
% 116.26/18.05 | | | | | End of split
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | Case 2:
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | (248) all_56_3 = e2
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | | REF_CLOSE: (10), (18), (19), (28), (29), (33), (36), (37), (42), (59),
% 116.26/18.05 | | | | | (65), (71), (82), (88), (101), (121), (123), (133), (134),
% 116.26/18.05 | | | | | (248) are inconsistent by sub-proof #199.
% 116.26/18.05 | | | | |
% 116.26/18.05 | | | | End of split
% 116.26/18.05 | | | |
% 116.26/18.05 | | | Case 2:
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | (249) all_56_6 = e1
% 116.26/18.05 | | | |
% 116.26/18.05 | | | | REF_CLOSE: (10), (18), (19), (28), (29), (33), (36), (37), (42), (48),
% 116.26/18.05 | | | | (59), (65), (71), (88), (101), (121), (123), (133), (134),
% 116.26/18.05 | | | | (249) are inconsistent by sub-proof #394.
% 116.26/18.05 | | | |
% 116.26/18.05 | | | End of split
% 116.26/18.05 | | |
% 116.26/18.05 | | End of split
% 116.26/18.05 | |
% 116.26/18.05 | Case 2:
% 116.26/18.05 | |
% 116.26/18.05 | | (250) all_56_12 = e2
% 116.26/18.05 | |
% 116.26/18.05 | | REF_CLOSE: (9), (26), (31), (37), (62), (80), (85), (89), (91), (94), (116),
% 116.26/18.05 | | (119), (124), (128), (131), (250) are inconsistent by sub-proof
% 116.26/18.05 | | #195.
% 116.26/18.05 | |
% 116.26/18.05 | End of split
% 116.26/18.05 |
% 116.26/18.05 End of proof
% 116.26/18.05
% 116.26/18.05 Sub-proof #195 shows that the following formulas are inconsistent:
% 116.26/18.05 ----------------------------------------------------------------
% 116.26/18.05 (1) op(e3, e2) = all_52_4
% 116.26/18.05 (2) all_56_12 = all_10_2
% 116.26/18.05 (3) op(all_10_1, all_10_2) = e1
% 116.26/18.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.05 (5) all_56_12 = e2
% 116.26/18.05 (6) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.05 (7) op(e3, all_10_2) = all_10_1
% 116.26/18.05 (8) all_54_1 = all_52_4
% 116.26/18.05 (9) op(e1, e2) = all_52_6
% 116.26/18.05 (10) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.05 (11) ~ (all_52_4 = all_52_6)
% 116.26/18.05 (12) all_24_1 = all_10_1
% 116.26/18.05 (13) all_24_2 = all_10_2
% 116.26/18.05 (14) ~ (all_52_4 = all_10_2)
% 116.26/18.05 (15) all_56_0 = all_52_4
% 116.26/18.05 (16) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/18.05
% 116.26/18.05 Begin of proof
% 116.26/18.05 |
% 116.26/18.05 | COMBINE_EQS: (2), (5) imply:
% 116.26/18.05 | (17) all_10_2 = e2
% 116.26/18.05 |
% 116.26/18.05 | SIMP: (17) implies:
% 116.26/18.05 | (18) all_10_2 = e2
% 116.26/18.05 |
% 116.26/18.05 | COMBINE_EQS: (13), (18) imply:
% 116.26/18.05 | (19) all_24_2 = e2
% 116.26/18.05 |
% 116.26/18.05 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 116.26/18.05 | (15), (16), (18), (19) are inconsistent by sub-proof #196.
% 116.26/18.05 |
% 116.26/18.05 End of proof
% 116.26/18.05
% 116.26/18.05 Sub-proof #196 shows that the following formulas are inconsistent:
% 116.26/18.05 ----------------------------------------------------------------
% 116.26/18.05 (1) op(e3, e2) = all_52_4
% 116.26/18.05 (2) op(all_10_1, all_10_2) = e1
% 116.26/18.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.05 (4) all_10_2 = e2
% 116.26/18.05 (5) all_56_12 = e2
% 116.26/18.05 (6) all_24_2 = e2
% 116.26/18.05 (7) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.05 (8) op(e3, all_10_2) = all_10_1
% 116.26/18.05 (9) all_54_1 = all_52_4
% 116.26/18.05 (10) op(e1, e2) = all_52_6
% 116.26/18.05 (11) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.05 (12) ~ (all_52_4 = all_52_6)
% 116.26/18.05 (13) all_24_1 = all_10_1
% 116.26/18.05 (14) ~ (all_52_4 = all_10_2)
% 116.26/18.05 (15) all_56_0 = all_52_4
% 116.26/18.05 (16) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.26/18.05
% 116.26/18.05 Begin of proof
% 116.26/18.05 |
% 116.26/18.05 | REDUCE: (4), (14) imply:
% 116.26/18.05 | (17) ~ (all_52_4 = e2)
% 116.26/18.05 |
% 116.26/18.05 | REDUCE: (2), (4) imply:
% 116.26/18.05 | (18) op(all_10_1, e2) = e1
% 116.26/18.05 |
% 116.26/18.05 | REDUCE: (4), (8) imply:
% 116.26/18.05 | (19) op(e3, e2) = all_10_1
% 116.26/18.05 |
% 116.26/18.05 | BETA: splitting (16) gives:
% 116.26/18.05 |
% 116.26/18.05 | Case 1:
% 116.26/18.05 | |
% 116.26/18.05 | | (20) ~ (all_56_0 = e3)
% 116.26/18.05 | |
% 116.26/18.05 | | REDUCE: (15), (20) imply:
% 116.26/18.05 | | (21) ~ (all_52_4 = e3)
% 116.26/18.05 | |
% 116.26/18.05 | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (13), (17), (18),
% 116.26/18.05 | | (19), (21) are inconsistent by sub-proof #197.
% 116.26/18.05 | |
% 116.26/18.05 | Case 2:
% 116.26/18.05 | |
% 116.26/18.05 | | (22) ~ (all_56_12 = e2)
% 116.26/18.05 | |
% 116.26/18.05 | | REDUCE: (5), (22) imply:
% 116.26/18.05 | | (23) $false
% 116.26/18.05 | |
% 116.26/18.05 | | CLOSE: (23) is inconsistent.
% 116.26/18.05 | |
% 116.26/18.05 | End of split
% 116.26/18.05 |
% 116.26/18.05 End of proof
% 116.26/18.05
% 116.26/18.05 Sub-proof #197 shows that the following formulas are inconsistent:
% 116.26/18.05 ----------------------------------------------------------------
% 116.26/18.05 (1) op(e3, e2) = all_52_4
% 116.26/18.05 (2) ~ (all_52_4 = e3)
% 116.26/18.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.05 (4) all_24_2 = e2
% 116.26/18.05 (5) ~ (all_24_1 = e0) | ~ (all_24_2 = e2)
% 116.26/18.05 (6) op(all_10_1, e2) = e1
% 116.26/18.06 (7) all_54_1 = all_52_4
% 116.26/18.06 (8) op(e1, e2) = all_52_6
% 116.26/18.06 (9) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.06 (10) ~ (all_52_4 = all_52_6)
% 116.26/18.06 (11) op(e3, e2) = all_10_1
% 116.26/18.06 (12) all_24_1 = all_10_1
% 116.26/18.06 (13) ~ (all_52_4 = e2)
% 116.26/18.06
% 116.26/18.06 Begin of proof
% 116.26/18.06 |
% 116.26/18.06 | BETA: splitting (5) gives:
% 116.26/18.06 |
% 116.26/18.06 | Case 1:
% 116.26/18.06 | |
% 116.26/18.06 | | (14) ~ (all_24_2 = e2)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (4), (14) imply:
% 116.26/18.06 | | (15) $false
% 116.26/18.06 | |
% 116.26/18.06 | | CLOSE: (15) is inconsistent.
% 116.26/18.06 | |
% 116.26/18.06 | Case 2:
% 116.26/18.06 | |
% 116.26/18.06 | | (16) ~ (all_24_1 = e0)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (12), (16) imply:
% 116.26/18.06 | | (17) ~ (all_10_1 = e0)
% 116.26/18.06 | |
% 116.26/18.06 | | GROUND_INST: instantiating (3) with all_52_4, all_10_1, e2, e3, simplifying
% 116.26/18.06 | | with (1), (11) gives:
% 116.26/18.06 | | (18) all_52_4 = all_10_1
% 116.26/18.06 | |
% 116.26/18.06 | | COMBINE_EQS: (7), (18) imply:
% 116.26/18.06 | | (19) all_54_1 = all_10_1
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (10), (18) imply:
% 116.26/18.06 | | (20) ~ (all_52_6 = all_10_1)
% 116.26/18.06 | |
% 116.26/18.06 | | SIMP: (20) implies:
% 116.26/18.06 | | (21) ~ (all_52_6 = all_10_1)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (2), (18) imply:
% 116.26/18.06 | | (22) ~ (all_10_1 = e3)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (13), (18) imply:
% 116.26/18.06 | | (23) ~ (all_10_1 = e2)
% 116.26/18.06 | |
% 116.26/18.06 | | BETA: splitting (9) gives:
% 116.26/18.06 | |
% 116.26/18.06 | | Case 1:
% 116.26/18.06 | | |
% 116.26/18.06 | | | (24) all_54_1 = e3
% 116.26/18.06 | | |
% 116.26/18.06 | | | REF_CLOSE: (19), (22), (24) are inconsistent by sub-proof #443.
% 116.26/18.06 | | |
% 116.26/18.06 | | Case 2:
% 116.26/18.06 | | |
% 116.26/18.06 | | | (25) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.26/18.06 | | |
% 116.26/18.06 | | | BETA: splitting (25) gives:
% 116.26/18.06 | | |
% 116.26/18.06 | | | Case 1:
% 116.26/18.06 | | | |
% 116.26/18.06 | | | | (26) all_54_1 = e2
% 116.26/18.06 | | | |
% 116.26/18.06 | | | | REF_CLOSE: (19), (23), (26) are inconsistent by sub-proof #442.
% 116.26/18.06 | | | |
% 116.26/18.06 | | | Case 2:
% 116.26/18.06 | | | |
% 116.26/18.06 | | | | (27) all_54_1 = e1 | all_54_1 = e0
% 116.26/18.06 | | | |
% 116.26/18.06 | | | | BETA: splitting (27) gives:
% 116.26/18.06 | | | |
% 116.26/18.06 | | | | Case 1:
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | (28) all_54_1 = e1
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | COMBINE_EQS: (19), (28) imply:
% 116.26/18.06 | | | | | (29) all_10_1 = e1
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | SIMP: (29) implies:
% 116.26/18.06 | | | | | (30) all_10_1 = e1
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | REDUCE: (21), (30) imply:
% 116.26/18.06 | | | | | (31) ~ (all_52_6 = e1)
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | REDUCE: (6), (30) imply:
% 116.26/18.06 | | | | | (32) op(e1, e2) = e1
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | GROUND_INST: instantiating (3) with all_52_6, e1, e2, e1, simplifying
% 116.26/18.06 | | | | | with (8), (32) gives:
% 116.26/18.06 | | | | | (33) all_52_6 = e1
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | REDUCE: (31), (33) imply:
% 116.26/18.06 | | | | | (34) $false
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | CLOSE: (34) is inconsistent.
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | Case 2:
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | (35) all_54_1 = e0
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | | REF_CLOSE: (17), (19), (35) are inconsistent by sub-proof #198.
% 116.26/18.06 | | | | |
% 116.26/18.06 | | | | End of split
% 116.26/18.06 | | | |
% 116.26/18.06 | | | End of split
% 116.26/18.06 | | |
% 116.26/18.06 | | End of split
% 116.26/18.06 | |
% 116.26/18.06 | End of split
% 116.26/18.06 |
% 116.26/18.06 End of proof
% 116.26/18.06
% 116.26/18.06 Sub-proof #198 shows that the following formulas are inconsistent:
% 116.26/18.06 ----------------------------------------------------------------
% 116.26/18.06 (1) all_54_1 = all_10_1
% 116.26/18.06 (2) all_54_1 = e0
% 116.26/18.06 (3) ~ (all_10_1 = e0)
% 116.26/18.06
% 116.26/18.06 Begin of proof
% 116.26/18.06 |
% 116.26/18.06 | COMBINE_EQS: (1), (2) imply:
% 116.26/18.06 | (4) all_10_1 = e0
% 116.26/18.06 |
% 116.26/18.06 | SIMP: (4) implies:
% 116.26/18.06 | (5) all_10_1 = e0
% 116.26/18.06 |
% 116.26/18.06 | REDUCE: (3), (5) imply:
% 116.26/18.06 | (6) $false
% 116.26/18.06 |
% 116.26/18.06 | CLOSE: (6) is inconsistent.
% 116.26/18.06 |
% 116.26/18.06 End of proof
% 116.26/18.06
% 116.26/18.06 Sub-proof #199 shows that the following formulas are inconsistent:
% 116.26/18.06 ----------------------------------------------------------------
% 116.26/18.06 (1) all_56_14 = all_6_2
% 116.26/18.06 (2) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.26/18.06 (3) ~ (all_6_1 = e3)
% 116.26/18.06 (4) all_58_0 = all_10_2
% 116.26/18.06 (5) all_54_11 = all_52_14
% 116.26/18.06 (6) ~ (all_52_14 = all_6_2)
% 116.26/18.06 (7) all_56_3 = e2
% 116.26/18.06 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.26/18.06 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.26/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.26/18.06 (10) all_54_10 = all_6_2
% 116.26/18.06 (11) op(e1, e0) = all_52_14
% 116.26/18.06 (12) op(e1, all_6_2) = all_6_1
% 116.26/18.06 (13) ~ (all_10_2 = e3)
% 116.26/18.06 (14) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.26/18.06 (15) ~ (all_6_2 = e2)
% 116.26/18.06 (16) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.26/18.06 (17) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.26/18.06 (18) all_56_8 = all_52_14
% 116.26/18.06 (19) ~ (all_6_2 = e1)
% 116.26/18.06 (20) ~ (all_6_1 = e2)
% 116.26/18.06
% 116.26/18.06 Begin of proof
% 116.26/18.06 |
% 116.26/18.06 | BETA: splitting (14) gives:
% 116.26/18.06 |
% 116.26/18.06 | Case 1:
% 116.26/18.06 | |
% 116.26/18.06 | | (21) ~ (all_56_3 = e2)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (7), (21) imply:
% 116.26/18.06 | | (22) $false
% 116.26/18.06 | |
% 116.26/18.06 | | CLOSE: (22) is inconsistent.
% 116.26/18.06 | |
% 116.26/18.06 | Case 2:
% 116.26/18.06 | |
% 116.26/18.06 | | (23) ~ (all_56_14 = e3)
% 116.26/18.06 | |
% 116.26/18.06 | | REDUCE: (1), (23) imply:
% 116.26/18.06 | | (24) ~ (all_6_2 = e3)
% 116.26/18.06 | |
% 116.26/18.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 116.26/18.06 | | (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 116.26/18.06 | | sub-proof #413.
% 116.26/18.06 | |
% 116.26/18.06 | End of split
% 116.26/18.06 |
% 116.26/18.06 End of proof
% 116.26/18.06
% 116.26/18.06 Sub-proof #200 shows that the following formulas are inconsistent:
% 116.26/18.06 ----------------------------------------------------------------
% 116.26/18.06 (1) all_58_10 = e2
% 116.26/18.06 (2) all_58_15 = e3
% 116.26/18.06 (3) ~ (e3 = e1)
% 116.26/18.06 (4) all_58_11 = all_52_14
% 116.26/18.06 (5) all_58_0 = e1
% 116.26/18.06 (6) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.26/18.06 (7) ~ (all_52_12 = e3)
% 116.26/18.06 (8) all_58_9 = all_52_12
% 116.26/18.06 (9) all_58_0 = e3
% 116.85/18.06 (10) ~ (all_52_14 = e3)
% 116.85/18.06 (11) ~ (e3 = e2)
% 116.85/18.06
% 116.85/18.06 Begin of proof
% 116.85/18.06 |
% 116.85/18.06 | COMBINE_EQS: (5), (9) imply:
% 116.85/18.06 | (12) e3 = e1
% 116.85/18.06 |
% 116.85/18.06 | SIMP: (12) implies:
% 116.85/18.06 | (13) e3 = e1
% 116.85/18.06 |
% 116.85/18.06 | COMBINE_EQS: (2), (13) imply:
% 116.85/18.06 | (14) all_58_15 = e1
% 116.85/18.06 |
% 116.85/18.06 | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (14) are inconsistent by
% 116.85/18.06 | sub-proof #201.
% 116.85/18.06 |
% 116.85/18.06 End of proof
% 116.85/18.06
% 116.85/18.06 Sub-proof #201 shows that the following formulas are inconsistent:
% 116.85/18.06 ----------------------------------------------------------------
% 116.85/18.06 (1) all_58_10 = e2
% 116.85/18.06 (2) ~ (e3 = e1)
% 116.85/18.06 (3) all_58_11 = all_52_14
% 116.85/18.06 (4) all_58_15 = e1
% 116.85/18.06 (5) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.85/18.06 (6) ~ (all_52_12 = e3)
% 116.85/18.06 (7) all_58_9 = all_52_12
% 116.85/18.06 (8) ~ (all_52_14 = e3)
% 116.85/18.06 (9) ~ (e3 = e2)
% 116.85/18.06
% 116.85/18.06 Begin of proof
% 116.85/18.06 |
% 116.85/18.06 | BETA: splitting (5) gives:
% 116.85/18.06 |
% 116.85/18.06 | Case 1:
% 116.85/18.06 | |
% 116.85/18.06 | | (10) all_58_9 = e3
% 116.85/18.06 | |
% 116.85/18.06 | | COMBINE_EQS: (7), (10) imply:
% 116.85/18.06 | | (11) all_52_12 = e3
% 116.85/18.06 | |
% 116.85/18.06 | | REDUCE: (6), (11) imply:
% 116.85/18.06 | | (12) $false
% 116.85/18.06 | |
% 116.85/18.06 | | CLOSE: (12) is inconsistent.
% 116.85/18.06 | |
% 116.85/18.06 | Case 2:
% 116.85/18.06 | |
% 116.85/18.06 | | (13) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.85/18.06 | |
% 116.85/18.06 | | BETA: splitting (13) gives:
% 116.85/18.06 | |
% 116.85/18.06 | | Case 1:
% 116.85/18.06 | | |
% 116.85/18.06 | | | (14) all_58_10 = e3
% 116.85/18.06 | | |
% 116.85/18.06 | | | COMBINE_EQS: (1), (14) imply:
% 116.85/18.06 | | | (15) e3 = e2
% 116.85/18.06 | | |
% 116.85/18.06 | | | REDUCE: (9), (15) imply:
% 116.85/18.06 | | | (16) $false
% 116.85/18.06 | | |
% 116.85/18.06 | | | CLOSE: (16) is inconsistent.
% 116.85/18.06 | | |
% 116.85/18.06 | | Case 2:
% 116.85/18.06 | | |
% 116.85/18.06 | | | (17) all_58_11 = e3 | all_58_15 = e3
% 116.85/18.06 | | |
% 116.85/18.06 | | | BETA: splitting (17) gives:
% 116.85/18.06 | | |
% 116.85/18.06 | | | Case 1:
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | (18) all_58_11 = e3
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | COMBINE_EQS: (3), (18) imply:
% 116.85/18.06 | | | | (19) all_52_14 = e3
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | SIMP: (19) implies:
% 116.85/18.06 | | | | (20) all_52_14 = e3
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | REDUCE: (8), (20) imply:
% 116.85/18.06 | | | | (21) $false
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | CLOSE: (21) is inconsistent.
% 116.85/18.06 | | | |
% 116.85/18.06 | | | Case 2:
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | (22) all_58_15 = e3
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | COMBINE_EQS: (4), (22) imply:
% 116.85/18.06 | | | | (23) e3 = e1
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | SIMP: (23) implies:
% 116.85/18.06 | | | | (24) e3 = e1
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | REDUCE: (2), (24) imply:
% 116.85/18.06 | | | | (25) $false
% 116.85/18.06 | | | |
% 116.85/18.06 | | | | CLOSE: (25) is inconsistent.
% 116.85/18.06 | | | |
% 116.85/18.06 | | | End of split
% 116.85/18.06 | | |
% 116.85/18.06 | | End of split
% 116.85/18.06 | |
% 116.85/18.06 | End of split
% 116.85/18.06 |
% 116.85/18.06 End of proof
% 116.85/18.06
% 116.85/18.06 Sub-proof #202 shows that the following formulas are inconsistent:
% 116.85/18.06 ----------------------------------------------------------------
% 116.85/18.06 (1) ~ (all_52_8 = all_10_2)
% 116.85/18.06 (2) all_56_14 = all_6_2
% 116.85/18.06 (3) all_54_0 = all_10_2
% 116.85/18.06 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.85/18.06 (5) ~ (all_6_1 = e3)
% 116.85/18.06 (6) all_56_12 = all_10_2
% 116.85/18.06 (7) all_58_0 = all_10_2
% 116.85/18.06 (8) all_54_11 = all_52_14
% 116.85/18.06 (9) ~ (all_52_14 = all_6_2)
% 116.85/18.06 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.85/18.06 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.06 (12) all_54_10 = all_6_2
% 116.85/18.06 (13) ~ (all_52_8 = all_6_2)
% 116.85/18.06 (14) all_58_4 = all_52_8
% 116.85/18.06 (15) op(e1, e0) = all_52_14
% 116.85/18.06 (16) op(e1, all_6_2) = all_6_1
% 116.85/18.06 (17) ~ (all_10_2 = e3)
% 116.85/18.06 (18) ~ (all_52_12 = e3)
% 116.85/18.06 (19) all_54_0 = e2
% 116.85/18.06 (20) all_58_1 = all_52_4
% 116.85/18.06 (21) ~ (all_6_2 = e2)
% 116.85/18.06 (22) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.85/18.06 (23) all_58_9 = all_52_12
% 116.85/18.06 (24) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.85/18.06 (25) all_56_8 = all_52_14
% 116.85/18.06 (26) all_56_0 = all_52_4
% 116.85/18.06 (27) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.85/18.06 (28) ~ (all_6_2 = e1)
% 116.85/18.06 (29) ~ (all_6_1 = e2)
% 116.85/18.06
% 116.85/18.06 Begin of proof
% 116.85/18.06 |
% 116.85/18.06 | COMBINE_EQS: (3), (19) imply:
% 116.85/18.06 | (30) all_10_2 = e2
% 116.85/18.06 |
% 116.85/18.06 | SIMP: (30) implies:
% 116.85/18.06 | (31) all_10_2 = e2
% 116.85/18.06 |
% 116.85/18.06 | COMBINE_EQS: (6), (31) imply:
% 116.85/18.06 | (32) all_56_12 = e2
% 116.85/18.06 |
% 116.85/18.06 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 116.85/18.06 | (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 116.85/18.06 | (27), (28), (29), (32) are inconsistent by sub-proof #204.
% 116.85/18.06 |
% 116.85/18.06 End of proof
% 116.85/18.06
% 116.85/18.06 Sub-proof #203 shows that the following formulas are inconsistent:
% 116.85/18.06 ----------------------------------------------------------------
% 116.85/18.06 (1) ~ (all_52_8 = all_10_2)
% 116.85/18.06 (2) all_54_2 = all_52_8
% 116.85/18.06 (3) all_58_7 = all_52_6
% 116.85/18.06 (4) ~ (all_52_1 = e2)
% 116.85/18.06 (5) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.85/18.06 (6) all_56_14 = all_6_2
% 116.85/18.06 (7) all_54_0 = all_10_2
% 116.85/18.06 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.06 (9) all_54_3 = all_52_12
% 116.85/18.06 (10) ~ (all_4_0 = e1)
% 116.85/18.06 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.85/18.06 (12) ~ (all_6_1 = e3)
% 116.85/18.06 (13) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.85/18.06 (14) ~ (all_52_4 = all_52_8)
% 116.85/18.06 (15) ~ (all_52_12 = all_10_2)
% 116.85/18.06 (16) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.85/18.06 (17) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.06 (18) all_56_12 = all_10_2
% 116.85/18.06 (19) all_58_0 = all_10_2
% 116.85/18.06 (20) all_54_11 = all_52_14
% 116.85/18.06 (21) all_54_13 = all_52_7
% 116.85/18.06 (22) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.85/18.06 (23) ~ (all_52_14 = all_6_2)
% 116.85/18.06 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.85/18.06 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.06 (26) ~ (all_52_7 = e3)
% 116.85/18.06 (27) all_54_10 = all_6_2
% 116.85/18.06 (28) op(e3, e0) = all_52_12
% 116.85/18.06 (29) ~ (all_52_8 = all_6_2)
% 116.85/18.06 (30) all_58_4 = all_52_8
% 116.85/18.06 (31) ~ (all_52_4 = all_52_7)
% 116.85/18.06 (32) all_58_11 = all_52_14
% 116.85/18.06 (33) all_16_1 = all_10_1
% 116.85/18.06 (34) op(e2, e3) = all_52_1
% 116.85/18.06 (35) ~ (all_10_2 = e1)
% 116.85/18.06 (36) ~ (all_52_7 = all_8_2)
% 116.85/18.06 (37) ~ (all_52_4 = all_8_2)
% 116.85/18.06 (38) op(e1, e0) = all_52_14
% 116.85/18.06 (39) ~ (all_16_1 = e2) | ~ (all_16_2 = e0)
% 116.85/18.06 (40) op(e1, all_6_2) = all_6_1
% 116.85/18.06 (41) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.85/18.06 (42) all_58_2 = all_52_1
% 116.85/18.06 (43) ~ (all_10_2 = e3)
% 116.85/18.06 (44) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.85/18.06 (45) all_58_6 = all_52_2
% 116.85/18.06 (46) ~ (all_52_2 = e1)
% 116.85/18.06 (47) ~ (all_52_1 = all_10_2)
% 116.85/18.06 (48) all_54_5 = all_8_2
% 116.85/18.06 (49) ~ (all_52_12 = e3)
% 116.85/18.06 (50) all_58_12 = all_4_1
% 116.85/18.06 (51) op(e3, all_10_2) = all_10_1
% 116.85/18.06 (52) ~ (all_52_6 = all_8_2)
% 116.85/18.06 (53) all_58_1 = all_52_4
% 116.85/18.06 (54) all_54_1 = all_52_4
% 116.85/18.06 (55) ~ (all_52_8 = e2)
% 116.85/18.06 (56) ~ (all_52_1 = all_8_2)
% 116.85/18.06 (57) op(all_4_1, e3) = all_4_0
% 116.85/18.06 (58) ~ (all_6_2 = e2)
% 116.85/18.06 (59) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.85/18.07 (60) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.07 (61) ~ (all_52_4 = all_52_12)
% 116.85/18.07 (62) all_58_8 = all_6_2
% 116.85/18.07 (63) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.85/18.07 (64) all_16_2 = all_10_2
% 116.85/18.07 (65) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.85/18.07 (66) all_58_9 = all_52_12
% 116.85/18.07 (67) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.07 (68) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.85/18.07 (69) ~ (all_52_8 = all_52_12)
% 116.85/18.07 (70) all_56_8 = all_52_14
% 116.85/18.07 (71) ~ (all_52_4 = all_10_2)
% 116.85/18.07 (72) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.85/18.07 (73) all_56_0 = all_52_4
% 116.85/18.07 (74) ~ (all_4_1 = e3)
% 116.85/18.07 (75) all_54_4 = all_52_1
% 116.85/18.07 (76) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.85/18.07 (77) ~ (all_6_2 = e1)
% 116.85/18.07 (78) ~ (all_6_1 = e2)
% 116.85/18.07 (79) ~ (all_52_6 = all_52_7)
% 116.85/18.07
% 116.85/18.07 Begin of proof
% 116.85/18.07 |
% 116.85/18.07 | BETA: splitting (44) gives:
% 116.85/18.07 |
% 116.85/18.07 | Case 1:
% 116.85/18.07 | |
% 116.85/18.07 | | (80) ~ (all_56_12 = e2)
% 116.85/18.07 | |
% 116.85/18.07 | | REDUCE: (18), (80) imply:
% 116.85/18.07 | | (81) ~ (all_10_2 = e2)
% 116.85/18.07 | |
% 116.85/18.07 | | BETA: splitting (63) gives:
% 116.85/18.07 | |
% 116.85/18.07 | | Case 1:
% 116.85/18.07 | | |
% 116.85/18.07 | | | (82) all_54_0 = e3
% 116.85/18.07 | | |
% 116.85/18.07 | | | REF_CLOSE: (7), (43), (82) are inconsistent by sub-proof #451.
% 116.85/18.07 | | |
% 116.85/18.07 | | Case 2:
% 116.85/18.07 | | |
% 116.85/18.07 | | | (83) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.85/18.07 | | |
% 116.85/18.07 | | | BETA: splitting (83) gives:
% 116.85/18.07 | | |
% 116.85/18.07 | | | Case 1:
% 116.85/18.07 | | | |
% 116.85/18.07 | | | | (84) all_54_0 = e2
% 116.85/18.07 | | | |
% 116.85/18.07 | | | | REF_CLOSE: (7), (81), (84) are inconsistent by sub-proof #450.
% 116.85/18.07 | | | |
% 116.85/18.07 | | | Case 2:
% 116.85/18.07 | | | |
% 116.85/18.07 | | | | (85) ~ (all_54_0 = e2)
% 116.85/18.07 | | | | (86) all_54_0 = e1 | all_54_0 = e0
% 116.85/18.07 | | | |
% 116.85/18.07 | | | | BETA: splitting (86) gives:
% 116.85/18.07 | | | |
% 116.85/18.07 | | | | Case 1:
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | (87) all_54_0 = e1
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REF_CLOSE: (7), (35), (87) are inconsistent by sub-proof #449.
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | Case 2:
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | (88) all_54_0 = e0
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | COMBINE_EQS: (7), (88) imply:
% 116.85/18.07 | | | | | (89) all_10_2 = e0
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | SIMP: (89) implies:
% 116.85/18.07 | | | | | (90) all_10_2 = e0
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | COMBINE_EQS: (64), (90) imply:
% 116.85/18.07 | | | | | (91) all_16_2 = e0
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | COMBINE_EQS: (19), (90) imply:
% 116.85/18.07 | | | | | (92) all_58_0 = e0
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (47), (90) imply:
% 116.85/18.07 | | | | | (93) ~ (all_52_1 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (71), (90) imply:
% 116.85/18.07 | | | | | (94) ~ (all_52_4 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (1), (90) imply:
% 116.85/18.07 | | | | | (95) ~ (all_52_8 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (15), (90) imply:
% 116.85/18.07 | | | | | (96) ~ (all_52_12 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (81), (90) imply:
% 116.85/18.07 | | | | | (97) ~ (e2 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | SIMP: (97) implies:
% 116.85/18.07 | | | | | (98) ~ (e2 = e0)
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | REDUCE: (51), (90) imply:
% 116.85/18.07 | | | | | (99) op(e3, e0) = all_10_1
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | BETA: splitting (41) gives:
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | | Case 1:
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | (100) ~ (all_56_8 = e1)
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | REDUCE: (70), (100) imply:
% 116.85/18.07 | | | | | | (101) ~ (all_52_14 = e1)
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | BETA: splitting (39) gives:
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | Case 1:
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | (102) ~ (all_16_1 = e2)
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | REDUCE: (33), (102) imply:
% 116.85/18.07 | | | | | | | (103) ~ (all_10_1 = e2)
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | BETA: splitting (59) gives:
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | Case 1:
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | | (104) all_58_6 = e1
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | | REF_CLOSE: (45), (46), (104) are inconsistent by sub-proof #452.
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | Case 2:
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | | (105) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | | BETA: splitting (105) gives:
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | | Case 1:
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | (106) all_58_7 = e1
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | COMBINE_EQS: (3), (106) imply:
% 116.85/18.07 | | | | | | | | | (107) all_52_6 = e1
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | REDUCE: (79), (107) imply:
% 116.85/18.07 | | | | | | | | | (108) ~ (all_52_7 = e1)
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | SIMP: (108) implies:
% 116.85/18.07 | | | | | | | | | (109) ~ (all_52_7 = e1)
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | REDUCE: (52), (107) imply:
% 116.85/18.07 | | | | | | | | | (110) ~ (all_8_2 = e1)
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | SIMP: (110) implies:
% 116.85/18.07 | | | | | | | | | (111) ~ (all_8_2 = e1)
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (13), (14), (16),
% 116.85/18.07 | | | | | | | | | (17), (21), (22), (25), (26), (28), (31), (34),
% 116.85/18.07 | | | | | | | | | (36), (37), (42), (48), (49), (50), (53), (54),
% 116.85/18.07 | | | | | | | | | (55), (56), (57), (60), (61), (67), (69), (72),
% 116.85/18.07 | | | | | | | | | (74), (75), (92), (93), (94), (95), (96), (98),
% 116.85/18.07 | | | | | | | | | (99), (103), (109), (111) are inconsistent by
% 116.85/18.07 | | | | | | | | | sub-proof #205.
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | Case 2:
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | (112) all_58_8 = e1 | all_58_11 = e1
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | | REF_CLOSE: (32), (62), (77), (101), (112) are inconsistent by
% 116.85/18.07 | | | | | | | | | sub-proof #445.
% 116.85/18.07 | | | | | | | | |
% 116.85/18.07 | | | | | | | | End of split
% 116.85/18.07 | | | | | | | |
% 116.85/18.07 | | | | | | | End of split
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | Case 2:
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | (113) ~ (all_16_2 = e0)
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | REDUCE: (91), (113) imply:
% 116.85/18.07 | | | | | | | (114) $false
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | | CLOSE: (114) is inconsistent.
% 116.85/18.07 | | | | | | |
% 116.85/18.07 | | | | | | End of split
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | Case 2:
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | (115) all_56_8 = e1
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | | REF_CLOSE: (7), (18), (35), (41), (81), (83), (115) are inconsistent
% 116.85/18.07 | | | | | | by sub-proof #385.
% 116.85/18.07 | | | | | |
% 116.85/18.07 | | | | | End of split
% 116.85/18.07 | | | | |
% 116.85/18.07 | | | | End of split
% 116.85/18.07 | | | |
% 116.85/18.07 | | | End of split
% 116.85/18.07 | | |
% 116.85/18.07 | | End of split
% 116.85/18.07 | |
% 116.85/18.07 | Case 2:
% 116.85/18.07 | |
% 116.85/18.07 | | (116) all_56_12 = e2
% 116.85/18.07 | |
% 116.85/18.07 | | REF_CLOSE: (1), (6), (11), (12), (19), (20), (23), (24), (25), (27), (29),
% 116.85/18.07 | | (30), (38), (40), (43), (49), (53), (58), (65), (66), (68), (70),
% 116.85/18.07 | | (73), (76), (77), (78), (116) are inconsistent by sub-proof #204.
% 116.85/18.07 | |
% 116.85/18.07 | End of split
% 116.85/18.07 |
% 116.85/18.07 End of proof
% 116.85/18.07
% 116.85/18.07 Sub-proof #204 shows that the following formulas are inconsistent:
% 116.85/18.07 ----------------------------------------------------------------
% 116.85/18.07 (1) ~ (all_52_8 = all_10_2)
% 116.85/18.07 (2) all_56_14 = all_6_2
% 116.85/18.07 (3) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.85/18.07 (4) ~ (all_6_1 = e3)
% 116.85/18.07 (5) all_58_0 = all_10_2
% 116.85/18.07 (6) all_54_11 = all_52_14
% 116.85/18.07 (7) ~ (all_52_14 = all_6_2)
% 116.85/18.07 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.85/18.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.07 (10) all_54_10 = all_6_2
% 116.85/18.07 (11) ~ (all_52_8 = all_6_2)
% 116.85/18.07 (12) all_58_4 = all_52_8
% 116.85/18.07 (13) all_56_12 = e2
% 116.85/18.07 (14) op(e1, e0) = all_52_14
% 116.85/18.07 (15) op(e1, all_6_2) = all_6_1
% 116.85/18.07 (16) ~ (all_10_2 = e3)
% 116.85/18.07 (17) ~ (all_52_12 = e3)
% 116.85/18.07 (18) all_58_1 = all_52_4
% 116.85/18.07 (19) ~ (all_6_2 = e2)
% 116.85/18.07 (20) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.85/18.07 (21) all_58_9 = all_52_12
% 116.85/18.07 (22) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.85/18.07 (23) all_56_8 = all_52_14
% 116.85/18.07 (24) all_56_0 = all_52_4
% 116.85/18.07 (25) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.85/18.07 (26) ~ (all_6_2 = e1)
% 116.85/18.07 (27) ~ (all_6_1 = e2)
% 116.85/18.07
% 116.85/18.07 Begin of proof
% 116.85/18.07 |
% 116.85/18.07 | BETA: splitting (25) gives:
% 116.85/18.07 |
% 116.85/18.07 | Case 1:
% 116.85/18.07 | |
% 116.85/18.07 | | (28) ~ (all_56_0 = e3)
% 116.85/18.07 | |
% 116.85/18.07 | | REDUCE: (24), (28) imply:
% 116.85/18.07 | | (29) ~ (all_52_4 = e3)
% 116.85/18.07 | |
% 116.85/18.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 116.85/18.07 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 116.85/18.07 | | (27), (29) are inconsistent by sub-proof #411.
% 116.85/18.07 | |
% 116.85/18.07 | Case 2:
% 116.85/18.07 | |
% 116.85/18.07 | | (30) ~ (all_56_12 = e2)
% 116.85/18.07 | |
% 116.85/18.07 | | REDUCE: (13), (30) imply:
% 116.85/18.07 | | (31) $false
% 116.85/18.07 | |
% 116.85/18.07 | | CLOSE: (31) is inconsistent.
% 116.85/18.07 | |
% 116.85/18.07 | End of split
% 116.85/18.07 |
% 116.85/18.07 End of proof
% 116.85/18.07
% 116.85/18.07 Sub-proof #205 shows that the following formulas are inconsistent:
% 116.85/18.07 ----------------------------------------------------------------
% 116.85/18.07 (1) all_54_2 = all_52_8
% 116.85/18.07 (2) ~ (all_52_1 = e2)
% 116.85/18.07 (3) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.85/18.07 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.07 (5) all_54_3 = all_52_12
% 116.85/18.07 (6) ~ (all_4_0 = e1)
% 116.85/18.07 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.85/18.07 (8) ~ (all_52_4 = all_52_8)
% 116.85/18.07 (9) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.85/18.07 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.07 (11) op(e3, e0) = all_10_1
% 116.85/18.07 (12) all_54_13 = all_52_7
% 116.85/18.07 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.85/18.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.07 (15) ~ (all_52_7 = e3)
% 116.85/18.07 (16) op(e3, e0) = all_52_12
% 116.85/18.07 (17) ~ (all_52_4 = all_52_7)
% 116.85/18.07 (18) ~ (all_52_12 = e0)
% 116.85/18.07 (19) op(e2, e3) = all_52_1
% 116.85/18.07 (20) ~ (all_52_7 = all_8_2)
% 116.85/18.07 (21) ~ (all_52_4 = all_8_2)
% 116.85/18.07 (22) all_58_2 = all_52_1
% 116.85/18.07 (23) all_54_5 = all_8_2
% 116.85/18.07 (24) ~ (all_52_12 = e3)
% 116.85/18.07 (25) all_58_12 = all_4_1
% 116.85/18.07 (26) ~ (all_10_1 = e2)
% 116.85/18.07 (27) all_58_1 = all_52_4
% 116.85/18.07 (28) ~ (all_52_4 = e0)
% 116.85/18.07 (29) ~ (all_8_2 = e1)
% 116.85/18.07 (30) ~ (all_52_1 = e0)
% 116.85/18.07 (31) all_54_1 = all_52_4
% 116.85/18.07 (32) ~ (all_52_8 = e2)
% 116.85/18.07 (33) ~ (all_52_1 = all_8_2)
% 116.85/18.07 (34) op(all_4_1, e3) = all_4_0
% 116.85/18.07 (35) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.07 (36) ~ (all_52_4 = all_52_12)
% 116.85/18.07 (37) all_58_0 = e0
% 116.85/18.07 (38) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.07 (39) ~ (e2 = e0)
% 116.85/18.07 (40) ~ (all_52_8 = all_52_12)
% 116.85/18.07 (41) ~ (all_52_7 = e1)
% 116.85/18.07 (42) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.85/18.07 (43) ~ (all_52_8 = e0)
% 116.85/18.07 (44) ~ (all_4_1 = e3)
% 116.85/18.07 (45) all_54_4 = all_52_1
% 116.85/18.07
% 116.85/18.07 Begin of proof
% 116.85/18.07 |
% 116.85/18.07 | GROUND_INST: instantiating (14) with all_52_12, all_10_1, e0, e3, simplifying
% 116.85/18.07 | with (11), (16) gives:
% 116.85/18.07 | (46) all_52_12 = all_10_1
% 116.85/18.07 |
% 116.85/18.07 | COMBINE_EQS: (5), (46) imply:
% 116.85/18.07 | (47) all_54_3 = all_10_1
% 116.85/18.07 |
% 116.85/18.07 | REDUCE: (36), (46) imply:
% 116.85/18.07 | (48) ~ (all_52_4 = all_10_1)
% 116.85/18.07 |
% 116.85/18.07 | REDUCE: (40), (46) imply:
% 116.85/18.07 | (49) ~ (all_52_8 = all_10_1)
% 116.85/18.07 |
% 116.85/18.07 | REDUCE: (24), (46) imply:
% 116.85/18.07 | (50) ~ (all_10_1 = e3)
% 116.85/18.07 |
% 116.85/18.07 | REDUCE: (18), (46) imply:
% 116.85/18.07 | (51) ~ (all_10_1 = e0)
% 116.85/18.07 |
% 116.85/18.07 | BETA: splitting (7) gives:
% 116.85/18.07 |
% 116.85/18.07 | Case 1:
% 116.85/18.07 | |
% 116.85/18.07 | | (52) all_54_3 = e3
% 116.85/18.07 | |
% 116.85/18.07 | | REF_CLOSE: (47), (50), (52) are inconsistent by sub-proof #215.
% 116.85/18.07 | |
% 116.85/18.07 | Case 2:
% 116.85/18.07 | |
% 116.85/18.07 | | (53) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.85/18.07 | |
% 116.85/18.07 | | BETA: splitting (53) gives:
% 116.85/18.07 | |
% 116.85/18.07 | | Case 1:
% 116.85/18.07 | | |
% 116.85/18.07 | | | (54) all_54_3 = e2
% 116.85/18.07 | | |
% 116.85/18.07 | | | REF_CLOSE: (26), (47), (54) are inconsistent by sub-proof #214.
% 116.85/18.07 | | |
% 116.85/18.07 | | Case 2:
% 116.85/18.07 | | |
% 116.85/18.07 | | | (55) all_54_3 = e1 | all_54_3 = e0
% 116.85/18.07 | | |
% 116.85/18.07 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (14),
% 116.85/18.07 | | | (15), (17), (19), (20), (21), (22), (23), (25), (27), (28),
% 116.85/18.07 | | | (29), (30), (31), (32), (33), (34), (35), (37), (38), (39),
% 116.85/18.07 | | | (41), (42), (43), (44), (45), (47), (48), (49), (51), (55) are
% 116.85/18.07 | | | inconsistent by sub-proof #206.
% 116.85/18.07 | | |
% 116.85/18.07 | | End of split
% 116.85/18.07 | |
% 116.85/18.07 | End of split
% 116.85/18.07 |
% 116.85/18.07 End of proof
% 116.85/18.07
% 116.85/18.07 Sub-proof #206 shows that the following formulas are inconsistent:
% 116.85/18.07 ----------------------------------------------------------------
% 116.85/18.07 (1) all_54_2 = all_52_8
% 116.85/18.07 (2) ~ (all_52_1 = e2)
% 116.85/18.07 (3) ~ (all_52_8 = all_10_1)
% 116.85/18.07 (4) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.85/18.07 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.07 (6) ~ (all_4_0 = e1)
% 116.85/18.07 (7) ~ (all_52_4 = all_10_1)
% 116.85/18.07 (8) ~ (all_52_4 = all_52_8)
% 116.85/18.07 (9) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.85/18.07 (10) all_54_3 = all_10_1
% 116.85/18.07 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.07 (12) all_54_13 = all_52_7
% 116.85/18.07 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.85/18.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.07 (15) ~ (all_52_7 = e3)
% 116.85/18.07 (16) ~ (all_52_4 = all_52_7)
% 116.85/18.07 (17) op(e2, e3) = all_52_1
% 116.85/18.07 (18) ~ (all_52_7 = all_8_2)
% 116.85/18.07 (19) ~ (all_52_4 = all_8_2)
% 116.85/18.07 (20) all_58_2 = all_52_1
% 116.85/18.07 (21) all_54_5 = all_8_2
% 116.85/18.07 (22) all_58_12 = all_4_1
% 116.85/18.07 (23) all_58_1 = all_52_4
% 116.85/18.07 (24) ~ (all_52_4 = e0)
% 116.85/18.07 (25) ~ (all_8_2 = e1)
% 116.85/18.07 (26) ~ (all_52_1 = e0)
% 116.85/18.08 (27) all_54_1 = all_52_4
% 116.85/18.08 (28) ~ (all_52_8 = e2)
% 116.85/18.08 (29) ~ (all_52_1 = all_8_2)
% 116.85/18.08 (30) op(all_4_1, e3) = all_4_0
% 116.85/18.08 (31) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.08 (32) ~ (all_10_1 = e0)
% 116.85/18.08 (33) all_58_0 = e0
% 116.85/18.08 (34) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 (35) ~ (e2 = e0)
% 116.85/18.08 (36) all_54_3 = e1 | all_54_3 = e0
% 116.85/18.08 (37) ~ (all_52_7 = e1)
% 116.85/18.08 (38) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.85/18.08 (39) ~ (all_52_8 = e0)
% 116.85/18.08 (40) ~ (all_4_1 = e3)
% 116.85/18.08 (41) all_54_4 = all_52_1
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | BETA: splitting (36) gives:
% 116.85/18.08 |
% 116.85/18.08 | Case 1:
% 116.85/18.08 | |
% 116.85/18.08 | | (42) all_54_3 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | COMBINE_EQS: (10), (42) imply:
% 116.85/18.08 | | (43) all_10_1 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | SIMP: (43) implies:
% 116.85/18.08 | | (44) all_10_1 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (7), (44) imply:
% 116.85/18.08 | | (45) ~ (all_52_4 = e1)
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (3), (44) imply:
% 116.85/18.08 | | (46) ~ (all_52_8 = e1)
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15),
% 116.85/18.08 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 116.85/18.08 | | (27), (28), (29), (30), (31), (33), (34), (35), (37), (38), (39),
% 116.85/18.08 | | (40), (41), (45), (46) are inconsistent by sub-proof #208.
% 116.85/18.08 | |
% 116.85/18.08 | Case 2:
% 116.85/18.08 | |
% 116.85/18.08 | | (47) all_54_3 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (10), (32), (47) are inconsistent by sub-proof #207.
% 116.85/18.08 | |
% 116.85/18.08 | End of split
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #207 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_3 = all_10_1
% 116.85/18.08 (2) all_54_3 = e0
% 116.85/18.08 (3) ~ (all_10_1 = e0)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | COMBINE_EQS: (1), (2) imply:
% 116.85/18.08 | (4) all_10_1 = e0
% 116.85/18.08 |
% 116.85/18.08 | SIMP: (4) implies:
% 116.85/18.08 | (5) all_10_1 = e0
% 116.85/18.08 |
% 116.85/18.08 | REDUCE: (3), (5) imply:
% 116.85/18.08 | (6) $false
% 116.85/18.08 |
% 116.85/18.08 | CLOSE: (6) is inconsistent.
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #208 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_2 = all_52_8
% 116.85/18.08 (2) ~ (all_52_1 = e2)
% 116.85/18.08 (3) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.85/18.08 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.08 (5) ~ (all_52_8 = e1)
% 116.85/18.08 (6) ~ (all_4_0 = e1)
% 116.85/18.08 (7) ~ (all_52_4 = all_52_8)
% 116.85/18.08 (8) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 116.85/18.08 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.08 (10) all_54_13 = all_52_7
% 116.85/18.08 (11) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 116.85/18.08 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.08 (13) ~ (all_52_7 = e3)
% 116.85/18.08 (14) ~ (all_52_4 = all_52_7)
% 116.85/18.08 (15) op(e2, e3) = all_52_1
% 116.85/18.08 (16) ~ (all_52_4 = e1)
% 116.85/18.08 (17) ~ (all_52_7 = all_8_2)
% 116.85/18.08 (18) ~ (all_52_4 = all_8_2)
% 116.85/18.08 (19) all_58_2 = all_52_1
% 116.85/18.08 (20) all_54_5 = all_8_2
% 116.85/18.08 (21) all_58_12 = all_4_1
% 116.85/18.08 (22) all_58_1 = all_52_4
% 116.85/18.08 (23) ~ (all_52_4 = e0)
% 116.85/18.08 (24) ~ (all_8_2 = e1)
% 116.85/18.08 (25) ~ (all_52_1 = e0)
% 116.85/18.08 (26) all_54_1 = all_52_4
% 116.85/18.08 (27) ~ (all_52_8 = e2)
% 116.85/18.08 (28) ~ (all_52_1 = all_8_2)
% 116.85/18.08 (29) op(all_4_1, e3) = all_4_0
% 116.85/18.08 (30) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.08 (31) all_58_0 = e0
% 116.85/18.08 (32) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 (33) ~ (e2 = e0)
% 116.85/18.08 (34) ~ (all_52_7 = e1)
% 116.85/18.08 (35) all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.85/18.08 (36) ~ (all_52_8 = e0)
% 116.85/18.08 (37) ~ (all_4_1 = e3)
% 116.85/18.08 (38) all_54_4 = all_52_1
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | BETA: splitting (32) gives:
% 116.85/18.08 |
% 116.85/18.08 | Case 1:
% 116.85/18.08 | |
% 116.85/18.08 | | (39) all_54_2 = e3
% 116.85/18.08 | |
% 116.85/18.08 | | COMBINE_EQS: (1), (39) imply:
% 116.85/18.08 | | (40) all_52_8 = e3
% 116.85/18.08 | |
% 116.85/18.08 | | SIMP: (40) implies:
% 116.85/18.08 | | (41) all_52_8 = e3
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (7), (41) imply:
% 116.85/18.08 | | (42) ~ (all_52_4 = e3)
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (27), (41) imply:
% 116.85/18.08 | | (43) ~ (e3 = e2)
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (36), (41) imply:
% 116.85/18.08 | | (44) ~ (e3 = e0)
% 116.85/18.08 | |
% 116.85/18.08 | | BETA: splitting (30) gives:
% 116.85/18.08 | |
% 116.85/18.08 | | Case 1:
% 116.85/18.08 | | |
% 116.85/18.08 | | | (45) all_54_1 = e3
% 116.85/18.08 | | |
% 116.85/18.08 | | | REF_CLOSE: (26), (42), (45) are inconsistent by sub-proof #222.
% 116.85/18.08 | | |
% 116.85/18.08 | | Case 2:
% 116.85/18.08 | | |
% 116.85/18.08 | | | (46) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.08 | | |
% 116.85/18.08 | | | BETA: splitting (35) gives:
% 116.85/18.08 | | |
% 116.85/18.08 | | | Case 1:
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | (47) all_58_0 = e2
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | REF_CLOSE: (31), (33), (47) are inconsistent by sub-proof #327.
% 116.85/18.08 | | | |
% 116.85/18.08 | | | Case 2:
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | (48) ~ (all_58_0 = e2)
% 116.85/18.08 | | | | (49) all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | REDUCE: (31), (48) imply:
% 116.85/18.08 | | | | (50) ~ (e2 = e0)
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | BETA: splitting (11) gives:
% 116.85/18.08 | | | |
% 116.85/18.08 | | | | Case 1:
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | (51) all_54_4 = e3
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | COMBINE_EQS: (38), (51) imply:
% 116.85/18.08 | | | | | (52) all_52_1 = e3
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | SIMP: (52) implies:
% 116.85/18.08 | | | | | (53) all_52_1 = e3
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | REDUCE: (28), (53) imply:
% 116.85/18.08 | | | | | (54) ~ (all_8_2 = e3)
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | SIMP: (54) implies:
% 116.85/18.08 | | | | | (55) ~ (all_8_2 = e3)
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | BETA: splitting (9) gives:
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | Case 1:
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | | (56) all_54_5 = e3
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | | REF_CLOSE: (20), (55), (56) are inconsistent by sub-proof #339.
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | Case 2:
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | | (57) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | | BETA: splitting (49) gives:
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | | Case 1:
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | (58) all_58_1 = e2
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | COMBINE_EQS: (22), (58) imply:
% 116.85/18.08 | | | | | | | (59) all_52_4 = e2
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | REDUCE: (14), (59) imply:
% 116.85/18.08 | | | | | | | (60) ~ (all_52_7 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | SIMP: (60) implies:
% 116.85/18.08 | | | | | | | (61) ~ (all_52_7 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | REDUCE: (18), (59) imply:
% 116.85/18.08 | | | | | | | (62) ~ (all_8_2 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | SIMP: (62) implies:
% 116.85/18.08 | | | | | | | (63) ~ (all_8_2 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | BETA: splitting (4) gives:
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | Case 1:
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | (64) all_54_13 = e3
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | COMBINE_EQS: (10), (64) imply:
% 116.85/18.08 | | | | | | | | (65) all_52_7 = e3
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | REDUCE: (13), (65) imply:
% 116.85/18.08 | | | | | | | | (66) $false
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | CLOSE: (66) is inconsistent.
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | Case 2:
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | (67) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | REF_CLOSE: (10), (17), (20), (24), (34), (57), (61), (63), (67)
% 116.85/18.08 | | | | | | | | are inconsistent by sub-proof #308.
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | End of split
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | Case 2:
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | (68) ~ (all_58_1 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | REDUCE: (22), (68) imply:
% 116.85/18.08 | | | | | | | (69) ~ (all_52_4 = e2)
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | BETA: splitting (46) gives:
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | | Case 1:
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | (70) all_54_1 = e2
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | REF_CLOSE: (26), (69), (70) are inconsistent by sub-proof #221.
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | Case 2:
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | (71) all_54_1 = e1 | all_54_1 = e0
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | | REF_CLOSE: (16), (23), (26), (71) are inconsistent by sub-proof
% 116.85/18.08 | | | | | | | | #213.
% 116.85/18.08 | | | | | | | |
% 116.85/18.08 | | | | | | | End of split
% 116.85/18.08 | | | | | | |
% 116.85/18.08 | | | | | | End of split
% 116.85/18.08 | | | | | |
% 116.85/18.08 | | | | | End of split
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | Case 2:
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | (72) ~ (all_54_4 = e3)
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | REDUCE: (38), (72) imply:
% 116.85/18.08 | | | | | (73) ~ (all_52_1 = e3)
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | | REF_CLOSE: (2), (3), (6), (8), (11), (12), (15), (19), (21), (25),
% 116.85/18.08 | | | | | (29), (31), (33), (37), (38), (43), (44), (73) are
% 116.85/18.08 | | | | | inconsistent by sub-proof #322.
% 116.85/18.08 | | | | |
% 116.85/18.08 | | | | End of split
% 116.85/18.08 | | | |
% 116.85/18.08 | | | End of split
% 116.85/18.08 | | |
% 116.85/18.08 | | End of split
% 116.85/18.08 | |
% 116.85/18.08 | Case 2:
% 116.85/18.08 | |
% 116.85/18.08 | | (74) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (1), (5), (27), (36), (74) are inconsistent by sub-proof #209.
% 116.85/18.08 | |
% 116.85/18.08 | End of split
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #209 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_2 = all_52_8
% 116.85/18.08 (2) ~ (all_52_8 = e1)
% 116.85/18.08 (3) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 (4) ~ (all_52_8 = e2)
% 116.85/18.08 (5) ~ (all_52_8 = e0)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | BETA: splitting (3) gives:
% 116.85/18.08 |
% 116.85/18.08 | Case 1:
% 116.85/18.08 | |
% 116.85/18.08 | | (6) all_54_2 = e2
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #212.
% 116.85/18.08 | |
% 116.85/18.08 | Case 2:
% 116.85/18.08 | |
% 116.85/18.08 | | (7) all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #210.
% 116.85/18.08 | |
% 116.85/18.08 | End of split
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #210 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_2 = e1 | all_54_2 = e0
% 116.85/18.08 (2) all_54_2 = all_52_8
% 116.85/18.08 (3) ~ (all_52_8 = e1)
% 116.85/18.08 (4) ~ (all_52_8 = e0)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | BETA: splitting (1) gives:
% 116.85/18.08 |
% 116.85/18.08 | Case 1:
% 116.85/18.08 | |
% 116.85/18.08 | | (5) all_54_2 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | COMBINE_EQS: (2), (5) imply:
% 116.85/18.08 | | (6) all_52_8 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | SIMP: (6) implies:
% 116.85/18.08 | | (7) all_52_8 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (3), (7) imply:
% 116.85/18.08 | | (8) $false
% 116.85/18.08 | |
% 116.85/18.08 | | CLOSE: (8) is inconsistent.
% 116.85/18.08 | |
% 116.85/18.08 | Case 2:
% 116.85/18.08 | |
% 116.85/18.08 | | (9) all_54_2 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #211.
% 116.85/18.08 | |
% 116.85/18.08 | End of split
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #211 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_2 = all_52_8
% 116.85/18.08 (2) all_54_2 = e0
% 116.85/18.08 (3) ~ (all_52_8 = e0)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | COMBINE_EQS: (1), (2) imply:
% 116.85/18.08 | (4) all_52_8 = e0
% 116.85/18.08 |
% 116.85/18.08 | SIMP: (4) implies:
% 116.85/18.08 | (5) all_52_8 = e0
% 116.85/18.08 |
% 116.85/18.08 | REDUCE: (3), (5) imply:
% 116.85/18.08 | (6) $false
% 116.85/18.08 |
% 116.85/18.08 | CLOSE: (6) is inconsistent.
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #212 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_2 = all_52_8
% 116.85/18.08 (2) all_54_2 = e2
% 116.85/18.08 (3) ~ (all_52_8 = e2)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | COMBINE_EQS: (1), (2) imply:
% 116.85/18.08 | (4) all_52_8 = e2
% 116.85/18.08 |
% 116.85/18.08 | SIMP: (4) implies:
% 116.85/18.08 | (5) all_52_8 = e2
% 116.85/18.08 |
% 116.85/18.08 | REDUCE: (3), (5) imply:
% 116.85/18.08 | (6) $false
% 116.85/18.08 |
% 116.85/18.08 | CLOSE: (6) is inconsistent.
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #213 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_1 = e1 | all_54_1 = e0
% 116.85/18.08 (2) all_54_1 = all_52_4
% 116.85/18.08 (3) ~ (all_52_4 = e1)
% 116.85/18.08 (4) ~ (all_52_4 = e0)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | BETA: splitting (1) gives:
% 116.85/18.08 |
% 116.85/18.08 | Case 1:
% 116.85/18.08 | |
% 116.85/18.08 | | (5) all_54_1 = e1
% 116.85/18.08 | |
% 116.85/18.08 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #220.
% 116.85/18.08 | |
% 116.85/18.08 | Case 2:
% 116.85/18.08 | |
% 116.85/18.08 | | (6) all_54_1 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | COMBINE_EQS: (2), (6) imply:
% 116.85/18.08 | | (7) all_52_4 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | SIMP: (7) implies:
% 116.85/18.08 | | (8) all_52_4 = e0
% 116.85/18.08 | |
% 116.85/18.08 | | REDUCE: (4), (8) imply:
% 116.85/18.08 | | (9) $false
% 116.85/18.08 | |
% 116.85/18.08 | | CLOSE: (9) is inconsistent.
% 116.85/18.08 | |
% 116.85/18.08 | End of split
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #214 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_3 = all_10_1
% 116.85/18.08 (2) all_54_3 = e2
% 116.85/18.08 (3) ~ (all_10_1 = e2)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | COMBINE_EQS: (1), (2) imply:
% 116.85/18.08 | (4) all_10_1 = e2
% 116.85/18.08 |
% 116.85/18.08 | SIMP: (4) implies:
% 116.85/18.08 | (5) all_10_1 = e2
% 116.85/18.08 |
% 116.85/18.08 | REDUCE: (3), (5) imply:
% 116.85/18.08 | (6) $false
% 116.85/18.08 |
% 116.85/18.08 | CLOSE: (6) is inconsistent.
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #215 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) all_54_3 = all_10_1
% 116.85/18.08 (2) all_54_3 = e3
% 116.85/18.08 (3) ~ (all_10_1 = e3)
% 116.85/18.08
% 116.85/18.08 Begin of proof
% 116.85/18.08 |
% 116.85/18.08 | COMBINE_EQS: (1), (2) imply:
% 116.85/18.08 | (4) all_10_1 = e3
% 116.85/18.08 |
% 116.85/18.08 | SIMP: (4) implies:
% 116.85/18.08 | (5) all_10_1 = e3
% 116.85/18.08 |
% 116.85/18.08 | REDUCE: (3), (5) imply:
% 116.85/18.08 | (6) $false
% 116.85/18.08 |
% 116.85/18.08 | CLOSE: (6) is inconsistent.
% 116.85/18.08 |
% 116.85/18.08 End of proof
% 116.85/18.08
% 116.85/18.08 Sub-proof #216 shows that the following formulas are inconsistent:
% 116.85/18.08 ----------------------------------------------------------------
% 116.85/18.08 (1) ~ (all_52_8 = all_10_2)
% 116.85/18.08 (2) op(e2, all_8_2) = e3
% 116.85/18.08 (3) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.85/18.08 (4) ~ (all_52_2 = all_10_2)
% 116.85/18.08 (5) ~ (all_52_6 = all_52_14)
% 116.85/18.08 (6) all_54_2 = all_52_8
% 116.85/18.08 (7) all_58_7 = all_52_6
% 116.85/18.08 (8) all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 116.85/18.08 (9) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 116.85/18.08 (10) ~ (all_52_8 = all_52_11)
% 116.85/18.08 (11) ~ (all_52_9 = all_8_2)
% 116.85/18.08 (12) all_28_1 = all_6_1
% 116.85/18.08 (13) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.85/18.08 (14) ~ (all_52_13 = all_52_14)
% 116.85/18.08 (15) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 116.85/18.09 (16) ~ (all_4_2 = e0)
% 116.85/18.09 (17) op(e3, e2) = all_52_4
% 116.85/18.09 (18) all_56_14 = all_6_2
% 116.85/18.09 (19) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.85/18.09 (20) all_56_3 = all_52_1
% 116.85/18.09 (21) all_38_1 = all_10_1
% 116.85/18.09 (22) all_54_0 = all_10_2
% 116.85/18.09 (23) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.85/18.09 (24) all_54_3 = all_52_12
% 116.85/18.09 (25) ~ (all_52_2 = all_52_6)
% 116.85/18.09 (26) op(e0, e2) = all_52_7
% 116.85/18.09 (27) ~ (all_52_7 = all_4_2)
% 116.85/18.09 (28) all_56_11 = all_52_11
% 116.85/18.09 (29) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 116.85/18.09 (30) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.85/18.09 (31) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.85/18.09 (32) ~ (all_52_4 = all_52_8)
% 116.85/18.09 (33) ~ (all_52_12 = all_10_2)
% 116.85/18.09 (34) ~ (e3 = e1)
% 116.85/18.09 (35) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.85/18.09 (36) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.09 (37) all_56_12 = all_10_2
% 116.85/18.09 (38) all_58_0 = all_10_2
% 116.85/18.09 (39) all_54_11 = all_52_14
% 116.85/18.09 (40) all_54_13 = all_52_7
% 116.85/18.09 (41) all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 116.85/18.09 (42) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.85/18.09 (43) ~ (all_52_14 = all_6_2)
% 116.85/18.09 (44) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 116.85/18.09 (45) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.85/18.09 (46) all_56_10 = all_52_7
% 116.85/18.09 (47) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.85/18.09 (48) op(all_6_1, all_6_2) = e2
% 116.85/18.09 (49) all_54_14 = all_52_11
% 116.85/18.09 (50) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.85/18.09 (51) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 116.85/18.09 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.85/18.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.85/18.09 (53) all_54_8 = all_52_2
% 116.85/18.09 (54) ~ (all_52_2 = all_6_2)
% 116.85/18.09 (55) all_32_2 = all_10_2
% 116.85/18.09 (56) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.85/18.09 (57) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 116.85/18.09 (58) all_54_10 = all_6_2
% 116.85/18.09 (59) op(e3, e0) = all_52_12
% 116.85/18.09 (60) all_38_0 = all_10_0
% 116.85/18.09 (61) ~ (all_52_8 = all_6_2)
% 116.85/18.09 (62) all_58_4 = all_52_8
% 116.85/18.09 (63) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.85/18.09 (64) ~ (all_52_4 = all_52_7)
% 116.85/18.09 (65) all_56_2 = all_52_12
% 116.85/18.09 (66) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.85/18.09 (67) all_58_3 = all_8_2
% 116.85/18.09 (68) all_54_6 = all_52_9
% 116.85/18.09 (69) ~ (all_10_0 = e2)
% 116.85/18.09 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.85/18.09 (71) all_58_11 = all_52_14
% 116.85/18.09 (72) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.85/18.09 (73) all_54_9 = all_52_6
% 116.85/18.09 (74) op(e3, e1) = all_52_8
% 116.85/18.09 (75) ~ (all_52_2 = all_52_3)
% 116.85/18.09 (76) op(all_10_1, all_10_2) = all_10_0
% 116.85/18.09 (77) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.85/18.09 (78) ~ (all_52_11 = all_6_2)
% 116.85/18.09 (79) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.85/18.09 (80) op(e2, e3) = all_52_1
% 116.85/18.09 (81) all_28_2 = all_6_2
% 116.85/18.09 (82) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.85/18.09 (83) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.85/18.09 (84) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.85/18.09 (85) ~ (all_52_7 = all_8_2)
% 116.85/18.09 (86) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.85/18.09 (87) ~ (all_52_4 = all_8_2)
% 116.85/18.09 (88) op(e1, e0) = all_52_14
% 116.85/18.09 (89) all_58_5 = all_52_9
% 116.85/18.09 (90) ~ (all_52_9 = all_52_13)
% 116.85/18.09 (91) all_56_9 = all_52_3
% 116.85/18.09 (92) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.85/18.09 (93) op(e1, all_6_2) = all_6_1
% 116.85/18.09 (94) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.85/18.09 (95) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.85/18.09 (96) all_32_0 = all_10_0
% 116.85/18.09 (97) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.85/18.09 (98) all_58_15 = all_4_2
% 116.85/18.09 (99) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.85/18.09 (100) all_58_2 = all_52_1
% 116.85/18.09 (101) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.85/18.09 (102) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.85/18.09 (103) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 116.85/18.09 (104) ~ (all_10_2 = e3)
% 116.85/18.09 (105) all_58_13 = all_52_7
% 116.85/18.09 (106) all_32_1 = all_10_1
% 116.85/18.09 (107) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.85/18.09 (108) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.85/18.09 (109) ~ (all_52_14 = all_4_2)
% 116.85/18.09 (110) all_58_6 = all_52_2
% 116.85/18.09 (111) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.85/18.09 (112) ~ (all_52_1 = all_10_2)
% 116.85/18.09 (113) all_54_5 = all_8_2
% 116.85/18.09 (114) all_56_15 = all_4_2
% 116.85/18.09 (115) all_58_10 = all_52_13
% 116.85/18.09 (116) ~ (all_52_13 = all_8_2)
% 116.85/18.09 (117) ~ (all_52_11 = all_4_2)
% 116.85/18.09 (118) ~ (all_8_0 = e1)
% 116.85/18.09 (119) op(e3, all_10_2) = all_10_1
% 116.85/18.09 (120) ~ (all_52_6 = all_8_2)
% 116.85/18.09 (121) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.85/18.09 (122) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 116.85/18.09 (123) all_38_2 = all_10_2
% 116.85/18.09 (124) all_58_1 = all_52_4
% 116.85/18.09 (125) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.85/18.09 (126) ~ (all_52_9 = all_52_11)
% 116.85/18.09 (127) all_58_14 = all_52_11
% 116.85/18.09 (128) all_54_1 = all_52_4
% 116.85/18.09 (129) all_56_13 = all_8_2
% 116.85/18.09 (130) op(e0, e1) = all_52_11
% 116.85/18.09 (131) ~ (all_52_1 = all_8_2)
% 116.85/18.09 (132) ~ (all_8_2 = e2)
% 116.85/18.09 (133) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.85/18.09 (134) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.85/18.09 (135) ~ (all_52_7 = all_52_11)
% 116.85/18.09 (136) op(e1, e2) = all_52_6
% 116.85/18.09 (137) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.85/18.09 (138) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.85/18.09 (139) all_56_7 = all_52_6
% 116.85/18.09 (140) ~ (all_52_9 = all_6_2)
% 116.85/18.09 (141) ~ (all_52_4 = all_52_6)
% 116.85/18.09 (142) ~ (all_52_1 = all_52_2)
% 116.85/18.09 (143) all_56_1 = all_52_8
% 116.85/18.09 (144) op(e0, all_4_2) = all_4_1
% 116.85/18.09 (145) all_58_8 = all_6_2
% 116.85/18.09 (146) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.85/18.09 (147) ~ (all_10_0 = e1)
% 116.85/18.09 (148) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.85/18.09 (149) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.85/18.09 (150) all_56_4 = all_52_9
% 116.85/18.09 (151) all_58_9 = all_52_12
% 116.85/18.09 (152) all_56_5 = all_52_13
% 116.85/18.09 (153) op(e2, e1) = all_52_9
% 116.85/18.09 (154) ~ (all_52_3 = all_4_2)
% 116.85/18.09 (155) ~ (all_52_6 = all_6_2)
% 116.85/18.09 (156) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.85/18.09 (157) op(e3, all_8_2) = all_8_0
% 116.85/18.09 (158) all_56_6 = all_52_2
% 116.85/18.09 (159) ~ (all_52_13 = all_4_2)
% 116.85/18.09 (160) ~ (e2 = e0)
% 116.85/18.09 (161) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.85/18.09 (162) all_58_12 = all_52_3
% 116.85/18.09 (163) ~ (all_52_2 = all_52_14)
% 116.85/18.09 (164) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.85/18.09 (165) ~ (all_52_8 = all_52_9)
% 116.85/18.09 (166) op(e2, e0) = all_52_13
% 116.85/18.09 (167) ~ (all_52_12 = all_4_2)
% 116.85/18.09 (168) ~ (all_52_3 = all_10_2)
% 116.85/18.09 (169) op(e1, e3) = all_52_2
% 116.85/18.09 (170) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.85/18.09 (171) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.85/18.09 (172) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.85/18.09 (173) ~ (all_52_8 = all_52_12)
% 116.85/18.09 (174) all_56_8 = all_52_14
% 116.85/18.09 (175) ~ (all_52_4 = all_10_2)
% 116.85/18.09 (176) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.85/18.09 (177) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.85/18.09 (178) all_56_0 = all_52_4
% 116.85/18.09 (179) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.85/18.09 (180) ~ (e3 = e2)
% 116.85/18.09 (181) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.85/18.09 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.85/18.09 (182) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.85/18.09 (183) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.85/18.09 (184) all_54_15 = all_4_2
% 116.85/18.09 (185) ~ (all_6_2 = e1)
% 116.85/18.09 (186) ~ (all_6_1 = e2)
% 116.85/18.09 (187) ~ (all_52_6 = all_52_7)
% 116.85/18.09 (188) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 116.85/18.09 (189) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.85/18.09 (190) ~ (all_52_3 = all_52_7)
% 116.85/18.09
% 116.85/18.09 Begin of proof
% 116.85/18.09 |
% 116.85/18.09 | BETA: splitting (9) gives:
% 116.85/18.09 |
% 116.85/18.09 | Case 1:
% 116.85/18.09 | |
% 116.85/18.09 | | (191) ~ (all_32_1 = e1)
% 116.85/18.09 | |
% 116.85/18.09 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), (16),
% 116.85/18.09 | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 116.85/18.09 | | (28), (29), (30), (31), (33), (35), (36), (37), (38), (39), (40),
% 116.85/18.09 | | (42), (43), (44), (45), (46), (48), (49), (50), (52), (53), (54),
% 116.85/18.09 | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 116.85/18.09 | | (67), (68), (69), (71), (72), (74), (75), (76), (77), (78), (79),
% 116.85/18.09 | | (81), (82), (83), (84), (86), (87), (88), (89), (90), (91), (92),
% 116.85/18.09 | | (93), (94), (95), (97), (98), (99), (100), (101), (102), (103),
% 116.85/18.09 | | (104), (105), (106), (107), (108), (109), (110), (112), (113),
% 116.85/18.09 | | (114), (115), (116), (117), (119), (120), (121), (122), (123),
% 116.85/18.09 | | (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 116.85/18.09 | | (133), (136), (137), (138), (139), (140), (141), (142), (143),
% 116.85/18.09 | | (144), (145), (146), (147), (149), (150), (151), (152), (153),
% 116.85/18.09 | | (155), (156), (158), (159), (160), (161), (162), (163), (164),
% 116.85/18.09 | | (165), (166), (167), (168), (169), (170), (172), (173), (174),
% 116.85/18.09 | | (175), (176), (177), (178), (179), (180), (181), (182), (183),
% 116.85/18.09 | | (184), (185), (186), (187), (188), (189), (191) are inconsistent
% 116.85/18.09 | | by sub-proof #254.
% 116.85/18.09 | |
% 116.85/18.09 | Case 2:
% 116.85/18.09 | |
% 116.85/18.09 | | (192) all_32_1 = e1
% 116.85/18.09 | | (193) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 116.85/18.09 | |
% 116.85/18.09 | | COMBINE_EQS: (106), (192) imply:
% 116.85/18.09 | | (194) all_10_1 = e1
% 116.85/18.09 | |
% 116.85/18.09 | | SIMP: (194) implies:
% 116.85/18.09 | | (195) all_10_1 = e1
% 116.85/18.09 | |
% 116.85/18.09 | | REDUCE: (76), (195) imply:
% 116.85/18.09 | | (196) op(e1, all_10_2) = all_10_0
% 116.85/18.09 | |
% 116.85/18.09 | | REDUCE: (119), (195) imply:
% 116.85/18.09 | | (197) op(e3, all_10_2) = e1
% 116.85/18.09 | |
% 116.85/18.09 | | BETA: splitting (107) gives:
% 116.85/18.09 | |
% 116.85/18.09 | | Case 1:
% 116.85/18.09 | | |
% 116.85/18.09 | | | (198) ~ (all_56_14 = e2)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (18), (198) imply:
% 116.85/18.09 | | | (199) ~ (all_6_2 = e2)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REF_CLOSE: (1), (3), (4), (7), (11), (12), (13), (16), (17), (18), (19),
% 116.85/18.09 | | | (20), (22), (25), (27), (30), (35), (36), (37), (38), (39),
% 116.85/18.09 | | | (42), (43), (47), (50), (52), (53), (54), (55), (58), (61),
% 116.85/18.09 | | | (62), (63), (65), (66), (67), (69), (70), (73), (74), (78),
% 116.85/18.09 | | | (81), (85), (86), (87), (88), (89), (93), (95), (96), (98),
% 116.85/18.09 | | | (100), (101), (103), (104), (105), (108), (113), (114), (115),
% 116.85/18.09 | | | (121), (124), (127), (129), (132), (135), (136), (139), (140),
% 116.85/18.09 | | | (145), (146), (149), (150), (151), (152), (155), (158), (162),
% 116.85/18.09 | | | (164), (168), (169), (171), (172), (174), (175), (177), (181),
% 116.85/18.09 | | | (184), (185), (186), (187), (193), (196), (197), (199) are
% 116.85/18.09 | | | inconsistent by sub-proof #249.
% 116.85/18.09 | | |
% 116.85/18.09 | | Case 2:
% 116.85/18.09 | | |
% 116.85/18.09 | | | (200) all_56_14 = e2
% 116.85/18.09 | | | (201) ~ (all_56_10 = e0)
% 116.85/18.09 | | |
% 116.85/18.09 | | | COMBINE_EQS: (18), (200) imply:
% 116.85/18.09 | | | (202) all_6_2 = e2
% 116.85/18.09 | | |
% 116.85/18.09 | | | SIMP: (202) implies:
% 116.85/18.09 | | | (203) all_6_2 = e2
% 116.85/18.09 | | |
% 116.85/18.09 | | | COMBINE_EQS: (145), (203) imply:
% 116.85/18.09 | | | (204) all_58_8 = e2
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (46), (201) imply:
% 116.85/18.09 | | | (205) ~ (all_52_7 = e0)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (54), (203) imply:
% 116.85/18.09 | | | (206) ~ (all_52_2 = e2)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (155), (203) imply:
% 116.85/18.09 | | | (207) ~ (all_52_6 = e2)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (140), (203) imply:
% 116.85/18.09 | | | (208) ~ (all_52_9 = e2)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (185), (203) imply:
% 116.85/18.09 | | | (209) ~ (e2 = e1)
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (48), (203) imply:
% 116.85/18.09 | | | (210) op(all_6_1, e2) = e2
% 116.85/18.09 | | |
% 116.85/18.09 | | | REDUCE: (93), (203) imply:
% 116.85/18.09 | | | (211) op(e1, e2) = all_6_1
% 116.85/18.09 | | |
% 116.85/18.09 | | | BETA: splitting (182) gives:
% 116.85/18.09 | | |
% 116.85/18.09 | | | Case 1:
% 116.85/18.09 | | | |
% 116.85/18.10 | | | | (212) ~ (all_56_0 = e3)
% 116.85/18.10 | | | |
% 116.85/18.10 | | | | REDUCE: (178), (212) imply:
% 116.85/18.10 | | | | (213) ~ (all_52_4 = e3)
% 116.85/18.10 | | | |
% 116.85/18.10 | | | | BETA: splitting (45) gives:
% 116.85/18.10 | | | |
% 116.85/18.10 | | | | Case 1:
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | (214) ~ (all_56_7 = e1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | REDUCE: (139), (214) imply:
% 116.85/18.10 | | | | | (215) ~ (all_52_6 = e1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | GROUND_INST: instantiating (52) with all_52_6, all_6_1, e2, e1,
% 116.85/18.10 | | | | | simplifying with (136), (211) gives:
% 116.85/18.10 | | | | | (216) all_52_6 = all_6_1
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | COMBINE_EQS: (73), (216) imply:
% 116.85/18.10 | | | | | (217) all_54_9 = all_6_1
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | COMBINE_EQS: (7), (216) imply:
% 116.85/18.10 | | | | | (218) all_58_7 = all_6_1
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | REDUCE: (25), (216) imply:
% 116.85/18.10 | | | | | (219) ~ (all_52_2 = all_6_1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | REDUCE: (187), (216) imply:
% 116.85/18.10 | | | | | (220) ~ (all_52_7 = all_6_1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | SIMP: (220) implies:
% 116.85/18.10 | | | | | (221) ~ (all_52_7 = all_6_1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | REDUCE: (120), (216) imply:
% 116.85/18.10 | | | | | (222) ~ (all_8_2 = all_6_1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | SIMP: (222) implies:
% 116.85/18.10 | | | | | (223) ~ (all_8_2 = all_6_1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | REDUCE: (215), (216) imply:
% 116.85/18.10 | | | | | (224) ~ (all_6_1 = e1)
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | BETA: splitting (103) gives:
% 116.85/18.10 | | | | |
% 116.85/18.10 | | | | | Case 1:
% 116.85/18.10 | | | | | |
% 116.85/18.10 | | | | | | (225) ~ (all_56_13 = e3)
% 116.85/18.10 | | | | | |
% 116.85/18.10 | | | | | | REDUCE: (129), (225) imply:
% 116.85/18.10 | | | | | | (226) ~ (all_8_2 = e3)
% 116.85/18.10 | | | | | |
% 116.85/18.10 | | | | | | BETA: splitting (92) gives:
% 116.85/18.10 | | | | | |
% 116.85/18.10 | | | | | | Case 1:
% 116.85/18.10 | | | | | | |
% 116.85/18.10 | | | | | | | (227) ~ (all_56_15 = e1)
% 116.85/18.10 | | | | | | |
% 116.85/18.10 | | | | | | | REDUCE: (114), (227) imply:
% 116.85/18.10 | | | | | | | (228) ~ (all_4_2 = e1)
% 116.85/18.10 | | | | | | |
% 116.85/18.10 | | | | | | | BETA: splitting (176) gives:
% 116.85/18.10 | | | | | | |
% 116.85/18.10 | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | |
% 116.85/18.10 | | | | | | | | (229) ~ (all_56_12 = e1)
% 116.85/18.10 | | | | | | | |
% 116.85/18.10 | | | | | | | | REDUCE: (37), (229) imply:
% 116.85/18.10 | | | | | | | | (230) ~ (all_10_2 = e1)
% 116.85/18.10 | | | | | | | |
% 116.85/18.10 | | | | | | | | BETA: splitting (79) gives:
% 116.85/18.10 | | | | | | | |
% 116.85/18.10 | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | |
% 116.85/18.10 | | | | | | | | | (231) ~ (all_56_13 = e1)
% 116.85/18.10 | | | | | | | | |
% 116.85/18.10 | | | | | | | | | REDUCE: (129), (231) imply:
% 116.85/18.10 | | | | | | | | | (232) ~ (all_8_2 = e1)
% 116.85/18.10 | | | | | | | | |
% 116.85/18.10 | | | | | | | | | BETA: splitting (36) gives:
% 116.85/18.10 | | | | | | | | |
% 116.85/18.10 | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | (233) all_54_5 = e3
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | REF_CLOSE: (113), (226), (233) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | #339.
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | (234) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | BETA: splitting (234) gives:
% 116.85/18.10 | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | (235) all_54_5 = e2
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | REF_CLOSE: (113), (132), (235) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | #338.
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | (236) ~ (all_54_5 = e2)
% 116.85/18.10 | | | | | | | | | | | (237) all_54_5 = e1 | all_54_5 = e0
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | BETA: splitting (237) gives:
% 116.85/18.10 | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | (238) all_54_5 = e1
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | REF_CLOSE: (113), (232), (238) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | | #337.
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | (239) all_54_5 = e0
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | COMBINE_EQS: (113), (239) imply:
% 116.85/18.10 | | | | | | | | | | | | (240) all_8_2 = e0
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | SIMP: (240) implies:
% 116.85/18.10 | | | | | | | | | | | | (241) all_8_2 = e0
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | COMBINE_EQS: (129), (241) imply:
% 116.85/18.10 | | | | | | | | | | | | (242) all_56_13 = e0
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | BETA: splitting (125) gives:
% 116.85/18.10 | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | (243) ~ (all_56_2 = e3)
% 116.85/18.10 | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | REDUCE: (65), (243) imply:
% 116.85/18.10 | | | | | | | | | | | | | (244) ~ (all_52_12 = e3)
% 116.85/18.10 | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | BETA: splitting (44) gives:
% 116.85/18.10 | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | (245) ~ (all_56_8 = e1)
% 116.85/18.10 | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | REDUCE: (174), (245) imply:
% 116.85/18.10 | | | | | | | | | | | | | | (246) ~ (all_52_14 = e1)
% 116.85/18.10 | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 116.85/18.10 | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | (247) all_58_6 = e1
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | COMBINE_EQS: (110), (247) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | (248) all_52_2 = e1
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | SIMP: (248) implies:
% 116.85/18.10 | | | | | | | | | | | | | | | (249) all_52_2 = e1
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | COMBINE_EQS: (158), (249) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | (250) all_56_6 = e1
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 116.85/18.10 | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | (251) ~ (all_56_6 = e1)
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | REDUCE: (250), (251) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | (252) $false
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | (253) ~ (all_56_15 = e3)
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | REDUCE: (114), (253) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | (254) ~ (all_4_2 = e3)
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | (255) all_54_15 = e3
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (255) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | (256) all_4_2 = e3
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | REDUCE: (254), (256) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | (257) $false
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | (258) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | (259) all_54_15 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (259) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | (260) all_4_2 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | REDUCE: (167), (260) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | (261) ~ (all_52_12 = e2)
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | REDUCE: (159), (260) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | (262) ~ (all_52_13 = e2)
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | (263) ~ (all_56_6 = e1)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | REDUCE: (250), (263) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | (264) $false
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (265) all_58_2 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (265) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (266) all_52_1 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (267) all_52_1 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (267) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (268) ~ (all_10_2 = e2)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | SIMP: (268) implies:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (269) ~ (all_10_2 = e2)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (267) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | (270) ~ (all_8_2 = e2)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | (271) all_54_0 = e3
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (104), (271) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | #451.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | (272) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | (273) all_54_5 = e3
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (226), (273) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | #339.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | (274) all_54_5 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (132), (274) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | #338.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | (275) all_54_5 = e1
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (232), (275) are inconsistent by sub-proof
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | #337.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (241) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | (276) op(e3, e0) = all_8_0
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_54_0 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (277) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_10_2 = e2
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (278) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | (279) $false
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_54_0 = e1 | all_54_0 = e0
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_9 = e1
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (281) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_52_12 = e1
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (282) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (283) op(e3, e0) = e1
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e1, all_8_0, e0, e3,
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (276), (283) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (284) all_8_0 = e1
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (284) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (285) $false
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (286) ~ (all_58_9 = e1)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (151), (286) imply:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_52_12 = e1)
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.85/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_54_3 = e3
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (244), (288) are inconsistent by sub-proof
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | #224.
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (24), (33), (230), (261), (280), (287),
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) are inconsistent by sub-proof #223.
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | (290) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (89), (115), (132), (208), (262), (290) are
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401.
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | (291) all_54_15 = e1 | all_54_15 = e0
% 116.97/18.10 | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (184), (228), (291) are inconsistent by
% 116.97/18.10 | | | | | | | | | | | | | | | | | | sub-proof #418.
% 116.97/18.10 | | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | (292) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.10 | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | | REF_CLOSE: (7), (71), (145), (185), (215), (246), (292) are
% 116.97/18.10 | | | | | | | | | | | | | | | inconsistent by sub-proof #354.
% 116.97/18.10 | | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | (293) ~ (all_56_13 = e0)
% 116.97/18.10 | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | REDUCE: (242), (293) imply:
% 116.97/18.10 | | | | | | | | | | | | | | (294) $false
% 116.97/18.10 | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 116.97/18.10 | | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | (295) all_56_2 = e3
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | REF_CLOSE: (113), (125), (129), (132), (232), (234), (295)
% 116.97/18.10 | | | | | | | | | | | | | are inconsistent by sub-proof #286.
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | | (296) all_56_13 = e1
% 116.97/18.10 | | | | | | | | | (297) ~ (all_56_11 = e0)
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | | REDUCE: (28), (297) imply:
% 116.97/18.10 | | | | | | | | | (298) ~ (all_52_11 = e0)
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | | BETA: splitting (51) gives:
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | | Case 1:
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | (299) ~ (all_56_1 = e3)
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | REDUCE: (143), (299) imply:
% 116.97/18.10 | | | | | | | | | | (300) ~ (all_52_8 = e3)
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | BETA: splitting (181) gives:
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | Case 1:
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | (301) all_58_15 = e0
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | COMBINE_EQS: (98), (301) imply:
% 116.97/18.10 | | | | | | | | | | | (302) all_4_2 = e0
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | REDUCE: (16), (302) imply:
% 116.97/18.10 | | | | | | | | | | | (303) $false
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | (304) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 116.97/18.10 | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 116.97/18.10 | | | | | | | | | | | e0)
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | ALPHA: (304) implies:
% 116.97/18.10 | | | | | | | | | | | (305) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | BETA: splitting (305) gives:
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | Case 1:
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | (306) all_58_12 = e0
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | COMBINE_EQS: (162), (306) imply:
% 116.97/18.10 | | | | | | | | | | | | (307) all_52_3 = e0
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | SIMP: (307) implies:
% 116.97/18.10 | | | | | | | | | | | | (308) all_52_3 = e0
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | COMBINE_EQS: (91), (308) imply:
% 116.97/18.10 | | | | | | | | | | | | (309) all_56_9 = e0
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | REDUCE: (154), (308) imply:
% 116.97/18.10 | | | | | | | | | | | | (310) ~ (all_4_2 = e0)
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | BETA: splitting (148) gives:
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | Case 1:
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | (311) ~ (all_56_15 = e3)
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | REDUCE: (114), (311) imply:
% 116.97/18.10 | | | | | | | | | | | | | (312) ~ (all_4_2 = e3)
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | REF_CLOSE: (1), (3), (16), (22), (33), (37), (38), (52),
% 116.97/18.10 | | | | | | | | | | | | | (62), (63), (65), (67), (74), (89), (100), (104),
% 116.97/18.10 | | | | | | | | | | | | | (112), (115), (124), (132), (146), (151), (159),
% 116.97/18.10 | | | | | | | | | | | | | (172), (177), (184), (197), (208), (213), (228),
% 116.97/18.10 | | | | | | | | | | | | | (300), (312) are inconsistent by sub-proof #243.
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | (313) ~ (all_56_9 = e0)
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | REDUCE: (309), (313) imply:
% 116.97/18.10 | | | | | | | | | | | | | (314) $false
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | | CLOSE: (314) is inconsistent.
% 116.97/18.10 | | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | (315) all_58_13 = e0 | all_58_14 = e0
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | | REF_CLOSE: (105), (127), (205), (298), (315) are inconsistent
% 116.97/18.10 | | | | | | | | | | | | by sub-proof #428.
% 116.97/18.10 | | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | (316) ~ (all_56_13 = e1)
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | REDUCE: (296), (316) imply:
% 116.97/18.10 | | | | | | | | | | (317) $false
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | | CLOSE: (317) is inconsistent.
% 116.97/18.10 | | | | | | | | | |
% 116.97/18.10 | | | | | | | | | End of split
% 116.97/18.10 | | | | | | | | |
% 116.97/18.10 | | | | | | | | End of split
% 116.97/18.10 | | | | | | | |
% 116.97/18.10 | | | | | | | Case 2:
% 116.97/18.10 | | | | | | | |
% 116.97/18.10 | | | | | | | | (318) all_56_12 = e1
% 116.97/18.10 | | | | | | | |
% 116.97/18.10 | | | | | | | | COMBINE_EQS: (37), (318) imply:
% 116.97/18.10 | | | | | | | | (319) all_10_2 = e1
% 116.97/18.10 | | | | | | | |
% 116.97/18.10 | | | | | | | | REF_CLOSE: (1), (52), (74), (197), (319) are inconsistent by
% 116.97/18.10 | | | | | | | | sub-proof #299.
% 116.97/18.10 | | | | | | | |
% 116.97/18.10 | | | | | | | End of split
% 116.97/18.10 | | | | | | |
% 116.97/18.10 | | | | | | Case 2:
% 116.97/18.10 | | | | | | |
% 116.97/18.10 | | | | | | | (320) all_56_15 = e1
% 116.97/18.10 | | | | | | | (321) ~ (all_56_11 = e0)
% 116.97/18.10 | | | | | | |
% 116.97/18.10 | | | | | | | COMBINE_EQS: (114), (320) imply:
% 116.97/18.11 | | | | | | | (322) all_4_2 = e1
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | SIMP: (322) implies:
% 116.97/18.11 | | | | | | | (323) all_4_2 = e1
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | COMBINE_EQS: (98), (323) imply:
% 116.97/18.11 | | | | | | | (324) all_58_15 = e1
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | REDUCE: (28), (321) imply:
% 116.97/18.11 | | | | | | | (325) ~ (all_52_11 = e0)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | REDUCE: (27), (323) imply:
% 116.97/18.11 | | | | | | | (326) ~ (all_52_7 = e1)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | REDUCE: (117), (323) imply:
% 116.97/18.11 | | | | | | | (327) ~ (all_52_11 = e1)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | REDUCE: (16), (323) imply:
% 116.97/18.11 | | | | | | | (328) ~ (e1 = e0)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | BETA: splitting (111) gives:
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | (329) ~ (all_56_1 = e3)
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | REDUCE: (143), (329) imply:
% 116.97/18.11 | | | | | | | | (330) ~ (all_52_8 = e3)
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | BETA: splitting (188) gives:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | (331) all_54_14 = e3
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | COMBINE_EQS: (49), (331) imply:
% 116.97/18.11 | | | | | | | | | (332) all_52_11 = e3
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | SIMP: (332) implies:
% 116.97/18.11 | | | | | | | | | (333) all_52_11 = e3
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | REDUCE: (135), (333) imply:
% 116.97/18.11 | | | | | | | | | (334) ~ (all_52_7 = e3)
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | BETA: splitting (23) gives:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (335) all_54_13 = e3
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | REF_CLOSE: (40), (334), (335) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | #336.
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (336) ~ (all_54_13 = e3)
% 116.97/18.11 | | | | | | | | | | (337) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | BETA: splitting (337) gives:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | (338) all_54_13 = e2
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | COMBINE_EQS: (40), (338) imply:
% 116.97/18.11 | | | | | | | | | | | (339) all_52_7 = e2
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | SIMP: (339) implies:
% 116.97/18.11 | | | | | | | | | | | (340) all_52_7 = e2
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | COMBINE_EQS: (105), (340) imply:
% 116.97/18.11 | | | | | | | | | | | (341) all_58_13 = e2
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (64), (340) imply:
% 116.97/18.11 | | | | | | | | | | | (342) ~ (all_52_4 = e2)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (334), (340) imply:
% 116.97/18.11 | | | | | | | | | | | (343) ~ (e3 = e2)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | BETA: splitting (133) gives:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | (344) all_58_1 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | COMBINE_EQS: (124), (344) imply:
% 116.97/18.11 | | | | | | | | | | | | (345) all_52_4 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | REDUCE: (213), (345) imply:
% 116.97/18.11 | | | | | | | | | | | | (346) $false
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | CLOSE: (346) is inconsistent.
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | (347) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | BETA: splitting (347) gives:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | (348) all_58_3 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | COMBINE_EQS: (67), (348) imply:
% 116.97/18.11 | | | | | | | | | | | | | (349) all_8_2 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | REDUCE: (226), (349) imply:
% 116.97/18.11 | | | | | | | | | | | | | (350) $false
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | (351) all_58_7 = e3 | all_58_13 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | REF_CLOSE: (17), (52), (180), (210), (218), (341), (342),
% 116.97/18.11 | | | | | | | | | | | | | (351) are inconsistent by sub-proof #263.
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | (352) all_54_13 = e1 | all_54_13 = e0
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REF_CLOSE: (40), (205), (326), (352) are inconsistent by
% 116.97/18.11 | | | | | | | | | | | sub-proof #333.
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | (353) ~ (all_54_14 = e3)
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | REDUCE: (49), (353) imply:
% 116.97/18.11 | | | | | | | | | (354) ~ (all_52_11 = e3)
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | BETA: splitting (181) gives:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (355) all_58_15 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | COMBINE_EQS: (324), (355) imply:
% 116.97/18.11 | | | | | | | | | | (356) e1 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | REDUCE: (328), (356) imply:
% 116.97/18.11 | | | | | | | | | | (357) $false
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | CLOSE: (357) is inconsistent.
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (358) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.97/18.11 | | | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | ALPHA: (358) implies:
% 116.97/18.11 | | | | | | | | | | (359) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | BETA: splitting (359) gives:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | (360) all_58_12 = e0
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | COMBINE_EQS: (162), (360) imply:
% 116.97/18.11 | | | | | | | | | | | (361) all_52_3 = e0
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | SIMP: (361) implies:
% 116.97/18.11 | | | | | | | | | | | (362) all_52_3 = e0
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (190), (362) imply:
% 116.97/18.11 | | | | | | | | | | | (363) ~ (all_52_7 = e0)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (168), (362) imply:
% 116.97/18.11 | | | | | | | | | | | (364) ~ (all_10_2 = e0)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | SIMP: (364) implies:
% 116.97/18.11 | | | | | | | | | | | (365) ~ (all_10_2 = e0)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | BETA: splitting (41) gives:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | (366) all_58_4 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | COMBINE_EQS: (62), (366) imply:
% 116.97/18.11 | | | | | | | | | | | | (367) all_52_8 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | REDUCE: (330), (367) imply:
% 116.97/18.11 | | | | | | | | | | | | (368) $false
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | (369) all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | BETA: splitting (369) gives:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | (370) all_58_5 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | COMBINE_EQS: (89), (370) imply:
% 116.97/18.11 | | | | | | | | | | | | | (371) all_52_9 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | (372) all_58_4 = e1
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | COMBINE_EQS: (62), (372) imply:
% 116.97/18.11 | | | | | | | | | | | | | | (373) all_52_8 = e1
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | REDUCE: (32), (373) imply:
% 116.97/18.11 | | | | | | | | | | | | | | (374) ~ (all_52_4 = e1)
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | REDUCE: (1), (373) imply:
% 116.97/18.11 | | | | | | | | | | | | | | (375) ~ (all_10_2 = e1)
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | SIMP: (375) implies:
% 116.97/18.11 | | | | | | | | | | | | | | (376) ~ (all_10_2 = e1)
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | (377) all_54_0 = e3
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | REF_CLOSE: (22), (104), (377) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | | #451.
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | (378) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | (379) all_54_0 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (379) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (380) all_10_2 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | SIMP: (380) implies:
% 116.97/18.11 | | | | | | | | | | | | | | | | (381) all_10_2 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (381) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (382) all_32_2 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (381) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (383) all_56_12 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | REDUCE: (175), (381) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (384) ~ (all_52_4 = e2)
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | REDUCE: (197), (381) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (385) op(e3, e2) = e1
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | REDUCE: (196), (381) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | (386) op(e1, e2) = all_10_0
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | (387) all_54_1 = e3
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (213), (387) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | | | | #222.
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | (388) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | (389) all_54_1 = e2
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (384), (389) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | | | | | #221.
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | (390) all_54_1 = e1 | all_54_1 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives:
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (391) all_54_1 = e1
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (374), (391) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | #220.
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (392) all_54_1 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (392) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (393) all_52_4 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | SIMP: (393) implies:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (394) all_52_4 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | REDUCE: (87), (394) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (395) ~ (all_8_2 = e0)
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | SIMP: (395) implies:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (396) ~ (all_8_2 = e0)
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | REDUCE: (374), (394) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (397) ~ (e1 = e0)
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (52), (67), (95), (96), (105), (124),
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (134), (136), (193), (205), (328), (382), (383),
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | (385), (386), (396) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | | | | | | #242.
% 116.97/18.11 | | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | (398) all_54_0 = e1 | all_54_0 = e0
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (365), (376), (398) are inconsistent by
% 116.97/18.11 | | | | | | | | | | | | | | | | sub-proof #423.
% 116.97/18.11 | | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | (399) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | (400) all_58_5 = e1
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | COMBINE_EQS: (370), (400) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | (401) e3 = e1
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | REDUCE: (34), (401) imply:
% 116.97/18.11 | | | | | | | | | | | | | | | (402) $false
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | CLOSE: (402) is inconsistent.
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | (403) all_58_8 = e1 | all_58_14 = e1
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | | REF_CLOSE: (127), (145), (185), (327), (403) are inconsistent
% 116.97/18.11 | | | | | | | | | | | | | | | by sub-proof #219.
% 116.97/18.11 | | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | (404) all_58_8 = e3 | all_58_14 = e3
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | BETA: splitting (404) gives:
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | (405) all_58_8 = e3
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | COMBINE_EQS: (204), (405) imply:
% 116.97/18.11 | | | | | | | | | | | | | | (406) e3 = e2
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | SIMP: (406) implies:
% 116.97/18.11 | | | | | | | | | | | | | | (407) e3 = e2
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | REDUCE: (180), (407) imply:
% 116.97/18.11 | | | | | | | | | | | | | | (408) $false
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | CLOSE: (408) is inconsistent.
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | (409) all_58_14 = e3
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | | REF_CLOSE: (127), (354), (409) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | | | | | #218.
% 116.97/18.11 | | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | (410) all_58_13 = e0 | all_58_14 = e0
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REF_CLOSE: (105), (127), (205), (325), (410) are inconsistent
% 116.97/18.11 | | | | | | | | | | | by sub-proof #428.
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | End of split
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | End of split
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | (411) ~ (all_56_15 = e1)
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | REDUCE: (320), (411) imply:
% 116.97/18.11 | | | | | | | | (412) $false
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | CLOSE: (412) is inconsistent.
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | End of split
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | End of split
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | Case 2:
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | (413) all_56_13 = e3
% 116.97/18.11 | | | | | | (414) ~ (all_56_9 = e0)
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | COMBINE_EQS: (129), (413) imply:
% 116.97/18.11 | | | | | | (415) all_8_2 = e3
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | SIMP: (415) implies:
% 116.97/18.11 | | | | | | (416) all_8_2 = e3
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | REDUCE: (91), (414) imply:
% 116.97/18.11 | | | | | | (417) ~ (all_52_3 = e0)
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | REDUCE: (223), (416) imply:
% 116.97/18.11 | | | | | | (418) ~ (all_6_1 = e3)
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | SIMP: (418) implies:
% 116.97/18.11 | | | | | | (419) ~ (all_6_1 = e3)
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | REDUCE: (2), (416) imply:
% 116.97/18.11 | | | | | | (420) op(e2, e3) = e3
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | BETA: splitting (97) gives:
% 116.97/18.11 | | | | | |
% 116.97/18.11 | | | | | | Case 1:
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | (421) ~ (all_56_6 = e1)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | REDUCE: (158), (421) imply:
% 116.97/18.11 | | | | | | | (422) ~ (all_52_2 = e1)
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | BETA: splitting (70) gives:
% 116.97/18.11 | | | | | | |
% 116.97/18.11 | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | (423) all_54_9 = e3
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | REF_CLOSE: (217), (419), (423) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | #230.
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | (424) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | BETA: splitting (424) gives:
% 116.97/18.11 | | | | | | | |
% 116.97/18.11 | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | (425) all_54_9 = e2
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | REF_CLOSE: (186), (217), (425) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | #229.
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | (426) all_54_9 = e1 | all_54_9 = e0
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | BETA: splitting (426) gives:
% 116.97/18.11 | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (427) all_54_9 = e1
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | REF_CLOSE: (217), (224), (427) are inconsistent by sub-proof
% 116.97/18.11 | | | | | | | | | | #228.
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | Case 2:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | (428) all_54_9 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | COMBINE_EQS: (217), (428) imply:
% 116.97/18.11 | | | | | | | | | | (429) all_6_1 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | SIMP: (429) implies:
% 116.97/18.11 | | | | | | | | | | (430) all_6_1 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | COMBINE_EQS: (218), (430) imply:
% 116.97/18.11 | | | | | | | | | | (431) all_58_7 = e0
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | REDUCE: (219), (430) imply:
% 116.97/18.11 | | | | | | | | | | (432) ~ (all_52_2 = e0)
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | REDUCE: (224), (430) imply:
% 116.97/18.11 | | | | | | | | | | (433) ~ (e1 = e0)
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | SIMP: (433) implies:
% 116.97/18.11 | | | | | | | | | | (434) ~ (e1 = e0)
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | BETA: splitting (86) gives:
% 116.97/18.11 | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | (435) all_54_8 = e3
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | COMBINE_EQS: (53), (435) imply:
% 116.97/18.11 | | | | | | | | | | | (436) all_52_2 = e3
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | SIMP: (436) implies:
% 116.97/18.11 | | | | | | | | | | | (437) all_52_2 = e3
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | COMBINE_EQS: (110), (437) imply:
% 116.97/18.11 | | | | | | | | | | | (438) all_58_6 = e3
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (142), (437) imply:
% 116.97/18.11 | | | | | | | | | | | (439) ~ (all_52_1 = e3)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | REDUCE: (4), (437) imply:
% 116.97/18.11 | | | | | | | | | | | (440) ~ (all_10_2 = e3)
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | BETA: splitting (181) gives:
% 116.97/18.11 | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | Case 1:
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | (441) all_58_15 = e0
% 116.97/18.11 | | | | | | | | | | | |
% 116.97/18.11 | | | | | | | | | | | | COMBINE_EQS: (98), (441) imply:
% 116.97/18.12 | | | | | | | | | | | | (442) all_4_2 = e0
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | REDUCE: (16), (442) imply:
% 116.97/18.12 | | | | | | | | | | | | (443) $false
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | (444) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 116.97/18.12 | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 116.97/18.12 | | | | | | | | | | | | e0)
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | ALPHA: (444) implies:
% 116.97/18.12 | | | | | | | | | | | | (445) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | BETA: splitting (445) gives:
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | (446) all_58_12 = e0
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | REF_CLOSE: (162), (417), (446) are inconsistent by sub-proof
% 116.97/18.12 | | | | | | | | | | | | | #362.
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | (447) ~ (all_58_12 = e0)
% 116.97/18.12 | | | | | | | | | | | | | (448) all_58_13 = e0 | all_58_14 = e0
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | BETA: splitting (137) gives:
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | (449) all_58_6 = e1
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | COMBINE_EQS: (438), (449) imply:
% 116.97/18.12 | | | | | | | | | | | | | | (450) e3 = e1
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | SIMP: (450) implies:
% 116.97/18.12 | | | | | | | | | | | | | | (451) e3 = e1
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | REDUCE: (34), (451) imply:
% 116.97/18.12 | | | | | | | | | | | | | | (452) $false
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | CLOSE: (452) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | (453) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | (454) all_58_7 = e1
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | REF_CLOSE: (431), (434), (454) are inconsistent by sub-proof
% 116.97/18.12 | | | | | | | | | | | | | | | #389.
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | (455) all_58_8 = e1 | all_58_11 = e1
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | (456) ~ (all_56_12 = e1)
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | REDUCE: (37), (456) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | (457) ~ (all_10_2 = e1)
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | (458) all_58_8 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (458) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | (459) e2 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | REDUCE: (209), (459) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | (460) $false
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | (461) all_58_11 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (461) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | (462) all_52_14 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (462) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | (463) all_56_8 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | (464) ~ (all_56_8 = e1)
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | REDUCE: (463), (464) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | (465) $false
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | (466) ~ (all_56_12 = e0)
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | REDUCE: (37), (466) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | (467) ~ (all_10_2 = e0)
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | (468) all_54_0 = e3
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (104), (468) are inconsistent by sub-proof
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | #451.
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | (469) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | (470) all_58_0 = e2
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (470) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | (471) all_10_2 = e2
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | (472) all_58_0 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (470), (472) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | (473) e2 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (473) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | (474) $false
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | CLOSE: (474) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | (475) all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (476) all_58_2 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (476) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (477) all_52_1 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (439), (477) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (478) ~ (e3 = e0)
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | SIMP: (478) implies:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (479) ~ (e3 = e0)
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (477) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (480) op(e2, e3) = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e0, e3, e3, e2,
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | simplifying with (420), (480) gives:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (481) e3 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (481) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (482) $false
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (482) is inconsistent.
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | (483) all_58_6 = e0 | all_58_12 = e0
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (162), (417), (432), (483) are inconsistent
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #217.
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | (484) ~ (all_58_0 = e2)
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (484) imply:
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | (485) ~ (all_10_2 = e2)
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (457), (467), (469), (485) are inconsistent
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | | by sub-proof #386.
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | (486) all_56_12 = e1
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | | REF_CLOSE: (28), (105), (127), (176), (205), (448), (486) are
% 116.97/18.12 | | | | | | | | | | | | | | | | inconsistent by sub-proof #361.
% 116.97/18.12 | | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | Case 2:
% 116.97/18.12 | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | (487) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.97/18.12 | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | | REF_CLOSE: (53), (206), (422), (432), (487) are inconsistent
% 116.97/18.12 | | | | | | | | | | | by sub-proof #381.
% 116.97/18.12 | | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | | |
% 116.97/18.12 | | | | | | | | | End of split
% 116.97/18.12 | | | | | | | | |
% 116.97/18.12 | | | | | | | | End of split
% 116.97/18.12 | | | | | | | |
% 116.97/18.12 | | | | | | | End of split
% 116.97/18.12 | | | | | | |
% 116.97/18.12 | | | | | | Case 2:
% 116.97/18.12 | | | | | | |
% 116.97/18.12 | | | | | | | (488) ~ (all_56_13 = e3)
% 116.97/18.12 | | | | | | |
% 116.97/18.12 | | | | | | | REDUCE: (413), (488) imply:
% 116.97/18.12 | | | | | | | (489) $false
% 116.97/18.12 | | | | | | |
% 116.97/18.12 | | | | | | | CLOSE: (489) is inconsistent.
% 116.97/18.12 | | | | | | |
% 116.97/18.12 | | | | | | End of split
% 116.97/18.12 | | | | | |
% 116.97/18.12 | | | | | End of split
% 116.97/18.12 | | | | |
% 116.97/18.12 | | | | Case 2:
% 116.97/18.12 | | | | |
% 116.97/18.12 | | | | | (490) ~ (all_56_14 = e2)
% 116.97/18.12 | | | | |
% 116.97/18.12 | | | | | REDUCE: (200), (490) imply:
% 116.97/18.12 | | | | | (491) $false
% 116.97/18.12 | | | | |
% 116.97/18.12 | | | | | CLOSE: (491) is inconsistent.
% 116.97/18.12 | | | | |
% 116.97/18.12 | | | | End of split
% 116.97/18.12 | | | |
% 116.97/18.12 | | | Case 2:
% 116.97/18.12 | | | |
% 116.97/18.12 | | | | (492) ~ (all_56_14 = e2)
% 116.97/18.12 | | | |
% 116.97/18.12 | | | | REDUCE: (200), (492) imply:
% 116.97/18.12 | | | | (493) $false
% 116.97/18.12 | | | |
% 116.97/18.12 | | | | CLOSE: (493) is inconsistent.
% 116.97/18.12 | | | |
% 116.97/18.12 | | | End of split
% 116.97/18.12 | | |
% 116.97/18.12 | | End of split
% 116.97/18.12 | |
% 116.97/18.12 | End of split
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #217 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) ~ (all_52_3 = e0)
% 116.97/18.12 (2) ~ (all_52_2 = e0)
% 116.97/18.12 (3) all_58_6 = all_52_2
% 116.97/18.12 (4) all_58_12 = all_52_3
% 116.97/18.12 (5) all_58_6 = e0 | all_58_12 = e0
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | BETA: splitting (5) gives:
% 116.97/18.12 |
% 116.97/18.12 | Case 1:
% 116.97/18.12 | |
% 116.97/18.12 | | (6) all_58_6 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | COMBINE_EQS: (3), (6) imply:
% 116.97/18.12 | | (7) all_52_2 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | REDUCE: (2), (7) imply:
% 116.97/18.12 | | (8) $false
% 116.97/18.12 | |
% 116.97/18.12 | | CLOSE: (8) is inconsistent.
% 116.97/18.12 | |
% 116.97/18.12 | Case 2:
% 116.97/18.12 | |
% 116.97/18.12 | | (9) all_58_12 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | COMBINE_EQS: (4), (9) imply:
% 116.97/18.12 | | (10) all_52_3 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | REDUCE: (1), (10) imply:
% 116.97/18.12 | | (11) $false
% 116.97/18.12 | |
% 116.97/18.12 | | CLOSE: (11) is inconsistent.
% 116.97/18.12 | |
% 116.97/18.12 | End of split
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #218 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_58_14 = all_52_11
% 116.97/18.12 (2) all_58_14 = e3
% 116.97/18.12 (3) ~ (all_52_11 = e3)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.12 | (4) all_52_11 = e3
% 116.97/18.12 |
% 116.97/18.12 | SIMP: (4) implies:
% 116.97/18.12 | (5) all_52_11 = e3
% 116.97/18.12 |
% 116.97/18.12 | REDUCE: (3), (5) imply:
% 116.97/18.12 | (6) $false
% 116.97/18.12 |
% 116.97/18.12 | CLOSE: (6) is inconsistent.
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #219 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_58_8 = e1 | all_58_14 = e1
% 116.97/18.12 (2) all_58_14 = all_52_11
% 116.97/18.12 (3) all_58_8 = all_6_2
% 116.97/18.12 (4) ~ (all_52_11 = e1)
% 116.97/18.12 (5) ~ (all_6_2 = e1)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | BETA: splitting (1) gives:
% 116.97/18.12 |
% 116.97/18.12 | Case 1:
% 116.97/18.12 | |
% 116.97/18.12 | | (6) all_58_8 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | COMBINE_EQS: (3), (6) imply:
% 116.97/18.12 | | (7) all_6_2 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | REDUCE: (5), (7) imply:
% 116.97/18.12 | | (8) $false
% 116.97/18.12 | |
% 116.97/18.12 | | CLOSE: (8) is inconsistent.
% 116.97/18.12 | |
% 116.97/18.12 | Case 2:
% 116.97/18.12 | |
% 116.97/18.12 | | (9) all_58_14 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | COMBINE_EQS: (2), (9) imply:
% 116.97/18.12 | | (10) all_52_11 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | SIMP: (10) implies:
% 116.97/18.12 | | (11) all_52_11 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | REDUCE: (4), (11) imply:
% 116.97/18.12 | | (12) $false
% 116.97/18.12 | |
% 116.97/18.12 | | CLOSE: (12) is inconsistent.
% 116.97/18.12 | |
% 116.97/18.12 | End of split
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #220 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_54_1 = all_52_4
% 116.97/18.12 (2) all_54_1 = e1
% 116.97/18.12 (3) ~ (all_52_4 = e1)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.12 | (4) all_52_4 = e1
% 116.97/18.12 |
% 116.97/18.12 | SIMP: (4) implies:
% 116.97/18.12 | (5) all_52_4 = e1
% 116.97/18.12 |
% 116.97/18.12 | REDUCE: (3), (5) imply:
% 116.97/18.12 | (6) $false
% 116.97/18.12 |
% 116.97/18.12 | CLOSE: (6) is inconsistent.
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #221 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_54_1 = all_52_4
% 116.97/18.12 (2) all_54_1 = e2
% 116.97/18.12 (3) ~ (all_52_4 = e2)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.12 | (4) all_52_4 = e2
% 116.97/18.12 |
% 116.97/18.12 | SIMP: (4) implies:
% 116.97/18.12 | (5) all_52_4 = e2
% 116.97/18.12 |
% 116.97/18.12 | REDUCE: (3), (5) imply:
% 116.97/18.12 | (6) $false
% 116.97/18.12 |
% 116.97/18.12 | CLOSE: (6) is inconsistent.
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #222 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_54_1 = all_52_4
% 116.97/18.12 (2) all_54_1 = e3
% 116.97/18.12 (3) ~ (all_52_4 = e3)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.12 | (4) all_52_4 = e3
% 116.97/18.12 |
% 116.97/18.12 | SIMP: (4) implies:
% 116.97/18.12 | (5) all_52_4 = e3
% 116.97/18.12 |
% 116.97/18.12 | REDUCE: (3), (5) imply:
% 116.97/18.12 | (6) $false
% 116.97/18.12 |
% 116.97/18.12 | CLOSE: (6) is inconsistent.
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #223 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_54_0 = all_10_2
% 116.97/18.12 (2) all_54_3 = all_52_12
% 116.97/18.12 (3) ~ (all_52_12 = all_10_2)
% 116.97/18.12 (4) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.97/18.12 (5) ~ (all_52_12 = e1)
% 116.97/18.12 (6) ~ (all_10_2 = e1)
% 116.97/18.12 (7) all_54_0 = e1 | all_54_0 = e0
% 116.97/18.12 (8) ~ (all_52_12 = e2)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | BETA: splitting (7) gives:
% 116.97/18.12 |
% 116.97/18.12 | Case 1:
% 116.97/18.12 | |
% 116.97/18.12 | | (9) all_54_0 = e1
% 116.97/18.12 | |
% 116.97/18.12 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #449.
% 116.97/18.12 | |
% 116.97/18.12 | Case 2:
% 116.97/18.12 | |
% 116.97/18.12 | | (10) all_54_0 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | COMBINE_EQS: (1), (10) imply:
% 116.97/18.12 | | (11) all_10_2 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | SIMP: (11) implies:
% 116.97/18.12 | | (12) all_10_2 = e0
% 116.97/18.12 | |
% 116.97/18.12 | | REDUCE: (3), (12) imply:
% 116.97/18.12 | | (13) ~ (all_52_12 = e0)
% 116.97/18.12 | |
% 116.97/18.12 | | REF_CLOSE: (2), (4), (5), (8), (13) are inconsistent by sub-proof #283.
% 116.97/18.12 | |
% 116.97/18.12 | End of split
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #224 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) all_54_3 = all_52_12
% 116.97/18.12 (2) all_54_3 = e3
% 116.97/18.12 (3) ~ (all_52_12 = e3)
% 116.97/18.12
% 116.97/18.12 Begin of proof
% 116.97/18.12 |
% 116.97/18.12 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.12 | (4) all_52_12 = e3
% 116.97/18.12 |
% 116.97/18.12 | SIMP: (4) implies:
% 116.97/18.12 | (5) all_52_12 = e3
% 116.97/18.12 |
% 116.97/18.12 | REDUCE: (3), (5) imply:
% 116.97/18.12 | (6) $false
% 116.97/18.12 |
% 116.97/18.12 | CLOSE: (6) is inconsistent.
% 116.97/18.12 |
% 116.97/18.12 End of proof
% 116.97/18.12
% 116.97/18.12 Sub-proof #225 shows that the following formulas are inconsistent:
% 116.97/18.12 ----------------------------------------------------------------
% 116.97/18.12 (1) ~ (all_52_2 = all_10_2)
% 116.97/18.12 (2) ~ (all_52_6 = all_52_14)
% 116.97/18.12 (3) all_58_7 = all_52_6
% 116.97/18.12 (4) all_36_2 = all_6_2
% 116.97/18.12 (5) all_28_1 = all_6_1
% 116.97/18.12 (6) ~ (all_52_13 = all_52_14)
% 116.97/18.12 (7) ~ (all_4_2 = e0)
% 116.97/18.12 (8) op(e3, e2) = all_52_4
% 116.97/18.12 (9) all_56_14 = all_6_2
% 116.97/18.12 (10) all_56_3 = all_52_1
% 116.97/18.12 (11) all_54_0 = all_10_2
% 116.97/18.12 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.12 (13) all_54_3 = all_52_12
% 116.97/18.12 (14) op(e0, e2) = all_52_7
% 116.97/18.12 (15) ~ (all_52_7 = all_4_2)
% 116.97/18.12 (16) all_56_11 = all_52_11
% 116.97/18.12 (17) all_4_0 = e1
% 116.97/18.12 (18) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.97/18.12 (19) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.97/18.12 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.12 (21) all_56_12 = all_10_2
% 116.97/18.12 (22) all_58_0 = all_10_2
% 116.97/18.12 (23) op(all_6_1, all_6_2) = all_6_0
% 116.97/18.12 (24) all_54_11 = all_52_14
% 116.97/18.12 (25) all_54_13 = all_52_7
% 116.97/18.12 (26) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.97/18.12 (27) all_36_1 = all_6_1
% 116.97/18.12 (28) ~ (all_52_14 = all_6_2)
% 116.97/18.12 (29) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.97/18.12 (30) all_56_10 = all_52_7
% 116.97/18.12 (31) op(all_4_1, all_4_2) = all_4_0
% 116.97/18.12 (32) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.97/18.12 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.12 (34) all_54_8 = all_52_2
% 116.97/18.12 (35) ~ (all_52_2 = all_6_2)
% 116.97/18.12 (36) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.97/18.12 (37) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.97/18.12 (38) all_44_2 = all_4_2
% 116.97/18.12 (39) all_54_10 = all_6_2
% 116.97/18.13 (40) all_36_0 = all_6_0
% 116.97/18.13 (41) op(e3, e0) = all_52_12
% 116.97/18.13 (42) all_58_4 = all_52_8
% 116.97/18.13 (43) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.13 (44) ~ (all_52_4 = all_52_7)
% 116.97/18.13 (45) all_56_2 = all_52_12
% 116.97/18.13 (46) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.97/18.13 (47) all_58_3 = all_8_2
% 116.97/18.13 (48) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 116.97/18.13 (49) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.97/18.13 (50) all_58_11 = all_52_14
% 116.97/18.13 (51) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.97/18.13 (52) all_54_9 = all_52_6
% 116.97/18.13 (53) ~ (all_52_2 = all_52_3)
% 116.97/18.13 (54) all_54_7 = all_52_13
% 116.97/18.13 (55) all_28_2 = all_6_2
% 116.97/18.13 (56) all_44_0 = all_4_0
% 116.97/18.13 (57) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.97/18.13 (58) ~ (all_52_7 = all_8_2)
% 116.97/18.13 (59) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.97/18.13 (60) ~ (all_52_4 = all_8_2)
% 116.97/18.13 (61) op(e1, e0) = all_52_14
% 116.97/18.13 (62) all_58_5 = all_52_9
% 116.97/18.13 (63) ~ (all_52_9 = all_52_13)
% 116.97/18.13 (64) all_40_0 = all_6_0
% 116.97/18.13 (65) ~ (all_44_0 = e1) | ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.13 (66) all_56_9 = all_52_3
% 116.97/18.13 (67) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.97/18.13 (68) op(e1, all_6_2) = all_6_1
% 116.97/18.13 (69) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.97/18.13 (70) all_58_15 = all_4_2
% 116.97/18.13 (71) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.97/18.13 (72) all_58_2 = all_52_1
% 116.97/18.13 (73) op(e0, e3) = all_52_3
% 116.97/18.13 (74) ~ (all_10_2 = e3)
% 116.97/18.13 (75) ~ (all_52_12 = all_52_13)
% 116.97/18.13 (76) all_58_13 = all_52_7
% 116.97/18.13 (77) all_40_1 = all_6_1
% 116.97/18.13 (78) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.97/18.13 (79) ~ (all_52_14 = all_4_2)
% 116.97/18.13 (80) all_58_6 = all_52_2
% 116.97/18.13 (81) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.97/18.13 (82) ~ (all_28_0 = e2) | ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.97/18.13 (83) ~ (all_52_1 = all_10_2)
% 116.97/18.13 (84) all_54_5 = all_8_2
% 116.97/18.13 (85) all_56_15 = all_4_2
% 116.97/18.13 (86) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 116.97/18.13 (87) all_58_10 = all_52_13
% 116.97/18.13 (88) ~ (all_52_13 = all_8_2)
% 116.97/18.13 (89) ~ (all_52_6 = all_8_2)
% 116.97/18.13 (90) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.97/18.13 (91) all_28_0 = all_6_0
% 116.97/18.13 (92) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 116.97/18.13 (93) all_58_1 = all_52_4
% 116.97/18.13 (94) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.97/18.13 (95) all_58_14 = all_52_11
% 116.97/18.13 (96) all_54_1 = all_52_4
% 116.97/18.13 (97) all_56_13 = all_8_2
% 116.97/18.13 (98) ~ (all_8_2 = e2)
% 116.97/18.13 (99) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.97/18.13 (100) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.13 (101) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.13 (102) op(e1, e2) = all_52_6
% 116.97/18.13 (103) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.13 (104) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.97/18.13 (105) all_56_7 = all_52_6
% 116.97/18.13 (106) ~ (all_52_9 = all_6_2)
% 116.97/18.13 (107) all_26_2 = all_4_2
% 116.97/18.13 (108) all_56_1 = all_52_8
% 116.97/18.13 (109) op(e0, all_4_2) = all_4_1
% 116.97/18.13 (110) all_58_8 = all_6_2
% 116.97/18.13 (111) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.13 (112) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.13 (113) all_40_2 = all_6_2
% 116.97/18.13 (114) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.97/18.13 (115) all_56_4 = all_52_9
% 116.97/18.13 (116) all_58_9 = all_52_12
% 116.97/18.13 (117) all_56_5 = all_52_13
% 116.97/18.13 (118) ~ (all_52_3 = all_4_2)
% 116.97/18.13 (119) ~ (all_52_6 = all_6_2)
% 116.97/18.13 (120) all_56_6 = all_52_2
% 116.97/18.13 (121) ~ (all_52_13 = all_4_2)
% 116.97/18.13 (122) all_58_12 = all_52_3
% 116.97/18.13 (123) ~ (all_52_2 = all_52_14)
% 116.97/18.13 (124) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.97/18.13 (125) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.13 (126) ~ (all_52_12 = all_4_2)
% 116.97/18.13 (127) ~ (all_52_3 = all_10_2)
% 116.97/18.13 (128) op(e1, e3) = all_52_2
% 116.97/18.13 (129) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.13 (130) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.97/18.13 (131) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.13 (132) all_44_1 = all_4_1
% 116.97/18.13 (133) all_56_8 = all_52_14
% 116.97/18.13 (134) all_26_1 = all_4_1
% 116.97/18.13 (135) ~ (all_52_4 = all_10_2)
% 116.97/18.13 (136) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.13 (137) all_56_0 = all_52_4
% 116.97/18.13 (138) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.97/18.13 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.97/18.13 (139) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.97/18.13 (140) all_54_15 = all_4_2
% 116.97/18.13 (141) ~ (all_6_2 = e1)
% 116.97/18.13 (142) ~ (all_6_1 = e2)
% 116.97/18.13 (143) ~ (all_52_6 = all_52_7)
% 116.97/18.13 (144) all_54_12 = all_52_3
% 116.97/18.13 (145) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.97/18.13
% 116.97/18.13 Begin of proof
% 116.97/18.13 |
% 116.97/18.13 | COMBINE_EQS: (17), (56) imply:
% 116.97/18.13 | (146) all_44_0 = e1
% 116.97/18.13 |
% 116.97/18.13 | REDUCE: (17), (31) imply:
% 116.97/18.13 | (147) op(all_4_1, all_4_2) = e1
% 116.97/18.13 |
% 116.97/18.13 | BETA: splitting (82) gives:
% 116.97/18.13 |
% 116.97/18.13 | Case 1:
% 116.97/18.13 | |
% 116.97/18.13 | | (148) ~ (all_28_0 = e2)
% 116.97/18.13 | |
% 116.97/18.13 | | REDUCE: (91), (148) imply:
% 116.97/18.13 | | (149) ~ (all_6_0 = e2)
% 116.97/18.13 | |
% 116.97/18.13 | | BETA: splitting (92) gives:
% 116.97/18.13 | |
% 116.97/18.13 | | Case 1:
% 116.97/18.13 | | |
% 116.97/18.13 | | | (150) ~ (all_36_1 = e3)
% 116.97/18.13 | | |
% 116.97/18.13 | | | REDUCE: (27), (150) imply:
% 116.97/18.13 | | | (151) ~ (all_6_1 = e3)
% 116.97/18.13 | | |
% 116.97/18.13 | | | BETA: splitting (37) gives:
% 116.97/18.13 | | |
% 116.97/18.13 | | | Case 1:
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | (152) ~ (all_40_0 = e3)
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | REDUCE: (64), (152) imply:
% 116.97/18.13 | | | | (153) ~ (all_6_0 = e3)
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | BETA: splitting (65) gives:
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | Case 1:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | (154) ~ (all_44_0 = e1)
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | REDUCE: (146), (154) imply:
% 116.97/18.13 | | | | | (155) $false
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | CLOSE: (155) is inconsistent.
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | Case 2:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | (156) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | BETA: splitting (78) gives:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | Case 1:
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | (157) ~ (all_56_14 = e2)
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REF_CLOSE: (6), (7), (9), (10), (12), (14), (15), (18), (22), (24),
% 116.97/18.13 | | | | | | (25), (28), (30), (32), (33), (34), (35), (38), (39),
% 116.97/18.13 | | | | | | (43), (46), (47), (53), (57), (59), (61), (62), (66),
% 116.97/18.13 | | | | | | (67), (68), (72), (73), (74), (79), (85), (87), (90),
% 116.97/18.13 | | | | | | (98), (101), (102), (107), (109), (112), (114), (115),
% 116.97/18.13 | | | | | | (117), (118), (120), (123), (124), (125), (128), (129),
% 116.97/18.13 | | | | | | (131), (132), (133), (134), (136), (140), (141), (142),
% 116.97/18.13 | | | | | | (143), (144), (147), (151), (156), (157) are inconsistent
% 116.97/18.13 | | | | | | by sub-proof #231.
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | Case 2:
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | (158) all_56_14 = e2
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | COMBINE_EQS: (9), (158) imply:
% 116.97/18.13 | | | | | | (159) all_6_2 = e2
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | SIMP: (159) implies:
% 116.97/18.13 | | | | | | (160) all_6_2 = e2
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REDUCE: (119), (160) imply:
% 116.97/18.13 | | | | | | (161) ~ (all_52_6 = e2)
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REDUCE: (23), (160) imply:
% 116.97/18.13 | | | | | | (162) op(all_6_1, e2) = all_6_0
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REDUCE: (68), (160) imply:
% 116.97/18.13 | | | | | | (163) op(e1, e2) = all_6_1
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | BETA: splitting (29) gives:
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | Case 1:
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | (164) ~ (all_56_7 = e1)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | REDUCE: (105), (164) imply:
% 116.97/18.13 | | | | | | | (165) ~ (all_52_6 = e1)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | GROUND_INST: instantiating (33) with all_52_6, all_6_1, e2, e1,
% 116.97/18.13 | | | | | | | simplifying with (102), (163) gives:
% 116.97/18.13 | | | | | | | (166) all_52_6 = all_6_1
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | COMBINE_EQS: (52), (166) imply:
% 116.97/18.13 | | | | | | | (167) all_54_9 = all_6_1
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | REDUCE: (143), (166) imply:
% 116.97/18.13 | | | | | | | (168) ~ (all_52_7 = all_6_1)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | SIMP: (168) implies:
% 116.97/18.13 | | | | | | | (169) ~ (all_52_7 = all_6_1)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | REDUCE: (165), (166) imply:
% 116.97/18.13 | | | | | | | (170) ~ (all_6_1 = e1)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | BETA: splitting (49) gives:
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | | (171) all_54_9 = e3
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | | REF_CLOSE: (151), (167), (171) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | #230.
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | | (172) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | | BETA: splitting (172) gives:
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | | (173) all_54_9 = e2
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | | REF_CLOSE: (142), (167), (173) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | | #229.
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | | (174) all_54_9 = e1 | all_54_9 = e0
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | | BETA: splitting (174) gives:
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | (175) all_54_9 = e1
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | REF_CLOSE: (167), (170), (175) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | | | #228.
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | (176) all_54_9 = e0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | COMBINE_EQS: (167), (176) imply:
% 116.97/18.13 | | | | | | | | | | (177) all_6_1 = e0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | SIMP: (177) implies:
% 116.97/18.13 | | | | | | | | | | (178) all_6_1 = e0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | REDUCE: (169), (178) imply:
% 116.97/18.13 | | | | | | | | | | (179) ~ (all_52_7 = e0)
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | REDUCE: (162), (178) imply:
% 116.97/18.13 | | | | | | | | | | (180) op(e0, e2) = all_6_0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | GROUND_INST: instantiating (33) with all_52_7, all_6_0, e2, e0,
% 116.97/18.13 | | | | | | | | | | simplifying with (14), (180) gives:
% 116.97/18.13 | | | | | | | | | | (181) all_52_7 = all_6_0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | COMBINE_EQS: (25), (181) imply:
% 116.97/18.13 | | | | | | | | | | (182) all_54_13 = all_6_0
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | REDUCE: (15), (181) imply:
% 116.97/18.13 | | | | | | | | | | (183) ~ (all_6_0 = all_4_2)
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | REDUCE: (179), (181) imply:
% 116.97/18.13 | | | | | | | | | | (184) ~ (all_6_0 = e0)
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | BETA: splitting (12) gives:
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | (185) all_54_13 = e3
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | REF_CLOSE: (153), (182), (185) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | | | | #380.
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | (186) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | BETA: splitting (186) gives:
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | (187) all_54_13 = e2
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | REF_CLOSE: (149), (182), (187) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | | | | | #379.
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | (188) all_54_13 = e1 | all_54_13 = e0
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | BETA: splitting (188) gives:
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | Case 1:
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | (189) all_54_13 = e1
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | COMBINE_EQS: (182), (189) imply:
% 116.97/18.13 | | | | | | | | | | | | | (190) all_6_0 = e1
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | SIMP: (190) implies:
% 116.97/18.13 | | | | | | | | | | | | | (191) all_6_0 = e1
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | REDUCE: (183), (191) imply:
% 116.97/18.13 | | | | | | | | | | | | | (192) ~ (all_4_2 = e1)
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | SIMP: (192) implies:
% 116.97/18.13 | | | | | | | | | | | | | (193) ~ (all_4_2 = e1)
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | REF_CLOSE: (7), (12), (14), (15), (25), (30), (33), (38),
% 116.97/18.13 | | | | | | | | | | | | | (43), (53), (66), (73), (85), (101), (102), (107),
% 116.97/18.13 | | | | | | | | | | | | | (109), (112), (118), (125), (128), (129), (132),
% 116.97/18.13 | | | | | | | | | | | | | (134), (140), (143), (144), (147), (156), (193)
% 116.97/18.13 | | | | | | | | | | | | | are inconsistent by sub-proof #232.
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | Case 2:
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | (194) all_54_13 = e0
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | | REF_CLOSE: (182), (184), (194) are inconsistent by sub-proof
% 116.97/18.13 | | | | | | | | | | | | | #378.
% 116.97/18.13 | | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | | End of split
% 116.97/18.13 | | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | | End of split
% 116.97/18.13 | | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | | End of split
% 116.97/18.13 | | | | | | | | | |
% 116.97/18.13 | | | | | | | | | End of split
% 116.97/18.13 | | | | | | | | |
% 116.97/18.13 | | | | | | | | End of split
% 116.97/18.13 | | | | | | | |
% 116.97/18.13 | | | | | | | End of split
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | Case 2:
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | (195) ~ (all_56_14 = e2)
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | REDUCE: (158), (195) imply:
% 116.97/18.13 | | | | | | | (196) $false
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | | CLOSE: (196) is inconsistent.
% 116.97/18.13 | | | | | | |
% 116.97/18.13 | | | | | | End of split
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | End of split
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | End of split
% 116.97/18.13 | | | |
% 116.97/18.13 | | | Case 2:
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | (197) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | BETA: splitting (65) gives:
% 116.97/18.13 | | | |
% 116.97/18.13 | | | | Case 1:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | (198) ~ (all_44_0 = e1)
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | REDUCE: (146), (198) imply:
% 116.97/18.13 | | | | | (199) $false
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | CLOSE: (199) is inconsistent.
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | Case 2:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | (200) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | BETA: splitting (78) gives:
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | | Case 1:
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | (201) ~ (all_56_14 = e2)
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REF_CLOSE: (6), (7), (9), (10), (12), (14), (15), (18), (22), (24),
% 116.97/18.13 | | | | | | (25), (28), (30), (32), (33), (34), (35), (38), (39),
% 116.97/18.13 | | | | | | (43), (46), (47), (53), (57), (59), (61), (62), (66),
% 116.97/18.13 | | | | | | (67), (68), (72), (73), (74), (79), (85), (87), (90),
% 116.97/18.13 | | | | | | (98), (101), (102), (107), (109), (112), (114), (115),
% 116.97/18.13 | | | | | | (117), (118), (120), (123), (124), (125), (128), (129),
% 116.97/18.13 | | | | | | (131), (132), (133), (134), (136), (140), (141), (142),
% 116.97/18.13 | | | | | | (143), (144), (147), (151), (200), (201) are inconsistent
% 116.97/18.13 | | | | | | by sub-proof #231.
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | Case 2:
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | (202) all_56_14 = e2
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | | REF_CLOSE: (9), (29), (33), (49), (52), (68), (77), (102), (105),
% 116.97/18.13 | | | | | | (113), (119), (151), (197), (202) are inconsistent by
% 116.97/18.13 | | | | | | sub-proof #372.
% 116.97/18.13 | | | | | |
% 116.97/18.13 | | | | | End of split
% 116.97/18.13 | | | | |
% 116.97/18.13 | | | | End of split
% 116.97/18.13 | | | |
% 116.97/18.13 | | | End of split
% 116.97/18.13 | | |
% 116.97/18.13 | | Case 2:
% 116.97/18.13 | | |
% 116.97/18.14 | | | (203) all_36_1 = e3
% 116.97/18.14 | | | (204) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 116.97/18.14 | | |
% 116.97/18.14 | | | COMBINE_EQS: (27), (203) imply:
% 116.97/18.14 | | | (205) all_6_1 = e3
% 116.97/18.14 | | |
% 116.97/18.14 | | | REDUCE: (23), (205) imply:
% 116.97/18.14 | | | (206) op(e3, all_6_2) = all_6_0
% 116.97/18.14 | | |
% 116.97/18.14 | | | REDUCE: (68), (205) imply:
% 116.97/18.14 | | | (207) op(e1, all_6_2) = e3
% 116.97/18.14 | | |
% 116.97/18.14 | | | BETA: splitting (65) gives:
% 116.97/18.14 | | |
% 116.97/18.14 | | | Case 1:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | (208) ~ (all_44_0 = e1)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (146), (208) imply:
% 116.97/18.14 | | | | (209) $false
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | CLOSE: (209) is inconsistent.
% 116.97/18.14 | | | |
% 116.97/18.14 | | | Case 2:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | (210) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | BETA: splitting (78) gives:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | Case 1:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | (211) ~ (all_56_14 = e2)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REDUCE: (9), (211) imply:
% 116.97/18.14 | | | | | (212) ~ (all_6_2 = e2)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | BETA: splitting (67) gives:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | Case 1:
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | (213) ~ (all_56_15 = e1)
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | REDUCE: (85), (213) imply:
% 116.97/18.14 | | | | | | (214) ~ (all_4_2 = e1)
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | REF_CLOSE: (7), (12), (14), (15), (25), (30), (33), (38), (43),
% 116.97/18.14 | | | | | | (53), (66), (73), (85), (101), (102), (107), (109),
% 116.97/18.14 | | | | | | (112), (118), (125), (128), (129), (132), (134), (140),
% 116.97/18.14 | | | | | | (143), (144), (147), (210), (214) are inconsistent by
% 116.97/18.14 | | | | | | sub-proof #232.
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | Case 2:
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | (215) all_56_15 = e1
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | COMBINE_EQS: (85), (215) imply:
% 116.97/18.14 | | | | | | (216) all_4_2 = e1
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | SIMP: (216) implies:
% 116.97/18.14 | | | | | | (217) all_4_2 = e1
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | REF_CLOSE: (3), (6), (9), (10), (13), (19), (32), (33), (35), (39),
% 116.97/18.14 | | | | | | (41), (45), (46), (47), (48), (50), (54), (57), (61),
% 116.97/18.14 | | | | | | (62), (72), (75), (79), (80), (86), (87), (90), (98),
% 116.97/18.14 | | | | | | (103), (110), (115), (117), (120), (121), (124), (126),
% 116.97/18.14 | | | | | | (128), (136), (141), (145), (149), (206), (207), (212),
% 116.97/18.14 | | | | | | (215), (217) are inconsistent by sub-proof #343.
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | End of split
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | Case 2:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | (218) all_56_14 = e2
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REF_CLOSE: (4), (7), (8), (9), (10), (12), (15), (20), (22), (25),
% 116.97/18.14 | | | | | (33), (36), (40), (42), (43), (44), (45), (47), (51), (58),
% 116.97/18.14 | | | | | (60), (62), (72), (74), (81), (84), (85), (87), (89), (93),
% 116.97/18.14 | | | | | (94), (96), (97), (98), (100), (102), (104), (106), (108),
% 116.97/18.14 | | | | | (116), (117), (131), (136), (137), (139), (140), (143),
% 116.97/18.14 | | | | | (149), (204), (206), (207), (218) are inconsistent by
% 116.97/18.14 | | | | | sub-proof #306.
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | End of split
% 116.97/18.14 | | | |
% 116.97/18.14 | | | End of split
% 116.97/18.14 | | |
% 116.97/18.14 | | End of split
% 116.97/18.14 | |
% 116.97/18.14 | Case 2:
% 116.97/18.14 | |
% 116.97/18.14 | | (219) all_28_0 = e2
% 116.97/18.14 | | (220) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.97/18.14 | |
% 116.97/18.14 | | COMBINE_EQS: (91), (219) imply:
% 116.97/18.14 | | (221) all_6_0 = e2
% 116.97/18.14 | |
% 116.97/18.14 | | REDUCE: (23), (221) imply:
% 116.97/18.14 | | (222) op(all_6_1, all_6_2) = e2
% 116.97/18.14 | |
% 116.97/18.14 | | BETA: splitting (65) gives:
% 116.97/18.14 | |
% 116.97/18.14 | | Case 1:
% 116.97/18.14 | | |
% 116.97/18.14 | | | (223) ~ (all_44_0 = e1)
% 116.97/18.14 | | |
% 116.97/18.14 | | | REDUCE: (146), (223) imply:
% 116.97/18.14 | | | (224) $false
% 116.97/18.14 | | |
% 116.97/18.14 | | | CLOSE: (224) is inconsistent.
% 116.97/18.14 | | |
% 116.97/18.14 | | Case 2:
% 116.97/18.14 | | |
% 116.97/18.14 | | | (225) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.14 | | |
% 116.97/18.14 | | | BETA: splitting (78) gives:
% 116.97/18.14 | | |
% 116.97/18.14 | | | Case 1:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | (226) ~ (all_56_14 = e2)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (9), (226) imply:
% 116.97/18.14 | | | | (227) ~ (all_6_2 = e2)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | BETA: splitting (67) gives:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | Case 1:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | (228) ~ (all_56_15 = e1)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REDUCE: (85), (228) imply:
% 116.97/18.14 | | | | | (229) ~ (all_4_2 = e1)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REF_CLOSE: (7), (12), (14), (15), (25), (30), (33), (38), (43), (53),
% 116.97/18.14 | | | | | (66), (73), (85), (101), (102), (107), (109), (112), (118),
% 116.97/18.14 | | | | | (125), (128), (129), (132), (134), (140), (143), (144),
% 116.97/18.14 | | | | | (147), (225), (229) are inconsistent by sub-proof #232.
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | Case 2:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | (230) all_56_15 = e1
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REF_CLOSE: (2), (3), (5), (6), (9), (10), (22), (24), (28), (32),
% 116.97/18.14 | | | | | (33), (35), (39), (46), (47), (50), (55), (57), (61), (62),
% 116.97/18.14 | | | | | (63), (68), (72), (74), (79), (80), (85), (87), (90), (98),
% 116.97/18.14 | | | | | (103), (110), (114), (115), (117), (119), (120), (121),
% 116.97/18.14 | | | | | (123), (124), (128), (131), (136), (141), (142), (145),
% 116.97/18.14 | | | | | (220), (227), (230) are inconsistent by sub-proof #269.
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | End of split
% 116.97/18.14 | | | |
% 116.97/18.14 | | | Case 2:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | (231) all_56_14 = e2
% 116.97/18.14 | | | | (232) ~ (all_56_10 = e0)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | COMBINE_EQS: (9), (231) imply:
% 116.97/18.14 | | | | (233) all_6_2 = e2
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | SIMP: (233) implies:
% 116.97/18.14 | | | | (234) all_6_2 = e2
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (30), (232) imply:
% 116.97/18.14 | | | | (235) ~ (all_52_7 = e0)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (119), (234) imply:
% 116.97/18.14 | | | | (236) ~ (all_52_6 = e2)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (106), (234) imply:
% 116.97/18.14 | | | | (237) ~ (all_52_9 = e2)
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (222), (234) imply:
% 116.97/18.14 | | | | (238) op(all_6_1, e2) = e2
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | REDUCE: (68), (234) imply:
% 116.97/18.14 | | | | (239) op(e1, e2) = all_6_1
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | BETA: splitting (139) gives:
% 116.97/18.14 | | | |
% 116.97/18.14 | | | | Case 1:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | (240) ~ (all_56_0 = e3)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | REDUCE: (137), (240) imply:
% 116.97/18.14 | | | | | (241) ~ (all_52_4 = e3)
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | BETA: splitting (29) gives:
% 116.97/18.14 | | | | |
% 116.97/18.14 | | | | | Case 1:
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | (242) ~ (all_56_7 = e1)
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | REDUCE: (105), (242) imply:
% 116.97/18.14 | | | | | | (243) ~ (all_52_6 = e1)
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | GROUND_INST: instantiating (33) with all_52_6, all_6_1, e2, e1,
% 116.97/18.14 | | | | | | simplifying with (102), (239) gives:
% 116.97/18.14 | | | | | | (244) all_52_6 = all_6_1
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | COMBINE_EQS: (3), (244) imply:
% 116.97/18.14 | | | | | | (245) all_58_7 = all_6_1
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | BETA: splitting (130) gives:
% 116.97/18.14 | | | | | |
% 116.97/18.14 | | | | | | Case 1:
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | (246) ~ (all_56_5 = e2)
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | REDUCE: (117), (246) imply:
% 116.97/18.14 | | | | | | | (247) ~ (all_52_13 = e2)
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | BETA: splitting (136) gives:
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | (248) all_58_2 = e2
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | COMBINE_EQS: (72), (248) imply:
% 116.97/18.14 | | | | | | | | (249) all_52_1 = e2
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | REDUCE: (83), (249) imply:
% 116.97/18.14 | | | | | | | | (250) ~ (all_10_2 = e2)
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | SIMP: (250) implies:
% 116.97/18.14 | | | | | | | | (251) ~ (all_10_2 = e2)
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | BETA: splitting (67) gives:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | (252) ~ (all_56_15 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (85), (252) imply:
% 116.97/18.14 | | | | | | | | | (253) ~ (all_4_2 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REF_CLOSE: (7), (12), (14), (15), (25), (30), (33), (38),
% 116.97/18.14 | | | | | | | | | (43), (53), (66), (73), (85), (101), (102), (107),
% 116.97/18.14 | | | | | | | | | (109), (112), (118), (125), (128), (129), (132),
% 116.97/18.14 | | | | | | | | | (134), (140), (143), (144), (147), (225), (253) are
% 116.97/18.14 | | | | | | | | | inconsistent by sub-proof #232.
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | Case 2:
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | (254) all_56_15 = e1
% 116.97/18.14 | | | | | | | | | (255) ~ (all_56_11 = e0)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | COMBINE_EQS: (85), (254) imply:
% 116.97/18.14 | | | | | | | | | (256) all_4_2 = e1
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | SIMP: (256) implies:
% 116.97/18.14 | | | | | | | | | (257) all_4_2 = e1
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | COMBINE_EQS: (70), (257) imply:
% 116.97/18.14 | | | | | | | | | (258) all_58_15 = e1
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (16), (255) imply:
% 116.97/18.14 | | | | | | | | | (259) ~ (all_52_11 = e0)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (79), (257) imply:
% 116.97/18.14 | | | | | | | | | (260) ~ (all_52_14 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (7), (257) imply:
% 116.97/18.14 | | | | | | | | | (261) ~ (e1 = e0)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REF_CLOSE: (1), (3), (11), (50), (74), (76), (80), (95),
% 116.97/18.14 | | | | | | | | | (103), (110), (111), (122), (127), (138), (141),
% 116.97/18.14 | | | | | | | | | (235), (243), (251), (258), (259), (260), (261) are
% 116.97/18.14 | | | | | | | | | inconsistent by sub-proof #255.
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | End of split
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | Case 2:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | (262) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | REF_CLOSE: (47), (62), (87), (98), (237), (247), (262) are
% 116.97/18.14 | | | | | | | | inconsistent by sub-proof #401.
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | End of split
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | Case 2:
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | (263) all_56_5 = e2
% 116.97/18.14 | | | | | | | (264) ~ (all_56_12 = e0)
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | COMBINE_EQS: (117), (263) imply:
% 116.97/18.14 | | | | | | | (265) all_52_13 = e2
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | REDUCE: (21), (264) imply:
% 116.97/18.14 | | | | | | | (266) ~ (all_10_2 = e0)
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | REDUCE: (88), (265) imply:
% 116.97/18.14 | | | | | | | (267) ~ (all_8_2 = e2)
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | BETA: splitting (51) gives:
% 116.97/18.14 | | | | | | |
% 116.97/18.14 | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | (268) ~ (all_56_5 = e2)
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | REDUCE: (263), (268) imply:
% 116.97/18.14 | | | | | | | | (269) $false
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | CLOSE: (269) is inconsistent.
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | Case 2:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | (270) ~ (all_56_13 = e0)
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | REDUCE: (97), (270) imply:
% 116.97/18.14 | | | | | | | | (271) ~ (all_8_2 = e0)
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | BETA: splitting (69) gives:
% 116.97/18.14 | | | | | | | |
% 116.97/18.14 | | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | (272) ~ (all_56_6 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (120), (272) imply:
% 116.97/18.14 | | | | | | | | | (273) ~ (all_52_2 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REF_CLOSE: (3), (7), (12), (14), (15), (25), (30), (33), (38),
% 116.97/18.14 | | | | | | | | | (43), (50), (53), (66), (73), (79), (80), (85),
% 116.97/18.14 | | | | | | | | | (101), (102), (103), (107), (109), (110), (112),
% 116.97/18.14 | | | | | | | | | (118), (125), (128), (129), (132), (134), (140),
% 116.97/18.14 | | | | | | | | | (141), (143), (144), (147), (225), (243), (273) are
% 116.97/18.14 | | | | | | | | | inconsistent by sub-proof #226.
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | Case 2:
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | (274) all_56_6 = e1
% 116.97/18.14 | | | | | | | | | (275) ~ (all_56_13 = e3)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | COMBINE_EQS: (120), (274) imply:
% 116.97/18.14 | | | | | | | | | (276) all_52_2 = e1
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (97), (275) imply:
% 116.97/18.14 | | | | | | | | | (277) ~ (all_8_2 = e3)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | REDUCE: (1), (276) imply:
% 116.97/18.14 | | | | | | | | | (278) ~ (all_10_2 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | SIMP: (278) implies:
% 116.97/18.14 | | | | | | | | | (279) ~ (all_10_2 = e1)
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | BETA: splitting (111) gives:
% 116.97/18.14 | | | | | | | | |
% 116.97/18.14 | | | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | (280) all_54_0 = e3
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | REF_CLOSE: (11), (74), (280) are inconsistent by sub-proof
% 116.97/18.14 | | | | | | | | | | #451.
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | Case 2:
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | (281) ~ (all_54_0 = e3)
% 116.97/18.14 | | | | | | | | | | (282) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | BETA: splitting (282) gives:
% 116.97/18.14 | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | (283) all_54_0 = e2
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | COMBINE_EQS: (11), (283) imply:
% 116.97/18.14 | | | | | | | | | | | (284) all_10_2 = e2
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | SIMP: (284) implies:
% 116.97/18.14 | | | | | | | | | | | (285) all_10_2 = e2
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | REDUCE: (127), (285) imply:
% 116.97/18.14 | | | | | | | | | | | (286) ~ (all_52_3 = e2)
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | REDUCE: (135), (285) imply:
% 116.97/18.14 | | | | | | | | | | | (287) ~ (all_52_4 = e2)
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | REDUCE: (74), (285) imply:
% 116.97/18.14 | | | | | | | | | | | (288) ~ (e3 = e2)
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | SIMP: (288) implies:
% 116.97/18.14 | | | | | | | | | | | (289) ~ (e3 = e2)
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | BETA: splitting (20) gives:
% 116.97/18.14 | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | Case 1:
% 116.97/18.14 | | | | | | | | | | | |
% 116.97/18.14 | | | | | | | | | | | | (290) all_54_5 = e3
% 116.97/18.14 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | REF_CLOSE: (84), (277), (290) are inconsistent by sub-proof
% 116.97/18.15 | | | | | | | | | | | | #339.
% 116.97/18.15 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | Case 2:
% 116.97/18.15 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | (291) ~ (all_54_5 = e3)
% 116.97/18.15 | | | | | | | | | | | | (292) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.15 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | BETA: splitting (292) gives:
% 116.97/18.15 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | Case 1:
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | (293) all_54_5 = e2
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | REF_CLOSE: (84), (98), (293) are inconsistent by sub-proof
% 116.97/18.15 | | | | | | | | | | | | | #338.
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | Case 2:
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | (294) ~ (all_54_5 = e2)
% 116.97/18.15 | | | | | | | | | | | | | (295) all_54_5 = e1 | all_54_5 = e0
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | BETA: splitting (71) gives:
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | Case 1:
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | (296) all_58_12 = e2
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | COMBINE_EQS: (122), (296) imply:
% 116.97/18.15 | | | | | | | | | | | | | | (297) all_52_3 = e2
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | SIMP: (297) implies:
% 116.97/18.15 | | | | | | | | | | | | | | (298) all_52_3 = e2
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | REDUCE: (286), (298) imply:
% 116.97/18.15 | | | | | | | | | | | | | | (299) $false
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | Case 2:
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | (300) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | | REF_CLOSE: (8), (26), (33), (44), (47), (76), (84), (93),
% 116.97/18.15 | | | | | | | | | | | | | | (98), (99), (142), (238), (241), (245), (271),
% 116.97/18.15 | | | | | | | | | | | | | | (277), (287), (289), (295), (300) are inconsistent
% 116.97/18.15 | | | | | | | | | | | | | | by sub-proof #262.
% 116.97/18.15 | | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | | End of split
% 116.97/18.15 | | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | | End of split
% 116.97/18.15 | | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | End of split
% 116.97/18.15 | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | Case 2:
% 116.97/18.15 | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | (301) all_54_0 = e1 | all_54_0 = e0
% 116.97/18.15 | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | | REF_CLOSE: (11), (266), (279), (301) are inconsistent by
% 116.97/18.15 | | | | | | | | | | | sub-proof #423.
% 116.97/18.15 | | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | | End of split
% 116.97/18.15 | | | | | | | | | |
% 116.97/18.15 | | | | | | | | | End of split
% 116.97/18.15 | | | | | | | | |
% 116.97/18.15 | | | | | | | | End of split
% 116.97/18.15 | | | | | | | |
% 116.97/18.15 | | | | | | | End of split
% 116.97/18.15 | | | | | | |
% 116.97/18.15 | | | | | | End of split
% 116.97/18.15 | | | | | |
% 116.97/18.15 | | | | | Case 2:
% 116.97/18.15 | | | | | |
% 116.97/18.15 | | | | | | (302) ~ (all_56_14 = e2)
% 116.97/18.15 | | | | | |
% 116.97/18.15 | | | | | | REDUCE: (231), (302) imply:
% 116.97/18.15 | | | | | | (303) $false
% 116.97/18.15 | | | | | |
% 116.97/18.15 | | | | | | CLOSE: (303) is inconsistent.
% 116.97/18.15 | | | | | |
% 116.97/18.15 | | | | | End of split
% 116.97/18.15 | | | | |
% 116.97/18.15 | | | | Case 2:
% 116.97/18.15 | | | | |
% 116.97/18.15 | | | | | (304) ~ (all_56_14 = e2)
% 116.97/18.15 | | | | |
% 116.97/18.15 | | | | | REDUCE: (231), (304) imply:
% 116.97/18.15 | | | | | (305) $false
% 116.97/18.15 | | | | |
% 116.97/18.15 | | | | | CLOSE: (305) is inconsistent.
% 116.97/18.15 | | | | |
% 116.97/18.15 | | | | End of split
% 116.97/18.15 | | | |
% 116.97/18.15 | | | End of split
% 116.97/18.15 | | |
% 116.97/18.15 | | End of split
% 116.97/18.15 | |
% 116.97/18.15 | End of split
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #226 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) all_58_7 = all_52_6
% 116.97/18.15 (2) ~ (all_4_2 = e0)
% 116.97/18.15 (3) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.15 (4) op(e0, e2) = all_52_7
% 116.97/18.15 (5) ~ (all_52_7 = all_4_2)
% 116.97/18.15 (6) all_54_13 = all_52_7
% 116.97/18.15 (7) all_56_10 = all_52_7
% 116.97/18.15 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.15 (9) all_44_2 = all_4_2
% 116.97/18.15 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.15 (11) all_58_11 = all_52_14
% 116.97/18.15 (12) ~ (all_52_2 = all_52_3)
% 116.97/18.15 (13) op(all_4_1, all_4_2) = e1
% 116.97/18.15 (14) all_56_9 = all_52_3
% 116.97/18.15 (15) op(e0, e3) = all_52_3
% 116.97/18.15 (16) ~ (all_52_14 = all_4_2)
% 116.97/18.15 (17) all_58_6 = all_52_2
% 116.97/18.15 (18) ~ (all_52_2 = e1)
% 116.97/18.15 (19) all_56_15 = all_4_2
% 116.97/18.15 (20) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.15 (21) op(e1, e2) = all_52_6
% 116.97/18.15 (22) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.15 (23) all_26_2 = all_4_2
% 116.97/18.15 (24) op(e0, all_4_2) = all_4_1
% 116.97/18.15 (25) all_58_8 = all_6_2
% 116.97/18.15 (26) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.15 (27) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.15 (28) ~ (all_52_3 = all_4_2)
% 116.97/18.15 (29) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.15 (30) op(e1, e3) = all_52_2
% 116.97/18.15 (31) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.15 (32) all_44_1 = all_4_1
% 116.97/18.15 (33) all_26_1 = all_4_1
% 116.97/18.15 (34) ~ (all_52_6 = e1)
% 116.97/18.15 (35) all_54_15 = all_4_2
% 116.97/18.15 (36) ~ (all_6_2 = e1)
% 116.97/18.15 (37) ~ (all_52_6 = all_52_7)
% 116.97/18.15 (38) all_54_12 = all_52_3
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | BETA: splitting (22) gives:
% 116.97/18.15 |
% 116.97/18.15 | Case 1:
% 116.97/18.15 | |
% 116.97/18.15 | | (39) all_58_6 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | REF_CLOSE: (17), (18), (39) are inconsistent by sub-proof #452.
% 116.97/18.15 | |
% 116.97/18.15 | Case 2:
% 116.97/18.15 | |
% 116.97/18.15 | | (40) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | BETA: splitting (40) gives:
% 116.97/18.15 | |
% 116.97/18.15 | | Case 1:
% 116.97/18.15 | | |
% 116.97/18.15 | | | (41) all_58_7 = e1
% 116.97/18.15 | | |
% 116.97/18.15 | | | COMBINE_EQS: (1), (41) imply:
% 116.97/18.15 | | | (42) all_52_6 = e1
% 116.97/18.15 | | |
% 116.97/18.15 | | | REDUCE: (34), (42) imply:
% 116.97/18.15 | | | (43) $false
% 116.97/18.15 | | |
% 116.97/18.15 | | | CLOSE: (43) is inconsistent.
% 116.97/18.15 | | |
% 116.97/18.15 | | Case 2:
% 116.97/18.15 | | |
% 116.97/18.15 | | | (44) all_58_8 = e1 | all_58_11 = e1
% 116.97/18.15 | | |
% 116.97/18.15 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 116.97/18.15 | | | (14), (15), (16), (19), (20), (21), (23), (24), (25), (26),
% 116.97/18.15 | | | (27), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 116.97/18.15 | | | (38), (44) are inconsistent by sub-proof #227.
% 116.97/18.15 | | |
% 116.97/18.15 | | End of split
% 116.97/18.15 | |
% 116.97/18.15 | End of split
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #227 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) ~ (all_4_2 = e0)
% 116.97/18.15 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.15 (3) op(e0, e2) = all_52_7
% 116.97/18.15 (4) ~ (all_52_7 = all_4_2)
% 116.97/18.15 (5) all_54_13 = all_52_7
% 116.97/18.15 (6) all_56_10 = all_52_7
% 116.97/18.15 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.15 (8) all_44_2 = all_4_2
% 116.97/18.15 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.15 (10) all_58_11 = all_52_14
% 116.97/18.15 (11) ~ (all_52_2 = all_52_3)
% 116.97/18.15 (12) op(all_4_1, all_4_2) = e1
% 116.97/18.15 (13) all_56_9 = all_52_3
% 116.97/18.15 (14) op(e0, e3) = all_52_3
% 116.97/18.15 (15) ~ (all_52_14 = all_4_2)
% 116.97/18.15 (16) all_56_15 = all_4_2
% 116.97/18.15 (17) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.15 (18) op(e1, e2) = all_52_6
% 116.97/18.15 (19) all_26_2 = all_4_2
% 116.97/18.15 (20) op(e0, all_4_2) = all_4_1
% 116.97/18.15 (21) all_58_8 = all_6_2
% 116.97/18.15 (22) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.15 (23) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.15 (24) ~ (all_52_3 = all_4_2)
% 116.97/18.15 (25) all_58_8 = e1 | all_58_11 = e1
% 116.97/18.15 (26) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.15 (27) op(e1, e3) = all_52_2
% 116.97/18.15 (28) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.15 (29) all_44_1 = all_4_1
% 116.97/18.15 (30) all_26_1 = all_4_1
% 116.97/18.15 (31) all_54_15 = all_4_2
% 116.97/18.15 (32) ~ (all_6_2 = e1)
% 116.97/18.15 (33) ~ (all_52_6 = all_52_7)
% 116.97/18.15 (34) all_54_12 = all_52_3
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | BETA: splitting (25) gives:
% 116.97/18.15 |
% 116.97/18.15 | Case 1:
% 116.97/18.15 | |
% 116.97/18.15 | | (35) all_58_8 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | COMBINE_EQS: (21), (35) imply:
% 116.97/18.15 | | (36) all_6_2 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | REDUCE: (32), (36) imply:
% 116.97/18.15 | | (37) $false
% 116.97/18.15 | |
% 116.97/18.15 | | CLOSE: (37) is inconsistent.
% 116.97/18.15 | |
% 116.97/18.15 | Case 2:
% 116.97/18.15 | |
% 116.97/18.15 | | (38) all_58_11 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | COMBINE_EQS: (10), (38) imply:
% 116.97/18.15 | | (39) all_52_14 = e1
% 116.97/18.15 | |
% 116.97/18.15 | | REDUCE: (15), (39) imply:
% 116.97/18.15 | | (40) ~ (all_4_2 = e1)
% 116.97/18.15 | |
% 116.97/18.15 | | SIMP: (40) implies:
% 116.97/18.15 | | (41) ~ (all_4_2 = e1)
% 116.97/18.15 | |
% 116.97/18.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 116.97/18.15 | | (14), (16), (17), (18), (19), (20), (22), (23), (24), (26), (27),
% 116.97/18.15 | | (28), (29), (30), (31), (33), (34), (41) are inconsistent by
% 116.97/18.15 | | sub-proof #232.
% 116.97/18.15 | |
% 116.97/18.15 | End of split
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #228 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) all_54_9 = all_6_1
% 116.97/18.15 (2) all_54_9 = e1
% 116.97/18.15 (3) ~ (all_6_1 = e1)
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.15 | (4) all_6_1 = e1
% 116.97/18.15 |
% 116.97/18.15 | SIMP: (4) implies:
% 116.97/18.15 | (5) all_6_1 = e1
% 116.97/18.15 |
% 116.97/18.15 | REDUCE: (3), (5) imply:
% 116.97/18.15 | (6) $false
% 116.97/18.15 |
% 116.97/18.15 | CLOSE: (6) is inconsistent.
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #229 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) all_54_9 = all_6_1
% 116.97/18.15 (2) all_54_9 = e2
% 116.97/18.15 (3) ~ (all_6_1 = e2)
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.15 | (4) all_6_1 = e2
% 116.97/18.15 |
% 116.97/18.15 | SIMP: (4) implies:
% 116.97/18.15 | (5) all_6_1 = e2
% 116.97/18.15 |
% 116.97/18.15 | REDUCE: (3), (5) imply:
% 116.97/18.15 | (6) $false
% 116.97/18.15 |
% 116.97/18.15 | CLOSE: (6) is inconsistent.
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #230 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) all_54_9 = all_6_1
% 116.97/18.15 (2) all_54_9 = e3
% 116.97/18.15 (3) ~ (all_6_1 = e3)
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.15 | (4) all_6_1 = e3
% 116.97/18.15 |
% 116.97/18.15 | SIMP: (4) implies:
% 116.97/18.15 | (5) all_6_1 = e3
% 116.97/18.15 |
% 116.97/18.15 | REDUCE: (3), (5) imply:
% 116.97/18.15 | (6) $false
% 116.97/18.15 |
% 116.97/18.15 | CLOSE: (6) is inconsistent.
% 116.97/18.15 |
% 116.97/18.15 End of proof
% 116.97/18.15
% 116.97/18.15 Sub-proof #231 shows that the following formulas are inconsistent:
% 116.97/18.15 ----------------------------------------------------------------
% 116.97/18.15 (1) ~ (all_52_13 = all_52_14)
% 116.97/18.15 (2) ~ (all_4_2 = e0)
% 116.97/18.15 (3) all_56_14 = all_6_2
% 116.97/18.15 (4) all_56_3 = all_52_1
% 116.97/18.15 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.15 (6) op(e0, e2) = all_52_7
% 116.97/18.15 (7) ~ (all_52_7 = all_4_2)
% 116.97/18.15 (8) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.97/18.15 (9) ~ (all_6_1 = e3)
% 116.97/18.15 (10) ~ (all_56_14 = e2)
% 116.97/18.15 (11) all_58_0 = all_10_2
% 116.97/18.15 (12) all_54_11 = all_52_14
% 116.97/18.15 (13) all_54_13 = all_52_7
% 116.97/18.15 (14) ~ (all_52_14 = all_6_2)
% 116.97/18.15 (15) all_56_10 = all_52_7
% 116.97/18.15 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.97/18.15 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.15 (18) all_54_8 = all_52_2
% 116.97/18.15 (19) ~ (all_52_2 = all_6_2)
% 116.97/18.15 (20) all_44_2 = all_4_2
% 116.97/18.15 (21) all_54_10 = all_6_2
% 116.97/18.15 (22) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.15 (23) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.97/18.15 (24) all_58_3 = all_8_2
% 116.97/18.15 (25) ~ (all_52_2 = all_52_3)
% 116.97/18.15 (26) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.97/18.15 (27) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.97/18.15 (28) op(e1, e0) = all_52_14
% 116.97/18.15 (29) all_58_5 = all_52_9
% 116.97/18.15 (30) op(all_4_1, all_4_2) = e1
% 116.97/18.15 (31) all_56_9 = all_52_3
% 116.97/18.15 (32) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.97/18.15 (33) op(e1, all_6_2) = all_6_1
% 116.97/18.15 (34) all_58_2 = all_52_1
% 116.97/18.15 (35) op(e0, e3) = all_52_3
% 116.97/18.15 (36) ~ (all_10_2 = e3)
% 116.97/18.15 (37) ~ (all_52_14 = all_4_2)
% 116.97/18.15 (38) all_56_15 = all_4_2
% 116.97/18.15 (39) all_58_10 = all_52_13
% 116.97/18.15 (40) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.97/18.15 (41) ~ (all_8_2 = e2)
% 116.97/18.15 (42) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.15 (43) op(e1, e2) = all_52_6
% 116.97/18.15 (44) all_26_2 = all_4_2
% 116.97/18.15 (45) op(e0, all_4_2) = all_4_1
% 116.97/18.15 (46) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.15 (47) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.15 (48) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.97/18.15 (49) all_56_4 = all_52_9
% 116.97/18.15 (50) all_56_5 = all_52_13
% 116.97/18.15 (51) ~ (all_52_3 = all_4_2)
% 116.97/18.15 (52) all_56_6 = all_52_2
% 116.97/18.15 (53) ~ (all_52_2 = all_52_14)
% 116.97/18.15 (54) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.97/18.15 (55) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.15 (56) op(e1, e3) = all_52_2
% 116.97/18.15 (57) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.15 (58) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.15 (59) all_44_1 = all_4_1
% 116.97/18.15 (60) all_56_8 = all_52_14
% 116.97/18.15 (61) all_26_1 = all_4_1
% 116.97/18.15 (62) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.15 (63) all_54_15 = all_4_2
% 116.97/18.15 (64) ~ (all_6_2 = e1)
% 116.97/18.15 (65) ~ (all_6_1 = e2)
% 116.97/18.15 (66) ~ (all_52_6 = all_52_7)
% 116.97/18.15 (67) all_54_12 = all_52_3
% 116.97/18.15
% 116.97/18.15 Begin of proof
% 116.97/18.15 |
% 116.97/18.15 | REDUCE: (3), (10) imply:
% 116.97/18.15 | (68) ~ (all_6_2 = e2)
% 116.97/18.15 |
% 116.97/18.15 | BETA: splitting (32) gives:
% 116.97/18.15 |
% 116.97/18.15 | Case 1:
% 116.97/18.15 | |
% 116.97/18.15 | | (69) ~ (all_56_15 = e1)
% 116.97/18.15 | |
% 116.97/18.15 | | REDUCE: (38), (69) imply:
% 116.97/18.15 | | (70) ~ (all_4_2 = e1)
% 116.97/18.15 | |
% 116.97/18.16 | | REF_CLOSE: (2), (5), (6), (7), (13), (15), (17), (20), (22), (25), (30),
% 116.97/18.16 | | (31), (35), (38), (42), (43), (44), (45), (46), (47), (51), (55),
% 116.97/18.16 | | (56), (57), (59), (61), (63), (66), (67), (70) are inconsistent
% 116.97/18.16 | | by sub-proof #232.
% 116.97/18.16 | |
% 116.97/18.16 | Case 2:
% 116.97/18.16 | |
% 116.97/18.16 | | (71) all_56_15 = e1
% 116.97/18.16 | |
% 116.97/18.16 | | REF_CLOSE: (1), (3), (4), (8), (9), (11), (12), (14), (16), (17), (18),
% 116.97/18.16 | | (19), (21), (23), (24), (26), (27), (28), (29), (33), (34), (36),
% 116.97/18.16 | | (37), (38), (39), (40), (41), (48), (49), (50), (52), (53), (54),
% 116.97/18.16 | | (56), (58), (60), (62), (64), (65), (68), (71) are inconsistent
% 116.97/18.16 | | by sub-proof #392.
% 116.97/18.16 | |
% 116.97/18.16 | End of split
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #232 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) ~ (all_4_2 = e0)
% 116.97/18.16 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.16 (3) ~ (all_4_2 = e1)
% 116.97/18.16 (4) op(e0, e2) = all_52_7
% 116.97/18.16 (5) ~ (all_52_7 = all_4_2)
% 116.97/18.16 (6) all_54_13 = all_52_7
% 116.97/18.16 (7) all_56_10 = all_52_7
% 116.97/18.16 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.16 (9) all_44_2 = all_4_2
% 116.97/18.16 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.16 (11) ~ (all_52_2 = all_52_3)
% 116.97/18.16 (12) op(all_4_1, all_4_2) = e1
% 116.97/18.16 (13) all_56_9 = all_52_3
% 116.97/18.16 (14) op(e0, e3) = all_52_3
% 116.97/18.16 (15) all_56_15 = all_4_2
% 116.97/18.16 (16) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.16 (17) op(e1, e2) = all_52_6
% 116.97/18.16 (18) all_26_2 = all_4_2
% 116.97/18.16 (19) op(e0, all_4_2) = all_4_1
% 116.97/18.16 (20) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.16 (21) ~ (all_44_1 = e3) | ~ (all_44_2 = e2)
% 116.97/18.16 (22) ~ (all_52_3 = all_4_2)
% 116.97/18.16 (23) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.16 (24) op(e1, e3) = all_52_2
% 116.97/18.16 (25) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.16 (26) all_44_1 = all_4_1
% 116.97/18.16 (27) all_26_1 = all_4_1
% 116.97/18.16 (28) all_54_15 = all_4_2
% 116.97/18.16 (29) ~ (all_52_6 = all_52_7)
% 116.97/18.16 (30) all_54_12 = all_52_3
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | BETA: splitting (25) gives:
% 116.97/18.16 |
% 116.97/18.16 | Case 1:
% 116.97/18.16 | |
% 116.97/18.16 | | (31) ~ (all_56_15 = e2)
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (15), (31) imply:
% 116.97/18.16 | | (32) ~ (all_4_2 = e2)
% 116.97/18.16 | |
% 116.97/18.16 | | REF_CLOSE: (1), (3), (8), (10), (11), (12), (13), (14), (15), (16), (18),
% 116.97/18.16 | | (19), (20), (22), (23), (24), (27), (28), (30), (32) are
% 116.97/18.16 | | inconsistent by sub-proof #236.
% 116.97/18.16 | |
% 116.97/18.16 | Case 2:
% 116.97/18.16 | |
% 116.97/18.16 | | (33) all_56_15 = e2
% 116.97/18.16 | | (34) ~ (all_56_10 = e0)
% 116.97/18.16 | |
% 116.97/18.16 | | COMBINE_EQS: (15), (33) imply:
% 116.97/18.16 | | (35) all_4_2 = e2
% 116.97/18.16 | |
% 116.97/18.16 | | SIMP: (35) implies:
% 116.97/18.16 | | (36) all_4_2 = e2
% 116.97/18.16 | |
% 116.97/18.16 | | COMBINE_EQS: (9), (36) imply:
% 116.97/18.16 | | (37) all_44_2 = e2
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (7), (34) imply:
% 116.97/18.16 | | (38) ~ (all_52_7 = e0)
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (5), (36) imply:
% 116.97/18.16 | | (39) ~ (all_52_7 = e2)
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (12), (36) imply:
% 116.97/18.16 | | (40) op(all_4_1, e2) = e1
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (19), (36) imply:
% 116.97/18.16 | | (41) op(e0, e2) = all_4_1
% 116.97/18.16 | |
% 116.97/18.16 | | BETA: splitting (21) gives:
% 116.97/18.16 | |
% 116.97/18.16 | | Case 1:
% 116.97/18.16 | | |
% 116.97/18.16 | | | (42) ~ (all_44_1 = e3)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (26), (42) imply:
% 116.97/18.16 | | | (43) ~ (all_4_1 = e3)
% 116.97/18.16 | | |
% 116.97/18.16 | | | GROUND_INST: instantiating (8) with all_52_7, all_4_1, e2, e0, simplifying
% 116.97/18.16 | | | with (4), (41) gives:
% 116.97/18.16 | | | (44) all_52_7 = all_4_1
% 116.97/18.16 | | |
% 116.97/18.16 | | | COMBINE_EQS: (6), (44) imply:
% 116.97/18.16 | | | (45) all_54_13 = all_4_1
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (29), (44) imply:
% 116.97/18.16 | | | (46) ~ (all_52_6 = all_4_1)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (39), (44) imply:
% 116.97/18.16 | | | (47) ~ (all_4_1 = e2)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (38), (44) imply:
% 116.97/18.16 | | | (48) ~ (all_4_1 = e0)
% 116.97/18.16 | | |
% 116.97/18.16 | | | BETA: splitting (2) gives:
% 116.97/18.16 | | |
% 116.97/18.16 | | | Case 1:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | (49) all_54_13 = e3
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REF_CLOSE: (43), (45), (49) are inconsistent by sub-proof #235.
% 116.97/18.16 | | | |
% 116.97/18.16 | | | Case 2:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | (50) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | BETA: splitting (50) gives:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | Case 1:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | (51) all_54_13 = e2
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | REF_CLOSE: (45), (47), (51) are inconsistent by sub-proof #234.
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | Case 2:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | (52) all_54_13 = e1 | all_54_13 = e0
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | BETA: splitting (52) gives:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | Case 1:
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | (53) all_54_13 = e1
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | COMBINE_EQS: (45), (53) imply:
% 116.97/18.16 | | | | | | (54) all_4_1 = e1
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | SIMP: (54) implies:
% 116.97/18.16 | | | | | | (55) all_4_1 = e1
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | REDUCE: (46), (55) imply:
% 116.97/18.16 | | | | | | (56) ~ (all_52_6 = e1)
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | REDUCE: (40), (55) imply:
% 116.97/18.16 | | | | | | (57) op(e1, e2) = e1
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | GROUND_INST: instantiating (8) with all_52_6, e1, e2, e1,
% 116.97/18.16 | | | | | | simplifying with (17), (57) gives:
% 116.97/18.16 | | | | | | (58) all_52_6 = e1
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | REDUCE: (56), (58) imply:
% 116.97/18.16 | | | | | | (59) $false
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | CLOSE: (59) is inconsistent.
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | Case 2:
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | (60) all_54_13 = e0
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | REF_CLOSE: (45), (48), (60) are inconsistent by sub-proof #233.
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | End of split
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | End of split
% 116.97/18.16 | | | |
% 116.97/18.16 | | | End of split
% 116.97/18.16 | | |
% 116.97/18.16 | | Case 2:
% 116.97/18.16 | | |
% 116.97/18.16 | | | (61) ~ (all_44_2 = e2)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (37), (61) imply:
% 116.97/18.16 | | | (62) $false
% 116.97/18.16 | | |
% 116.97/18.16 | | | CLOSE: (62) is inconsistent.
% 116.97/18.16 | | |
% 116.97/18.16 | | End of split
% 116.97/18.16 | |
% 116.97/18.16 | End of split
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #233 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_13 = all_4_1
% 116.97/18.16 (2) all_54_13 = e0
% 116.97/18.16 (3) ~ (all_4_1 = e0)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e0
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e0
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #234 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_13 = all_4_1
% 116.97/18.16 (2) all_54_13 = e2
% 116.97/18.16 (3) ~ (all_4_1 = e2)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e2
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e2
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #235 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_13 = all_4_1
% 116.97/18.16 (2) all_54_13 = e3
% 116.97/18.16 (3) ~ (all_4_1 = e3)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e3
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e3
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #236 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) ~ (all_4_2 = e0)
% 116.97/18.16 (2) ~ (all_4_2 = e1)
% 116.97/18.16 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.16 (4) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.16 (5) ~ (all_52_2 = all_52_3)
% 116.97/18.16 (6) op(all_4_1, all_4_2) = e1
% 116.97/18.16 (7) all_56_9 = all_52_3
% 116.97/18.16 (8) op(e0, e3) = all_52_3
% 116.97/18.16 (9) all_56_15 = all_4_2
% 116.97/18.16 (10) ~ (all_26_1 = e2) | ~ (all_26_2 = e3)
% 116.97/18.16 (11) all_26_2 = all_4_2
% 116.97/18.16 (12) op(e0, all_4_2) = all_4_1
% 116.97/18.16 (13) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.16 (14) ~ (all_52_3 = all_4_2)
% 116.97/18.16 (15) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.16 (16) op(e1, e3) = all_52_2
% 116.97/18.16 (17) ~ (all_4_2 = e2)
% 116.97/18.16 (18) all_26_1 = all_4_1
% 116.97/18.16 (19) all_54_15 = all_4_2
% 116.97/18.16 (20) all_54_12 = all_52_3
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | BETA: splitting (4) gives:
% 116.97/18.16 |
% 116.97/18.16 | Case 1:
% 116.97/18.16 | |
% 116.97/18.16 | | (21) all_54_15 = e3
% 116.97/18.16 | |
% 116.97/18.16 | | COMBINE_EQS: (19), (21) imply:
% 116.97/18.16 | | (22) all_4_2 = e3
% 116.97/18.16 | |
% 116.97/18.16 | | SIMP: (22) implies:
% 116.97/18.16 | | (23) all_4_2 = e3
% 116.97/18.16 | |
% 116.97/18.16 | | COMBINE_EQS: (11), (23) imply:
% 116.97/18.16 | | (24) all_26_2 = e3
% 116.97/18.16 | |
% 116.97/18.16 | | COMBINE_EQS: (9), (23) imply:
% 116.97/18.16 | | (25) all_56_15 = e3
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (14), (23) imply:
% 116.97/18.16 | | (26) ~ (all_52_3 = e3)
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (6), (23) imply:
% 116.97/18.16 | | (27) op(all_4_1, e3) = e1
% 116.97/18.16 | |
% 116.97/18.16 | | REDUCE: (12), (23) imply:
% 116.97/18.16 | | (28) op(e0, e3) = all_4_1
% 116.97/18.16 | |
% 116.97/18.16 | | BETA: splitting (13) gives:
% 116.97/18.16 | |
% 116.97/18.16 | | Case 1:
% 116.97/18.16 | | |
% 116.97/18.16 | | | (29) ~ (all_56_15 = e3)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (25), (29) imply:
% 116.97/18.16 | | | (30) $false
% 116.97/18.16 | | |
% 116.97/18.16 | | | CLOSE: (30) is inconsistent.
% 116.97/18.16 | | |
% 116.97/18.16 | | Case 2:
% 116.97/18.16 | | |
% 116.97/18.16 | | | (31) ~ (all_56_9 = e0)
% 116.97/18.16 | | |
% 116.97/18.16 | | | REDUCE: (7), (31) imply:
% 116.97/18.16 | | | (32) ~ (all_52_3 = e0)
% 116.97/18.16 | | |
% 116.97/18.16 | | | BETA: splitting (10) gives:
% 116.97/18.16 | | |
% 116.97/18.16 | | | Case 1:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | (33) ~ (all_26_1 = e2)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REDUCE: (18), (33) imply:
% 116.97/18.16 | | | | (34) ~ (all_4_1 = e2)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | GROUND_INST: instantiating (3) with all_52_3, all_4_1, e3, e0,
% 116.97/18.16 | | | | simplifying with (8), (28) gives:
% 116.97/18.16 | | | | (35) all_52_3 = all_4_1
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | COMBINE_EQS: (20), (35) imply:
% 116.97/18.16 | | | | (36) all_54_12 = all_4_1
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REDUCE: (5), (35) imply:
% 116.97/18.16 | | | | (37) ~ (all_52_2 = all_4_1)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REDUCE: (26), (35) imply:
% 116.97/18.16 | | | | (38) ~ (all_4_1 = e3)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REDUCE: (32), (35) imply:
% 116.97/18.16 | | | | (39) ~ (all_4_1 = e0)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | BETA: splitting (15) gives:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | Case 1:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | (40) all_54_12 = e3
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | REF_CLOSE: (36), (38), (40) are inconsistent by sub-proof #239.
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | Case 2:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | (41) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | BETA: splitting (41) gives:
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | | Case 1:
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | (42) all_54_12 = e2
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | REF_CLOSE: (34), (36), (42) are inconsistent by sub-proof #238.
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | Case 2:
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | (43) all_54_12 = e1 | all_54_12 = e0
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | BETA: splitting (43) gives:
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | | Case 1:
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | (44) all_54_12 = e1
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | COMBINE_EQS: (36), (44) imply:
% 116.97/18.16 | | | | | | | (45) all_4_1 = e1
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | SIMP: (45) implies:
% 116.97/18.16 | | | | | | | (46) all_4_1 = e1
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | REDUCE: (37), (46) imply:
% 116.97/18.16 | | | | | | | (47) ~ (all_52_2 = e1)
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | REDUCE: (27), (46) imply:
% 116.97/18.16 | | | | | | | (48) op(e1, e3) = e1
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | GROUND_INST: instantiating (3) with all_52_2, e1, e3, e1,
% 116.97/18.16 | | | | | | | simplifying with (16), (48) gives:
% 116.97/18.16 | | | | | | | (49) all_52_2 = e1
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | REDUCE: (47), (49) imply:
% 116.97/18.16 | | | | | | | (50) $false
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | CLOSE: (50) is inconsistent.
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | Case 2:
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | (51) all_54_12 = e0
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | | REF_CLOSE: (36), (39), (51) are inconsistent by sub-proof #237.
% 116.97/18.16 | | | | | | |
% 116.97/18.16 | | | | | | End of split
% 116.97/18.16 | | | | | |
% 116.97/18.16 | | | | | End of split
% 116.97/18.16 | | | | |
% 116.97/18.16 | | | | End of split
% 116.97/18.16 | | | |
% 116.97/18.16 | | | Case 2:
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | (52) ~ (all_26_2 = e3)
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | REDUCE: (24), (52) imply:
% 116.97/18.16 | | | | (53) $false
% 116.97/18.16 | | | |
% 116.97/18.16 | | | | CLOSE: (53) is inconsistent.
% 116.97/18.16 | | | |
% 116.97/18.16 | | | End of split
% 116.97/18.16 | | |
% 116.97/18.16 | | End of split
% 116.97/18.16 | |
% 116.97/18.16 | Case 2:
% 116.97/18.16 | |
% 116.97/18.16 | | (54) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.16 | |
% 116.97/18.16 | | REF_CLOSE: (1), (2), (17), (19), (54) are inconsistent by sub-proof #417.
% 116.97/18.16 | |
% 116.97/18.16 | End of split
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #237 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_12 = all_4_1
% 116.97/18.16 (2) all_54_12 = e0
% 116.97/18.16 (3) ~ (all_4_1 = e0)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e0
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e0
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #238 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_12 = all_4_1
% 116.97/18.16 (2) all_54_12 = e2
% 116.97/18.16 (3) ~ (all_4_1 = e2)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e2
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e2
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #239 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) all_54_12 = all_4_1
% 116.97/18.16 (2) all_54_12 = e3
% 116.97/18.16 (3) ~ (all_4_1 = e3)
% 116.97/18.16
% 116.97/18.16 Begin of proof
% 116.97/18.16 |
% 116.97/18.16 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.16 | (4) all_4_1 = e3
% 116.97/18.16 |
% 116.97/18.16 | SIMP: (4) implies:
% 116.97/18.16 | (5) all_4_1 = e3
% 116.97/18.16 |
% 116.97/18.16 | REDUCE: (3), (5) imply:
% 116.97/18.16 | (6) $false
% 116.97/18.16 |
% 116.97/18.16 | CLOSE: (6) is inconsistent.
% 116.97/18.16 |
% 116.97/18.16 End of proof
% 116.97/18.16
% 116.97/18.16 Sub-proof #240 shows that the following formulas are inconsistent:
% 116.97/18.16 ----------------------------------------------------------------
% 116.97/18.16 (1) ~ (all_52_8 = all_10_2)
% 116.97/18.17 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.97/18.17 (3) ~ (all_52_2 = all_10_2)
% 116.97/18.17 (4) ~ (all_52_6 = all_52_14)
% 116.97/18.17 (5) all_54_2 = all_52_8
% 116.97/18.17 (6) all_58_7 = all_52_6
% 116.97/18.17 (7) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 116.97/18.17 (8) ~ (all_52_8 = all_52_11)
% 116.97/18.17 (9) ~ (all_52_9 = all_8_2)
% 116.97/18.17 (10) all_28_1 = all_6_1
% 116.97/18.17 (11) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.97/18.17 (12) ~ (all_52_13 = all_52_14)
% 116.97/18.17 (13) ~ (all_4_2 = e0)
% 116.97/18.17 (14) op(e3, e2) = all_52_4
% 116.97/18.17 (15) all_56_14 = all_6_2
% 116.97/18.17 (16) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.97/18.17 (17) all_56_3 = all_52_1
% 116.97/18.17 (18) all_38_1 = all_10_1
% 116.97/18.17 (19) all_54_0 = all_10_2
% 116.97/18.17 (20) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 116.97/18.17 (21) all_54_3 = all_52_12
% 116.97/18.17 (22) ~ (all_52_2 = all_52_6)
% 116.97/18.17 (23) op(e0, e2) = all_52_7
% 116.97/18.17 (24) ~ (all_52_7 = all_4_2)
% 116.97/18.17 (25) all_56_11 = all_52_11
% 116.97/18.17 (26) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 116.97/18.17 (27) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.97/18.17 (28) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 116.97/18.17 (29) ~ (all_52_4 = all_52_8)
% 116.97/18.17 (30) ~ (all_52_12 = all_10_2)
% 116.97/18.17 (31) ~ (e3 = e1)
% 116.97/18.17 (32) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.97/18.17 (33) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.17 (34) all_56_12 = all_10_2
% 116.97/18.17 (35) all_58_0 = all_10_2
% 116.97/18.17 (36) op(all_6_1, all_6_2) = all_6_0
% 116.97/18.17 (37) all_54_11 = all_52_14
% 116.97/18.17 (38) all_54_13 = all_52_7
% 116.97/18.17 (39) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.97/18.17 (40) ~ (all_52_14 = all_6_2)
% 116.97/18.17 (41) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 116.97/18.17 (42) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 116.97/18.17 (43) all_56_10 = all_52_7
% 116.97/18.17 (44) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.97/18.17 (45) all_54_14 = all_52_11
% 116.97/18.17 (46) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 116.97/18.17 (47) ~ (all_56_1 = e3) | ~ (all_56_13 = e1)
% 116.97/18.17 (48) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.17 (49) ~ (all_8_1 = e3)
% 116.97/18.17 (50) all_54_8 = all_52_2
% 116.97/18.17 (51) ~ (all_52_2 = all_6_2)
% 116.97/18.17 (52) all_32_2 = all_10_2
% 116.97/18.17 (53) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 116.97/18.17 (54) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 116.97/18.17 (55) all_54_10 = all_6_2
% 116.97/18.17 (56) op(e3, e0) = all_52_12
% 116.97/18.17 (57) all_38_0 = all_10_0
% 116.97/18.17 (58) ~ (all_52_8 = all_6_2)
% 116.97/18.17 (59) all_58_4 = all_52_8
% 116.97/18.17 (60) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.17 (61) ~ (all_52_4 = all_52_7)
% 116.97/18.17 (62) all_56_2 = all_52_12
% 116.97/18.17 (63) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 116.97/18.17 (64) all_58_3 = all_8_2
% 116.97/18.17 (65) all_54_6 = all_52_9
% 116.97/18.17 (66) ~ (all_10_0 = e2)
% 116.97/18.17 (67) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 116.97/18.17 (68) all_58_11 = all_52_14
% 116.97/18.17 (69) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 116.97/18.17 (70) all_54_9 = all_52_6
% 116.97/18.17 (71) op(e3, e1) = all_52_8
% 116.97/18.17 (72) ~ (all_52_2 = all_52_3)
% 116.97/18.17 (73) op(all_10_1, all_10_2) = all_10_0
% 116.97/18.17 (74) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 116.97/18.17 (75) ~ (all_52_11 = all_6_2)
% 116.97/18.17 (76) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 116.97/18.17 (77) all_28_2 = all_6_2
% 116.97/18.17 (78) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 116.97/18.17 (79) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 116.97/18.17 (80) all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.97/18.17 (81) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 116.97/18.17 (82) ~ (all_52_7 = all_8_2)
% 116.97/18.17 (83) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 116.97/18.17 (84) ~ (all_52_4 = all_8_2)
% 116.97/18.17 (85) op(e1, e0) = all_52_14
% 116.97/18.17 (86) all_58_5 = all_52_9
% 116.97/18.17 (87) ~ (all_52_9 = all_52_13)
% 116.97/18.17 (88) all_56_9 = all_52_3
% 116.97/18.17 (89) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 116.97/18.17 (90) op(e1, all_6_2) = all_6_1
% 116.97/18.17 (91) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 116.97/18.17 (92) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.97/18.17 (93) all_32_0 = all_10_0
% 116.97/18.17 (94) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 116.97/18.17 (95) all_58_15 = all_4_2
% 116.97/18.17 (96) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 116.97/18.17 (97) all_58_2 = all_52_1
% 116.97/18.17 (98) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 116.97/18.17 (99) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 116.97/18.17 (100) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 116.97/18.17 (101) ~ (all_10_2 = e3)
% 116.97/18.17 (102) all_58_13 = all_52_7
% 116.97/18.17 (103) all_32_1 = all_10_1
% 116.97/18.17 (104) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 116.97/18.17 (105) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 116.97/18.17 (106) ~ (all_52_14 = all_4_2)
% 116.97/18.17 (107) all_58_6 = all_52_2
% 116.97/18.17 (108) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 116.97/18.17 (109) ~ (all_52_1 = all_10_2)
% 116.97/18.17 (110) all_54_5 = all_8_2
% 116.97/18.17 (111) all_56_15 = all_4_2
% 116.97/18.17 (112) all_58_10 = all_52_13
% 116.97/18.17 (113) ~ (all_52_13 = all_8_2)
% 116.97/18.17 (114) op(e2, all_8_2) = all_8_1
% 116.97/18.17 (115) ~ (all_52_11 = all_4_2)
% 116.97/18.17 (116) op(e3, all_10_2) = all_10_1
% 116.97/18.17 (117) ~ (all_52_6 = all_8_2)
% 116.97/18.17 (118) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 116.97/18.17 (119) all_6_0 = e2
% 116.97/18.17 (120) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 116.97/18.17 (121) all_38_2 = all_10_2
% 116.97/18.17 (122) all_58_1 = all_52_4
% 116.97/18.17 (123) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.97/18.17 (124) ~ (all_52_9 = all_52_11)
% 116.97/18.17 (125) all_58_14 = all_52_11
% 116.97/18.17 (126) all_54_1 = all_52_4
% 116.97/18.17 (127) all_56_13 = all_8_2
% 116.97/18.17 (128) op(e0, e1) = all_52_11
% 116.97/18.17 (129) ~ (all_52_1 = all_8_2)
% 116.97/18.17 (130) ~ (all_8_2 = e2)
% 116.97/18.17 (131) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.97/18.17 (132) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.17 (133) ~ (all_52_7 = all_52_11)
% 116.97/18.17 (134) op(e1, e2) = all_52_6
% 116.97/18.17 (135) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.17 (136) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 116.97/18.17 (137) all_56_7 = all_52_6
% 116.97/18.17 (138) ~ (all_52_9 = all_6_2)
% 116.97/18.17 (139) ~ (all_52_4 = all_52_6)
% 116.97/18.17 (140) ~ (all_52_1 = all_52_2)
% 116.97/18.17 (141) ~ (all_52_4 = all_52_12)
% 116.97/18.17 (142) all_56_1 = all_52_8
% 116.97/18.17 (143) op(e0, all_4_2) = all_4_1
% 116.97/18.17 (144) all_58_8 = all_6_2
% 116.97/18.17 (145) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.17 (146) ~ (all_10_0 = e1)
% 116.97/18.17 (147) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 116.97/18.17 (148) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 116.97/18.17 (149) all_56_4 = all_52_9
% 116.97/18.17 (150) all_58_9 = all_52_12
% 116.97/18.17 (151) all_56_5 = all_52_13
% 116.97/18.17 (152) op(e2, e1) = all_52_9
% 116.97/18.17 (153) ~ (all_52_6 = all_6_2)
% 116.97/18.17 (154) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 116.97/18.17 (155) all_56_6 = all_52_2
% 116.97/18.17 (156) ~ (all_52_13 = all_4_2)
% 116.97/18.17 (157) ~ (e2 = e0)
% 116.97/18.17 (158) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 116.97/18.17 (159) all_58_12 = all_52_3
% 116.97/18.17 (160) ~ (all_52_2 = all_52_14)
% 116.97/18.17 (161) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 116.97/18.17 (162) ~ (all_52_8 = all_52_9)
% 116.97/18.17 (163) op(e2, e0) = all_52_13
% 116.97/18.17 (164) ~ (all_52_12 = all_4_2)
% 116.97/18.17 (165) ~ (all_52_3 = all_10_2)
% 116.97/18.17 (166) op(e1, e3) = all_52_2
% 116.97/18.17 (167) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 116.97/18.17 (168) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 116.97/18.17 (169) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.17 (170) ~ (all_52_8 = all_52_12)
% 116.97/18.17 (171) all_56_8 = all_52_14
% 116.97/18.17 (172) ~ (all_52_4 = all_10_2)
% 116.97/18.17 (173) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 116.97/18.17 (174) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.17 (175) all_56_0 = all_52_4
% 116.97/18.17 (176) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.97/18.17 (177) ~ (e3 = e2)
% 116.97/18.17 (178) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.97/18.17 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 116.97/18.17 (179) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 116.97/18.17 (180) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 116.97/18.17 (181) all_54_15 = all_4_2
% 116.97/18.17 (182) ~ (all_6_2 = e1)
% 116.97/18.17 (183) ~ (all_6_1 = e2)
% 116.97/18.17 (184) ~ (all_52_6 = all_52_7)
% 116.97/18.17 (185) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 116.97/18.17 (186) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 116.97/18.17 (187) ~ (e1 = e0)
% 116.97/18.17
% 116.97/18.17 Begin of proof
% 116.97/18.17 |
% 116.97/18.17 | REDUCE: (36), (119) imply:
% 116.97/18.17 | (188) op(all_6_1, all_6_2) = e2
% 116.97/18.17 |
% 116.97/18.17 | BETA: splitting (7) gives:
% 116.97/18.17 |
% 116.97/18.17 | Case 1:
% 116.97/18.17 | |
% 116.97/18.17 | | (189) ~ (all_32_1 = e1)
% 116.97/18.17 | |
% 116.97/18.17 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 116.97/18.17 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 116.97/18.17 | | (25), (26), (27), (28), (30), (32), (33), (34), (35), (37), (38),
% 116.97/18.17 | | (39), (40), (41), (42), (43), (45), (46), (48), (50), (51), (53),
% 116.97/18.17 | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 116.97/18.17 | | (65), (66), (68), (69), (71), (72), (73), (74), (75), (76), (77),
% 116.97/18.17 | | (78), (79), (81), (83), (84), (85), (86), (87), (88), (89), (90),
% 116.97/18.17 | | (91), (92), (94), (95), (96), (97), (98), (99), (100), (101),
% 116.97/18.17 | | (102), (103), (104), (105), (106), (107), (109), (110), (111),
% 116.97/18.17 | | (112), (113), (115), (116), (117), (118), (120), (121), (122),
% 116.97/18.17 | | (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 116.97/18.17 | | (134), (135), (136), (137), (138), (139), (140), (142), (143),
% 116.97/18.17 | | (144), (145), (146), (148), (149), (150), (151), (152), (153),
% 116.97/18.17 | | (154), (155), (156), (157), (158), (159), (160), (161), (162),
% 116.97/18.17 | | (163), (164), (165), (166), (167), (169), (170), (171), (172),
% 116.97/18.17 | | (173), (174), (175), (176), (177), (178), (179), (180), (181),
% 116.97/18.17 | | (182), (183), (184), (185), (186), (188), (189) are inconsistent
% 116.97/18.17 | | by sub-proof #254.
% 116.97/18.17 | |
% 116.97/18.17 | Case 2:
% 116.97/18.17 | |
% 116.97/18.17 | | (190) all_32_1 = e1
% 116.97/18.17 | | (191) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 116.97/18.17 | |
% 116.97/18.17 | | COMBINE_EQS: (103), (190) imply:
% 116.97/18.17 | | (192) all_10_1 = e1
% 116.97/18.17 | |
% 116.97/18.17 | | SIMP: (192) implies:
% 116.97/18.17 | | (193) all_10_1 = e1
% 116.97/18.17 | |
% 116.97/18.17 | | REDUCE: (73), (193) imply:
% 116.97/18.17 | | (194) op(e1, all_10_2) = all_10_0
% 116.97/18.17 | |
% 116.97/18.17 | | REDUCE: (116), (193) imply:
% 116.97/18.17 | | (195) op(e3, all_10_2) = e1
% 116.97/18.17 | |
% 116.97/18.17 | | BETA: splitting (104) gives:
% 116.97/18.17 | |
% 116.97/18.17 | | Case 1:
% 116.97/18.17 | | |
% 116.97/18.17 | | | (196) ~ (all_56_14 = e2)
% 116.97/18.17 | | |
% 116.97/18.17 | | | REDUCE: (15), (196) imply:
% 116.97/18.17 | | | (197) ~ (all_6_2 = e2)
% 116.97/18.17 | | |
% 116.97/18.17 | | | REF_CLOSE: (1), (2), (3), (6), (9), (10), (11), (13), (14), (15), (16),
% 116.97/18.17 | | | (17), (19), (22), (24), (27), (32), (33), (34), (35), (37),
% 116.97/18.17 | | | (39), (40), (44), (46), (48), (50), (51), (52), (55), (58),
% 116.97/18.17 | | | (59), (60), (62), (63), (64), (66), (67), (70), (71), (75),
% 116.97/18.17 | | | (77), (82), (83), (84), (85), (86), (90), (92), (93), (95),
% 116.97/18.17 | | | (97), (98), (100), (101), (102), (105), (110), (111), (112),
% 116.97/18.17 | | | (118), (122), (125), (127), (130), (133), (134), (137), (138),
% 116.97/18.17 | | | (144), (145), (148), (149), (150), (151), (153), (155), (159),
% 116.97/18.17 | | | (161), (165), (166), (168), (169), (171), (172), (174), (178),
% 116.97/18.17 | | | (181), (182), (183), (184), (191), (194), (195), (197) are
% 116.97/18.17 | | | inconsistent by sub-proof #249.
% 116.97/18.17 | | |
% 116.97/18.17 | | Case 2:
% 116.97/18.17 | | |
% 116.97/18.17 | | | (198) all_56_14 = e2
% 116.97/18.17 | | | (199) ~ (all_56_10 = e0)
% 116.97/18.17 | | |
% 116.97/18.17 | | | COMBINE_EQS: (15), (198) imply:
% 116.97/18.17 | | | (200) all_6_2 = e2
% 116.97/18.17 | | |
% 116.97/18.17 | | | SIMP: (200) implies:
% 116.97/18.17 | | | (201) all_6_2 = e2
% 116.97/18.17 | | |
% 116.97/18.17 | | | REDUCE: (43), (199) imply:
% 116.97/18.17 | | | (202) ~ (all_52_7 = e0)
% 116.97/18.17 | | |
% 116.97/18.17 | | | REDUCE: (153), (201) imply:
% 116.97/18.17 | | | (203) ~ (all_52_6 = e2)
% 116.97/18.17 | | |
% 116.97/18.17 | | | REDUCE: (138), (201) imply:
% 116.97/18.17 | | | (204) ~ (all_52_9 = e2)
% 116.97/18.17 | | |
% 116.97/18.17 | | | REDUCE: (90), (201) imply:
% 116.97/18.17 | | | (205) op(e1, e2) = all_6_1
% 116.97/18.17 | | |
% 116.97/18.17 | | | BETA: splitting (42) gives:
% 116.97/18.17 | | |
% 116.97/18.17 | | | Case 1:
% 116.97/18.17 | | | |
% 116.97/18.17 | | | | (206) ~ (all_56_7 = e1)
% 116.97/18.17 | | | |
% 116.97/18.17 | | | | REDUCE: (137), (206) imply:
% 116.97/18.17 | | | | (207) ~ (all_52_6 = e1)
% 116.97/18.17 | | | |
% 116.97/18.17 | | | | BETA: splitting (179) gives:
% 116.97/18.17 | | | |
% 116.97/18.17 | | | | Case 1:
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | (208) ~ (all_56_0 = e3)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | REDUCE: (175), (208) imply:
% 116.97/18.17 | | | | | (209) ~ (all_52_4 = e3)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | GROUND_INST: instantiating (48) with all_52_6, all_6_1, e2, e1,
% 116.97/18.17 | | | | | simplifying with (134), (205) gives:
% 116.97/18.17 | | | | | (210) all_52_6 = all_6_1
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | COMBINE_EQS: (6), (210) imply:
% 116.97/18.17 | | | | | (211) all_58_7 = all_6_1
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | REDUCE: (139), (210) imply:
% 116.97/18.17 | | | | | (212) ~ (all_52_4 = all_6_1)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | REDUCE: (4), (210) imply:
% 116.97/18.17 | | | | | (213) ~ (all_52_14 = all_6_1)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | SIMP: (213) implies:
% 116.97/18.17 | | | | | (214) ~ (all_52_14 = all_6_1)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | REDUCE: (207), (210) imply:
% 116.97/18.17 | | | | | (215) ~ (all_6_1 = e1)
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | BETA: splitting (147) gives:
% 116.97/18.17 | | | | |
% 116.97/18.17 | | | | | Case 1:
% 116.97/18.17 | | | | | |
% 116.97/18.17 | | | | | | (216) ~ (all_56_15 = e3)
% 116.97/18.17 | | | | | |
% 116.97/18.17 | | | | | | REDUCE: (111), (216) imply:
% 116.97/18.17 | | | | | | (217) ~ (all_4_2 = e3)
% 116.97/18.17 | | | | | |
% 116.97/18.17 | | | | | | BETA: splitting (2) gives:
% 116.97/18.17 | | | | | |
% 116.97/18.17 | | | | | | Case 1:
% 116.97/18.17 | | | | | | |
% 116.97/18.17 | | | | | | | (218) ~ (all_56_2 = e3)
% 116.97/18.17 | | | | | | |
% 116.97/18.17 | | | | | | | REDUCE: (62), (218) imply:
% 116.97/18.17 | | | | | | | (219) ~ (all_52_12 = e3)
% 116.97/18.17 | | | | | | |
% 116.97/18.17 | | | | | | | BETA: splitting (169) gives:
% 116.97/18.17 | | | | | | |
% 116.97/18.18 | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | (220) all_58_0 = e3
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | COMBINE_EQS: (35), (220) imply:
% 116.97/18.18 | | | | | | | | (221) all_10_2 = e3
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | REDUCE: (101), (221) imply:
% 116.97/18.18 | | | | | | | | (222) $false
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | CLOSE: (222) is inconsistent.
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | (223) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | BETA: splitting (223) gives:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | (224) all_58_1 = e3
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | COMBINE_EQS: (122), (224) imply:
% 116.97/18.18 | | | | | | | | | (225) all_52_4 = e3
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | REDUCE: (209), (225) imply:
% 116.97/18.18 | | | | | | | | | (226) $false
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | CLOSE: (226) is inconsistent.
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | (227) all_58_4 = e3 | all_58_9 = e3
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | BETA: splitting (227) gives:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | (228) all_58_4 = e3
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | COMBINE_EQS: (59), (228) imply:
% 116.97/18.18 | | | | | | | | | | (229) all_52_8 = e3
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | COMBINE_EQS: (142), (229) imply:
% 116.97/18.18 | | | | | | | | | | (230) all_56_1 = e3
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | BETA: splitting (108) gives:
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | (231) ~ (all_56_1 = e3)
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | REDUCE: (230), (231) imply:
% 116.97/18.18 | | | | | | | | | | | (232) $false
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | (233) ~ (all_56_15 = e1)
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | REDUCE: (111), (233) imply:
% 116.97/18.18 | | | | | | | | | | | (234) ~ (all_4_2 = e1)
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | BETA: splitting (47) gives:
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | (235) ~ (all_56_1 = e3)
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | REDUCE: (230), (235) imply:
% 116.97/18.18 | | | | | | | | | | | | (236) $false
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | (237) ~ (all_56_13 = e1)
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | REDUCE: (127), (237) imply:
% 116.97/18.18 | | | | | | | | | | | | (238) ~ (all_8_2 = e1)
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | BETA: splitting (60) gives:
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | (239) all_54_15 = e3
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | COMBINE_EQS: (181), (239) imply:
% 116.97/18.18 | | | | | | | | | | | | | (240) all_4_2 = e3
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | REDUCE: (217), (240) imply:
% 116.97/18.18 | | | | | | | | | | | | | (241) $false
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | (242) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | BETA: splitting (242) gives:
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | (243) all_54_15 = e2
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | COMBINE_EQS: (181), (243) imply:
% 116.97/18.18 | | | | | | | | | | | | | | (244) all_4_2 = e2
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | COMBINE_EQS: (95), (244) imply:
% 116.97/18.18 | | | | | | | | | | | | | | (245) all_58_15 = e2
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | REDUCE: (24), (244) imply:
% 116.97/18.18 | | | | | | | | | | | | | | (246) ~ (all_52_7 = e2)
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | REDUCE: (156), (244) imply:
% 116.97/18.18 | | | | | | | | | | | | | | (247) ~ (all_52_13 = e2)
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | REDUCE: (234), (244) imply:
% 116.97/18.18 | | | | | | | | | | | | | | (248) ~ (e2 = e1)
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | (249) all_58_1 = e2
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | COMBINE_EQS: (122), (249) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | (250) all_52_4 = e2
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | REDUCE: (84), (250) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | (251) ~ (all_8_2 = e2)
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | REDUCE: (212), (250) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | (252) ~ (all_6_1 = e2)
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | REDUCE: (209), (250) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | (253) ~ (e3 = e2)
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | (254) all_58_1 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (254) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | (255) e2 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | REDUCE: (248), (255) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | (256) $false
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | (257) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | (258) all_58_2 = e2
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (258) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | (259) all_52_1 = e2
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (259) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | (260) all_56_3 = e2
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | (261) all_58_3 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (261) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | (262) all_8_2 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | REDUCE: (238), (262) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | (263) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | (264) all_58_7 = e1 | all_58_13 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (265) all_58_7 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (265) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (266) all_6_1 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | REDUCE: (215), (266) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (267) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (268) all_58_13 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (268) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (269) all_52_7 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | SIMP: (269) implies:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (270) all_52_7 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | REDUCE: (82), (270) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | (271) ~ (all_8_2 = e1)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | (272) ~ (all_56_3 = e2)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (260), (272) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | (273) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | (274) ~ (all_56_13 = e3)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (274) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | (275) ~ (all_8_2 = e3)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | (276) all_54_5 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (275), (276) are inconsistent by sub-proof
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | #339.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | (277) ~ (all_54_5 = e3)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | (278) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | (279) all_58_1 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (177), (249), (279) are inconsistent by sub-proof
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | #390.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | (280) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | (281) all_58_3 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (281) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | (282) all_8_2 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (282) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | (283) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | (284) all_58_7 = e3 | all_58_13 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_7 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (285) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (286) all_6_1 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (286) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (287) ~ (all_52_14 = e3)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_9 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (110), (123), (127), (130), (150), (238),
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | (278), (288) are inconsistent by sub-proof #248.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_10 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (290) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_52_13 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (291) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (292) op(e2, e0) = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_1 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (293) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e2 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (294) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (295) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_58_3 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (64), (297) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_8_2 = e0
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (298) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) op(e2, e0) = all_8_1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (49), (292), (299) are inconsistent by
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #247.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) ~ (all_58_3 = e0)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (300) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) ~ (all_8_2 = e0)
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (130), (238), (278), (301) are inconsistent
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #310.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_58_11 = e3 | all_58_15 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (177), (245), (287), (302) are inconsistent
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #245.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (303) all_58_13 = e3
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (303) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (304) e3 = e1
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (304) imply:
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | (305) $false
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | (306) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (86), (112), (130), (204), (247), (306) are
% 116.97/18.18 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401.
% 116.97/18.18 | | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | (307) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | | REF_CLOSE: (64), (102), (130), (183), (211), (246), (307) are
% 116.97/18.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #264.
% 116.97/18.18 | | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | (308) all_54_15 = e1 | all_54_15 = e0
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | | REF_CLOSE: (13), (181), (234), (308) are inconsistent by
% 116.97/18.18 | | | | | | | | | | | | | | sub-proof #418.
% 116.97/18.18 | | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | (309) all_58_9 = e3
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | COMBINE_EQS: (150), (309) imply:
% 116.97/18.18 | | | | | | | | | | (310) all_52_12 = e3
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | REDUCE: (219), (310) imply:
% 116.97/18.18 | | | | | | | | | | (311) $false
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | CLOSE: (311) is inconsistent.
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | End of split
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | End of split
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | Case 2:
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | (312) all_56_2 = e3
% 116.97/18.18 | | | | | | | (313) ~ (all_56_12 = e0)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | COMBINE_EQS: (62), (312) imply:
% 116.97/18.18 | | | | | | | (314) all_52_12 = e3
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | REDUCE: (34), (313) imply:
% 116.97/18.18 | | | | | | | (315) ~ (all_10_2 = e0)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | REDUCE: (170), (314) imply:
% 116.97/18.18 | | | | | | | (316) ~ (all_52_8 = e3)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | REDUCE: (30), (314) imply:
% 116.97/18.18 | | | | | | | (317) ~ (all_10_2 = e3)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | REDUCE: (164), (314) imply:
% 116.97/18.18 | | | | | | | (318) ~ (all_4_2 = e3)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | BETA: splitting (123) gives:
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | (319) ~ (all_56_2 = e3)
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | REDUCE: (312), (319) imply:
% 116.97/18.18 | | | | | | | | (320) $false
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | CLOSE: (320) is inconsistent.
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | (321) ~ (all_56_13 = e0)
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | REDUCE: (127), (321) imply:
% 116.97/18.18 | | | | | | | | (322) ~ (all_8_2 = e0)
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | BETA: splitting (89) gives:
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | (323) ~ (all_56_15 = e1)
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | REDUCE: (111), (323) imply:
% 116.97/18.18 | | | | | | | | | (324) ~ (all_4_2 = e1)
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | REF_CLOSE: (1), (2), (13), (19), (30), (34), (35), (48), (59),
% 116.97/18.18 | | | | | | | | | (60), (62), (64), (71), (86), (97), (101), (109),
% 116.97/18.18 | | | | | | | | | (112), (122), (130), (145), (150), (156), (169),
% 116.97/18.18 | | | | | | | | | (174), (181), (195), (204), (209), (217), (316),
% 116.97/18.18 | | | | | | | | | (324) are inconsistent by sub-proof #243.
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | (325) all_56_15 = e1
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | COMBINE_EQS: (111), (325) imply:
% 116.97/18.18 | | | | | | | | | (326) all_4_2 = e1
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | SIMP: (326) implies:
% 116.97/18.18 | | | | | | | | | (327) all_4_2 = e1
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | REDUCE: (106), (327) imply:
% 116.97/18.18 | | | | | | | | | (328) ~ (all_52_14 = e1)
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | BETA: splitting (135) gives:
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | | Case 1:
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | (329) all_58_6 = e1
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | COMBINE_EQS: (107), (329) imply:
% 116.97/18.18 | | | | | | | | | | (330) all_52_2 = e1
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | SIMP: (330) implies:
% 116.97/18.18 | | | | | | | | | | (331) all_52_2 = e1
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | REDUCE: (3), (331) imply:
% 116.97/18.18 | | | | | | | | | | (332) ~ (all_10_2 = e1)
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | SIMP: (332) implies:
% 116.97/18.18 | | | | | | | | | | (333) ~ (all_10_2 = e1)
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | REF_CLOSE: (6), (14), (19), (34), (48), (52), (64), (92),
% 116.97/18.18 | | | | | | | | | | (93), (101), (102), (122), (132), (134), (145),
% 116.97/18.18 | | | | | | | | | | (187), (191), (194), (195), (202), (315), (322),
% 116.97/18.18 | | | | | | | | | | (333) are inconsistent by sub-proof #241.
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | Case 2:
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | (334) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | | REF_CLOSE: (6), (68), (144), (182), (207), (328), (334) are
% 116.97/18.18 | | | | | | | | | | inconsistent by sub-proof #354.
% 116.97/18.18 | | | | | | | | | |
% 116.97/18.18 | | | | | | | | | End of split
% 116.97/18.18 | | | | | | | | |
% 116.97/18.18 | | | | | | | | End of split
% 116.97/18.18 | | | | | | | |
% 116.97/18.18 | | | | | | | End of split
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | End of split
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | Case 2:
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | (335) all_56_15 = e3
% 116.97/18.18 | | | | | | (336) ~ (all_56_9 = e0)
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | COMBINE_EQS: (111), (335) imply:
% 116.97/18.18 | | | | | | (337) all_4_2 = e3
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | SIMP: (337) implies:
% 116.97/18.18 | | | | | | (338) all_4_2 = e3
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | COMBINE_EQS: (95), (338) imply:
% 116.97/18.18 | | | | | | (339) all_58_15 = e3
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | REDUCE: (88), (336) imply:
% 116.97/18.18 | | | | | | (340) ~ (all_52_3 = e0)
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | REDUCE: (13), (338) imply:
% 116.97/18.18 | | | | | | (341) ~ (e3 = e0)
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | BETA: splitting (53) gives:
% 116.97/18.18 | | | | | |
% 116.97/18.18 | | | | | | Case 1:
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | (342) ~ (all_56_3 = e2)
% 116.97/18.18 | | | | | | |
% 116.97/18.18 | | | | | | | REDUCE: (17), (342) imply:
% 116.97/18.19 | | | | | | | (343) ~ (all_52_1 = e2)
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | | BETA: splitting (178) gives:
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | (344) all_58_15 = e0
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | COMBINE_EQS: (339), (344) imply:
% 116.97/18.19 | | | | | | | | (345) e3 = e0
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | REDUCE: (341), (345) imply:
% 116.97/18.19 | | | | | | | | (346) $false
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | CLOSE: (346) is inconsistent.
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | (347) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 116.97/18.19 | | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | ALPHA: (347) implies:
% 116.97/18.19 | | | | | | | | (348) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | BETA: splitting (348) gives:
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | | (349) all_58_12 = e0
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | | REF_CLOSE: (159), (340), (349) are inconsistent by sub-proof
% 116.97/18.19 | | | | | | | | | #362.
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | | (350) all_58_13 = e0 | all_58_14 = e0
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | | BETA: splitting (173) gives:
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | (351) ~ (all_56_12 = e1)
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | REDUCE: (34), (351) imply:
% 116.97/18.19 | | | | | | | | | | (352) ~ (all_10_2 = e1)
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | BETA: splitting (174) gives:
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | (353) all_58_2 = e2
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | COMBINE_EQS: (97), (353) imply:
% 116.97/18.19 | | | | | | | | | | | (354) all_52_1 = e2
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | REDUCE: (343), (354) imply:
% 116.97/18.19 | | | | | | | | | | | (355) $false
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | CLOSE: (355) is inconsistent.
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | (356) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | BETA: splitting (356) gives:
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | (357) all_58_3 = e2
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | COMBINE_EQS: (64), (357) imply:
% 116.97/18.19 | | | | | | | | | | | | (358) all_8_2 = e2
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | REDUCE: (130), (358) imply:
% 116.97/18.19 | | | | | | | | | | | | (359) $false
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | (360) all_58_5 = e2 | all_58_10 = e2
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | BETA: splitting (360) gives:
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | (361) all_58_5 = e2
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | COMBINE_EQS: (86), (361) imply:
% 116.97/18.19 | | | | | | | | | | | | | (362) all_52_9 = e2
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | REDUCE: (204), (362) imply:
% 116.97/18.19 | | | | | | | | | | | | | (363) $false
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | CLOSE: (363) is inconsistent.
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | (364) all_58_10 = e2
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | COMBINE_EQS: (112), (364) imply:
% 116.97/18.19 | | | | | | | | | | | | | (365) all_52_13 = e2
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | COMBINE_EQS: (151), (365) imply:
% 116.97/18.19 | | | | | | | | | | | | | (366) all_56_5 = e2
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | BETA: splitting (69) gives:
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | (367) ~ (all_56_5 = e2)
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | REDUCE: (366), (367) imply:
% 116.97/18.19 | | | | | | | | | | | | | | (368) $false
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | (369) ~ (all_56_13 = e0)
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | REDUCE: (127), (369) imply:
% 116.97/18.19 | | | | | | | | | | | | | | (370) ~ (all_8_2 = e0)
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | Case 1:
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | (371) ~ (all_56_5 = e2)
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | REDUCE: (366), (371) imply:
% 116.97/18.19 | | | | | | | | | | | | | | | (372) $false
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent.
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | (373) ~ (all_56_12 = e0)
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | REDUCE: (34), (373) imply:
% 116.97/18.19 | | | | | | | | | | | | | | | (374) ~ (all_10_2 = e0)
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (19), (34), (48), (52), (64), (92),
% 116.97/18.19 | | | | | | | | | | | | | | | (93), (101), (102), (122), (132), (134), (145),
% 116.97/18.19 | | | | | | | | | | | | | | | (187), (191), (194), (195), (202), (352), (370),
% 116.97/18.19 | | | | | | | | | | | | | | | (374) are inconsistent by sub-proof #241.
% 116.97/18.19 | | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | Case 2:
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | (375) all_56_12 = e1
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | | REF_CLOSE: (25), (102), (125), (173), (202), (350), (375) are
% 116.97/18.19 | | | | | | | | | | inconsistent by sub-proof #361.
% 116.97/18.19 | | | | | | | | | |
% 116.97/18.19 | | | | | | | | | End of split
% 116.97/18.19 | | | | | | | | |
% 116.97/18.19 | | | | | | | | End of split
% 116.97/18.19 | | | | | | | |
% 116.97/18.19 | | | | | | | End of split
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | Case 2:
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | | (376) ~ (all_56_15 = e3)
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | | REDUCE: (335), (376) imply:
% 116.97/18.19 | | | | | | | (377) $false
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | | CLOSE: (377) is inconsistent.
% 116.97/18.19 | | | | | | |
% 116.97/18.19 | | | | | | End of split
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | End of split
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | Case 2:
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | (378) ~ (all_56_14 = e2)
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | REDUCE: (198), (378) imply:
% 116.97/18.19 | | | | | (379) $false
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | CLOSE: (379) is inconsistent.
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | End of split
% 116.97/18.19 | | | |
% 116.97/18.19 | | | Case 2:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | (380) ~ (all_56_14 = e2)
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | REDUCE: (198), (380) imply:
% 116.97/18.19 | | | | (381) $false
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | CLOSE: (381) is inconsistent.
% 116.97/18.19 | | | |
% 116.97/18.19 | | | End of split
% 116.97/18.19 | | |
% 116.97/18.19 | | End of split
% 116.97/18.19 | |
% 116.97/18.19 | End of split
% 116.97/18.19 |
% 116.97/18.19 End of proof
% 116.97/18.19
% 116.97/18.19 Sub-proof #241 shows that the following formulas are inconsistent:
% 116.97/18.19 ----------------------------------------------------------------
% 116.97/18.19 (1) all_58_7 = all_52_6
% 116.97/18.19 (2) op(e3, e2) = all_52_4
% 116.97/18.19 (3) all_54_0 = all_10_2
% 116.97/18.19 (4) op(e3, all_10_2) = e1
% 116.97/18.19 (5) all_56_12 = all_10_2
% 116.97/18.19 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.19 (7) all_32_2 = all_10_2
% 116.97/18.19 (8) all_58_3 = all_8_2
% 116.97/18.19 (9) ~ (all_8_2 = e0)
% 116.97/18.19 (10) ~ (all_10_2 = e1)
% 116.97/18.19 (11) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.97/18.19 (12) all_32_0 = all_10_0
% 116.97/18.19 (13) ~ (all_10_2 = e3)
% 116.97/18.19 (14) all_58_13 = all_52_7
% 116.97/18.19 (15) ~ (all_52_7 = e0)
% 116.97/18.19 (16) all_58_1 = all_52_4
% 116.97/18.19 (17) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.19 (18) op(e1, e2) = all_52_6
% 116.97/18.19 (19) ~ (all_10_2 = e0)
% 116.97/18.19 (20) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 116.97/18.19 (21) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.19 (22) op(e1, all_10_2) = all_10_0
% 116.97/18.19 (23) ~ (e1 = e0)
% 116.97/18.19
% 116.97/18.19 Begin of proof
% 116.97/18.19 |
% 116.97/18.19 | BETA: splitting (21) gives:
% 116.97/18.19 |
% 116.97/18.19 | Case 1:
% 116.97/18.19 | |
% 116.97/18.19 | | (24) all_54_0 = e3
% 116.97/18.19 | |
% 116.97/18.19 | | REF_CLOSE: (3), (13), (24) are inconsistent by sub-proof #451.
% 116.97/18.19 | |
% 116.97/18.19 | Case 2:
% 116.97/18.19 | |
% 116.97/18.19 | | (25) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.19 | |
% 116.97/18.19 | | BETA: splitting (25) gives:
% 116.97/18.19 | |
% 116.97/18.19 | | Case 1:
% 116.97/18.19 | | |
% 116.97/18.19 | | | (26) all_54_0 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (3), (26) imply:
% 116.97/18.19 | | | (27) all_10_2 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | SIMP: (27) implies:
% 116.97/18.19 | | | (28) all_10_2 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (7), (28) imply:
% 116.97/18.19 | | | (29) all_32_2 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (5), (28) imply:
% 116.97/18.19 | | | (30) all_56_12 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | REDUCE: (4), (28) imply:
% 116.97/18.19 | | | (31) op(e3, e2) = e1
% 116.97/18.19 | | |
% 116.97/18.19 | | | REDUCE: (22), (28) imply:
% 116.97/18.19 | | | (32) op(e1, e2) = all_10_0
% 116.97/18.19 | | |
% 116.97/18.19 | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (12), (14), (15), (16), (17),
% 116.97/18.19 | | | (18), (20), (23), (29), (30), (31), (32) are inconsistent by
% 116.97/18.19 | | | sub-proof #242.
% 116.97/18.19 | | |
% 116.97/18.19 | | Case 2:
% 116.97/18.19 | | |
% 116.97/18.19 | | | (33) all_54_0 = e1 | all_54_0 = e0
% 116.97/18.19 | | |
% 116.97/18.19 | | | REF_CLOSE: (3), (10), (19), (33) are inconsistent by sub-proof #423.
% 116.97/18.19 | | |
% 116.97/18.19 | | End of split
% 116.97/18.19 | |
% 116.97/18.19 | End of split
% 116.97/18.19 |
% 116.97/18.19 End of proof
% 116.97/18.19
% 116.97/18.19 Sub-proof #242 shows that the following formulas are inconsistent:
% 116.97/18.19 ----------------------------------------------------------------
% 116.97/18.19 (1) all_58_7 = all_52_6
% 116.97/18.19 (2) op(e3, e2) = all_52_4
% 116.97/18.19 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.19 (4) all_56_12 = e2
% 116.97/18.19 (5) all_58_3 = all_8_2
% 116.97/18.19 (6) ~ (all_8_2 = e0)
% 116.97/18.19 (7) op(e3, e2) = e1
% 116.97/18.19 (8) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 116.97/18.19 (9) all_32_0 = all_10_0
% 116.97/18.19 (10) all_58_13 = all_52_7
% 116.97/18.19 (11) ~ (all_52_7 = e0)
% 116.97/18.19 (12) op(e1, e2) = all_10_0
% 116.97/18.19 (13) all_58_1 = all_52_4
% 116.97/18.19 (14) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.19 (15) op(e1, e2) = all_52_6
% 116.97/18.19 (16) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 116.97/18.19 (17) all_32_2 = e2
% 116.97/18.19 (18) ~ (e1 = e0)
% 116.97/18.19
% 116.97/18.19 Begin of proof
% 116.97/18.19 |
% 116.97/18.19 | BETA: splitting (16) gives:
% 116.97/18.19 |
% 116.97/18.19 | Case 1:
% 116.97/18.19 | |
% 116.97/18.19 | | (19) ~ (all_32_2 = e2)
% 116.97/18.19 | |
% 116.97/18.19 | | REDUCE: (17), (19) imply:
% 116.97/18.19 | | (20) $false
% 116.97/18.19 | |
% 116.97/18.19 | | CLOSE: (20) is inconsistent.
% 116.97/18.19 | |
% 116.97/18.19 | Case 2:
% 116.97/18.19 | |
% 116.97/18.19 | | (21) ~ (all_32_0 = e0)
% 116.97/18.19 | |
% 116.97/18.19 | | REDUCE: (9), (21) imply:
% 116.97/18.19 | | (22) ~ (all_10_0 = e0)
% 116.97/18.19 | |
% 116.97/18.19 | | BETA: splitting (8) gives:
% 116.97/18.19 | |
% 116.97/18.19 | | Case 1:
% 116.97/18.19 | | |
% 116.97/18.19 | | |
% 116.97/18.19 | | | GROUND_INST: instantiating (3) with all_52_6, all_10_0, e2, e1,
% 116.97/18.19 | | | simplifying with (12), (15) gives:
% 116.97/18.19 | | | (23) all_52_6 = all_10_0
% 116.97/18.19 | | |
% 116.97/18.19 | | | GROUND_INST: instantiating (3) with all_52_4, e1, e2, e3, simplifying with
% 116.97/18.19 | | | (2), (7) gives:
% 116.97/18.19 | | | (24) all_52_4 = e1
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (1), (23) imply:
% 116.97/18.19 | | | (25) all_58_7 = all_10_0
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (13), (24) imply:
% 116.97/18.19 | | | (26) all_58_1 = e1
% 116.97/18.19 | | |
% 116.97/18.19 | | | BETA: splitting (14) gives:
% 116.97/18.19 | | |
% 116.97/18.19 | | | Case 1:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | (27) all_58_1 = e0
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | COMBINE_EQS: (26), (27) imply:
% 116.97/18.19 | | | | (28) e1 = e0
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | REDUCE: (18), (28) imply:
% 116.97/18.19 | | | | (29) $false
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | CLOSE: (29) is inconsistent.
% 116.97/18.19 | | | |
% 116.97/18.19 | | | Case 2:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | (30) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | BETA: splitting (30) gives:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | Case 1:
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | (31) all_58_3 = e0
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | COMBINE_EQS: (5), (31) imply:
% 116.97/18.19 | | | | | (32) all_8_2 = e0
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | REDUCE: (6), (32) imply:
% 116.97/18.19 | | | | | (33) $false
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | CLOSE: (33) is inconsistent.
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | Case 2:
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | (34) all_58_7 = e0 | all_58_13 = e0
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | BETA: splitting (34) gives:
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | | Case 1:
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | (35) all_58_7 = e0
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | COMBINE_EQS: (25), (35) imply:
% 116.97/18.19 | | | | | | (36) all_10_0 = e0
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | REDUCE: (22), (36) imply:
% 116.97/18.19 | | | | | | (37) $false
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | CLOSE: (37) is inconsistent.
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | Case 2:
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | (38) all_58_13 = e0
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | | REF_CLOSE: (10), (11), (38) are inconsistent by sub-proof #430.
% 116.97/18.19 | | | | | |
% 116.97/18.19 | | | | | End of split
% 116.97/18.19 | | | | |
% 116.97/18.19 | | | | End of split
% 116.97/18.19 | | | |
% 116.97/18.19 | | | End of split
% 116.97/18.19 | | |
% 116.97/18.19 | | Case 2:
% 116.97/18.19 | | |
% 116.97/18.19 | | | (39) ~ (all_56_12 = e2)
% 116.97/18.19 | | |
% 116.97/18.19 | | | REDUCE: (4), (39) imply:
% 116.97/18.19 | | | (40) $false
% 116.97/18.19 | | |
% 116.97/18.19 | | | CLOSE: (40) is inconsistent.
% 116.97/18.19 | | |
% 116.97/18.19 | | End of split
% 116.97/18.19 | |
% 116.97/18.19 | End of split
% 116.97/18.19 |
% 116.97/18.19 End of proof
% 116.97/18.19
% 116.97/18.19 Sub-proof #243 shows that the following formulas are inconsistent:
% 116.97/18.19 ----------------------------------------------------------------
% 116.97/18.19 (1) ~ (all_52_8 = all_10_2)
% 116.97/18.19 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.97/18.19 (3) ~ (all_52_9 = e2)
% 116.97/18.19 (4) ~ (all_4_2 = e0)
% 116.97/18.19 (5) all_54_0 = all_10_2
% 116.97/18.19 (6) ~ (all_4_2 = e1)
% 116.97/18.19 (7) ~ (all_52_4 = e3)
% 116.97/18.19 (8) ~ (all_52_12 = all_10_2)
% 116.97/18.19 (9) op(e3, all_10_2) = e1
% 116.97/18.19 (10) all_56_12 = all_10_2
% 116.97/18.19 (11) all_58_0 = all_10_2
% 116.97/18.19 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.19 (13) all_58_4 = all_52_8
% 116.97/18.19 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.19 (15) all_56_2 = all_52_12
% 116.97/18.19 (16) all_58_3 = all_8_2
% 116.97/18.19 (17) op(e3, e1) = all_52_8
% 116.97/18.19 (18) ~ (all_4_2 = e3)
% 116.97/18.19 (19) all_58_5 = all_52_9
% 116.97/18.19 (20) all_58_2 = all_52_1
% 116.97/18.19 (21) ~ (all_10_2 = e3)
% 116.97/18.19 (22) ~ (all_52_1 = all_10_2)
% 116.97/18.19 (23) all_58_10 = all_52_13
% 116.97/18.19 (24) all_58_1 = all_52_4
% 116.97/18.19 (25) ~ (all_52_8 = e3)
% 116.97/18.19 (26) ~ (all_8_2 = e2)
% 116.97/18.19 (27) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.19 (28) all_58_9 = all_52_12
% 116.97/18.19 (29) ~ (all_52_13 = all_4_2)
% 116.97/18.19 (30) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.19 (31) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.19 (32) all_54_15 = all_4_2
% 116.97/18.19
% 116.97/18.19 Begin of proof
% 116.97/18.19 |
% 116.97/18.19 | BETA: splitting (14) gives:
% 116.97/18.19 |
% 116.97/18.19 | Case 1:
% 116.97/18.19 | |
% 116.97/18.19 | | (33) all_54_15 = e3
% 116.97/18.19 | |
% 116.97/18.19 | | COMBINE_EQS: (32), (33) imply:
% 116.97/18.19 | | (34) all_4_2 = e3
% 116.97/18.19 | |
% 116.97/18.19 | | REDUCE: (18), (34) imply:
% 116.97/18.19 | | (35) $false
% 116.97/18.19 | |
% 116.97/18.19 | | CLOSE: (35) is inconsistent.
% 116.97/18.19 | |
% 116.97/18.19 | Case 2:
% 116.97/18.19 | |
% 116.97/18.19 | | (36) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 116.97/18.19 | |
% 116.97/18.19 | | BETA: splitting (36) gives:
% 116.97/18.19 | |
% 116.97/18.19 | | Case 1:
% 116.97/18.19 | | |
% 116.97/18.19 | | | (37) all_54_15 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | COMBINE_EQS: (32), (37) imply:
% 116.97/18.19 | | | (38) all_4_2 = e2
% 116.97/18.19 | | |
% 116.97/18.19 | | | REDUCE: (29), (38) imply:
% 116.97/18.19 | | | (39) ~ (all_52_13 = e2)
% 116.97/18.19 | | |
% 116.97/18.19 | | | BETA: splitting (31) gives:
% 116.97/18.19 | | |
% 116.97/18.19 | | | Case 1:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | (40) all_58_2 = e2
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | COMBINE_EQS: (20), (40) imply:
% 116.97/18.19 | | | | (41) all_52_1 = e2
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | SIMP: (41) implies:
% 116.97/18.19 | | | | (42) all_52_1 = e2
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | REDUCE: (22), (42) imply:
% 116.97/18.19 | | | | (43) ~ (all_10_2 = e2)
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | SIMP: (43) implies:
% 116.97/18.19 | | | | (44) ~ (all_10_2 = e2)
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (12), (13), (15),
% 116.97/18.19 | | | | (17), (21), (24), (25), (27), (28), (30), (44) are
% 116.97/18.19 | | | | inconsistent by sub-proof #244.
% 116.97/18.19 | | | |
% 116.97/18.19 | | | Case 2:
% 116.97/18.19 | | | |
% 116.97/18.19 | | | | (45) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 116.97/18.19 | | | |
% 116.97/18.20 | | | | REF_CLOSE: (3), (16), (19), (23), (26), (39), (45) are inconsistent by
% 116.97/18.20 | | | | sub-proof #401.
% 116.97/18.20 | | | |
% 116.97/18.20 | | | End of split
% 116.97/18.20 | | |
% 116.97/18.20 | | Case 2:
% 116.97/18.20 | | |
% 116.97/18.20 | | | (46) all_54_15 = e1 | all_54_15 = e0
% 116.97/18.20 | | |
% 116.97/18.20 | | | REF_CLOSE: (4), (6), (32), (46) are inconsistent by sub-proof #418.
% 116.97/18.20 | | |
% 116.97/18.20 | | End of split
% 116.97/18.20 | |
% 116.97/18.20 | End of split
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #244 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) ~ (all_52_8 = all_10_2)
% 116.97/18.20 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.97/18.20 (3) all_54_0 = all_10_2
% 116.97/18.20 (4) ~ (all_52_4 = e3)
% 116.97/18.20 (5) ~ (all_52_12 = all_10_2)
% 116.97/18.20 (6) op(e3, all_10_2) = e1
% 116.97/18.20 (7) all_56_12 = all_10_2
% 116.97/18.20 (8) all_58_0 = all_10_2
% 116.97/18.20 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.20 (10) ~ (all_10_2 = e2)
% 116.97/18.20 (11) all_58_4 = all_52_8
% 116.97/18.20 (12) all_56_2 = all_52_12
% 116.97/18.20 (13) op(e3, e1) = all_52_8
% 116.97/18.20 (14) ~ (all_10_2 = e3)
% 116.97/18.20 (15) all_58_1 = all_52_4
% 116.97/18.20 (16) ~ (all_52_8 = e3)
% 116.97/18.20 (17) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 116.97/18.20 (18) all_58_9 = all_52_12
% 116.97/18.20 (19) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.20
% 116.97/18.20 Begin of proof
% 116.97/18.20 |
% 116.97/18.20 | BETA: splitting (19) gives:
% 116.97/18.20 |
% 116.97/18.20 | Case 1:
% 116.97/18.20 | |
% 116.97/18.20 | | (20) all_58_0 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | COMBINE_EQS: (8), (20) imply:
% 116.97/18.20 | | (21) all_10_2 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | REDUCE: (14), (21) imply:
% 116.97/18.20 | | (22) $false
% 116.97/18.20 | |
% 116.97/18.20 | | CLOSE: (22) is inconsistent.
% 116.97/18.20 | |
% 116.97/18.20 | Case 2:
% 116.97/18.20 | |
% 116.97/18.20 | | (23) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | BETA: splitting (23) gives:
% 116.97/18.20 | |
% 116.97/18.20 | | Case 1:
% 116.97/18.20 | | |
% 116.97/18.20 | | | (24) all_58_1 = e3
% 116.97/18.20 | | |
% 116.97/18.20 | | | COMBINE_EQS: (15), (24) imply:
% 116.97/18.20 | | | (25) all_52_4 = e3
% 116.97/18.20 | | |
% 116.97/18.20 | | | REDUCE: (4), (25) imply:
% 116.97/18.20 | | | (26) $false
% 116.97/18.20 | | |
% 116.97/18.20 | | | CLOSE: (26) is inconsistent.
% 116.97/18.20 | | |
% 116.97/18.20 | | Case 2:
% 116.97/18.20 | | |
% 116.97/18.20 | | | (27) all_58_4 = e3 | all_58_9 = e3
% 116.97/18.20 | | |
% 116.97/18.20 | | | BETA: splitting (27) gives:
% 116.97/18.20 | | |
% 116.97/18.20 | | | Case 1:
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | (28) all_58_4 = e3
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | COMBINE_EQS: (11), (28) imply:
% 116.97/18.20 | | | | (29) all_52_8 = e3
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | REDUCE: (16), (29) imply:
% 116.97/18.20 | | | | (30) $false
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | CLOSE: (30) is inconsistent.
% 116.97/18.20 | | | |
% 116.97/18.20 | | | Case 2:
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | (31) all_58_9 = e3
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | COMBINE_EQS: (18), (31) imply:
% 116.97/18.20 | | | | (32) all_52_12 = e3
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | COMBINE_EQS: (12), (32) imply:
% 116.97/18.20 | | | | (33) all_56_2 = e3
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | REDUCE: (5), (32) imply:
% 116.97/18.20 | | | | (34) ~ (all_10_2 = e3)
% 116.97/18.20 | | | |
% 116.97/18.20 | | | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (13), (14), (17), (33)
% 116.97/18.20 | | | | are inconsistent by sub-proof #297.
% 116.97/18.20 | | | |
% 116.97/18.20 | | | End of split
% 116.97/18.20 | | |
% 116.97/18.20 | | End of split
% 116.97/18.20 | |
% 116.97/18.20 | End of split
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #245 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) all_58_11 = all_52_14
% 116.97/18.20 (2) all_58_15 = e2
% 116.97/18.20 (3) ~ (all_52_14 = e3)
% 116.97/18.20 (4) all_58_11 = e3 | all_58_15 = e3
% 116.97/18.20 (5) ~ (e3 = e2)
% 116.97/18.20
% 116.97/18.20 Begin of proof
% 116.97/18.20 |
% 116.97/18.20 | BETA: splitting (4) gives:
% 116.97/18.20 |
% 116.97/18.20 | Case 1:
% 116.97/18.20 | |
% 116.97/18.20 | | (6) all_58_11 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | COMBINE_EQS: (1), (6) imply:
% 116.97/18.20 | | (7) all_52_14 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | REDUCE: (3), (7) imply:
% 116.97/18.20 | | (8) $false
% 116.97/18.20 | |
% 116.97/18.20 | | CLOSE: (8) is inconsistent.
% 116.97/18.20 | |
% 116.97/18.20 | Case 2:
% 116.97/18.20 | |
% 116.97/18.20 | | (9) all_58_15 = e3
% 116.97/18.20 | |
% 116.97/18.20 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #246.
% 116.97/18.20 | |
% 116.97/18.20 | End of split
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #246 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) all_58_15 = e3
% 116.97/18.20 (2) all_58_15 = e2
% 116.97/18.20 (3) ~ (e3 = e2)
% 116.97/18.20
% 116.97/18.20 Begin of proof
% 116.97/18.20 |
% 116.97/18.20 | COMBINE_EQS: (1), (2) imply:
% 116.97/18.20 | (4) e3 = e2
% 116.97/18.20 |
% 116.97/18.20 | SIMP: (4) implies:
% 116.97/18.20 | (5) e3 = e2
% 116.97/18.20 |
% 116.97/18.20 | REDUCE: (3), (5) imply:
% 116.97/18.20 | (6) $false
% 116.97/18.20 |
% 116.97/18.20 | CLOSE: (6) is inconsistent.
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #247 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 116.97/18.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 116.97/18.20 (2) op(e2, e0) = all_8_1
% 116.97/18.20 (3) op(e2, e0) = e3
% 116.97/18.20 (4) ~ (all_8_1 = e3)
% 116.97/18.20
% 116.97/18.20 Begin of proof
% 116.97/18.20 |
% 116.97/18.20 | GROUND_INST: instantiating (1) with e3, all_8_1, e0, e2, simplifying with (2),
% 116.97/18.20 | (3) gives:
% 116.97/18.20 | (5) all_8_1 = e3
% 116.97/18.20 |
% 116.97/18.20 | REDUCE: (4), (5) imply:
% 116.97/18.20 | (6) $false
% 116.97/18.20 |
% 116.97/18.20 | CLOSE: (6) is inconsistent.
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #248 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.20 (2) all_58_9 = e3
% 116.97/18.20 (3) all_56_2 = all_52_12
% 116.97/18.20 (4) all_54_5 = all_8_2
% 116.97/18.20 (5) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 116.97/18.20 (6) ~ (all_8_2 = e1)
% 116.97/18.20 (7) all_56_13 = all_8_2
% 116.97/18.20 (8) ~ (all_8_2 = e2)
% 116.97/18.20 (9) all_58_9 = all_52_12
% 116.97/18.20
% 116.97/18.20 Begin of proof
% 116.97/18.20 |
% 116.97/18.20 | COMBINE_EQS: (2), (9) imply:
% 116.97/18.20 | (10) all_52_12 = e3
% 116.97/18.20 |
% 116.97/18.20 | COMBINE_EQS: (3), (10) imply:
% 116.97/18.20 | (11) all_56_2 = e3
% 116.97/18.20 |
% 116.97/18.20 | REF_CLOSE: (1), (4), (5), (6), (7), (8), (11) are inconsistent by sub-proof
% 116.97/18.20 | #286.
% 116.97/18.20 |
% 116.97/18.20 End of proof
% 116.97/18.20
% 116.97/18.20 Sub-proof #249 shows that the following formulas are inconsistent:
% 116.97/18.20 ----------------------------------------------------------------
% 116.97/18.20 (1) ~ (all_52_8 = all_10_2)
% 116.97/18.20 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 116.97/18.20 (3) ~ (all_52_2 = all_10_2)
% 116.97/18.20 (4) all_58_7 = all_52_6
% 116.97/18.20 (5) ~ (all_52_9 = all_8_2)
% 116.97/18.20 (6) all_28_1 = all_6_1
% 116.97/18.20 (7) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 116.97/18.20 (8) ~ (all_4_2 = e0)
% 116.97/18.20 (9) op(e3, e2) = all_52_4
% 116.97/18.20 (10) all_56_14 = all_6_2
% 116.97/18.20 (11) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 116.97/18.20 (12) all_56_3 = all_52_1
% 116.97/18.20 (13) all_54_0 = all_10_2
% 116.97/18.20 (14) ~ (all_52_2 = all_52_6)
% 116.97/18.20 (15) ~ (all_52_7 = all_4_2)
% 116.97/18.20 (16) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 116.97/18.20 (17) op(e3, all_10_2) = e1
% 116.97/18.20 (18) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 116.97/18.20 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 116.97/18.20 (20) all_56_12 = all_10_2
% 116.97/18.20 (21) all_58_0 = all_10_2
% 116.97/18.20 (22) all_54_11 = all_52_14
% 116.97/18.20 (23) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 116.97/18.20 (24) ~ (all_52_14 = all_6_2)
% 116.97/18.20 (25) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 116.97/18.20 (26) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.20 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.20 (28) all_54_8 = all_52_2
% 117.27/18.20 (29) ~ (all_52_2 = all_6_2)
% 117.27/18.20 (30) all_32_2 = all_10_2
% 117.27/18.20 (31) all_54_10 = all_6_2
% 117.27/18.20 (32) ~ (all_52_8 = all_6_2)
% 117.27/18.20 (33) all_58_4 = all_52_8
% 117.27/18.20 (34) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.27/18.20 (35) all_56_2 = all_52_12
% 117.27/18.20 (36) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.20 (37) all_58_3 = all_8_2
% 117.27/18.20 (38) ~ (all_10_0 = e2)
% 117.27/18.20 (39) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.27/18.20 (40) all_54_9 = all_52_6
% 117.27/18.20 (41) op(e3, e1) = all_52_8
% 117.27/18.20 (42) ~ (all_52_11 = all_6_2)
% 117.27/18.20 (43) all_28_2 = all_6_2
% 117.27/18.20 (44) ~ (all_52_7 = all_8_2)
% 117.27/18.20 (45) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.27/18.20 (46) ~ (all_52_4 = all_8_2)
% 117.27/18.20 (47) op(e1, e0) = all_52_14
% 117.27/18.20 (48) all_58_5 = all_52_9
% 117.27/18.20 (49) op(e1, all_6_2) = all_6_1
% 117.27/18.20 (50) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.27/18.20 (51) all_32_0 = all_10_0
% 117.27/18.20 (52) all_58_15 = all_4_2
% 117.27/18.20 (53) all_58_2 = all_52_1
% 117.27/18.20 (54) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.27/18.20 (55) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.27/18.20 (56) ~ (all_10_2 = e3)
% 117.27/18.20 (57) all_58_13 = all_52_7
% 117.27/18.20 (58) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.27/18.20 (59) all_54_5 = all_8_2
% 117.27/18.20 (60) all_56_15 = all_4_2
% 117.27/18.20 (61) all_58_10 = all_52_13
% 117.27/18.20 (62) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.20 (63) all_58_1 = all_52_4
% 117.27/18.20 (64) all_58_14 = all_52_11
% 117.27/18.20 (65) all_56_13 = all_8_2
% 117.27/18.20 (66) ~ (all_8_2 = e2)
% 117.27/18.20 (67) ~ (all_6_2 = e2)
% 117.27/18.20 (68) ~ (all_52_7 = all_52_11)
% 117.27/18.20 (69) op(e1, e2) = all_52_6
% 117.27/18.20 (70) all_56_7 = all_52_6
% 117.27/18.20 (71) ~ (all_52_9 = all_6_2)
% 117.27/18.20 (72) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.27/18.20 (73) all_58_8 = all_6_2
% 117.27/18.20 (74) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.20 (75) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.20 (76) all_56_4 = all_52_9
% 117.27/18.20 (77) all_58_9 = all_52_12
% 117.27/18.20 (78) all_56_5 = all_52_13
% 117.27/18.20 (79) op(e1, all_10_2) = all_10_0
% 117.27/18.20 (80) ~ (all_52_6 = all_6_2)
% 117.27/18.20 (81) all_56_6 = all_52_2
% 117.27/18.20 (82) all_58_12 = all_52_3
% 117.27/18.20 (83) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.27/18.20 (84) ~ (all_52_3 = all_10_2)
% 117.27/18.20 (85) op(e1, e3) = all_52_2
% 117.27/18.20 (86) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 117.27/18.20 (87) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.20 (88) all_56_8 = all_52_14
% 117.27/18.20 (89) ~ (all_52_4 = all_10_2)
% 117.27/18.20 (90) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.20 (91) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.20 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.20 (92) all_54_15 = all_4_2
% 117.27/18.20 (93) ~ (all_6_2 = e1)
% 117.27/18.20 (94) ~ (all_6_1 = e2)
% 117.27/18.20 (95) ~ (all_52_6 = all_52_7)
% 117.27/18.20
% 117.27/18.20 Begin of proof
% 117.27/18.20 |
% 117.27/18.20 | BETA: splitting (58) gives:
% 117.27/18.20 |
% 117.27/18.20 | Case 1:
% 117.27/18.20 | |
% 117.27/18.20 | | (96) ~ (all_56_12 = e2)
% 117.27/18.20 | |
% 117.27/18.20 | | REDUCE: (20), (96) imply:
% 117.27/18.20 | | (97) ~ (all_10_2 = e2)
% 117.27/18.20 | |
% 117.27/18.20 | | BETA: splitting (86) gives:
% 117.27/18.20 | |
% 117.27/18.20 | | Case 1:
% 117.27/18.20 | | |
% 117.27/18.20 | | | (98) ~ (all_56_5 = e2)
% 117.27/18.20 | | |
% 117.27/18.20 | | | REDUCE: (78), (98) imply:
% 117.27/18.20 | | | (99) ~ (all_52_13 = e2)
% 117.27/18.20 | | |
% 117.27/18.20 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (13), (16),
% 117.27/18.20 | | | (18), (19), (20), (21), (22), (24), (26), (27), (28), (29),
% 117.27/18.20 | | | (31), (32), (33), (35), (36), (37), (42), (43), (44), (45),
% 117.27/18.20 | | | (46), (47), (48), (49), (52), (53), (54), (55), (56), (57),
% 117.27/18.20 | | | (59), (61), (62), (63), (64), (65), (66), (67), (71), (74),
% 117.27/18.20 | | | (75), (76), (77), (81), (82), (84), (85), (87), (88), (90),
% 117.27/18.20 | | | (91), (93), (94), (97), (99) are inconsistent by sub-proof
% 117.27/18.20 | | | #250.
% 117.27/18.20 | | |
% 117.27/18.20 | | Case 2:
% 117.27/18.20 | | |
% 117.27/18.20 | | | (100) ~ (all_56_12 = e0)
% 117.27/18.20 | | |
% 117.27/18.20 | | | REDUCE: (20), (100) imply:
% 117.27/18.20 | | | (101) ~ (all_10_2 = e0)
% 117.27/18.20 | | |
% 117.27/18.20 | | | REF_CLOSE: (1), (13), (17), (27), (41), (56), (74), (97), (101) are
% 117.27/18.20 | | | inconsistent by sub-proof #298.
% 117.27/18.20 | | |
% 117.27/18.20 | | End of split
% 117.27/18.20 | |
% 117.27/18.20 | Case 2:
% 117.27/18.20 | |
% 117.27/18.20 | | (102) all_56_12 = e2
% 117.27/18.20 | |
% 117.27/18.20 | | COMBINE_EQS: (20), (102) imply:
% 117.27/18.20 | | (103) all_10_2 = e2
% 117.27/18.20 | |
% 117.27/18.20 | | COMBINE_EQS: (30), (103) imply:
% 117.27/18.20 | | (104) all_32_2 = e2
% 117.27/18.20 | |
% 117.27/18.20 | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (14), (15), (17), (23), (25), (26),
% 117.27/18.20 | | (27), (28), (29), (31), (33), (34), (37), (38), (39), (40), (45),
% 117.27/18.20 | | (48), (50), (51), (57), (60), (63), (64), (66), (67), (68), (69),
% 117.27/18.20 | | (70), (71), (72), (73), (76), (79), (80), (81), (83), (89), (92),
% 117.27/18.20 | | (93), (95), (102), (103), (104) are inconsistent by sub-proof
% 117.27/18.20 | | #292.
% 117.27/18.20 | |
% 117.27/18.20 | End of split
% 117.27/18.20 |
% 117.27/18.20 End of proof
% 117.27/18.20
% 117.27/18.20 Sub-proof #250 shows that the following formulas are inconsistent:
% 117.27/18.20 ----------------------------------------------------------------
% 117.27/18.20 (1) ~ (all_52_8 = all_10_2)
% 117.27/18.20 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.27/18.20 (3) ~ (all_52_2 = all_10_2)
% 117.27/18.20 (4) ~ (all_52_9 = all_8_2)
% 117.27/18.20 (5) all_28_1 = all_6_1
% 117.27/18.20 (6) ~ (all_4_2 = e0)
% 117.27/18.20 (7) all_56_14 = all_6_2
% 117.27/18.20 (8) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.20 (9) all_56_3 = all_52_1
% 117.27/18.20 (10) all_54_0 = all_10_2
% 117.27/18.20 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.20 (12) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.27/18.20 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.20 (14) all_56_12 = all_10_2
% 117.27/18.20 (15) all_58_0 = all_10_2
% 117.27/18.20 (16) all_54_11 = all_52_14
% 117.27/18.20 (17) ~ (all_52_14 = all_6_2)
% 117.27/18.20 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.20 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.20 (20) all_54_8 = all_52_2
% 117.27/18.20 (21) ~ (all_52_2 = all_6_2)
% 117.27/18.20 (22) ~ (all_10_2 = e2)
% 117.27/18.20 (23) all_54_10 = all_6_2
% 117.27/18.21 (24) ~ (all_52_8 = all_6_2)
% 117.27/18.21 (25) all_58_4 = all_52_8
% 117.27/18.21 (26) all_56_2 = all_52_12
% 117.27/18.21 (27) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.21 (28) all_58_3 = all_8_2
% 117.27/18.21 (29) ~ (all_52_11 = all_6_2)
% 117.27/18.21 (30) all_28_2 = all_6_2
% 117.27/18.21 (31) ~ (all_52_7 = all_8_2)
% 117.27/18.21 (32) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.27/18.21 (33) ~ (all_52_4 = all_8_2)
% 117.27/18.21 (34) op(e1, e0) = all_52_14
% 117.27/18.21 (35) all_58_5 = all_52_9
% 117.27/18.21 (36) op(e1, all_6_2) = all_6_1
% 117.27/18.21 (37) all_58_15 = all_4_2
% 117.27/18.21 (38) all_58_2 = all_52_1
% 117.27/18.21 (39) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.27/18.21 (40) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.27/18.21 (41) ~ (all_10_2 = e3)
% 117.27/18.21 (42) all_58_13 = all_52_7
% 117.27/18.21 (43) all_54_5 = all_8_2
% 117.27/18.21 (44) ~ (all_52_13 = e2)
% 117.27/18.21 (45) all_58_10 = all_52_13
% 117.27/18.21 (46) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.21 (47) all_58_1 = all_52_4
% 117.27/18.21 (48) all_58_14 = all_52_11
% 117.27/18.21 (49) all_56_13 = all_8_2
% 117.27/18.21 (50) ~ (all_8_2 = e2)
% 117.27/18.21 (51) ~ (all_6_2 = e2)
% 117.27/18.21 (52) ~ (all_52_9 = all_6_2)
% 117.27/18.21 (53) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.21 (54) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.21 (55) all_56_4 = all_52_9
% 117.27/18.21 (56) all_58_9 = all_52_12
% 117.27/18.21 (57) all_56_6 = all_52_2
% 117.27/18.21 (58) all_58_12 = all_52_3
% 117.27/18.21 (59) ~ (all_52_3 = all_10_2)
% 117.27/18.21 (60) op(e1, e3) = all_52_2
% 117.27/18.21 (61) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.21 (62) all_56_8 = all_52_14
% 117.27/18.21 (63) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.21 (64) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.21 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.21 (65) ~ (all_6_2 = e1)
% 117.27/18.21 (66) ~ (all_6_1 = e2)
% 117.27/18.21
% 117.27/18.21 Begin of proof
% 117.27/18.21 |
% 117.27/18.21 | BETA: splitting (40) gives:
% 117.27/18.21 |
% 117.27/18.21 | Case 1:
% 117.27/18.21 | |
% 117.27/18.21 | | (67) ~ (all_56_13 = e3)
% 117.27/18.21 | |
% 117.27/18.21 | | REDUCE: (49), (67) imply:
% 117.27/18.21 | | (68) ~ (all_8_2 = e3)
% 117.27/18.21 | |
% 117.27/18.21 | | BETA: splitting (12) gives:
% 117.27/18.21 | |
% 117.27/18.21 | | Case 1:
% 117.27/18.21 | | |
% 117.27/18.21 | | | (69) ~ (all_56_4 = e2)
% 117.27/18.21 | | |
% 117.27/18.21 | | | REDUCE: (55), (69) imply:
% 117.27/18.21 | | | (70) ~ (all_52_9 = e2)
% 117.27/18.21 | | |
% 117.27/18.21 | | | BETA: splitting (63) gives:
% 117.27/18.21 | | |
% 117.27/18.21 | | | Case 1:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (71) all_58_2 = e2
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | REF_CLOSE: (5), (7), (8), (9), (11), (15), (16), (17), (18), (19), (23),
% 117.27/18.21 | | | | (30), (34), (36), (38), (41), (46), (51), (54), (61), (62),
% 117.27/18.21 | | | | (65), (66), (71) are inconsistent by sub-proof #253.
% 117.27/18.21 | | | |
% 117.27/18.21 | | | Case 2:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (72) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | REF_CLOSE: (28), (35), (44), (45), (50), (70), (72) are inconsistent by
% 117.27/18.21 | | | | sub-proof #401.
% 117.27/18.21 | | | |
% 117.27/18.21 | | | End of split
% 117.27/18.21 | | |
% 117.27/18.21 | | Case 2:
% 117.27/18.21 | | |
% 117.27/18.21 | | | (73) all_56_4 = e2
% 117.27/18.21 | | | (74) ~ (all_56_13 = e1)
% 117.27/18.21 | | |
% 117.27/18.21 | | | COMBINE_EQS: (55), (73) imply:
% 117.27/18.21 | | | (75) all_52_9 = e2
% 117.27/18.21 | | |
% 117.27/18.21 | | | REDUCE: (49), (74) imply:
% 117.27/18.21 | | | (76) ~ (all_8_2 = e1)
% 117.27/18.21 | | |
% 117.27/18.21 | | | REDUCE: (4), (75) imply:
% 117.27/18.21 | | | (77) ~ (all_8_2 = e2)
% 117.27/18.21 | | |
% 117.27/18.21 | | | REDUCE: (52), (75) imply:
% 117.27/18.21 | | | (78) ~ (all_6_2 = e2)
% 117.27/18.21 | | |
% 117.27/18.21 | | | BETA: splitting (13) gives:
% 117.27/18.21 | | |
% 117.27/18.21 | | | Case 1:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (79) all_54_5 = e3
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | REF_CLOSE: (43), (68), (79) are inconsistent by sub-proof #339.
% 117.27/18.21 | | | |
% 117.27/18.21 | | | Case 2:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (80) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | BETA: splitting (39) gives:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | Case 1:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | (81) ~ (all_56_4 = e2)
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | REDUCE: (73), (81) imply:
% 117.27/18.21 | | | | | (82) $false
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | CLOSE: (82) is inconsistent.
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | Case 2:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | (83) ~ (all_56_12 = e1)
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | REDUCE: (14), (83) imply:
% 117.27/18.21 | | | | | (84) ~ (all_10_2 = e1)
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | BETA: splitting (80) gives:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | Case 1:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | (85) all_54_5 = e2
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | REF_CLOSE: (43), (50), (85) are inconsistent by sub-proof #338.
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | Case 2:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | (86) all_54_5 = e1 | all_54_5 = e0
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | BETA: splitting (86) gives:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | Case 1:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | (87) all_54_5 = e1
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | REF_CLOSE: (43), (76), (87) are inconsistent by sub-proof #337.
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | Case 2:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | (88) all_54_5 = e0
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | COMBINE_EQS: (43), (88) imply:
% 117.27/18.21 | | | | | | | (89) all_8_2 = e0
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | SIMP: (89) implies:
% 117.27/18.21 | | | | | | | (90) all_8_2 = e0
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | REDUCE: (31), (90) imply:
% 117.27/18.21 | | | | | | | (91) ~ (all_52_7 = e0)
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | BETA: splitting (53) gives:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | (92) all_54_0 = e3
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | REF_CLOSE: (10), (41), (92) are inconsistent by sub-proof #451.
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | (93) ~ (all_54_0 = e3)
% 117.27/18.21 | | | | | | | | (94) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | BETA: splitting (94) gives:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | (95) all_54_0 = e2
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | REF_CLOSE: (10), (22), (95) are inconsistent by sub-proof
% 117.27/18.21 | | | | | | | | | #450.
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | (96) all_54_0 = e1 | all_54_0 = e0
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | BETA: splitting (96) gives:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | (97) all_54_0 = e1
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REF_CLOSE: (10), (84), (97) are inconsistent by sub-proof
% 117.27/18.21 | | | | | | | | | | #449.
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | (98) all_54_0 = e0
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | COMBINE_EQS: (10), (98) imply:
% 117.27/18.21 | | | | | | | | | | (99) all_10_2 = e0
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | SIMP: (99) implies:
% 117.27/18.21 | | | | | | | | | | (100) all_10_2 = e0
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REDUCE: (3), (100) imply:
% 117.27/18.21 | | | | | | | | | | (101) ~ (all_52_2 = e0)
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REDUCE: (59), (100) imply:
% 117.27/18.21 | | | | | | | | | | (102) ~ (all_52_3 = e0)
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | BETA: splitting (64) gives:
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | (103) all_58_15 = e0
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | COMBINE_EQS: (37), (103) imply:
% 117.27/18.21 | | | | | | | | | | | (104) all_4_2 = e0
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | REDUCE: (6), (104) imply:
% 117.27/18.21 | | | | | | | | | | | (105) $false
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | CLOSE: (105) is inconsistent.
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | (106) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 117.27/18.21 | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 117.27/18.21 | | | | | | | | | | | e0)
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | ALPHA: (106) implies:
% 117.27/18.21 | | | | | | | | | | | (107) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | BETA: splitting (107) gives:
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | (108) all_58_12 = e0
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | COMBINE_EQS: (58), (108) imply:
% 117.27/18.21 | | | | | | | | | | | | (109) all_52_3 = e0
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | REDUCE: (102), (109) imply:
% 117.27/18.21 | | | | | | | | | | | | (110) $false
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | (111) all_58_13 = e0 | all_58_14 = e0
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | BETA: splitting (111) gives:
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | (112) all_58_13 = e0
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | COMBINE_EQS: (42), (112) imply:
% 117.27/18.21 | | | | | | | | | | | | | (113) all_52_7 = e0
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | REDUCE: (91), (113) imply:
% 117.27/18.21 | | | | | | | | | | | | | (114) $false
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | (115) all_58_14 = e0
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | COMBINE_EQS: (48), (115) imply:
% 117.27/18.21 | | | | | | | | | | | | | (116) all_52_11 = e0
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | REDUCE: (29), (116) imply:
% 117.27/18.21 | | | | | | | | | | | | | (117) ~ (all_6_2 = e0)
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | SIMP: (117) implies:
% 117.27/18.21 | | | | | | | | | | | | | (118) ~ (all_6_2 = e0)
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | BETA: splitting (18) gives:
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | (119) all_54_10 = e3
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | COMBINE_EQS: (23), (119) imply:
% 117.27/18.21 | | | | | | | | | | | | | | (120) all_6_2 = e3
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | SIMP: (120) implies:
% 117.27/18.21 | | | | | | | | | | | | | | (121) all_6_2 = e3
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | REDUCE: (21), (121) imply:
% 117.27/18.21 | | | | | | | | | | | | | | (122) ~ (all_52_2 = e3)
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | REDUCE: (36), (121) imply:
% 117.27/18.21 | | | | | | | | | | | | | | (123) op(e1, e3) = all_6_1
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | | (124) ~ (all_56_6 = e1)
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | | REDUCE: (57), (124) imply:
% 117.27/18.21 | | | | | | | | | | | | | | | (125) ~ (all_52_2 = e1)
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (32), (60), (66), (101), (122), (123),
% 117.27/18.21 | | | | | | | | | | | | | | | (125) are inconsistent by sub-proof #395.
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | | (126) all_56_6 = e1
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (11), (15), (16), (17), (18), (19),
% 117.27/18.21 | | | | | | | | | | | | | | | (23), (27), (30), (34), (36), (41), (51), (54),
% 117.27/18.21 | | | | | | | | | | | | | | | (61), (62), (65), (66), (126) are inconsistent by
% 117.27/18.21 | | | | | | | | | | | | | | | sub-proof #252.
% 117.27/18.21 | | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | (127) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | | REF_CLOSE: (23), (51), (65), (118), (127) are inconsistent by
% 117.27/18.21 | | | | | | | | | | | | | | sub-proof #435.
% 117.27/18.21 | | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | End of split
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | End of split
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | End of split
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | End of split
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | End of split
% 117.27/18.21 | | | |
% 117.27/18.21 | | | End of split
% 117.27/18.21 | | |
% 117.27/18.21 | | End of split
% 117.27/18.21 | |
% 117.27/18.21 | Case 2:
% 117.27/18.21 | |
% 117.27/18.21 | | (128) all_56_13 = e3
% 117.27/18.21 | |
% 117.27/18.21 | | COMBINE_EQS: (49), (128) imply:
% 117.27/18.21 | | (129) all_8_2 = e3
% 117.27/18.21 | |
% 117.27/18.21 | | COMBINE_EQS: (28), (129) imply:
% 117.27/18.21 | | (130) all_58_3 = e3
% 117.27/18.21 | |
% 117.27/18.21 | | REDUCE: (33), (129) imply:
% 117.27/18.21 | | (131) ~ (all_52_4 = e3)
% 117.27/18.21 | |
% 117.27/18.21 | | REDUCE: (50), (129) imply:
% 117.27/18.21 | | (132) ~ (e3 = e2)
% 117.27/18.21 | |
% 117.27/18.21 | | BETA: splitting (63) gives:
% 117.27/18.21 | |
% 117.27/18.21 | | Case 1:
% 117.27/18.21 | | |
% 117.27/18.21 | | | (133) all_58_2 = e2
% 117.27/18.21 | | |
% 117.27/18.21 | | | REF_CLOSE: (5), (7), (8), (9), (11), (15), (16), (17), (18), (19), (23),
% 117.27/18.21 | | | (30), (34), (36), (38), (41), (46), (51), (54), (61), (62),
% 117.27/18.21 | | | (65), (66), (133) are inconsistent by sub-proof #253.
% 117.27/18.21 | | |
% 117.27/18.21 | | Case 2:
% 117.27/18.21 | | |
% 117.27/18.21 | | | (134) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.21 | | |
% 117.27/18.21 | | | BETA: splitting (134) gives:
% 117.27/18.21 | | |
% 117.27/18.21 | | | Case 1:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (135) all_58_3 = e2
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | COMBINE_EQS: (130), (135) imply:
% 117.27/18.21 | | | | (136) e3 = e2
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | REDUCE: (132), (136) imply:
% 117.27/18.21 | | | | (137) $false
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | CLOSE: (137) is inconsistent.
% 117.27/18.21 | | | |
% 117.27/18.21 | | | Case 2:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | (138) all_58_5 = e2 | all_58_10 = e2
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | BETA: splitting (138) gives:
% 117.27/18.21 | | | |
% 117.27/18.21 | | | | Case 1:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | (139) all_58_5 = e2
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | COMBINE_EQS: (35), (139) imply:
% 117.27/18.21 | | | | | (140) all_52_9 = e2
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | COMBINE_EQS: (55), (140) imply:
% 117.27/18.21 | | | | | (141) all_56_4 = e2
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | REDUCE: (52), (140) imply:
% 117.27/18.21 | | | | | (142) ~ (all_6_2 = e2)
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | BETA: splitting (39) gives:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | Case 1:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | (143) ~ (all_56_4 = e2)
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | REDUCE: (141), (143) imply:
% 117.27/18.21 | | | | | | (144) $false
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | CLOSE: (144) is inconsistent.
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | Case 2:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | (145) ~ (all_56_12 = e1)
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | REDUCE: (14), (145) imply:
% 117.27/18.21 | | | | | | (146) ~ (all_10_2 = e1)
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | BETA: splitting (53) gives:
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | | Case 1:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | (147) all_54_0 = e3
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | REF_CLOSE: (10), (41), (147) are inconsistent by sub-proof #451.
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | Case 2:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | (148) ~ (all_54_0 = e3)
% 117.27/18.21 | | | | | | | (149) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | BETA: splitting (149) gives:
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | (150) all_54_0 = e2
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | REF_CLOSE: (10), (22), (150) are inconsistent by sub-proof #450.
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | (151) all_54_0 = e1 | all_54_0 = e0
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | BETA: splitting (151) gives:
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | (152) all_54_0 = e1
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | REF_CLOSE: (10), (146), (152) are inconsistent by sub-proof
% 117.27/18.21 | | | | | | | | | #449.
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | (153) all_54_0 = e0
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | COMBINE_EQS: (10), (153) imply:
% 117.27/18.21 | | | | | | | | | (154) all_10_2 = e0
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | SIMP: (154) implies:
% 117.27/18.21 | | | | | | | | | (155) all_10_2 = e0
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | COMBINE_EQS: (14), (155) imply:
% 117.27/18.21 | | | | | | | | | (156) all_56_12 = e0
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | BETA: splitting (2) gives:
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | | Case 1:
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | (157) ~ (all_56_2 = e3)
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REDUCE: (26), (157) imply:
% 117.27/18.21 | | | | | | | | | | (158) ~ (all_52_12 = e3)
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (11), (15), (16), (17), (18),
% 117.27/18.21 | | | | | | | | | | (19), (23), (24), (25), (30), (34), (36), (41),
% 117.27/18.21 | | | | | | | | | | (47), (51), (54), (56), (61), (62), (65), (66),
% 117.27/18.21 | | | | | | | | | | (131), (158) are inconsistent by sub-proof #251.
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | Case 2:
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | (159) ~ (all_56_12 = e0)
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | REDUCE: (156), (159) imply:
% 117.27/18.21 | | | | | | | | | | (160) $false
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | | CLOSE: (160) is inconsistent.
% 117.27/18.21 | | | | | | | | | |
% 117.27/18.21 | | | | | | | | | End of split
% 117.27/18.21 | | | | | | | | |
% 117.27/18.21 | | | | | | | | End of split
% 117.27/18.21 | | | | | | | |
% 117.27/18.21 | | | | | | | End of split
% 117.27/18.21 | | | | | | |
% 117.27/18.21 | | | | | | End of split
% 117.27/18.21 | | | | | |
% 117.27/18.21 | | | | | End of split
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | Case 2:
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | (161) all_58_10 = e2
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | COMBINE_EQS: (45), (161) imply:
% 117.27/18.21 | | | | | (162) all_52_13 = e2
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | REDUCE: (44), (162) imply:
% 117.27/18.21 | | | | | (163) $false
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | | CLOSE: (163) is inconsistent.
% 117.27/18.21 | | | | |
% 117.27/18.21 | | | | End of split
% 117.27/18.21 | | | |
% 117.27/18.21 | | | End of split
% 117.27/18.21 | | |
% 117.27/18.21 | | End of split
% 117.27/18.21 | |
% 117.27/18.21 | End of split
% 117.27/18.21 |
% 117.27/18.21 End of proof
% 117.27/18.21
% 117.27/18.21 Sub-proof #251 shows that the following formulas are inconsistent:
% 117.27/18.21 ----------------------------------------------------------------
% 117.27/18.21 (1) ~ (all_52_8 = all_10_2)
% 117.27/18.21 (2) all_28_1 = all_6_1
% 117.27/18.21 (3) all_56_14 = all_6_2
% 117.27/18.22 (4) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.22 (5) ~ (all_52_4 = e3)
% 117.27/18.22 (6) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.22 (7) all_58_0 = all_10_2
% 117.27/18.22 (8) all_54_11 = all_52_14
% 117.27/18.22 (9) ~ (all_52_14 = all_6_2)
% 117.27/18.22 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.22 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.22 (12) all_54_10 = all_6_2
% 117.27/18.22 (13) ~ (all_52_8 = all_6_2)
% 117.27/18.22 (14) all_58_4 = all_52_8
% 117.27/18.22 (15) all_28_2 = all_6_2
% 117.27/18.22 (16) op(e1, e0) = all_52_14
% 117.27/18.22 (17) op(e1, all_6_2) = all_6_1
% 117.27/18.22 (18) ~ (all_10_2 = e3)
% 117.27/18.22 (19) ~ (all_52_12 = e3)
% 117.27/18.22 (20) all_58_1 = all_52_4
% 117.27/18.22 (21) ~ (all_6_2 = e2)
% 117.27/18.22 (22) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.22 (23) all_58_9 = all_52_12
% 117.27/18.22 (24) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.22 (25) all_56_8 = all_52_14
% 117.27/18.22 (26) ~ (all_6_2 = e1)
% 117.27/18.22 (27) ~ (all_6_1 = e2)
% 117.27/18.22
% 117.27/18.22 Begin of proof
% 117.27/18.22 |
% 117.27/18.22 | BETA: splitting (24) gives:
% 117.27/18.22 |
% 117.27/18.22 | Case 1:
% 117.27/18.22 | |
% 117.27/18.22 | | (28) all_58_0 = e3
% 117.27/18.22 | |
% 117.27/18.22 | | COMBINE_EQS: (7), (28) imply:
% 117.27/18.22 | | (29) all_10_2 = e3
% 117.27/18.22 | |
% 117.27/18.22 | | REDUCE: (18), (29) imply:
% 117.27/18.22 | | (30) $false
% 117.27/18.22 | |
% 117.27/18.22 | | CLOSE: (30) is inconsistent.
% 117.27/18.22 | |
% 117.27/18.22 | Case 2:
% 117.27/18.22 | |
% 117.27/18.22 | | (31) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.22 | |
% 117.27/18.22 | | BETA: splitting (31) gives:
% 117.27/18.22 | |
% 117.27/18.22 | | Case 1:
% 117.27/18.22 | | |
% 117.27/18.22 | | | (32) all_58_1 = e3
% 117.27/18.22 | | |
% 117.27/18.22 | | | COMBINE_EQS: (20), (32) imply:
% 117.27/18.22 | | | (33) all_52_4 = e3
% 117.27/18.22 | | |
% 117.27/18.22 | | | REDUCE: (5), (33) imply:
% 117.27/18.22 | | | (34) $false
% 117.27/18.22 | | |
% 117.27/18.22 | | | CLOSE: (34) is inconsistent.
% 117.27/18.22 | | |
% 117.27/18.22 | | Case 2:
% 117.27/18.22 | | |
% 117.27/18.22 | | | (35) all_58_4 = e3 | all_58_9 = e3
% 117.27/18.22 | | |
% 117.27/18.22 | | | BETA: splitting (35) gives:
% 117.27/18.22 | | |
% 117.27/18.22 | | | Case 1:
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | (36) all_58_4 = e3
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | COMBINE_EQS: (14), (36) imply:
% 117.27/18.22 | | | | (37) all_52_8 = e3
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | REDUCE: (1), (37) imply:
% 117.27/18.22 | | | | (38) ~ (all_10_2 = e3)
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | REDUCE: (13), (37) imply:
% 117.27/18.22 | | | | (39) ~ (all_6_2 = e3)
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | SIMP: (39) implies:
% 117.27/18.22 | | | | (40) ~ (all_6_2 = e3)
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | BETA: splitting (10) gives:
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | Case 1:
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | | (41) all_54_10 = e3
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | | REF_CLOSE: (12), (40), (41) are inconsistent by sub-proof #352.
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | Case 2:
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | | (42) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), (15), (16),
% 117.27/18.22 | | | | | (17), (18), (21), (22), (24), (25), (26), (27), (42) are
% 117.27/18.22 | | | | | inconsistent by sub-proof #259.
% 117.27/18.22 | | | | |
% 117.27/18.22 | | | | End of split
% 117.27/18.22 | | | |
% 117.27/18.22 | | | Case 2:
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | (43) all_58_9 = e3
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | COMBINE_EQS: (23), (43) imply:
% 117.27/18.22 | | | | (44) all_52_12 = e3
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | REDUCE: (19), (44) imply:
% 117.27/18.22 | | | | (45) $false
% 117.27/18.22 | | | |
% 117.27/18.22 | | | | CLOSE: (45) is inconsistent.
% 117.27/18.22 | | | |
% 117.27/18.22 | | | End of split
% 117.27/18.22 | | |
% 117.27/18.22 | | End of split
% 117.27/18.22 | |
% 117.27/18.22 | End of split
% 117.27/18.22 |
% 117.27/18.22 End of proof
% 117.27/18.22
% 117.27/18.22 Sub-proof #252 shows that the following formulas are inconsistent:
% 117.27/18.22 ----------------------------------------------------------------
% 117.27/18.22 (1) all_28_1 = all_6_1
% 117.27/18.22 (2) all_56_14 = all_6_2
% 117.27/18.22 (3) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.22 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.22 (5) all_58_0 = all_10_2
% 117.27/18.22 (6) all_54_11 = all_52_14
% 117.27/18.22 (7) ~ (all_52_14 = all_6_2)
% 117.27/18.22 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.22 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.22 (10) all_54_10 = all_6_2
% 117.27/18.22 (11) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.22 (12) all_56_6 = e1
% 117.27/18.22 (13) all_28_2 = all_6_2
% 117.27/18.22 (14) op(e1, e0) = all_52_14
% 117.27/18.22 (15) op(e1, all_6_2) = all_6_1
% 117.27/18.22 (16) ~ (all_10_2 = e3)
% 117.27/18.22 (17) ~ (all_6_2 = e2)
% 117.27/18.22 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.22 (19) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.22 (20) all_56_8 = all_52_14
% 117.27/18.22 (21) ~ (all_6_2 = e1)
% 117.27/18.22 (22) ~ (all_6_1 = e2)
% 117.27/18.22
% 117.27/18.22 Begin of proof
% 117.27/18.22 |
% 117.27/18.22 | BETA: splitting (11) gives:
% 117.27/18.22 |
% 117.27/18.22 | Case 1:
% 117.27/18.22 | |
% 117.27/18.22 | | (23) ~ (all_56_6 = e1)
% 117.27/18.22 | |
% 117.27/18.22 | | REDUCE: (12), (23) imply:
% 117.27/18.22 | | (24) $false
% 117.27/18.22 | |
% 117.27/18.22 | | CLOSE: (24) is inconsistent.
% 117.27/18.22 | |
% 117.27/18.22 | Case 2:
% 117.27/18.22 | |
% 117.27/18.22 | | (25) ~ (all_56_14 = e3)
% 117.27/18.22 | |
% 117.27/18.22 | | REDUCE: (2), (25) imply:
% 117.27/18.22 | | (26) ~ (all_6_2 = e3)
% 117.27/18.22 | |
% 117.27/18.22 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 117.27/18.22 | | (15), (16), (17), (18), (19), (20), (21), (22), (26) are
% 117.27/18.22 | | inconsistent by sub-proof #258.
% 117.27/18.22 | |
% 117.27/18.22 | End of split
% 117.27/18.22 |
% 117.27/18.22 End of proof
% 117.27/18.22
% 117.27/18.22 Sub-proof #253 shows that the following formulas are inconsistent:
% 117.27/18.22 ----------------------------------------------------------------
% 117.27/18.22 (1) all_28_1 = all_6_1
% 117.27/18.22 (2) all_56_14 = all_6_2
% 117.27/18.22 (3) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.22 (4) all_56_3 = all_52_1
% 117.27/18.22 (5) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.22 (6) all_58_0 = all_10_2
% 117.27/18.22 (7) all_54_11 = all_52_14
% 117.27/18.22 (8) ~ (all_52_14 = all_6_2)
% 117.27/18.22 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.22 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.22 (11) all_54_10 = all_6_2
% 117.27/18.22 (12) all_28_2 = all_6_2
% 117.27/18.22 (13) op(e1, e0) = all_52_14
% 117.27/18.22 (14) op(e1, all_6_2) = all_6_1
% 117.27/18.22 (15) all_58_2 = all_52_1
% 117.27/18.22 (16) ~ (all_10_2 = e3)
% 117.27/18.22 (17) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.22 (18) ~ (all_6_2 = e2)
% 117.27/18.22 (19) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.22 (20) all_58_2 = e2
% 117.27/18.22 (21) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.22 (22) all_56_8 = all_52_14
% 117.27/18.22 (23) ~ (all_6_2 = e1)
% 117.27/18.22 (24) ~ (all_6_1 = e2)
% 117.27/18.22
% 117.27/18.22 Begin of proof
% 117.27/18.22 |
% 117.27/18.22 | COMBINE_EQS: (15), (20) imply:
% 117.27/18.22 | (25) all_52_1 = e2
% 117.27/18.22 |
% 117.27/18.22 | COMBINE_EQS: (4), (25) imply:
% 117.27/18.22 | (26) all_56_3 = e2
% 117.27/18.22 |
% 117.27/18.22 | BETA: splitting (17) gives:
% 117.27/18.22 |
% 117.27/18.22 | Case 1:
% 117.27/18.22 | |
% 117.27/18.22 | | (27) ~ (all_56_3 = e2)
% 117.27/18.22 | |
% 117.27/18.22 | | REDUCE: (26), (27) imply:
% 117.27/18.22 | | (28) $false
% 117.27/18.22 | |
% 117.27/18.22 | | CLOSE: (28) is inconsistent.
% 117.27/18.22 | |
% 117.27/18.22 | Case 2:
% 117.27/18.22 | |
% 117.27/18.22 | | (29) ~ (all_56_14 = e3)
% 117.27/18.22 | |
% 117.27/18.22 | | REDUCE: (2), (29) imply:
% 117.27/18.22 | | (30) ~ (all_6_2 = e3)
% 117.27/18.22 | |
% 117.27/18.22 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.27/18.22 | | (14), (16), (18), (19), (21), (22), (23), (24), (30) are
% 117.27/18.22 | | inconsistent by sub-proof #258.
% 117.27/18.22 | |
% 117.27/18.22 | End of split
% 117.27/18.22 |
% 117.27/18.22 End of proof
% 117.27/18.22
% 117.27/18.22 Sub-proof #254 shows that the following formulas are inconsistent:
% 117.27/18.22 ----------------------------------------------------------------
% 117.27/18.22 (1) ~ (all_52_8 = all_10_2)
% 117.27/18.22 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.27/18.22 (3) ~ (all_52_2 = all_10_2)
% 117.27/18.22 (4) ~ (all_52_6 = all_52_14)
% 117.27/18.22 (5) all_54_2 = all_52_8
% 117.27/18.22 (6) all_58_7 = all_52_6
% 117.27/18.22 (7) ~ (all_52_8 = all_52_11)
% 117.27/18.22 (8) ~ (all_52_9 = all_8_2)
% 117.27/18.22 (9) all_28_1 = all_6_1
% 117.27/18.22 (10) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.27/18.22 (11) ~ (all_52_13 = all_52_14)
% 117.27/18.22 (12) ~ (all_4_2 = e0)
% 117.27/18.22 (13) op(e3, e2) = all_52_4
% 117.27/18.22 (14) all_56_14 = all_6_2
% 117.27/18.22 (15) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.22 (16) all_56_3 = all_52_1
% 117.27/18.22 (17) all_38_1 = all_10_1
% 117.27/18.22 (18) all_54_0 = all_10_2
% 117.27/18.22 (19) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.27/18.22 (20) all_54_3 = all_52_12
% 117.27/18.22 (21) ~ (all_52_2 = all_52_6)
% 117.27/18.22 (22) op(e0, e2) = all_52_7
% 117.27/18.22 (23) ~ (all_52_7 = all_4_2)
% 117.27/18.22 (24) all_56_11 = all_52_11
% 117.27/18.22 (25) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 117.27/18.22 (26) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.22 (27) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.27/18.22 (28) ~ (all_52_12 = all_10_2)
% 117.27/18.22 (29) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.27/18.22 (30) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.22 (31) all_56_12 = all_10_2
% 117.27/18.22 (32) all_58_0 = all_10_2
% 117.27/18.22 (33) all_54_11 = all_52_14
% 117.27/18.22 (34) all_54_13 = all_52_7
% 117.27/18.22 (35) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.22 (36) ~ (all_52_14 = all_6_2)
% 117.27/18.22 (37) ~ (all_56_8 = e1) | ~ (all_56_13 = e0)
% 117.27/18.22 (38) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.27/18.22 (39) all_56_10 = all_52_7
% 117.27/18.22 (40) op(all_6_1, all_6_2) = e2
% 117.27/18.22 (41) all_54_14 = all_52_11
% 117.27/18.22 (42) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.22 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.22 (44) all_54_8 = all_52_2
% 117.27/18.22 (45) ~ (all_52_2 = all_6_2)
% 117.27/18.22 (46) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.27/18.22 (47) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 117.27/18.22 (48) all_54_10 = all_6_2
% 117.27/18.22 (49) op(e3, e0) = all_52_12
% 117.27/18.22 (50) ~ (all_32_1 = e1)
% 117.27/18.22 (51) all_38_0 = all_10_0
% 117.27/18.22 (52) ~ (all_52_8 = all_6_2)
% 117.27/18.22 (53) all_58_4 = all_52_8
% 117.27/18.22 (54) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.27/18.22 (55) ~ (all_52_4 = all_52_7)
% 117.27/18.22 (56) all_56_2 = all_52_12
% 117.27/18.22 (57) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.22 (58) all_58_3 = all_8_2
% 117.27/18.22 (59) all_54_6 = all_52_9
% 117.27/18.22 (60) ~ (all_10_0 = e2)
% 117.27/18.22 (61) all_58_11 = all_52_14
% 117.27/18.22 (62) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 117.27/18.22 (63) op(e3, e1) = all_52_8
% 117.27/18.22 (64) ~ (all_52_2 = all_52_3)
% 117.27/18.22 (65) op(all_10_1, all_10_2) = all_10_0
% 117.27/18.22 (66) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.27/18.22 (67) ~ (all_52_11 = all_6_2)
% 117.27/18.22 (68) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.27/18.22 (69) all_28_2 = all_6_2
% 117.27/18.22 (70) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.27/18.22 (71) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.27/18.22 (72) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.22 (73) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.27/18.22 (74) ~ (all_52_4 = all_8_2)
% 117.27/18.22 (75) op(e1, e0) = all_52_14
% 117.27/18.22 (76) all_58_5 = all_52_9
% 117.27/18.22 (77) ~ (all_52_9 = all_52_13)
% 117.27/18.22 (78) all_56_9 = all_52_3
% 117.27/18.22 (79) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 117.27/18.22 (80) op(e1, all_6_2) = all_6_1
% 117.27/18.22 (81) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.27/18.22 (82) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.27/18.22 (83) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.27/18.22 (84) all_58_15 = all_4_2
% 117.27/18.22 (85) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 117.27/18.22 (86) all_58_2 = all_52_1
% 117.27/18.22 (87) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.27/18.22 (88) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.27/18.22 (89) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.27/18.22 (90) ~ (all_10_2 = e3)
% 117.27/18.22 (91) all_58_13 = all_52_7
% 117.27/18.22 (92) all_32_1 = all_10_1
% 117.27/18.22 (93) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 117.27/18.22 (94) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.27/18.22 (95) ~ (all_52_14 = all_4_2)
% 117.27/18.22 (96) all_58_6 = all_52_2
% 117.27/18.22 (97) ~ (all_52_1 = all_10_2)
% 117.27/18.22 (98) all_54_5 = all_8_2
% 117.27/18.22 (99) all_56_15 = all_4_2
% 117.27/18.22 (100) all_58_10 = all_52_13
% 117.27/18.22 (101) ~ (all_52_13 = all_8_2)
% 117.27/18.22 (102) ~ (all_52_11 = all_4_2)
% 117.27/18.22 (103) op(e3, all_10_2) = all_10_1
% 117.27/18.22 (104) ~ (all_52_6 = all_8_2)
% 117.27/18.22 (105) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.22 (106) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.27/18.22 (107) all_38_2 = all_10_2
% 117.27/18.22 (108) all_58_1 = all_52_4
% 117.27/18.22 (109) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.27/18.22 (110) ~ (all_52_9 = all_52_11)
% 117.27/18.22 (111) all_58_14 = all_52_11
% 117.27/18.22 (112) all_54_1 = all_52_4
% 117.27/18.22 (113) all_56_13 = all_8_2
% 117.27/18.22 (114) op(e0, e1) = all_52_11
% 117.27/18.22 (115) ~ (all_52_1 = all_8_2)
% 117.27/18.22 (116) ~ (all_8_2 = e2)
% 117.27/18.22 (117) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.22 (118) op(e1, e2) = all_52_6
% 117.27/18.22 (119) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.22 (120) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.27/18.22 (121) all_56_7 = all_52_6
% 117.27/18.22 (122) ~ (all_52_9 = all_6_2)
% 117.27/18.22 (123) ~ (all_52_4 = all_52_6)
% 117.27/18.22 (124) ~ (all_52_1 = all_52_2)
% 117.27/18.22 (125) all_56_1 = all_52_8
% 117.27/18.22 (126) op(e0, all_4_2) = all_4_1
% 117.27/18.22 (127) all_58_8 = all_6_2
% 117.27/18.22 (128) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.22 (129) ~ (all_10_0 = e1)
% 117.27/18.23 (130) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.23 (131) all_56_4 = all_52_9
% 117.27/18.23 (132) all_58_9 = all_52_12
% 117.27/18.23 (133) all_56_5 = all_52_13
% 117.27/18.23 (134) op(e2, e1) = all_52_9
% 117.27/18.23 (135) ~ (all_52_6 = all_6_2)
% 117.27/18.23 (136) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.27/18.23 (137) all_56_6 = all_52_2
% 117.27/18.23 (138) ~ (all_52_13 = all_4_2)
% 117.27/18.23 (139) ~ (e2 = e0)
% 117.27/18.23 (140) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.27/18.23 (141) all_58_12 = all_52_3
% 117.27/18.23 (142) ~ (all_52_2 = all_52_14)
% 117.27/18.23 (143) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.27/18.23 (144) ~ (all_52_8 = all_52_9)
% 117.27/18.23 (145) op(e2, e0) = all_52_13
% 117.27/18.23 (146) ~ (all_52_12 = all_4_2)
% 117.27/18.23 (147) ~ (all_52_3 = all_10_2)
% 117.27/18.23 (148) op(e1, e3) = all_52_2
% 117.27/18.23 (149) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.27/18.23 (150) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.23 (151) ~ (all_52_8 = all_52_12)
% 117.27/18.23 (152) all_56_8 = all_52_14
% 117.27/18.23 (153) ~ (all_52_4 = all_10_2)
% 117.27/18.23 (154) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.27/18.23 (155) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.23 (156) all_56_0 = all_52_4
% 117.27/18.23 (157) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.27/18.23 (158) ~ (e3 = e2)
% 117.27/18.23 (159) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.23 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.23 (160) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.27/18.23 (161) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.27/18.23 (162) all_54_15 = all_4_2
% 117.27/18.23 (163) ~ (all_6_2 = e1)
% 117.27/18.23 (164) ~ (all_6_1 = e2)
% 117.27/18.23 (165) ~ (all_52_6 = all_52_7)
% 117.27/18.23 (166) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.27/18.23 (167) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.27/18.23
% 117.27/18.23 Begin of proof
% 117.27/18.23 |
% 117.27/18.23 | REDUCE: (50), (92) imply:
% 117.27/18.23 | (168) ~ (all_10_1 = e1)
% 117.27/18.23 |
% 117.27/18.23 | BETA: splitting (47) gives:
% 117.27/18.23 |
% 117.27/18.23 | Case 1:
% 117.27/18.23 | |
% 117.27/18.23 | | (169) ~ (all_38_1 = e2)
% 117.27/18.23 | |
% 117.27/18.23 | | REDUCE: (17), (169) imply:
% 117.27/18.23 | | (170) ~ (all_10_1 = e2)
% 117.27/18.23 | |
% 117.27/18.23 | | BETA: splitting (93) gives:
% 117.27/18.23 | |
% 117.27/18.23 | | Case 1:
% 117.27/18.23 | | |
% 117.27/18.23 | | | (171) ~ (all_56_14 = e2)
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (14), (171) imply:
% 117.27/18.23 | | | (172) ~ (all_6_2 = e2)
% 117.27/18.23 | | |
% 117.27/18.23 | | | BETA: splitting (94) gives:
% 117.27/18.23 | | |
% 117.27/18.23 | | | Case 1:
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | (173) ~ (all_56_12 = e2)
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | REDUCE: (31), (173) imply:
% 117.27/18.23 | | | | (174) ~ (all_10_2 = e2)
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | BETA: splitting (79) gives:
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | Case 1:
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | (175) ~ (all_56_15 = e1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (99), (175) imply:
% 117.27/18.23 | | | | | (176) ~ (all_4_2 = e1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (12), (13), (14), (16), (18),
% 117.27/18.23 | | | | | (20), (22), (24), (25), (27), (28), (29), (30), (31), (35),
% 117.27/18.23 | | | | | (41), (42), (43), (48), (49), (53), (54), (55), (56), (58),
% 117.27/18.23 | | | | | (60), (63), (65), (66), (68), (70), (71), (72), (76), (78),
% 117.27/18.23 | | | | | (82), (84), (86), (87), (90), (91), (97), (98), (100),
% 117.27/18.23 | | | | | (102), (103), (108), (109), (110), (111), (112), (113),
% 117.27/18.23 | | | | | (114), (115), (116), (120), (121), (125), (127), (128),
% 117.27/18.23 | | | | | (129), (131), (133), (135), (136), (138), (141), (146),
% 117.27/18.23 | | | | | (151), (153), (154), (155), (156), (157), (159), (161),
% 117.27/18.23 | | | | | (162), (163), (166), (168), (170), (174), (176) are
% 117.27/18.23 | | | | | inconsistent by sub-proof #280.
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | Case 2:
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | (177) all_56_15 = e1
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REF_CLOSE: (4), (6), (9), (11), (14), (15), (16), (32), (33), (36),
% 117.27/18.23 | | | | | (42), (43), (45), (48), (57), (58), (61), (69), (72), (75),
% 117.27/18.23 | | | | | (76), (77), (80), (86), (90), (95), (96), (99), (100),
% 117.27/18.23 | | | | | (105), (116), (119), (127), (130), (131), (133), (135),
% 117.27/18.23 | | | | | (137), (138), (142), (143), (148), (150), (155), (163),
% 117.27/18.23 | | | | | (164), (167), (172), (177) are inconsistent by sub-proof
% 117.27/18.23 | | | | | #269.
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | End of split
% 117.27/18.23 | | | |
% 117.27/18.23 | | | Case 2:
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | (178) all_56_12 = e2
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | COMBINE_EQS: (31), (178) imply:
% 117.27/18.23 | | | | (179) all_10_2 = e2
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | REF_CLOSE: (6), (12), (13), (14), (22), (24), (29), (35), (42), (43),
% 117.27/18.23 | | | | (48), (55), (58), (60), (65), (66), (68), (72), (76), (78),
% 117.27/18.23 | | | | (82), (84), (86), (91), (97), (100), (103), (108), (111),
% 117.27/18.23 | | | | (112), (113), (116), (120), (121), (129), (131), (133),
% 117.27/18.23 | | | | (135), (141), (153), (155), (156), (157), (159), (161),
% 117.27/18.23 | | | | (163), (168), (178), (179) are inconsistent by sub-proof
% 117.27/18.23 | | | | #425.
% 117.27/18.23 | | | |
% 117.27/18.23 | | | End of split
% 117.27/18.23 | | |
% 117.27/18.23 | | Case 2:
% 117.27/18.23 | | |
% 117.27/18.23 | | | (180) all_56_14 = e2
% 117.27/18.23 | | | (181) ~ (all_56_10 = e0)
% 117.27/18.23 | | |
% 117.27/18.23 | | | COMBINE_EQS: (14), (180) imply:
% 117.27/18.23 | | | (182) all_6_2 = e2
% 117.27/18.23 | | |
% 117.27/18.23 | | | SIMP: (182) implies:
% 117.27/18.23 | | | (183) all_6_2 = e2
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (39), (181) imply:
% 117.27/18.23 | | | (184) ~ (all_52_7 = e0)
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (135), (183) imply:
% 117.27/18.23 | | | (185) ~ (all_52_6 = e2)
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (122), (183) imply:
% 117.27/18.23 | | | (186) ~ (all_52_9 = e2)
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (67), (183) imply:
% 117.27/18.23 | | | (187) ~ (all_52_11 = e2)
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (40), (183) imply:
% 117.27/18.23 | | | (188) op(all_6_1, e2) = e2
% 117.27/18.23 | | |
% 117.27/18.23 | | | REDUCE: (80), (183) imply:
% 117.27/18.23 | | | (189) op(e1, e2) = all_6_1
% 117.27/18.23 | | |
% 117.27/18.23 | | | BETA: splitting (160) gives:
% 117.27/18.23 | | |
% 117.27/18.23 | | | Case 1:
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | (190) ~ (all_56_0 = e3)
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | REDUCE: (156), (190) imply:
% 117.27/18.23 | | | | (191) ~ (all_52_4 = e3)
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | BETA: splitting (38) gives:
% 117.27/18.23 | | | |
% 117.27/18.23 | | | | Case 1:
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | (192) ~ (all_56_7 = e1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (121), (192) imply:
% 117.27/18.23 | | | | | (193) ~ (all_52_6 = e1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | GROUND_INST: instantiating (43) with all_52_6, all_6_1, e2, e1,
% 117.27/18.23 | | | | | simplifying with (118), (189) gives:
% 117.27/18.23 | | | | | (194) all_52_6 = all_6_1
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | COMBINE_EQS: (6), (194) imply:
% 117.27/18.23 | | | | | (195) all_58_7 = all_6_1
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (21), (194) imply:
% 117.27/18.23 | | | | | (196) ~ (all_52_2 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (123), (194) imply:
% 117.27/18.23 | | | | | (197) ~ (all_52_4 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (165), (194) imply:
% 117.27/18.23 | | | | | (198) ~ (all_52_7 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | SIMP: (198) implies:
% 117.27/18.23 | | | | | (199) ~ (all_52_7 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | REDUCE: (104), (194) imply:
% 117.27/18.23 | | | | | (200) ~ (all_8_2 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | SIMP: (200) implies:
% 117.27/18.23 | | | | | (201) ~ (all_8_2 = all_6_1)
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | BETA: splitting (89) gives:
% 117.27/18.23 | | | | |
% 117.27/18.23 | | | | | Case 1:
% 117.27/18.23 | | | | | |
% 117.27/18.23 | | | | | | (202) ~ (all_56_13 = e3)
% 117.27/18.23 | | | | | |
% 117.27/18.23 | | | | | | REDUCE: (113), (202) imply:
% 117.27/18.23 | | | | | | (203) ~ (all_8_2 = e3)
% 117.27/18.23 | | | | | |
% 117.27/18.23 | | | | | | BETA: splitting (62) gives:
% 117.27/18.23 | | | | | |
% 117.27/18.23 | | | | | | Case 1:
% 117.27/18.23 | | | | | | |
% 117.27/18.23 | | | | | | | (204) ~ (all_56_5 = e2)
% 117.27/18.23 | | | | | | |
% 117.27/18.23 | | | | | | | REDUCE: (133), (204) imply:
% 117.27/18.23 | | | | | | | (205) ~ (all_52_13 = e2)
% 117.27/18.23 | | | | | | |
% 117.27/18.23 | | | | | | | BETA: splitting (155) gives:
% 117.27/18.23 | | | | | | |
% 117.27/18.23 | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | (206) all_58_2 = e2
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | COMBINE_EQS: (86), (206) imply:
% 117.27/18.23 | | | | | | | | (207) all_52_1 = e2
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | COMBINE_EQS: (16), (207) imply:
% 117.27/18.23 | | | | | | | | (208) all_56_3 = e2
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | REDUCE: (124), (207) imply:
% 117.27/18.23 | | | | | | | | (209) ~ (all_52_2 = e2)
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | SIMP: (209) implies:
% 117.27/18.23 | | | | | | | | (210) ~ (all_52_2 = e2)
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | REDUCE: (97), (207) imply:
% 117.27/18.23 | | | | | | | | (211) ~ (all_10_2 = e2)
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | SIMP: (211) implies:
% 117.27/18.23 | | | | | | | | (212) ~ (all_10_2 = e2)
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | REDUCE: (115), (207) imply:
% 117.27/18.23 | | | | | | | | (213) ~ (all_8_2 = e2)
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | BETA: splitting (46) gives:
% 117.27/18.23 | | | | | | | |
% 117.27/18.23 | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | (214) ~ (all_56_3 = e2)
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | REDUCE: (208), (214) imply:
% 117.27/18.23 | | | | | | | | | (215) $false
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | CLOSE: (215) is inconsistent.
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | (216) ~ (all_56_15 = e3)
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | REDUCE: (99), (216) imply:
% 117.27/18.23 | | | | | | | | | (217) ~ (all_4_2 = e3)
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | BETA: splitting (79) gives:
% 117.27/18.23 | | | | | | | | |
% 117.27/18.23 | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | (218) ~ (all_56_15 = e1)
% 117.27/18.23 | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | REDUCE: (99), (218) imply:
% 117.27/18.23 | | | | | | | | | | (219) ~ (all_4_2 = e1)
% 117.27/18.23 | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | BETA: splitting (54) gives:
% 117.27/18.23 | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | (220) all_54_15 = e3
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | REF_CLOSE: (162), (217), (220) are inconsistent by sub-proof
% 117.27/18.23 | | | | | | | | | | | #312.
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | (221) ~ (all_54_15 = e3)
% 117.27/18.23 | | | | | | | | | | | (222) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | BETA: splitting (222) gives:
% 117.27/18.23 | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | (223) all_54_15 = e2
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | COMBINE_EQS: (162), (223) imply:
% 117.27/18.23 | | | | | | | | | | | | (224) all_4_2 = e2
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | SIMP: (224) implies:
% 117.27/18.23 | | | | | | | | | | | | (225) all_4_2 = e2
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | REDUCE: (23), (225) imply:
% 117.27/18.23 | | | | | | | | | | | | (226) ~ (all_52_7 = e2)
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | REDUCE: (126), (225) imply:
% 117.27/18.23 | | | | | | | | | | | | (227) op(e0, e2) = all_4_1
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | BETA: splitting (35) gives:
% 117.27/18.23 | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | (228) all_58_1 = e2
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | COMBINE_EQS: (108), (228) imply:
% 117.27/18.23 | | | | | | | | | | | | | (229) all_52_4 = e2
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | REDUCE: (197), (229) imply:
% 117.27/18.23 | | | | | | | | | | | | | (230) ~ (all_6_1 = e2)
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | REDUCE: (191), (229) imply:
% 117.27/18.23 | | | | | | | | | | | | | (231) ~ (e3 = e2)
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_52_7, all_4_1, e2, e0,
% 117.27/18.23 | | | | | | | | | | | | | simplifying with (22), (227) gives:
% 117.27/18.23 | | | | | | | | | | | | | (232) all_52_7 = all_4_1
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | COMBINE_EQS: (34), (232) imply:
% 117.27/18.23 | | | | | | | | | | | | | (233) all_54_13 = all_4_1
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | COMBINE_EQS: (91), (232) imply:
% 117.27/18.23 | | | | | | | | | | | | | (234) all_58_13 = all_4_1
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | REDUCE: (199), (232) imply:
% 117.27/18.23 | | | | | | | | | | | | | (235) ~ (all_6_1 = all_4_1)
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | SIMP: (235) implies:
% 117.27/18.23 | | | | | | | | | | | | | (236) ~ (all_6_1 = all_4_1)
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | BETA: splitting (81) gives:
% 117.27/18.23 | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | (237) ~ (all_56_8 = e1)
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | REDUCE: (152), (237) imply:
% 117.27/18.23 | | | | | | | | | | | | | | (238) ~ (all_52_14 = e1)
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (12), (13), (14), (18), (20), (22),
% 117.27/18.23 | | | | | | | | | | | | | | (24), (27), (28), (29), (31), (35), (42), (43),
% 117.27/18.23 | | | | | | | | | | | | | | (45), (48), (49), (55), (56), (58), (60), (61),
% 117.27/18.23 | | | | | | | | | | | | | | (65), (66), (68), (72), (76), (78), (82), (84),
% 117.27/18.23 | | | | | | | | | | | | | | (86), (90), (91), (96), (97), (100), (103), (108),
% 117.27/18.23 | | | | | | | | | | | | | | (111), (112), (113), (116), (119), (120), (121),
% 117.27/18.23 | | | | | | | | | | | | | | (127), (128), (129), (131), (133), (135), (141),
% 117.27/18.23 | | | | | | | | | | | | | | (153), (155), (156), (157), (159), (161), (163),
% 117.27/18.23 | | | | | | | | | | | | | | (168), (170), (193), (212), (238) are inconsistent
% 117.27/18.23 | | | | | | | | | | | | | | by sub-proof #353.
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | (239) all_56_8 = e1
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | COMBINE_EQS: (152), (239) imply:
% 117.27/18.23 | | | | | | | | | | | | | | (240) all_52_14 = e1
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | SIMP: (240) implies:
% 117.27/18.23 | | | | | | | | | | | | | | (241) all_52_14 = e1
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | REDUCE: (142), (241) imply:
% 117.27/18.23 | | | | | | | | | | | | | | (242) ~ (all_52_2 = e1)
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 117.27/18.23 | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | (243) ~ (all_56_8 = e1)
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | REDUCE: (239), (243) imply:
% 117.27/18.23 | | | | | | | | | | | | | | | (244) $false
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | (245) ~ (all_56_13 = e0)
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | REDUCE: (113), (245) imply:
% 117.27/18.23 | | | | | | | | | | | | | | | (246) ~ (all_8_2 = e0)
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 117.27/18.23 | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | (247) all_54_5 = e3
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | REF_CLOSE: (98), (203), (247) are inconsistent by sub-proof
% 117.27/18.23 | | | | | | | | | | | | | | | | #339.
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | (248) ~ (all_54_5 = e3)
% 117.27/18.23 | | | | | | | | | | | | | | | | (249) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 117.27/18.23 | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.23 | | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | | (250) all_54_5 = e2
% 117.27/18.23 | | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (116), (250) are inconsistent by sub-proof
% 117.27/18.23 | | | | | | | | | | | | | | | | | #338.
% 117.27/18.23 | | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.23 | | | | | | | | | | | | | | | | |
% 117.27/18.23 | | | | | | | | | | | | | | | | | (251) ~ (all_54_5 = e2)
% 117.27/18.24 | | | | | | | | | | | | | | | | | (252) all_54_5 = e1 | all_54_5 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (253) all_54_5 = e1
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (253) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (254) all_8_2 = e1
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (255) all_8_2 = e1
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (255) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (256) all_58_3 = e1
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | REDUCE: (203), (255) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (257) ~ (e3 = e1)
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | SIMP: (257) implies:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (258) ~ (e3 = e1)
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (259) all_54_13 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (259) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (260) all_4_1 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | REDUCE: (236), (260) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (261) ~ (all_6_1 = e3)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (12), (13),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (14), (16), (18), (20), (22), (24), (25), (26),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (35),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (36), (41), (42), (43), (48), (49), (52), (53),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (54), (55), (56), (58), (59), (60), (61), (63),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (65), (66), (68), (70), (71), (72), (75), (76),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (78), (80), (81), (82), (84), (86), (87), (90),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (91), (96), (97), (98), (99), (100), (102), (103),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (106), (108), (109), (110), (111), (112), (113),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (114), (115), (116), (119), (120), (121), (122),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (125), (127), (128), (129), (130), (131), (132),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (133), (135), (136), (137), (138), (140), (141),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (144), (146), (149), (150), (151), (152), (153),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (154), (155), (156), (157), (159), (161), (162),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (163), (164), (166), (168), (170), (219), (261)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #267.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (262) ~ (all_54_13 = e3)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | REDUCE: (233), (262) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | (263) ~ (all_4_1 = e3)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | (264) all_58_1 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (228), (264) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | #390.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | (265) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | (266) all_58_3 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (258), (266) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | #266.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | (267) all_58_7 = e3 | all_58_13 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (268) all_58_7 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (268) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (269) all_6_1 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (269) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (270) ~ (all_52_2 = e3)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | (271) all_54_8 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (270), (271) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | #399.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | (272) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | (273) all_54_8 = e2
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (210), (273) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | #382.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | (274) all_54_8 = e1 | all_54_8 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_54_8 = e1
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (242), (275) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | #397.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_54_8 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (276) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_52_2 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_52_2 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (278) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_52_3 = e0)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_52_3 = e0)
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (18), (24), (31), (39), (54), (81), (84),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (90), (91), (99), (111), (128), (141), (149),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (154), (159), (162), (212), (217), (219), (239),
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | | (280) are inconsistent by sub-proof #360.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (281) all_58_13 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (234), (281) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (282) all_4_1 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | SIMP: (282) implies:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (283) all_4_1 = e3
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (283) imply:
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | (284) $false
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | (285) all_54_5 = e0
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (98), (246), (285) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | | | | | | | | | | #311.
% 117.27/18.24 | | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | (286) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.24 | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | | REF_CLOSE: (58), (91), (116), (164), (195), (226), (286) are
% 117.27/18.24 | | | | | | | | | | | | | inconsistent by sub-proof #264.
% 117.27/18.24 | | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | (287) all_54_15 = e1 | all_54_15 = e0
% 117.27/18.24 | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | | REF_CLOSE: (12), (162), (219), (287) are inconsistent by
% 117.27/18.24 | | | | | | | | | | | | sub-proof #418.
% 117.27/18.24 | | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | (288) all_56_15 = e1
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | COMBINE_EQS: (99), (288) imply:
% 117.27/18.24 | | | | | | | | | | (289) all_4_2 = e1
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | SIMP: (289) implies:
% 117.27/18.24 | | | | | | | | | | (290) all_4_2 = e1
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | REDUCE: (95), (290) imply:
% 117.27/18.24 | | | | | | | | | | (291) ~ (all_52_14 = e1)
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | REF_CLOSE: (2), (3), (6), (12), (13), (14), (18), (20), (22),
% 117.27/18.24 | | | | | | | | | | (24), (27), (28), (29), (31), (35), (42), (43),
% 117.27/18.24 | | | | | | | | | | (45), (48), (49), (55), (56), (58), (60), (61),
% 117.27/18.24 | | | | | | | | | | (65), (66), (68), (72), (76), (78), (82), (84),
% 117.27/18.24 | | | | | | | | | | (86), (90), (91), (96), (97), (100), (103), (108),
% 117.27/18.24 | | | | | | | | | | (111), (112), (113), (116), (119), (120), (121),
% 117.27/18.24 | | | | | | | | | | (127), (128), (129), (131), (133), (135), (141),
% 117.27/18.24 | | | | | | | | | | (153), (155), (156), (157), (159), (161), (163),
% 117.27/18.24 | | | | | | | | | | (168), (170), (193), (212), (291) are inconsistent
% 117.27/18.24 | | | | | | | | | | by sub-proof #353.
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | End of split
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | (292) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | REF_CLOSE: (58), (76), (100), (116), (186), (205), (292) are
% 117.27/18.24 | | | | | | | | inconsistent by sub-proof #401.
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | End of split
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | Case 2:
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | (293) all_56_5 = e2
% 117.27/18.24 | | | | | | | (294) ~ (all_56_13 = e0)
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | REF_CLOSE: (12), (13), (24), (30), (35), (43), (55), (58), (68),
% 117.27/18.24 | | | | | | | (84), (85), (91), (98), (101), (108), (111), (113),
% 117.27/18.24 | | | | | | | (117), (133), (138), (139), (158), (159), (184), (187),
% 117.27/18.24 | | | | | | | (188), (191), (195), (199), (203), (293), (294) are
% 117.27/18.24 | | | | | | | inconsistent by sub-proof #260.
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | End of split
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | Case 2:
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | (295) all_56_13 = e3
% 117.27/18.24 | | | | | | (296) ~ (all_56_9 = e0)
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | COMBINE_EQS: (113), (295) imply:
% 117.27/18.24 | | | | | | (297) all_8_2 = e3
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | SIMP: (297) implies:
% 117.27/18.24 | | | | | | (298) all_8_2 = e3
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | REDUCE: (78), (296) imply:
% 117.27/18.24 | | | | | | (299) ~ (all_52_3 = e0)
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | REDUCE: (201), (298) imply:
% 117.27/18.24 | | | | | | (300) ~ (all_6_1 = e3)
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | SIMP: (300) implies:
% 117.27/18.24 | | | | | | (301) ~ (all_6_1 = e3)
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | BETA: splitting (159) gives:
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | | Case 1:
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | (302) all_58_15 = e0
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | COMBINE_EQS: (84), (302) imply:
% 117.27/18.24 | | | | | | | (303) all_4_2 = e0
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | REDUCE: (12), (303) imply:
% 117.27/18.24 | | | | | | | (304) $false
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | CLOSE: (304) is inconsistent.
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | Case 2:
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | (305) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.24 | | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | ALPHA: (305) implies:
% 117.27/18.24 | | | | | | | (306) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | BETA: splitting (306) gives:
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | (307) all_58_12 = e0
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | COMBINE_EQS: (141), (307) imply:
% 117.27/18.24 | | | | | | | | (308) all_52_3 = e0
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | REDUCE: (299), (308) imply:
% 117.27/18.24 | | | | | | | | (309) $false
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | CLOSE: (309) is inconsistent.
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | (310) all_58_13 = e0 | all_58_14 = e0
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | BETA: splitting (310) gives:
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | (311) all_58_13 = e0
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | REF_CLOSE: (91), (184), (311) are inconsistent by sub-proof
% 117.27/18.24 | | | | | | | | | #430.
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | (312) all_58_14 = e0
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | COMBINE_EQS: (111), (312) imply:
% 117.27/18.24 | | | | | | | | | (313) all_52_11 = e0
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | SIMP: (313) implies:
% 117.27/18.24 | | | | | | | | | (314) all_52_11 = e0
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | COMBINE_EQS: (24), (314) imply:
% 117.27/18.24 | | | | | | | | | (315) all_56_11 = e0
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | REDUCE: (102), (314) imply:
% 117.27/18.24 | | | | | | | | | (316) ~ (all_4_2 = e0)
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | BETA: splitting (79) gives:
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | | Case 1:
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | (317) ~ (all_56_15 = e1)
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | REDUCE: (99), (317) imply:
% 117.27/18.24 | | | | | | | | | | (318) ~ (all_4_2 = e1)
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (12), (13),
% 117.27/18.24 | | | | | | | | | | (14), (16), (18), (20), (22), (24), (25), (26),
% 117.27/18.24 | | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (35),
% 117.27/18.24 | | | | | | | | | | (36), (41), (42), (43), (48), (49), (52), (53),
% 117.27/18.24 | | | | | | | | | | (54), (55), (56), (58), (59), (60), (61), (63),
% 117.27/18.24 | | | | | | | | | | (65), (66), (68), (70), (71), (72), (75), (76),
% 117.27/18.24 | | | | | | | | | | (78), (80), (81), (82), (84), (86), (87), (90),
% 117.27/18.24 | | | | | | | | | | (91), (96), (97), (98), (99), (100), (102), (103),
% 117.27/18.24 | | | | | | | | | | (106), (108), (109), (110), (111), (112), (113),
% 117.27/18.24 | | | | | | | | | | (114), (115), (116), (119), (120), (121), (122),
% 117.27/18.24 | | | | | | | | | | (125), (127), (128), (129), (130), (131), (132),
% 117.27/18.24 | | | | | | | | | | (133), (135), (136), (137), (138), (140), (141),
% 117.27/18.24 | | | | | | | | | | (144), (146), (149), (150), (151), (152), (153),
% 117.27/18.24 | | | | | | | | | | (154), (155), (156), (157), (159), (161), (162),
% 117.27/18.24 | | | | | | | | | | (163), (164), (166), (168), (170), (301), (318)
% 117.27/18.24 | | | | | | | | | | are inconsistent by sub-proof #267.
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | Case 2:
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | (319) ~ (all_56_11 = e0)
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | REDUCE: (315), (319) imply:
% 117.27/18.24 | | | | | | | | | | (320) $false
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | | CLOSE: (320) is inconsistent.
% 117.27/18.24 | | | | | | | | | |
% 117.27/18.24 | | | | | | | | | End of split
% 117.27/18.24 | | | | | | | | |
% 117.27/18.24 | | | | | | | | End of split
% 117.27/18.24 | | | | | | | |
% 117.27/18.24 | | | | | | | End of split
% 117.27/18.24 | | | | | | |
% 117.27/18.24 | | | | | | End of split
% 117.27/18.24 | | | | | |
% 117.27/18.24 | | | | | End of split
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | Case 2:
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | | (321) ~ (all_56_14 = e2)
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | | REDUCE: (180), (321) imply:
% 117.27/18.24 | | | | | (322) $false
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | | CLOSE: (322) is inconsistent.
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | End of split
% 117.27/18.24 | | | |
% 117.27/18.24 | | | Case 2:
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | (323) ~ (all_56_14 = e2)
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | REDUCE: (180), (323) imply:
% 117.27/18.24 | | | | (324) $false
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | CLOSE: (324) is inconsistent.
% 117.27/18.24 | | | |
% 117.27/18.24 | | | End of split
% 117.27/18.24 | | |
% 117.27/18.24 | | End of split
% 117.27/18.24 | |
% 117.27/18.24 | Case 2:
% 117.27/18.24 | |
% 117.27/18.24 | | (325) all_38_1 = e2
% 117.27/18.24 | | (326) ~ (all_38_0 = e0) | ~ (all_38_2 = e1)
% 117.27/18.24 | |
% 117.27/18.24 | | COMBINE_EQS: (17), (325) imply:
% 117.27/18.24 | | (327) all_10_1 = e2
% 117.27/18.24 | |
% 117.27/18.24 | | SIMP: (327) implies:
% 117.27/18.24 | | (328) all_10_1 = e2
% 117.27/18.24 | |
% 117.27/18.24 | | REDUCE: (168), (328) imply:
% 117.27/18.24 | | (329) ~ (e2 = e1)
% 117.27/18.24 | |
% 117.27/18.24 | | REDUCE: (65), (328) imply:
% 117.27/18.24 | | (330) op(e2, all_10_2) = all_10_0
% 117.27/18.24 | |
% 117.27/18.24 | | REDUCE: (103), (328) imply:
% 117.27/18.24 | | (331) op(e3, all_10_2) = e2
% 117.27/18.24 | |
% 117.27/18.24 | | BETA: splitting (93) gives:
% 117.27/18.24 | |
% 117.27/18.24 | | Case 1:
% 117.27/18.24 | | |
% 117.27/18.24 | | | (332) ~ (all_56_14 = e2)
% 117.27/18.24 | | |
% 117.27/18.24 | | | REDUCE: (14), (332) imply:
% 117.27/18.24 | | | (333) ~ (all_6_2 = e2)
% 117.27/18.24 | | |
% 117.27/18.24 | | | BETA: splitting (94) gives:
% 117.27/18.24 | | |
% 117.27/18.24 | | | Case 1:
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | (334) ~ (all_56_12 = e2)
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | REDUCE: (31), (334) imply:
% 117.27/18.24 | | | | (335) ~ (all_10_2 = e2)
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | BETA: splitting (79) gives:
% 117.27/18.24 | | | |
% 117.27/18.24 | | | | Case 1:
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | | (336) ~ (all_56_15 = e1)
% 117.27/18.24 | | | | |
% 117.27/18.24 | | | | | REDUCE: (99), (336) imply:
% 117.27/18.24 | | | | | (337) ~ (all_4_2 = e1)
% 117.27/18.24 | | | | |
% 117.27/18.25 | | | | | REF_CLOSE: (9), (12), (14), (15), (18), (26), (31), (32), (33), (36),
% 117.27/18.25 | | | | | (42), (43), (48), (49), (51), (52), (54), (59), (61), (63),
% 117.27/18.25 | | | | | (69), (75), (80), (81), (84), (87), (88), (90), (100),
% 117.27/18.25 | | | | | (107), (122), (128), (129), (130), (131), (132), (134),
% 117.27/18.25 | | | | | (140), (145), (146), (150), (152), (154), (162), (163),
% 117.27/18.25 | | | | | (164), (326), (329), (330), (331), (335), (337) are
% 117.27/18.25 | | | | | inconsistent by sub-proof #257.
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | Case 2:
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | (338) all_56_15 = e1
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | REF_CLOSE: (4), (6), (9), (11), (14), (15), (16), (32), (33), (36),
% 117.27/18.25 | | | | | (42), (43), (45), (48), (57), (58), (61), (69), (72), (75),
% 117.27/18.25 | | | | | (76), (77), (80), (86), (90), (95), (96), (99), (100),
% 117.27/18.25 | | | | | (105), (116), (119), (127), (130), (131), (133), (135),
% 117.27/18.25 | | | | | (137), (138), (142), (143), (148), (150), (155), (163),
% 117.27/18.25 | | | | | (164), (167), (333), (338) are inconsistent by sub-proof
% 117.27/18.25 | | | | | #269.
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | End of split
% 117.27/18.25 | | | |
% 117.27/18.25 | | | Case 2:
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | (339) all_56_12 = e2
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | COMBINE_EQS: (31), (339) imply:
% 117.27/18.25 | | | | (340) all_10_2 = e2
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | REDUCE: (153), (340) imply:
% 117.27/18.25 | | | | (341) ~ (all_52_4 = e2)
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | REDUCE: (331), (340) imply:
% 117.27/18.25 | | | | (342) op(e3, e2) = e2
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | REF_CLOSE: (13), (43), (341), (342) are inconsistent by sub-proof #301.
% 117.27/18.25 | | | |
% 117.27/18.25 | | | End of split
% 117.27/18.25 | | |
% 117.27/18.25 | | Case 2:
% 117.27/18.25 | | |
% 117.27/18.25 | | | (343) all_56_14 = e2
% 117.27/18.25 | | | (344) ~ (all_56_10 = e0)
% 117.27/18.25 | | |
% 117.27/18.25 | | | COMBINE_EQS: (14), (343) imply:
% 117.27/18.25 | | | (345) all_6_2 = e2
% 117.27/18.25 | | |
% 117.27/18.25 | | | SIMP: (345) implies:
% 117.27/18.25 | | | (346) all_6_2 = e2
% 117.27/18.25 | | |
% 117.27/18.25 | | | COMBINE_EQS: (127), (346) imply:
% 117.27/18.25 | | | (347) all_58_8 = e2
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (39), (344) imply:
% 117.27/18.25 | | | (348) ~ (all_52_7 = e0)
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (135), (346) imply:
% 117.27/18.25 | | | (349) ~ (all_52_6 = e2)
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (122), (346) imply:
% 117.27/18.25 | | | (350) ~ (all_52_9 = e2)
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (67), (346) imply:
% 117.27/18.25 | | | (351) ~ (all_52_11 = e2)
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (40), (346) imply:
% 117.27/18.25 | | | (352) op(all_6_1, e2) = e2
% 117.27/18.25 | | |
% 117.27/18.25 | | | REDUCE: (80), (346) imply:
% 117.27/18.25 | | | (353) op(e1, e2) = all_6_1
% 117.27/18.25 | | |
% 117.27/18.25 | | | BETA: splitting (160) gives:
% 117.27/18.25 | | |
% 117.27/18.25 | | | Case 1:
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | (354) ~ (all_56_0 = e3)
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | REDUCE: (156), (354) imply:
% 117.27/18.25 | | | | (355) ~ (all_52_4 = e3)
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | BETA: splitting (38) gives:
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | Case 1:
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | (356) ~ (all_56_7 = e1)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | REDUCE: (121), (356) imply:
% 117.27/18.25 | | | | | (357) ~ (all_52_6 = e1)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | GROUND_INST: instantiating (43) with all_52_6, all_6_1, e2, e1,
% 117.27/18.25 | | | | | simplifying with (118), (353) gives:
% 117.27/18.25 | | | | | (358) all_52_6 = all_6_1
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | COMBINE_EQS: (6), (358) imply:
% 117.27/18.25 | | | | | (359) all_58_7 = all_6_1
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | REDUCE: (165), (358) imply:
% 117.27/18.25 | | | | | (360) ~ (all_52_7 = all_6_1)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | SIMP: (360) implies:
% 117.27/18.25 | | | | | (361) ~ (all_52_7 = all_6_1)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | REDUCE: (357), (358) imply:
% 117.27/18.25 | | | | | (362) ~ (all_6_1 = e1)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | BETA: splitting (89) gives:
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | Case 1:
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | (363) ~ (all_56_13 = e3)
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | REDUCE: (113), (363) imply:
% 117.27/18.25 | | | | | | (364) ~ (all_8_2 = e3)
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | BETA: splitting (62) gives:
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | Case 1:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | (365) ~ (all_56_5 = e2)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | REDUCE: (133), (365) imply:
% 117.27/18.25 | | | | | | | (366) ~ (all_52_13 = e2)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | BETA: splitting (155) gives:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | (367) all_58_2 = e2
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | COMBINE_EQS: (86), (367) imply:
% 117.27/18.25 | | | | | | | | (368) all_52_1 = e2
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | REDUCE: (97), (368) imply:
% 117.27/18.25 | | | | | | | | (369) ~ (all_10_2 = e2)
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | SIMP: (369) implies:
% 117.27/18.25 | | | | | | | | (370) ~ (all_10_2 = e2)
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | BETA: splitting (79) gives:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | (371) ~ (all_56_15 = e1)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REDUCE: (99), (371) imply:
% 117.27/18.25 | | | | | | | | | (372) ~ (all_4_2 = e1)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REF_CLOSE: (9), (12), (14), (15), (18), (26), (31), (32),
% 117.27/18.25 | | | | | | | | | (33), (36), (42), (43), (48), (49), (51), (52),
% 117.27/18.25 | | | | | | | | | (54), (59), (61), (63), (69), (75), (80), (81),
% 117.27/18.25 | | | | | | | | | (84), (87), (88), (90), (100), (107), (122), (128),
% 117.27/18.25 | | | | | | | | | (129), (130), (131), (132), (134), (140), (145),
% 117.27/18.25 | | | | | | | | | (146), (150), (152), (154), (162), (163), (164),
% 117.27/18.25 | | | | | | | | | (326), (329), (330), (331), (370), (372) are
% 117.27/18.25 | | | | | | | | | inconsistent by sub-proof #257.
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | (373) all_56_15 = e1
% 117.27/18.25 | | | | | | | | | (374) ~ (all_56_11 = e0)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | COMBINE_EQS: (99), (373) imply:
% 117.27/18.25 | | | | | | | | | (375) all_4_2 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | SIMP: (375) implies:
% 117.27/18.25 | | | | | | | | | (376) all_4_2 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | COMBINE_EQS: (84), (376) imply:
% 117.27/18.25 | | | | | | | | | (377) all_58_15 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REDUCE: (24), (374) imply:
% 117.27/18.25 | | | | | | | | | (378) ~ (all_52_11 = e0)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REDUCE: (95), (376) imply:
% 117.27/18.25 | | | | | | | | | (379) ~ (all_52_14 = e1)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REDUCE: (12), (376) imply:
% 117.27/18.25 | | | | | | | | | (380) ~ (e1 = e0)
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REF_CLOSE: (3), (6), (18), (61), (90), (91), (96), (111),
% 117.27/18.25 | | | | | | | | | (119), (127), (128), (141), (147), (159), (163),
% 117.27/18.25 | | | | | | | | | (348), (357), (370), (377), (378), (379), (380) are
% 117.27/18.25 | | | | | | | | | inconsistent by sub-proof #255.
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | End of split
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | (381) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | REF_CLOSE: (58), (76), (100), (116), (350), (366), (381) are
% 117.27/18.25 | | | | | | | | inconsistent by sub-proof #401.
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | End of split
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | Case 2:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | (382) all_56_5 = e2
% 117.27/18.25 | | | | | | | (383) ~ (all_56_13 = e0)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | REF_CLOSE: (12), (13), (24), (30), (35), (43), (55), (58), (68),
% 117.27/18.25 | | | | | | | (84), (85), (91), (98), (101), (108), (111), (113),
% 117.27/18.25 | | | | | | | (117), (133), (138), (139), (158), (159), (348), (351),
% 117.27/18.25 | | | | | | | (352), (355), (359), (361), (364), (382), (383) are
% 117.27/18.25 | | | | | | | inconsistent by sub-proof #260.
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | End of split
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | Case 2:
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | (384) all_56_13 = e3
% 117.27/18.25 | | | | | | (385) ~ (all_56_9 = e0)
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | REDUCE: (78), (385) imply:
% 117.27/18.25 | | | | | | (386) ~ (all_52_3 = e0)
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | BETA: splitting (83) gives:
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | | Case 1:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | (387) ~ (all_56_6 = e1)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | REDUCE: (137), (387) imply:
% 117.27/18.25 | | | | | | | (388) ~ (all_52_2 = e1)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | BETA: splitting (119) gives:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | (389) all_58_6 = e1
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | REF_CLOSE: (96), (388), (389) are inconsistent by sub-proof
% 117.27/18.25 | | | | | | | | #452.
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | (390) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | BETA: splitting (390) gives:
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | (391) all_58_7 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | COMBINE_EQS: (359), (391) imply:
% 117.27/18.25 | | | | | | | | | (392) all_6_1 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | REDUCE: (362), (392) imply:
% 117.27/18.25 | | | | | | | | | (393) $false
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | CLOSE: (393) is inconsistent.
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | (394) all_58_8 = e1 | all_58_11 = e1
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | BETA: splitting (394) gives:
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | (395) all_58_8 = e1
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | COMBINE_EQS: (347), (395) imply:
% 117.27/18.25 | | | | | | | | | | (396) e2 = e1
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | REDUCE: (329), (396) imply:
% 117.27/18.25 | | | | | | | | | | (397) $false
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | CLOSE: (397) is inconsistent.
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | (398) all_58_11 = e1
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | COMBINE_EQS: (61), (398) imply:
% 117.27/18.25 | | | | | | | | | | (399) all_52_14 = e1
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | COMBINE_EQS: (152), (399) imply:
% 117.27/18.25 | | | | | | | | | | (400) all_56_8 = e1
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | BETA: splitting (159) gives:
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | (401) all_58_15 = e0
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | COMBINE_EQS: (84), (401) imply:
% 117.27/18.25 | | | | | | | | | | | (402) all_4_2 = e0
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | REDUCE: (12), (402) imply:
% 117.27/18.25 | | | | | | | | | | | (403) $false
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | CLOSE: (403) is inconsistent.
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | (404) ~ (all_58_15 = e0)
% 117.27/18.25 | | | | | | | | | | | (405) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 117.27/18.25 | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 117.27/18.25 | | | | | | | | | | | e0)
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | ALPHA: (405) implies:
% 117.27/18.25 | | | | | | | | | | | (406) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | BETA: splitting (81) gives:
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | (407) ~ (all_56_8 = e1)
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | REDUCE: (400), (407) imply:
% 117.27/18.25 | | | | | | | | | | | | (408) $false
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | CLOSE: (408) is inconsistent.
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | (409) ~ (all_56_12 = e0)
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | REDUCE: (31), (409) imply:
% 117.27/18.25 | | | | | | | | | | | | (410) ~ (all_10_2 = e0)
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | BETA: splitting (406) gives:
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | (411) all_58_12 = e0
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | COMBINE_EQS: (141), (411) imply:
% 117.27/18.25 | | | | | | | | | | | | | (412) all_52_3 = e0
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | REDUCE: (386), (412) imply:
% 117.27/18.25 | | | | | | | | | | | | | (413) $false
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | (414) all_58_13 = e0 | all_58_14 = e0
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | Case 1:
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | | (415) ~ (all_56_12 = e1)
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | | REDUCE: (31), (415) imply:
% 117.27/18.25 | | | | | | | | | | | | | | (416) ~ (all_10_2 = e1)
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (13), (14), (18), (22), (24), (29),
% 117.27/18.25 | | | | | | | | | | | | | | (31), (35), (42), (43), (48), (55), (58), (60),
% 117.27/18.25 | | | | | | | | | | | | | | (65), (66), (68), (72), (76), (78), (82), (84),
% 117.27/18.25 | | | | | | | | | | | | | | (86), (90), (91), (97), (100), (103), (108),
% 117.27/18.25 | | | | | | | | | | | | | | (111), (112), (113), (116), (120), (121), (128),
% 117.27/18.25 | | | | | | | | | | | | | | (129), (131), (133), (135), (141), (153), (155),
% 117.27/18.25 | | | | | | | | | | | | | | (156), (157), (159), (161), (163), (168), (410),
% 117.27/18.25 | | | | | | | | | | | | | | (416) are inconsistent by sub-proof #422.
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | Case 2:
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | | (417) all_56_12 = e1
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | | REF_CLOSE: (24), (91), (111), (154), (348), (414), (417) are
% 117.27/18.25 | | | | | | | | | | | | | | inconsistent by sub-proof #361.
% 117.27/18.25 | | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | | End of split
% 117.27/18.25 | | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | | End of split
% 117.27/18.25 | | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | | End of split
% 117.27/18.25 | | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | | End of split
% 117.27/18.25 | | | | | | | | | |
% 117.27/18.25 | | | | | | | | | End of split
% 117.27/18.25 | | | | | | | | |
% 117.27/18.25 | | | | | | | | End of split
% 117.27/18.25 | | | | | | | |
% 117.27/18.25 | | | | | | | End of split
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | Case 2:
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | (418) ~ (all_56_13 = e3)
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | REDUCE: (384), (418) imply:
% 117.27/18.25 | | | | | | | (419) $false
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | | CLOSE: (419) is inconsistent.
% 117.27/18.25 | | | | | | |
% 117.27/18.25 | | | | | | End of split
% 117.27/18.25 | | | | | |
% 117.27/18.25 | | | | | End of split
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | Case 2:
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | (420) ~ (all_56_14 = e2)
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | REDUCE: (343), (420) imply:
% 117.27/18.25 | | | | | (421) $false
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | | CLOSE: (421) is inconsistent.
% 117.27/18.25 | | | | |
% 117.27/18.25 | | | | End of split
% 117.27/18.25 | | | |
% 117.27/18.25 | | | Case 2:
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | (422) ~ (all_56_14 = e2)
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | REDUCE: (343), (422) imply:
% 117.27/18.25 | | | | (423) $false
% 117.27/18.25 | | | |
% 117.27/18.25 | | | | CLOSE: (423) is inconsistent.
% 117.27/18.25 | | | |
% 117.27/18.25 | | | End of split
% 117.27/18.25 | | |
% 117.27/18.25 | | End of split
% 117.27/18.25 | |
% 117.27/18.25 | End of split
% 117.27/18.25 |
% 117.27/18.25 End of proof
% 117.27/18.25
% 117.27/18.25 Sub-proof #255 shows that the following formulas are inconsistent:
% 117.27/18.25 ----------------------------------------------------------------
% 117.27/18.25 (1) ~ (all_52_2 = all_10_2)
% 117.27/18.25 (2) all_58_7 = all_52_6
% 117.27/18.25 (3) all_54_0 = all_10_2
% 117.27/18.25 (4) ~ (all_10_2 = e2)
% 117.27/18.25 (5) ~ (all_52_14 = e1)
% 117.27/18.25 (6) all_58_11 = all_52_14
% 117.27/18.25 (7) all_58_15 = e1
% 117.27/18.25 (8) ~ (all_10_2 = e3)
% 117.27/18.25 (9) all_58_13 = all_52_7
% 117.27/18.25 (10) ~ (all_52_7 = e0)
% 117.27/18.25 (11) all_58_6 = all_52_2
% 117.27/18.25 (12) all_58_14 = all_52_11
% 117.27/18.25 (13) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.25 (14) all_58_8 = all_6_2
% 117.27/18.25 (15) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.25 (16) all_58_12 = all_52_3
% 117.27/18.25 (17) ~ (all_52_3 = all_10_2)
% 117.27/18.25 (18) ~ (all_52_6 = e1)
% 117.27/18.25 (19) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.25 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.25 (20) ~ (all_52_11 = e0)
% 117.27/18.25 (21) ~ (all_6_2 = e1)
% 117.27/18.25 (22) ~ (e1 = e0)
% 117.27/18.25
% 117.27/18.25 Begin of proof
% 117.27/18.25 |
% 117.27/18.25 | BETA: splitting (19) gives:
% 117.27/18.25 |
% 117.27/18.25 | Case 1:
% 117.27/18.25 | |
% 117.27/18.25 | | (23) all_58_15 = e0
% 117.27/18.25 | |
% 117.27/18.25 | | COMBINE_EQS: (7), (23) imply:
% 117.27/18.25 | | (24) e1 = e0
% 117.27/18.25 | |
% 117.27/18.25 | | REDUCE: (22), (24) imply:
% 117.27/18.25 | | (25) $false
% 117.27/18.25 | |
% 117.27/18.25 | | CLOSE: (25) is inconsistent.
% 117.27/18.25 | |
% 117.27/18.25 | Case 2:
% 117.27/18.25 | |
% 117.27/18.25 | | (26) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 117.27/18.25 | | | all_58_13 = e0 | all_58_14 = e0)
% 117.27/18.25 | |
% 117.27/18.25 | | ALPHA: (26) implies:
% 117.27/18.25 | | (27) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.27/18.25 | |
% 117.27/18.25 | | BETA: splitting (13) gives:
% 117.27/18.25 | |
% 117.27/18.25 | | Case 1:
% 117.27/18.25 | | |
% 117.27/18.26 | | | (28) all_58_6 = e1
% 117.27/18.26 | | |
% 117.27/18.26 | | | COMBINE_EQS: (11), (28) imply:
% 117.27/18.26 | | | (29) all_52_2 = e1
% 117.27/18.26 | | |
% 117.27/18.26 | | | SIMP: (29) implies:
% 117.27/18.26 | | | (30) all_52_2 = e1
% 117.27/18.26 | | |
% 117.27/18.26 | | | REDUCE: (1), (30) imply:
% 117.27/18.26 | | | (31) ~ (all_10_2 = e1)
% 117.27/18.26 | | |
% 117.27/18.26 | | | SIMP: (31) implies:
% 117.27/18.26 | | | (32) ~ (all_10_2 = e1)
% 117.27/18.26 | | |
% 117.27/18.26 | | | BETA: splitting (27) gives:
% 117.27/18.26 | | |
% 117.27/18.26 | | | Case 1:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (33) all_58_12 = e0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | COMBINE_EQS: (16), (33) imply:
% 117.27/18.26 | | | | (34) all_52_3 = e0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | SIMP: (34) implies:
% 117.27/18.26 | | | | (35) all_52_3 = e0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (17), (35) imply:
% 117.27/18.26 | | | | (36) ~ (all_10_2 = e0)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | SIMP: (36) implies:
% 117.27/18.26 | | | | (37) ~ (all_10_2 = e0)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REF_CLOSE: (3), (4), (8), (15), (32), (37) are inconsistent by sub-proof
% 117.27/18.26 | | | | #256.
% 117.27/18.26 | | | |
% 117.27/18.26 | | | Case 2:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (38) all_58_13 = e0 | all_58_14 = e0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REF_CLOSE: (9), (10), (12), (20), (38) are inconsistent by sub-proof
% 117.27/18.26 | | | | #428.
% 117.27/18.26 | | | |
% 117.27/18.26 | | | End of split
% 117.27/18.26 | | |
% 117.27/18.26 | | Case 2:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (39) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.26 | | |
% 117.27/18.26 | | | REF_CLOSE: (2), (5), (6), (14), (18), (21), (39) are inconsistent by
% 117.27/18.26 | | | sub-proof #354.
% 117.27/18.26 | | |
% 117.27/18.26 | | End of split
% 117.27/18.26 | |
% 117.27/18.26 | End of split
% 117.27/18.26 |
% 117.27/18.26 End of proof
% 117.27/18.26
% 117.27/18.26 Sub-proof #256 shows that the following formulas are inconsistent:
% 117.27/18.26 ----------------------------------------------------------------
% 117.27/18.26 (1) all_54_0 = all_10_2
% 117.27/18.26 (2) ~ (all_10_2 = e2)
% 117.27/18.26 (3) ~ (all_10_2 = e1)
% 117.27/18.26 (4) ~ (all_10_2 = e3)
% 117.27/18.26 (5) ~ (all_10_2 = e0)
% 117.27/18.26 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.26
% 117.27/18.26 Begin of proof
% 117.27/18.26 |
% 117.27/18.26 | BETA: splitting (6) gives:
% 117.27/18.26 |
% 117.27/18.26 | Case 1:
% 117.27/18.26 | |
% 117.27/18.26 | | (7) all_54_0 = e3
% 117.27/18.26 | |
% 117.27/18.26 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #451.
% 117.27/18.26 | |
% 117.27/18.26 | Case 2:
% 117.27/18.26 | |
% 117.27/18.26 | | (8) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.26 | |
% 117.27/18.26 | | BETA: splitting (8) gives:
% 117.27/18.26 | |
% 117.27/18.26 | | Case 1:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (9) all_54_0 = e2
% 117.27/18.26 | | |
% 117.27/18.26 | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #450.
% 117.27/18.26 | | |
% 117.27/18.26 | | Case 2:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (10) all_54_0 = e1 | all_54_0 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #423.
% 117.27/18.26 | | |
% 117.27/18.26 | | End of split
% 117.27/18.26 | |
% 117.27/18.26 | End of split
% 117.27/18.26 |
% 117.27/18.26 End of proof
% 117.27/18.26
% 117.27/18.26 Sub-proof #257 shows that the following formulas are inconsistent:
% 117.27/18.26 ----------------------------------------------------------------
% 117.27/18.26 (1) all_28_1 = all_6_1
% 117.27/18.26 (2) ~ (all_4_2 = e0)
% 117.27/18.26 (3) all_56_14 = all_6_2
% 117.27/18.26 (4) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.26 (5) all_54_0 = all_10_2
% 117.27/18.26 (6) ~ (all_4_2 = e1)
% 117.27/18.26 (7) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.26 (8) all_56_12 = all_10_2
% 117.27/18.26 (9) all_58_0 = all_10_2
% 117.27/18.26 (10) all_54_11 = all_52_14
% 117.27/18.26 (11) ~ (all_52_14 = all_6_2)
% 117.27/18.26 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.26 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.26 (14) ~ (all_10_2 = e2)
% 117.27/18.26 (15) all_54_10 = all_6_2
% 117.27/18.26 (16) ~ (e2 = e1)
% 117.27/18.26 (17) op(e3, e0) = all_52_12
% 117.27/18.26 (18) all_38_0 = all_10_0
% 117.27/18.26 (19) ~ (all_52_8 = all_6_2)
% 117.27/18.26 (20) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.27/18.26 (21) all_54_6 = all_52_9
% 117.27/18.26 (22) all_58_11 = all_52_14
% 117.27/18.26 (23) op(e3, e1) = all_52_8
% 117.27/18.26 (24) ~ (all_38_0 = e0) | ~ (all_38_2 = e1)
% 117.27/18.26 (25) all_28_2 = all_6_2
% 117.27/18.26 (26) op(e1, e0) = all_52_14
% 117.27/18.26 (27) op(e1, all_6_2) = all_6_1
% 117.27/18.26 (28) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.27/18.26 (29) all_58_15 = all_4_2
% 117.27/18.26 (30) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.27/18.26 (31) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.27/18.26 (32) ~ (all_10_2 = e3)
% 117.27/18.26 (33) op(e2, all_10_2) = all_10_0
% 117.27/18.26 (34) all_58_10 = all_52_13
% 117.27/18.26 (35) op(e3, all_10_2) = e2
% 117.27/18.26 (36) all_38_2 = all_10_2
% 117.27/18.26 (37) ~ (all_52_9 = all_6_2)
% 117.27/18.26 (38) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.26 (39) ~ (all_10_0 = e1)
% 117.27/18.26 (40) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.26 (41) all_56_4 = all_52_9
% 117.27/18.26 (42) all_58_9 = all_52_12
% 117.27/18.26 (43) op(e2, e1) = all_52_9
% 117.27/18.26 (44) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.27/18.26 (45) op(e2, e0) = all_52_13
% 117.27/18.26 (46) ~ (all_52_12 = all_4_2)
% 117.27/18.26 (47) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.26 (48) all_56_8 = all_52_14
% 117.27/18.26 (49) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.27/18.26 (50) all_54_15 = all_4_2
% 117.27/18.26 (51) ~ (all_6_2 = e1)
% 117.27/18.26 (52) ~ (all_6_1 = e2)
% 117.27/18.26
% 117.27/18.26 Begin of proof
% 117.27/18.26 |
% 117.27/18.26 | BETA: splitting (49) gives:
% 117.27/18.26 |
% 117.27/18.26 | Case 1:
% 117.27/18.26 | |
% 117.27/18.26 | | (53) ~ (all_56_12 = e1)
% 117.27/18.26 | |
% 117.27/18.26 | | REDUCE: (8), (53) imply:
% 117.27/18.26 | | (54) ~ (all_10_2 = e1)
% 117.27/18.26 | |
% 117.27/18.26 | | REF_CLOSE: (2), (5), (6), (8), (13), (14), (16), (17), (20), (22), (28),
% 117.27/18.26 | | (29), (31), (32), (33), (34), (35), (38), (39), (42), (45), (46),
% 117.27/18.26 | | (48), (50), (54) are inconsistent by sub-proof #367.
% 117.27/18.26 | |
% 117.27/18.26 | Case 2:
% 117.27/18.26 | |
% 117.27/18.26 | | (55) all_56_12 = e1
% 117.27/18.26 | |
% 117.27/18.26 | | COMBINE_EQS: (8), (55) imply:
% 117.27/18.26 | | (56) all_10_2 = e1
% 117.27/18.26 | |
% 117.27/18.26 | | COMBINE_EQS: (36), (56) imply:
% 117.27/18.26 | | (57) all_38_2 = e1
% 117.27/18.26 | |
% 117.27/18.26 | | REDUCE: (35), (56) imply:
% 117.27/18.26 | | (58) op(e3, e1) = e2
% 117.27/18.26 | |
% 117.27/18.26 | | REDUCE: (33), (56) imply:
% 117.27/18.26 | | (59) op(e2, e1) = all_10_0
% 117.27/18.26 | |
% 117.27/18.26 | | BETA: splitting (30) gives:
% 117.27/18.26 | |
% 117.27/18.26 | | Case 1:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (60) ~ (all_56_4 = e2)
% 117.27/18.26 | | |
% 117.27/18.26 | | | REDUCE: (41), (60) imply:
% 117.27/18.26 | | | (61) ~ (all_52_9 = e2)
% 117.27/18.26 | | |
% 117.27/18.26 | | | BETA: splitting (24) gives:
% 117.27/18.26 | | |
% 117.27/18.26 | | | Case 1:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (62) ~ (all_38_2 = e1)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (57), (62) imply:
% 117.27/18.26 | | | | (63) $false
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | CLOSE: (63) is inconsistent.
% 117.27/18.26 | | | |
% 117.27/18.26 | | | Case 2:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (64) ~ (all_38_0 = e0)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (18), (64) imply:
% 117.27/18.26 | | | | (65) ~ (all_10_0 = e0)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | GROUND_INST: instantiating (13) with all_52_9, all_10_0, e1, e2,
% 117.27/18.26 | | | | simplifying with (43), (59) gives:
% 117.27/18.26 | | | | (66) all_52_9 = all_10_0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | GROUND_INST: instantiating (13) with all_52_8, e2, e1, e3, simplifying
% 117.27/18.26 | | | | with (23), (58) gives:
% 117.27/18.26 | | | | (67) all_52_8 = e2
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | COMBINE_EQS: (21), (66) imply:
% 117.27/18.26 | | | | (68) all_54_6 = all_10_0
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (19), (67) imply:
% 117.27/18.26 | | | | (69) ~ (all_6_2 = e2)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | SIMP: (69) implies:
% 117.27/18.26 | | | | (70) ~ (all_6_2 = e2)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (37), (66) imply:
% 117.27/18.26 | | | | (71) ~ (all_10_0 = all_6_2)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (61), (66) imply:
% 117.27/18.26 | | | | (72) ~ (all_10_0 = e2)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | BETA: splitting (44) gives:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | Case 1:
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | (73) all_54_6 = e3
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | COMBINE_EQS: (68), (73) imply:
% 117.27/18.26 | | | | | (74) all_10_0 = e3
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | SIMP: (74) implies:
% 117.27/18.26 | | | | | (75) all_10_0 = e3
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | REDUCE: (71), (75) imply:
% 117.27/18.26 | | | | | (76) ~ (all_6_2 = e3)
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | SIMP: (76) implies:
% 117.27/18.26 | | | | | (77) ~ (all_6_2 = e3)
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (10), (11), (12), (13), (15),
% 117.27/18.26 | | | | | (25), (26), (27), (32), (40), (47), (48), (51), (52), (70),
% 117.27/18.26 | | | | | (77) are inconsistent by sub-proof #258.
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | Case 2:
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | (78) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | | REF_CLOSE: (39), (65), (68), (72), (78) are inconsistent by sub-proof
% 117.27/18.26 | | | | | #365.
% 117.27/18.26 | | | | |
% 117.27/18.26 | | | | End of split
% 117.27/18.26 | | | |
% 117.27/18.26 | | | End of split
% 117.27/18.26 | | |
% 117.27/18.26 | | Case 2:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (79) ~ (all_56_12 = e1)
% 117.27/18.26 | | |
% 117.27/18.26 | | | REDUCE: (55), (79) imply:
% 117.27/18.26 | | | (80) $false
% 117.27/18.26 | | |
% 117.27/18.26 | | | CLOSE: (80) is inconsistent.
% 117.27/18.26 | | |
% 117.27/18.26 | | End of split
% 117.27/18.26 | |
% 117.27/18.26 | End of split
% 117.27/18.26 |
% 117.27/18.26 End of proof
% 117.27/18.26
% 117.27/18.26 Sub-proof #258 shows that the following formulas are inconsistent:
% 117.27/18.26 ----------------------------------------------------------------
% 117.27/18.26 (1) all_28_1 = all_6_1
% 117.27/18.26 (2) all_56_14 = all_6_2
% 117.27/18.26 (3) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.26 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.26 (5) all_58_0 = all_10_2
% 117.27/18.26 (6) all_54_11 = all_52_14
% 117.27/18.26 (7) ~ (all_52_14 = all_6_2)
% 117.27/18.26 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.26 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.26 (10) all_54_10 = all_6_2
% 117.27/18.26 (11) all_28_2 = all_6_2
% 117.27/18.26 (12) op(e1, e0) = all_52_14
% 117.27/18.26 (13) op(e1, all_6_2) = all_6_1
% 117.27/18.26 (14) ~ (all_10_2 = e3)
% 117.27/18.26 (15) ~ (all_6_2 = e2)
% 117.27/18.26 (16) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.26 (17) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.26 (18) all_56_8 = all_52_14
% 117.27/18.26 (19) ~ (all_6_2 = e3)
% 117.27/18.26 (20) ~ (all_6_2 = e1)
% 117.27/18.26 (21) ~ (all_6_1 = e2)
% 117.27/18.26
% 117.27/18.26 Begin of proof
% 117.27/18.26 |
% 117.27/18.26 | BETA: splitting (8) gives:
% 117.27/18.26 |
% 117.27/18.26 | Case 1:
% 117.27/18.26 | |
% 117.27/18.26 | | (22) all_54_10 = e3
% 117.27/18.26 | |
% 117.27/18.26 | | REF_CLOSE: (10), (19), (22) are inconsistent by sub-proof #352.
% 117.27/18.26 | |
% 117.27/18.26 | Case 2:
% 117.27/18.26 | |
% 117.27/18.26 | | (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.26 | |
% 117.27/18.26 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 117.27/18.26 | | (14), (15), (16), (17), (18), (20), (21), (23) are inconsistent
% 117.27/18.26 | | by sub-proof #259.
% 117.27/18.26 | |
% 117.27/18.26 | End of split
% 117.27/18.26 |
% 117.27/18.26 End of proof
% 117.27/18.26
% 117.27/18.26 Sub-proof #259 shows that the following formulas are inconsistent:
% 117.27/18.26 ----------------------------------------------------------------
% 117.27/18.26 (1) all_28_1 = all_6_1
% 117.27/18.26 (2) all_56_14 = all_6_2
% 117.27/18.26 (3) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.26 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.26 (5) all_58_0 = all_10_2
% 117.27/18.26 (6) all_54_11 = all_52_14
% 117.27/18.26 (7) ~ (all_52_14 = all_6_2)
% 117.27/18.26 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.26 (9) all_54_10 = all_6_2
% 117.27/18.26 (10) all_28_2 = all_6_2
% 117.27/18.26 (11) op(e1, e0) = all_52_14
% 117.27/18.26 (12) op(e1, all_6_2) = all_6_1
% 117.27/18.26 (13) ~ (all_10_2 = e3)
% 117.27/18.26 (14) ~ (all_6_2 = e2)
% 117.27/18.26 (15) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.26 (16) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.26 (17) all_56_8 = all_52_14
% 117.27/18.26 (18) ~ (all_6_2 = e1)
% 117.27/18.26 (19) ~ (all_6_1 = e2)
% 117.27/18.26 (20) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.26
% 117.27/18.26 Begin of proof
% 117.27/18.26 |
% 117.27/18.26 | BETA: splitting (20) gives:
% 117.27/18.26 |
% 117.27/18.26 | Case 1:
% 117.27/18.26 | |
% 117.27/18.26 | | (21) all_54_10 = e2
% 117.27/18.26 | |
% 117.27/18.26 | | REF_CLOSE: (9), (14), (21) are inconsistent by sub-proof #438.
% 117.27/18.26 | |
% 117.27/18.26 | Case 2:
% 117.27/18.26 | |
% 117.27/18.26 | | (22) all_54_10 = e1 | all_54_10 = e0
% 117.27/18.26 | |
% 117.27/18.26 | | BETA: splitting (22) gives:
% 117.27/18.26 | |
% 117.27/18.26 | | Case 1:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (23) all_54_10 = e1
% 117.27/18.26 | | |
% 117.27/18.26 | | | REF_CLOSE: (9), (18), (23) are inconsistent by sub-proof #437.
% 117.27/18.26 | | |
% 117.27/18.26 | | Case 2:
% 117.27/18.26 | | |
% 117.27/18.26 | | | (24) all_54_10 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | COMBINE_EQS: (9), (24) imply:
% 117.27/18.26 | | | (25) all_6_2 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | SIMP: (25) implies:
% 117.27/18.26 | | | (26) all_6_2 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | COMBINE_EQS: (10), (26) imply:
% 117.27/18.26 | | | (27) all_28_2 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | COMBINE_EQS: (2), (26) imply:
% 117.27/18.26 | | | (28) all_56_14 = e0
% 117.27/18.26 | | |
% 117.27/18.26 | | | REDUCE: (7), (26) imply:
% 117.27/18.26 | | | (29) ~ (all_52_14 = e0)
% 117.27/18.26 | | |
% 117.27/18.26 | | | REDUCE: (12), (26) imply:
% 117.27/18.26 | | | (30) op(e1, e0) = all_6_1
% 117.27/18.26 | | |
% 117.27/18.26 | | | BETA: splitting (4) gives:
% 117.27/18.26 | | |
% 117.27/18.26 | | | Case 1:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (31) ~ (all_56_8 = e1)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (17), (31) imply:
% 117.27/18.26 | | | | (32) ~ (all_52_14 = e1)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (13), (15), (16), (19), (27),
% 117.27/18.26 | | | | (29), (30), (32) are inconsistent by sub-proof #279.
% 117.27/18.26 | | | |
% 117.27/18.26 | | | Case 2:
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | (33) ~ (all_56_14 = e0)
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | REDUCE: (28), (33) imply:
% 117.27/18.26 | | | | (34) $false
% 117.27/18.26 | | | |
% 117.27/18.26 | | | | CLOSE: (34) is inconsistent.
% 117.27/18.26 | | | |
% 117.27/18.26 | | | End of split
% 117.27/18.26 | | |
% 117.27/18.26 | | End of split
% 117.27/18.26 | |
% 117.27/18.26 | End of split
% 117.27/18.26 |
% 117.27/18.26 End of proof
% 117.27/18.26
% 117.27/18.26 Sub-proof #260 shows that the following formulas are inconsistent:
% 117.27/18.26 ----------------------------------------------------------------
% 117.27/18.26 (1) ~ (all_4_2 = e0)
% 117.27/18.26 (2) op(e3, e2) = all_52_4
% 117.27/18.26 (3) op(all_6_1, e2) = e2
% 117.27/18.26 (4) all_56_11 = all_52_11
% 117.27/18.26 (5) ~ (all_52_4 = e3)
% 117.27/18.27 (6) ~ (all_52_7 = all_6_1)
% 117.27/18.27 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.27 (8) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.27 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.27 (10) ~ (all_52_4 = all_52_7)
% 117.27/18.27 (11) all_58_3 = all_8_2
% 117.27/18.27 (12) ~ (all_8_2 = e3)
% 117.27/18.27 (13) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.27/18.27 (14) all_58_15 = all_4_2
% 117.27/18.27 (15) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 117.27/18.27 (16) all_58_13 = all_52_7
% 117.27/18.27 (17) ~ (all_52_7 = e0)
% 117.27/18.27 (18) all_54_5 = all_8_2
% 117.27/18.27 (19) ~ (all_52_11 = e2)
% 117.27/18.27 (20) ~ (all_52_13 = all_8_2)
% 117.27/18.27 (21) all_56_5 = e2
% 117.27/18.27 (22) all_58_1 = all_52_4
% 117.27/18.27 (23) all_58_14 = all_52_11
% 117.27/18.27 (24) all_56_13 = all_8_2
% 117.27/18.27 (25) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 (26) all_56_5 = all_52_13
% 117.27/18.27 (27) ~ (all_52_13 = all_4_2)
% 117.27/18.27 (28) ~ (e2 = e0)
% 117.27/18.27 (29) ~ (all_56_13 = e0)
% 117.27/18.27 (30) all_58_7 = all_6_1
% 117.27/18.27 (31) ~ (e3 = e2)
% 117.27/18.27 (32) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.27 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.27
% 117.27/18.27 Begin of proof
% 117.27/18.27 |
% 117.27/18.27 | COMBINE_EQS: (21), (26) imply:
% 117.27/18.27 | (33) all_52_13 = e2
% 117.27/18.27 |
% 117.27/18.27 | REDUCE: (24), (29) imply:
% 117.27/18.27 | (34) ~ (all_8_2 = e0)
% 117.27/18.27 |
% 117.27/18.27 | REDUCE: (20), (33) imply:
% 117.27/18.27 | (35) ~ (all_8_2 = e2)
% 117.27/18.27 |
% 117.27/18.27 | SIMP: (35) implies:
% 117.27/18.27 | (36) ~ (all_8_2 = e2)
% 117.27/18.27 |
% 117.27/18.27 | REDUCE: (27), (33) imply:
% 117.27/18.27 | (37) ~ (all_4_2 = e2)
% 117.27/18.27 |
% 117.27/18.27 | SIMP: (37) implies:
% 117.27/18.27 | (38) ~ (all_4_2 = e2)
% 117.27/18.27 |
% 117.27/18.27 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 117.27/18.27 | (13), (14), (15), (16), (17), (18), (19), (22), (23), (24), (25),
% 117.27/18.27 | (28), (30), (31), (32), (34), (36), (38) are inconsistent by
% 117.27/18.27 | sub-proof #261.
% 117.27/18.27 |
% 117.27/18.27 End of proof
% 117.27/18.27
% 117.27/18.27 Sub-proof #261 shows that the following formulas are inconsistent:
% 117.27/18.27 ----------------------------------------------------------------
% 117.27/18.27 (1) ~ (all_4_2 = e0)
% 117.27/18.27 (2) op(e3, e2) = all_52_4
% 117.27/18.27 (3) op(all_6_1, e2) = e2
% 117.27/18.27 (4) all_56_11 = all_52_11
% 117.27/18.27 (5) ~ (all_52_4 = e3)
% 117.27/18.27 (6) ~ (all_52_7 = all_6_1)
% 117.27/18.27 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.27 (8) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.27 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.27 (10) ~ (all_52_4 = all_52_7)
% 117.27/18.27 (11) all_58_3 = all_8_2
% 117.27/18.27 (12) ~ (all_8_2 = e0)
% 117.27/18.27 (13) ~ (all_8_2 = e3)
% 117.27/18.27 (14) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.27/18.27 (15) all_58_15 = all_4_2
% 117.27/18.27 (16) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 117.27/18.27 (17) all_58_13 = all_52_7
% 117.27/18.27 (18) ~ (all_52_7 = e0)
% 117.27/18.27 (19) all_54_5 = all_8_2
% 117.27/18.27 (20) ~ (all_52_11 = e2)
% 117.27/18.27 (21) all_58_1 = all_52_4
% 117.27/18.27 (22) all_58_14 = all_52_11
% 117.27/18.27 (23) all_56_13 = all_8_2
% 117.27/18.27 (24) ~ (all_8_2 = e2)
% 117.27/18.27 (25) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 (26) ~ (e2 = e0)
% 117.27/18.27 (27) ~ (all_4_2 = e2)
% 117.27/18.27 (28) all_58_7 = all_6_1
% 117.27/18.27 (29) ~ (e3 = e2)
% 117.27/18.27 (30) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.27 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.27
% 117.27/18.27 Begin of proof
% 117.27/18.27 |
% 117.27/18.27 | BETA: splitting (7) gives:
% 117.27/18.27 |
% 117.27/18.27 | Case 1:
% 117.27/18.27 | |
% 117.27/18.27 | | (31) all_54_5 = e3
% 117.27/18.27 | |
% 117.27/18.27 | | REF_CLOSE: (13), (19), (31) are inconsistent by sub-proof #339.
% 117.27/18.27 | |
% 117.27/18.27 | Case 2:
% 117.27/18.27 | |
% 117.27/18.27 | | (32) ~ (all_54_5 = e3)
% 117.27/18.27 | | (33) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.27 | |
% 117.27/18.27 | | BETA: splitting (33) gives:
% 117.27/18.27 | |
% 117.27/18.27 | | Case 1:
% 117.27/18.27 | | |
% 117.27/18.27 | | | (34) all_54_5 = e2
% 117.27/18.27 | | |
% 117.27/18.27 | | | REF_CLOSE: (19), (24), (34) are inconsistent by sub-proof #338.
% 117.27/18.27 | | |
% 117.27/18.27 | | Case 2:
% 117.27/18.27 | | |
% 117.27/18.27 | | | (35) ~ (all_54_5 = e2)
% 117.27/18.27 | | | (36) all_54_5 = e1 | all_54_5 = e0
% 117.27/18.27 | | |
% 117.27/18.27 | | | BETA: splitting (36) gives:
% 117.27/18.27 | | |
% 117.27/18.27 | | | Case 1:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | (37) all_54_5 = e1
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | COMBINE_EQS: (19), (37) imply:
% 117.27/18.27 | | | | (38) all_8_2 = e1
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | SIMP: (38) implies:
% 117.27/18.27 | | | | (39) all_8_2 = e1
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | COMBINE_EQS: (23), (39) imply:
% 117.27/18.27 | | | | (40) all_56_13 = e1
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | BETA: splitting (14) gives:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | Case 1:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | (41) ~ (all_56_13 = e1)
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | REDUCE: (40), (41) imply:
% 117.27/18.27 | | | | | (42) $false
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | CLOSE: (42) is inconsistent.
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | Case 2:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | (43) ~ (all_56_11 = e0)
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | REDUCE: (4), (43) imply:
% 117.27/18.27 | | | | | (44) ~ (all_52_11 = e0)
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | BETA: splitting (30) gives:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | Case 1:
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | (45) all_58_15 = e0
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | COMBINE_EQS: (15), (45) imply:
% 117.27/18.27 | | | | | | (46) all_4_2 = e0
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | REDUCE: (1), (46) imply:
% 117.27/18.27 | | | | | | (47) $false
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | CLOSE: (47) is inconsistent.
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | Case 2:
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | (48) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.27 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | ALPHA: (48) implies:
% 117.27/18.27 | | | | | | (49) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | BETA: splitting (49) gives:
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | Case 1:
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | | (50) all_58_12 = e0
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | | BETA: splitting (16) gives:
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | | Case 1:
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | (51) all_58_12 = e2
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | COMBINE_EQS: (50), (51) imply:
% 117.27/18.27 | | | | | | | | (52) e2 = e0
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | REDUCE: (26), (52) imply:
% 117.27/18.27 | | | | | | | | (53) $false
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | CLOSE: (53) is inconsistent.
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | Case 2:
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | (54) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | BETA: splitting (54) gives:
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | | Case 1:
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | (55) all_58_13 = e2
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | COMBINE_EQS: (17), (55) imply:
% 117.27/18.27 | | | | | | | | | (56) all_52_7 = e2
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | SIMP: (56) implies:
% 117.27/18.27 | | | | | | | | | (57) all_52_7 = e2
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | REDUCE: (10), (57) imply:
% 117.27/18.27 | | | | | | | | | (58) ~ (all_52_4 = e2)
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | REDUCE: (6), (57) imply:
% 117.27/18.27 | | | | | | | | | (59) ~ (all_6_1 = e2)
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | SIMP: (59) implies:
% 117.27/18.27 | | | | | | | | | (60) ~ (all_6_1 = e2)
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (9), (10), (11), (12), (13),
% 117.27/18.27 | | | | | | | | | (17), (19), (21), (24), (25), (28), (29), (36),
% 117.27/18.27 | | | | | | | | | (54), (58), (60) are inconsistent by sub-proof
% 117.27/18.27 | | | | | | | | | #262.
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | Case 2:
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | (61) all_58_14 = e2 | all_58_15 = e2
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | BETA: splitting (61) gives:
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | | Case 1:
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | (62) all_58_14 = e2
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | REF_CLOSE: (20), (22), (62) are inconsistent by sub-proof
% 117.27/18.27 | | | | | | | | | | #295.
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | Case 2:
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | (63) all_58_15 = e2
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | COMBINE_EQS: (15), (63) imply:
% 117.27/18.27 | | | | | | | | | | (64) all_4_2 = e2
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | REDUCE: (27), (64) imply:
% 117.27/18.27 | | | | | | | | | | (65) $false
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | | CLOSE: (65) is inconsistent.
% 117.27/18.27 | | | | | | | | | |
% 117.27/18.27 | | | | | | | | | End of split
% 117.27/18.27 | | | | | | | | |
% 117.27/18.27 | | | | | | | | End of split
% 117.27/18.27 | | | | | | | |
% 117.27/18.27 | | | | | | | End of split
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | Case 2:
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | | (66) all_58_13 = e0 | all_58_14 = e0
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | | REF_CLOSE: (17), (18), (22), (44), (66) are inconsistent by
% 117.27/18.27 | | | | | | | sub-proof #428.
% 117.27/18.27 | | | | | | |
% 117.27/18.27 | | | | | | End of split
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | End of split
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | End of split
% 117.27/18.27 | | | |
% 117.27/18.27 | | | Case 2:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | (67) all_54_5 = e0
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | REF_CLOSE: (12), (19), (67) are inconsistent by sub-proof #311.
% 117.27/18.27 | | | |
% 117.27/18.27 | | | End of split
% 117.27/18.27 | | |
% 117.27/18.27 | | End of split
% 117.27/18.27 | |
% 117.27/18.27 | End of split
% 117.27/18.27 |
% 117.27/18.27 End of proof
% 117.27/18.27
% 117.27/18.27 Sub-proof #262 shows that the following formulas are inconsistent:
% 117.27/18.27 ----------------------------------------------------------------
% 117.27/18.27 (1) op(e3, e2) = all_52_4
% 117.27/18.27 (2) op(all_6_1, e2) = e2
% 117.27/18.27 (3) ~ (all_52_4 = e3)
% 117.27/18.27 (4) all_54_5 = e1 | all_54_5 = e0
% 117.27/18.27 (5) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 117.27/18.27 (6) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.27 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.27 (8) ~ (all_52_4 = all_52_7)
% 117.27/18.27 (9) all_58_3 = all_8_2
% 117.27/18.27 (10) ~ (all_8_2 = e0)
% 117.27/18.27 (11) ~ (all_8_2 = e3)
% 117.27/18.27 (12) all_58_13 = all_52_7
% 117.27/18.27 (13) all_54_5 = all_8_2
% 117.27/18.27 (14) all_58_1 = all_52_4
% 117.27/18.27 (15) ~ (all_8_2 = e2)
% 117.27/18.27 (16) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 (17) all_58_7 = all_6_1
% 117.27/18.27 (18) ~ (e3 = e2)
% 117.27/18.27 (19) ~ (all_6_1 = e2)
% 117.27/18.27 (20) ~ (all_52_4 = e2)
% 117.27/18.27
% 117.27/18.27 Begin of proof
% 117.27/18.27 |
% 117.27/18.27 | BETA: splitting (6) gives:
% 117.27/18.27 |
% 117.27/18.27 | Case 1:
% 117.27/18.27 | |
% 117.27/18.27 | | (21) all_58_1 = e2
% 117.27/18.27 | |
% 117.27/18.27 | | COMBINE_EQS: (14), (21) imply:
% 117.27/18.27 | | (22) all_52_4 = e2
% 117.27/18.27 | |
% 117.27/18.27 | | REDUCE: (20), (22) imply:
% 117.27/18.27 | | (23) $false
% 117.27/18.27 | |
% 117.27/18.27 | | CLOSE: (23) is inconsistent.
% 117.27/18.27 | |
% 117.27/18.27 | Case 2:
% 117.27/18.27 | |
% 117.27/18.27 | | (24) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.27 | |
% 117.27/18.27 | | BETA: splitting (4) gives:
% 117.27/18.27 | |
% 117.27/18.27 | | Case 1:
% 117.27/18.27 | | |
% 117.27/18.27 | | | (25) all_54_5 = e1
% 117.27/18.27 | | |
% 117.27/18.27 | | | COMBINE_EQS: (13), (25) imply:
% 117.27/18.27 | | | (26) all_8_2 = e1
% 117.27/18.27 | | |
% 117.27/18.27 | | | SIMP: (26) implies:
% 117.27/18.27 | | | (27) all_8_2 = e1
% 117.27/18.27 | | |
% 117.27/18.27 | | | COMBINE_EQS: (9), (27) imply:
% 117.27/18.27 | | | (28) all_58_3 = e1
% 117.27/18.27 | | |
% 117.27/18.27 | | | REDUCE: (11), (27) imply:
% 117.27/18.27 | | | (29) ~ (e3 = e1)
% 117.27/18.27 | | |
% 117.27/18.27 | | | SIMP: (29) implies:
% 117.27/18.27 | | | (30) ~ (e3 = e1)
% 117.27/18.27 | | |
% 117.27/18.27 | | | BETA: splitting (5) gives:
% 117.27/18.27 | | |
% 117.27/18.27 | | | Case 1:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | (31) all_58_13 = e2
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | COMBINE_EQS: (12), (31) imply:
% 117.27/18.27 | | | | (32) all_52_7 = e2
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | SIMP: (32) implies:
% 117.27/18.27 | | | | (33) all_52_7 = e2
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | BETA: splitting (16) gives:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | Case 1:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | (34) all_58_1 = e3
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | COMBINE_EQS: (14), (34) imply:
% 117.27/18.27 | | | | | (35) all_52_4 = e3
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | REDUCE: (3), (35) imply:
% 117.27/18.27 | | | | | (36) $false
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | CLOSE: (36) is inconsistent.
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | Case 2:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | (37) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | BETA: splitting (37) gives:
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | | Case 1:
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | (38) all_58_3 = e3
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | REF_CLOSE: (28), (30), (38) are inconsistent by sub-proof #266.
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | Case 2:
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | (39) all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | | REF_CLOSE: (1), (2), (7), (17), (18), (20), (31), (39) are
% 117.27/18.27 | | | | | | inconsistent by sub-proof #263.
% 117.27/18.27 | | | | | |
% 117.27/18.27 | | | | | End of split
% 117.27/18.27 | | | | |
% 117.27/18.27 | | | | End of split
% 117.27/18.27 | | | |
% 117.27/18.27 | | | Case 2:
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | (40) ~ (all_58_13 = e2)
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | REDUCE: (12), (40) imply:
% 117.27/18.27 | | | | (41) ~ (all_52_7 = e2)
% 117.27/18.27 | | | |
% 117.27/18.27 | | | | REF_CLOSE: (9), (12), (15), (17), (19), (24), (41) are inconsistent by
% 117.27/18.27 | | | | sub-proof #264.
% 117.27/18.27 | | | |
% 117.27/18.27 | | | End of split
% 117.27/18.27 | | |
% 117.27/18.27 | | Case 2:
% 117.27/18.27 | | |
% 117.27/18.27 | | | (42) all_54_5 = e0
% 117.27/18.27 | | |
% 117.27/18.27 | | | REF_CLOSE: (10), (13), (42) are inconsistent by sub-proof #311.
% 117.27/18.27 | | |
% 117.27/18.27 | | End of split
% 117.27/18.27 | |
% 117.27/18.27 | End of split
% 117.27/18.27 |
% 117.27/18.27 End of proof
% 117.27/18.27
% 117.27/18.27 Sub-proof #263 shows that the following formulas are inconsistent:
% 117.27/18.27 ----------------------------------------------------------------
% 117.27/18.27 (1) op(e3, e2) = all_52_4
% 117.27/18.27 (2) op(all_6_1, e2) = e2
% 117.27/18.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.27 (4) all_58_13 = e2
% 117.27/18.27 (5) all_58_7 = all_6_1
% 117.27/18.27 (6) all_58_7 = e3 | all_58_13 = e3
% 117.27/18.27 (7) ~ (e3 = e2)
% 117.27/18.27 (8) ~ (all_52_4 = e2)
% 117.27/18.27
% 117.27/18.27 Begin of proof
% 117.27/18.27 |
% 117.27/18.27 | BETA: splitting (6) gives:
% 117.27/18.27 |
% 117.27/18.27 | Case 1:
% 117.27/18.27 | |
% 117.27/18.27 | | (9) all_58_7 = e3
% 117.27/18.27 | |
% 117.27/18.27 | | COMBINE_EQS: (5), (9) imply:
% 117.27/18.27 | | (10) all_6_1 = e3
% 117.27/18.27 | |
% 117.27/18.27 | | REDUCE: (2), (10) imply:
% 117.27/18.27 | | (11) op(e3, e2) = e2
% 117.27/18.27 | |
% 117.27/18.27 | | REF_CLOSE: (1), (3), (8), (11) are inconsistent by sub-proof #301.
% 117.27/18.27 | |
% 117.27/18.27 | Case 2:
% 117.27/18.27 | |
% 117.27/18.27 | | (12) all_58_13 = e3
% 117.27/18.27 | |
% 117.27/18.27 | | COMBINE_EQS: (4), (12) imply:
% 117.27/18.27 | | (13) e3 = e2
% 117.27/18.27 | |
% 117.27/18.27 | | REDUCE: (7), (13) imply:
% 117.27/18.27 | | (14) $false
% 117.27/18.27 | |
% 117.27/18.27 | | CLOSE: (14) is inconsistent.
% 117.27/18.27 | |
% 117.27/18.27 | End of split
% 117.27/18.27 |
% 117.27/18.27 End of proof
% 117.27/18.27
% 117.27/18.27 Sub-proof #264 shows that the following formulas are inconsistent:
% 117.27/18.27 ----------------------------------------------------------------
% 117.27/18.27 (1) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.27 (2) all_58_3 = all_8_2
% 117.27/18.27 (3) all_58_13 = all_52_7
% 117.27/18.27 (4) ~ (all_52_7 = e2)
% 117.27/18.28 (5) ~ (all_8_2 = e2)
% 117.27/18.28 (6) all_58_7 = all_6_1
% 117.27/18.28 (7) ~ (all_6_1 = e2)
% 117.27/18.28
% 117.27/18.28 Begin of proof
% 117.27/18.28 |
% 117.27/18.28 | BETA: splitting (1) gives:
% 117.27/18.28 |
% 117.27/18.28 | Case 1:
% 117.27/18.28 | |
% 117.27/18.28 | | (8) all_58_3 = e2
% 117.27/18.28 | |
% 117.27/18.28 | | COMBINE_EQS: (2), (8) imply:
% 117.27/18.28 | | (9) all_8_2 = e2
% 117.27/18.28 | |
% 117.27/18.28 | | REDUCE: (5), (9) imply:
% 117.27/18.28 | | (10) $false
% 117.27/18.28 | |
% 117.27/18.28 | | CLOSE: (10) is inconsistent.
% 117.27/18.28 | |
% 117.27/18.28 | Case 2:
% 117.27/18.28 | |
% 117.27/18.28 | | (11) all_58_7 = e2 | all_58_13 = e2
% 117.27/18.28 | |
% 117.27/18.28 | | BETA: splitting (11) gives:
% 117.27/18.28 | |
% 117.27/18.28 | | Case 1:
% 117.27/18.28 | | |
% 117.27/18.28 | | | (12) all_58_7 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | COMBINE_EQS: (6), (12) imply:
% 117.27/18.28 | | | (13) all_6_1 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | REDUCE: (7), (13) imply:
% 117.27/18.28 | | | (14) $false
% 117.27/18.28 | | |
% 117.27/18.28 | | | CLOSE: (14) is inconsistent.
% 117.27/18.28 | | |
% 117.27/18.28 | | Case 2:
% 117.27/18.28 | | |
% 117.27/18.28 | | | (15) all_58_13 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #265.
% 117.27/18.28 | | |
% 117.27/18.28 | | End of split
% 117.27/18.28 | |
% 117.27/18.28 | End of split
% 117.27/18.28 |
% 117.27/18.28 End of proof
% 117.27/18.28
% 117.27/18.28 Sub-proof #265 shows that the following formulas are inconsistent:
% 117.27/18.28 ----------------------------------------------------------------
% 117.27/18.28 (1) all_58_13 = all_52_7
% 117.27/18.28 (2) all_58_13 = e2
% 117.27/18.28 (3) ~ (all_52_7 = e2)
% 117.27/18.28
% 117.27/18.28 Begin of proof
% 117.27/18.28 |
% 117.27/18.28 | COMBINE_EQS: (1), (2) imply:
% 117.27/18.28 | (4) all_52_7 = e2
% 117.27/18.28 |
% 117.27/18.28 | SIMP: (4) implies:
% 117.27/18.28 | (5) all_52_7 = e2
% 117.27/18.28 |
% 117.27/18.28 | REDUCE: (3), (5) imply:
% 117.27/18.28 | (6) $false
% 117.27/18.28 |
% 117.27/18.28 | CLOSE: (6) is inconsistent.
% 117.27/18.28 |
% 117.27/18.28 End of proof
% 117.27/18.28
% 117.27/18.28 Sub-proof #266 shows that the following formulas are inconsistent:
% 117.27/18.28 ----------------------------------------------------------------
% 117.27/18.28 (1) all_58_3 = e3
% 117.27/18.28 (2) all_58_3 = e1
% 117.27/18.28 (3) ~ (e3 = e1)
% 117.27/18.28
% 117.27/18.28 Begin of proof
% 117.27/18.28 |
% 117.27/18.28 | COMBINE_EQS: (1), (2) imply:
% 117.27/18.28 | (4) e3 = e1
% 117.27/18.28 |
% 117.27/18.28 | SIMP: (4) implies:
% 117.27/18.28 | (5) e3 = e1
% 117.27/18.28 |
% 117.27/18.28 | REDUCE: (3), (5) imply:
% 117.27/18.28 | (6) $false
% 117.27/18.28 |
% 117.27/18.28 | CLOSE: (6) is inconsistent.
% 117.27/18.28 |
% 117.27/18.28 End of proof
% 117.27/18.28
% 117.27/18.28 Sub-proof #267 shows that the following formulas are inconsistent:
% 117.27/18.28 ----------------------------------------------------------------
% 117.27/18.28 (1) ~ (all_52_8 = all_10_2)
% 117.27/18.28 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.27/18.28 (3) all_54_2 = all_52_8
% 117.27/18.28 (4) all_58_7 = all_52_6
% 117.27/18.28 (5) ~ (all_52_8 = all_52_11)
% 117.27/18.28 (6) ~ (all_52_9 = all_8_2)
% 117.27/18.28 (7) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.27/18.28 (8) ~ (all_4_2 = e0)
% 117.27/18.28 (9) op(e3, e2) = all_52_4
% 117.27/18.28 (10) all_56_14 = all_6_2
% 117.27/18.28 (11) all_56_3 = all_52_1
% 117.27/18.28 (12) all_54_0 = all_10_2
% 117.27/18.28 (13) all_54_3 = all_52_12
% 117.27/18.28 (14) ~ (all_4_2 = e1)
% 117.27/18.28 (15) op(e0, e2) = all_52_7
% 117.27/18.28 (16) all_56_11 = all_52_11
% 117.27/18.28 (17) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 117.27/18.28 (18) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.27/18.28 (19) ~ (all_6_1 = e3)
% 117.27/18.28 (20) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.27/18.28 (21) ~ (all_52_12 = all_10_2)
% 117.27/18.28 (22) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.27/18.28 (23) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.27/18.28 (24) all_56_12 = all_10_2
% 117.27/18.28 (25) all_58_0 = all_10_2
% 117.27/18.28 (26) all_54_11 = all_52_14
% 117.27/18.28 (27) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.27/18.28 (28) ~ (all_52_14 = all_6_2)
% 117.27/18.28 (29) all_54_14 = all_52_11
% 117.27/18.28 (30) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.28 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.28 (32) all_54_10 = all_6_2
% 117.27/18.28 (33) op(e3, e0) = all_52_12
% 117.27/18.28 (34) ~ (all_52_8 = all_6_2)
% 117.27/18.28 (35) all_58_4 = all_52_8
% 117.27/18.28 (36) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.27/18.28 (37) ~ (all_52_4 = all_52_7)
% 117.27/18.28 (38) all_56_2 = all_52_12
% 117.27/18.28 (39) all_58_3 = all_8_2
% 117.27/18.28 (40) all_54_6 = all_52_9
% 117.27/18.28 (41) ~ (all_10_0 = e2)
% 117.27/18.28 (42) all_58_11 = all_52_14
% 117.27/18.28 (43) op(e3, e1) = all_52_8
% 117.27/18.28 (44) op(all_10_1, all_10_2) = all_10_0
% 117.27/18.28 (45) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.27/18.28 (46) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.27/18.28 (47) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.27/18.28 (48) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.27/18.28 (49) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.28 (50) op(e1, e0) = all_52_14
% 117.27/18.28 (51) all_58_5 = all_52_9
% 117.27/18.28 (52) all_56_9 = all_52_3
% 117.27/18.28 (53) op(e1, all_6_2) = all_6_1
% 117.27/18.28 (54) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.27/18.28 (55) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.27/18.28 (56) all_58_15 = all_4_2
% 117.27/18.28 (57) all_58_2 = all_52_1
% 117.27/18.28 (58) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.27/18.28 (59) ~ (all_10_2 = e3)
% 117.27/18.28 (60) all_58_13 = all_52_7
% 117.27/18.28 (61) all_58_6 = all_52_2
% 117.27/18.28 (62) ~ (all_52_1 = all_10_2)
% 117.27/18.28 (63) all_54_5 = all_8_2
% 117.27/18.28 (64) all_56_15 = all_4_2
% 117.27/18.28 (65) all_58_10 = all_52_13
% 117.27/18.28 (66) ~ (all_52_11 = all_4_2)
% 117.27/18.28 (67) op(e3, all_10_2) = all_10_1
% 117.27/18.28 (68) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.27/18.28 (69) ~ (all_10_1 = e2)
% 117.27/18.28 (70) all_58_1 = all_52_4
% 117.27/18.28 (71) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.27/18.28 (72) ~ (all_52_9 = all_52_11)
% 117.27/18.28 (73) all_58_14 = all_52_11
% 117.27/18.28 (74) all_54_1 = all_52_4
% 117.27/18.28 (75) all_56_13 = all_8_2
% 117.27/18.28 (76) op(e0, e1) = all_52_11
% 117.27/18.28 (77) ~ (all_52_1 = all_8_2)
% 117.27/18.28 (78) ~ (all_8_2 = e2)
% 117.27/18.28 (79) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.28 (80) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.27/18.28 (81) all_56_7 = all_52_6
% 117.27/18.28 (82) ~ (all_52_9 = all_6_2)
% 117.27/18.28 (83) all_56_1 = all_52_8
% 117.27/18.28 (84) all_58_8 = all_6_2
% 117.27/18.28 (85) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.27/18.28 (86) ~ (all_10_0 = e1)
% 117.27/18.28 (87) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.28 (88) all_56_4 = all_52_9
% 117.27/18.28 (89) all_58_9 = all_52_12
% 117.27/18.28 (90) all_56_5 = all_52_13
% 117.27/18.28 (91) ~ (all_52_6 = all_6_2)
% 117.27/18.28 (92) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.27/18.28 (93) all_56_6 = all_52_2
% 117.27/18.28 (94) ~ (all_52_13 = all_4_2)
% 117.27/18.28 (95) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.27/18.28 (96) all_58_12 = all_52_3
% 117.27/18.28 (97) ~ (all_52_8 = all_52_9)
% 117.27/18.28 (98) ~ (all_52_12 = all_4_2)
% 117.27/18.28 (99) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.27/18.28 (100) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.28 (101) ~ (all_52_8 = all_52_12)
% 117.27/18.28 (102) all_56_8 = all_52_14
% 117.27/18.28 (103) ~ (all_52_4 = all_10_2)
% 117.27/18.28 (104) ~ (all_10_1 = e1)
% 117.27/18.28 (105) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.27/18.28 (106) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.28 (107) all_56_0 = all_52_4
% 117.27/18.28 (108) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.27/18.28 (109) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.27/18.28 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.27/18.28 (110) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.27/18.28 (111) all_54_15 = all_4_2
% 117.27/18.28 (112) ~ (all_6_2 = e1)
% 117.27/18.28 (113) ~ (all_6_1 = e2)
% 117.27/18.28 (114) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.27/18.28
% 117.27/18.28 Begin of proof
% 117.27/18.28 |
% 117.27/18.28 | BETA: splitting (105) gives:
% 117.27/18.28 |
% 117.27/18.28 | Case 1:
% 117.27/18.28 | |
% 117.27/18.28 | | (115) ~ (all_56_12 = e1)
% 117.27/18.28 | |
% 117.27/18.28 | | REDUCE: (24), (115) imply:
% 117.27/18.28 | | (116) ~ (all_10_2 = e1)
% 117.27/18.28 | |
% 117.27/18.28 | | BETA: splitting (99) gives:
% 117.27/18.28 | |
% 117.27/18.28 | | Case 1:
% 117.27/18.28 | | |
% 117.27/18.28 | | | (117) ~ (all_56_15 = e2)
% 117.27/18.28 | | |
% 117.27/18.28 | | | REDUCE: (64), (117) imply:
% 117.27/18.28 | | | (118) ~ (all_4_2 = e2)
% 117.27/18.28 | | |
% 117.27/18.28 | | | REF_CLOSE: (4), (7), (8), (9), (10), (12), (13), (14), (15), (16), (20),
% 117.27/18.28 | | | (21), (22), (24), (27), (28), (30), (31), (32), (33), (36),
% 117.27/18.28 | | | (37), (39), (41), (42), (44), (45), (46), (49), (51), (52),
% 117.27/18.28 | | | (54), (55), (56), (57), (59), (60), (61), (62), (64), (65),
% 117.27/18.28 | | | (67), (69), (70), (73), (74), (75), (78), (79), (80), (81),
% 117.27/18.28 | | | (84), (85), (86), (88), (90), (91), (93), (96), (98), (102),
% 117.27/18.28 | | | (103), (104), (106), (107), (108), (109), (110), (111), (112),
% 117.27/18.28 | | | (116), (118) are inconsistent by sub-proof #416.
% 117.27/18.28 | | |
% 117.27/18.28 | | Case 2:
% 117.27/18.28 | | |
% 117.27/18.28 | | | (119) all_56_15 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | COMBINE_EQS: (64), (119) imply:
% 117.27/18.28 | | | (120) all_4_2 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | SIMP: (120) implies:
% 117.27/18.28 | | | (121) all_4_2 = e2
% 117.27/18.28 | | |
% 117.27/18.28 | | | REDUCE: (94), (121) imply:
% 117.27/18.28 | | | (122) ~ (all_52_13 = e2)
% 117.27/18.28 | | |
% 117.27/18.28 | | | BETA: splitting (68) gives:
% 117.27/18.28 | | |
% 117.27/18.28 | | | Case 1:
% 117.27/18.28 | | | |
% 117.27/18.28 | | | | (123) ~ (all_56_0 = e3)
% 117.27/18.28 | | | |
% 117.27/18.28 | | | | REDUCE: (107), (123) imply:
% 117.27/18.28 | | | | (124) ~ (all_52_4 = e3)
% 117.27/18.28 | | | |
% 117.27/18.28 | | | | BETA: splitting (100) gives:
% 117.27/18.28 | | | |
% 117.27/18.28 | | | | Case 1:
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | (125) all_58_0 = e3
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | COMBINE_EQS: (25), (125) imply:
% 117.27/18.28 | | | | | (126) all_10_2 = e3
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | REDUCE: (59), (126) imply:
% 117.27/18.28 | | | | | (127) $false
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | CLOSE: (127) is inconsistent.
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | Case 2:
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | (128) ~ (all_58_0 = e3)
% 117.27/18.28 | | | | | (129) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | BETA: splitting (129) gives:
% 117.27/18.28 | | | | |
% 117.27/18.28 | | | | | Case 1:
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | (130) all_58_1 = e3
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | COMBINE_EQS: (70), (130) imply:
% 117.27/18.28 | | | | | | (131) all_52_4 = e3
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | REDUCE: (124), (131) imply:
% 117.27/18.28 | | | | | | (132) $false
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | CLOSE: (132) is inconsistent.
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | Case 2:
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | (133) all_58_4 = e3 | all_58_9 = e3
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | BETA: splitting (133) gives:
% 117.27/18.28 | | | | | |
% 117.27/18.28 | | | | | | Case 1:
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | (134) all_58_4 = e3
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | COMBINE_EQS: (35), (134) imply:
% 117.27/18.28 | | | | | | | (135) all_52_8 = e3
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | REDUCE: (97), (135) imply:
% 117.27/18.28 | | | | | | | (136) ~ (all_52_9 = e3)
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | SIMP: (136) implies:
% 117.27/18.28 | | | | | | | (137) ~ (all_52_9 = e3)
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | REDUCE: (101), (135) imply:
% 117.27/18.28 | | | | | | | (138) ~ (all_52_12 = e3)
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | SIMP: (138) implies:
% 117.27/18.28 | | | | | | | (139) ~ (all_52_12 = e3)
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | REDUCE: (1), (135) imply:
% 117.27/18.28 | | | | | | | (140) ~ (all_10_2 = e3)
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | BETA: splitting (95) gives:
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | Case 1:
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | | (141) all_54_6 = e3
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | | REF_CLOSE: (40), (137), (141) are inconsistent by sub-proof
% 117.27/18.28 | | | | | | | | #268.
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | Case 2:
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | | (142) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | | BETA: splitting (142) gives:
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | | Case 1:
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | (143) all_54_6 = e2
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | COMBINE_EQS: (40), (143) imply:
% 117.27/18.28 | | | | | | | | | (144) all_52_9 = e2
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | SIMP: (144) implies:
% 117.27/18.28 | | | | | | | | | (145) all_52_9 = e2
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | REDUCE: (82), (145) imply:
% 117.27/18.28 | | | | | | | | | (146) ~ (all_6_2 = e2)
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | SIMP: (146) implies:
% 117.27/18.28 | | | | | | | | | (147) ~ (all_6_2 = e2)
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | REF_CLOSE: (1), (10), (18), (19), (25), (26), (28), (30),
% 117.27/18.28 | | | | | | | | | (31), (32), (34), (35), (50), (53), (87), (89),
% 117.27/18.28 | | | | | | | | | (100), (102), (112), (113), (133), (139), (147) are
% 117.27/18.28 | | | | | | | | | inconsistent by sub-proof #412.
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | Case 2:
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | (148) ~ (all_54_6 = e2)
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | REDUCE: (40), (148) imply:
% 117.27/18.28 | | | | | | | | | (149) ~ (all_52_9 = e2)
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | BETA: splitting (106) gives:
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | | Case 1:
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | (150) all_58_2 = e2
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | COMBINE_EQS: (57), (150) imply:
% 117.27/18.28 | | | | | | | | | | (151) all_52_1 = e2
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | SIMP: (151) implies:
% 117.27/18.28 | | | | | | | | | | (152) all_52_1 = e2
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | REDUCE: (62), (152) imply:
% 117.27/18.28 | | | | | | | | | | (153) ~ (all_10_2 = e2)
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | SIMP: (153) implies:
% 117.27/18.28 | | | | | | | | | | (154) ~ (all_10_2 = e2)
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | REF_CLOSE: (12), (13), (20), (21), (31), (33), (59), (67),
% 117.27/18.28 | | | | | | | | | | (69), (85), (104), (116), (139), (154) are
% 117.27/18.28 | | | | | | | | | | inconsistent by sub-proof #446.
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | Case 2:
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | (155) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | | REF_CLOSE: (39), (51), (65), (78), (122), (149), (155) are
% 117.27/18.28 | | | | | | | | | | inconsistent by sub-proof #401.
% 117.27/18.28 | | | | | | | | | |
% 117.27/18.28 | | | | | | | | | End of split
% 117.27/18.28 | | | | | | | | |
% 117.27/18.28 | | | | | | | | End of split
% 117.27/18.28 | | | | | | | |
% 117.27/18.28 | | | | | | | End of split
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | Case 2:
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | (156) all_58_9 = e3
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | COMBINE_EQS: (89), (156) imply:
% 117.27/18.28 | | | | | | | (157) all_52_12 = e3
% 117.27/18.28 | | | | | | |
% 117.27/18.28 | | | | | | | COMBINE_EQS: (38), (157) imply:
% 117.27/18.28 | | | | | | | (158) all_56_2 = e3
% 117.27/18.28 | | | | | | |
% 117.27/18.29 | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (12), (15), (16), (22), (24),
% 117.27/18.29 | | | | | | | (27), (30), (31), (32), (37), (39), (41), (44), (45),
% 117.27/18.29 | | | | | | | (46), (49), (51), (52), (55), (56), (57), (59), (60),
% 117.27/18.29 | | | | | | | (62), (65), (67), (70), (73), (74), (75), (78), (80),
% 117.27/18.29 | | | | | | | (81), (85), (86), (88), (90), (91), (96), (103), (104),
% 117.27/18.29 | | | | | | | (106), (107), (108), (109), (110), (112), (116), (158)
% 117.27/18.29 | | | | | | | are inconsistent by sub-proof #356.
% 117.27/18.29 | | | | | | |
% 117.27/18.29 | | | | | | End of split
% 117.27/18.29 | | | | | |
% 117.27/18.29 | | | | | End of split
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | End of split
% 117.27/18.29 | | | |
% 117.27/18.29 | | | Case 2:
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | (159) ~ (all_56_15 = e2)
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | REDUCE: (119), (159) imply:
% 117.27/18.29 | | | | (160) $false
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | CLOSE: (160) is inconsistent.
% 117.27/18.29 | | | |
% 117.27/18.29 | | | End of split
% 117.27/18.29 | | |
% 117.27/18.29 | | End of split
% 117.27/18.29 | |
% 117.27/18.29 | Case 2:
% 117.27/18.29 | |
% 117.27/18.29 | | (161) all_56_12 = e1
% 117.27/18.29 | |
% 117.27/18.29 | | COMBINE_EQS: (24), (161) imply:
% 117.27/18.29 | | (162) all_10_2 = e1
% 117.27/18.29 | |
% 117.27/18.29 | | SIMP: (162) implies:
% 117.27/18.29 | | (163) all_10_2 = e1
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (1), (163) imply:
% 117.27/18.29 | | (164) ~ (all_52_8 = e1)
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (21), (163) imply:
% 117.27/18.29 | | (165) ~ (all_52_12 = e1)
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (44), (163) imply:
% 117.27/18.29 | | (166) op(all_10_1, e1) = all_10_0
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (67), (163) imply:
% 117.27/18.29 | | (167) op(e3, e1) = all_10_1
% 117.27/18.29 | |
% 117.27/18.29 | | REF_CLOSE: (3), (5), (6), (8), (11), (13), (14), (17), (20), (23), (29),
% 117.27/18.29 | | (31), (35), (36), (38), (39), (41), (43), (47), (48), (51), (57),
% 117.27/18.29 | | (58), (63), (65), (66), (69), (71), (72), (73), (75), (76), (77),
% 117.27/18.29 | | (78), (83), (84), (86), (88), (92), (94), (98), (101), (106),
% 117.27/18.29 | | (111), (112), (114), (161), (164), (165), (166), (167) are
% 117.27/18.29 | | inconsistent by sub-proof #282.
% 117.27/18.29 | |
% 117.27/18.29 | End of split
% 117.27/18.29 |
% 117.27/18.29 End of proof
% 117.27/18.29
% 117.27/18.29 Sub-proof #268 shows that the following formulas are inconsistent:
% 117.27/18.29 ----------------------------------------------------------------
% 117.27/18.29 (1) all_54_6 = all_52_9
% 117.27/18.29 (2) all_54_6 = e3
% 117.27/18.29 (3) ~ (all_52_9 = e3)
% 117.27/18.29
% 117.27/18.29 Begin of proof
% 117.27/18.29 |
% 117.27/18.29 | COMBINE_EQS: (1), (2) imply:
% 117.27/18.29 | (4) all_52_9 = e3
% 117.27/18.29 |
% 117.27/18.29 | SIMP: (4) implies:
% 117.27/18.29 | (5) all_52_9 = e3
% 117.27/18.29 |
% 117.27/18.29 | REDUCE: (3), (5) imply:
% 117.27/18.29 | (6) $false
% 117.27/18.29 |
% 117.27/18.29 | CLOSE: (6) is inconsistent.
% 117.27/18.29 |
% 117.27/18.29 End of proof
% 117.27/18.29
% 117.27/18.29 Sub-proof #269 shows that the following formulas are inconsistent:
% 117.27/18.29 ----------------------------------------------------------------
% 117.27/18.29 (1) ~ (all_52_6 = all_52_14)
% 117.27/18.29 (2) all_58_7 = all_52_6
% 117.27/18.29 (3) all_28_1 = all_6_1
% 117.27/18.29 (4) ~ (all_52_13 = all_52_14)
% 117.27/18.29 (5) all_56_14 = all_6_2
% 117.27/18.29 (6) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.29 (7) all_56_3 = all_52_1
% 117.27/18.29 (8) all_58_0 = all_10_2
% 117.27/18.29 (9) all_54_11 = all_52_14
% 117.27/18.29 (10) ~ (all_52_14 = all_6_2)
% 117.27/18.29 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.29 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.29 (13) ~ (all_52_2 = all_6_2)
% 117.27/18.29 (14) all_54_10 = all_6_2
% 117.27/18.29 (15) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.29 (16) all_58_3 = all_8_2
% 117.27/18.29 (17) all_58_11 = all_52_14
% 117.27/18.29 (18) all_28_2 = all_6_2
% 117.27/18.29 (19) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.29 (20) all_56_15 = e1
% 117.27/18.29 (21) op(e1, e0) = all_52_14
% 117.27/18.29 (22) all_58_5 = all_52_9
% 117.27/18.29 (23) ~ (all_52_9 = all_52_13)
% 117.27/18.29 (24) op(e1, all_6_2) = all_6_1
% 117.27/18.29 (25) all_58_2 = all_52_1
% 117.27/18.29 (26) ~ (all_10_2 = e3)
% 117.27/18.29 (27) ~ (all_52_14 = all_4_2)
% 117.27/18.29 (28) all_58_6 = all_52_2
% 117.27/18.29 (29) all_56_15 = all_4_2
% 117.27/18.29 (30) all_58_10 = all_52_13
% 117.27/18.29 (31) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.29 (32) ~ (all_8_2 = e2)
% 117.27/18.29 (33) ~ (all_6_2 = e2)
% 117.27/18.29 (34) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.29 (35) all_58_8 = all_6_2
% 117.27/18.29 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.29 (37) all_56_4 = all_52_9
% 117.27/18.29 (38) all_56_5 = all_52_13
% 117.27/18.29 (39) ~ (all_52_6 = all_6_2)
% 117.27/18.29 (40) all_56_6 = all_52_2
% 117.27/18.29 (41) ~ (all_52_13 = all_4_2)
% 117.27/18.29 (42) ~ (all_52_2 = all_52_14)
% 117.27/18.29 (43) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.27/18.29 (44) op(e1, e3) = all_52_2
% 117.27/18.29 (45) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.29 (46) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.29 (47) ~ (all_6_2 = e1)
% 117.27/18.29 (48) ~ (all_6_1 = e2)
% 117.27/18.29 (49) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.27/18.29
% 117.27/18.29 Begin of proof
% 117.27/18.29 |
% 117.27/18.29 | COMBINE_EQS: (20), (29) imply:
% 117.27/18.29 | (50) all_4_2 = e1
% 117.27/18.29 |
% 117.27/18.29 | SIMP: (50) implies:
% 117.27/18.29 | (51) all_4_2 = e1
% 117.27/18.29 |
% 117.27/18.29 | REDUCE: (41), (51) imply:
% 117.27/18.29 | (52) ~ (all_52_13 = e1)
% 117.27/18.29 |
% 117.27/18.29 | REDUCE: (27), (51) imply:
% 117.27/18.29 | (53) ~ (all_52_14 = e1)
% 117.27/18.29 |
% 117.27/18.29 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 117.27/18.29 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 117.27/18.29 | (24), (25), (26), (28), (30), (31), (32), (33), (34), (35), (36),
% 117.27/18.29 | (37), (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 117.27/18.29 | (49), (52), (53) are inconsistent by sub-proof #270.
% 117.27/18.29 |
% 117.27/18.29 End of proof
% 117.27/18.29
% 117.27/18.29 Sub-proof #270 shows that the following formulas are inconsistent:
% 117.27/18.29 ----------------------------------------------------------------
% 117.27/18.29 (1) ~ (all_52_6 = all_52_14)
% 117.27/18.29 (2) all_58_7 = all_52_6
% 117.27/18.29 (3) all_28_1 = all_6_1
% 117.27/18.29 (4) ~ (all_52_13 = all_52_14)
% 117.27/18.29 (5) all_56_14 = all_6_2
% 117.27/18.29 (6) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.29 (7) all_56_3 = all_52_1
% 117.27/18.29 (8) all_58_0 = all_10_2
% 117.27/18.29 (9) all_54_11 = all_52_14
% 117.27/18.29 (10) ~ (all_52_14 = all_6_2)
% 117.27/18.29 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.29 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.29 (13) ~ (all_52_2 = all_6_2)
% 117.27/18.29 (14) all_54_10 = all_6_2
% 117.27/18.29 (15) ~ (all_52_14 = e1)
% 117.27/18.29 (16) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.29 (17) all_58_3 = all_8_2
% 117.27/18.29 (18) all_58_11 = all_52_14
% 117.27/18.29 (19) all_28_2 = all_6_2
% 117.27/18.29 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.29 (21) all_56_15 = e1
% 117.27/18.29 (22) op(e1, e0) = all_52_14
% 117.27/18.29 (23) all_58_5 = all_52_9
% 117.27/18.29 (24) ~ (all_52_9 = all_52_13)
% 117.27/18.29 (25) op(e1, all_6_2) = all_6_1
% 117.27/18.29 (26) all_58_2 = all_52_1
% 117.27/18.29 (27) ~ (all_10_2 = e3)
% 117.27/18.29 (28) all_58_6 = all_52_2
% 117.27/18.29 (29) ~ (all_52_13 = e1)
% 117.27/18.29 (30) all_58_10 = all_52_13
% 117.27/18.29 (31) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.29 (32) ~ (all_8_2 = e2)
% 117.27/18.29 (33) ~ (all_6_2 = e2)
% 117.27/18.29 (34) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.29 (35) all_58_8 = all_6_2
% 117.27/18.29 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.29 (37) all_56_4 = all_52_9
% 117.27/18.29 (38) all_56_5 = all_52_13
% 117.27/18.29 (39) ~ (all_52_6 = all_6_2)
% 117.27/18.29 (40) all_56_6 = all_52_2
% 117.27/18.29 (41) ~ (all_52_2 = all_52_14)
% 117.27/18.29 (42) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.27/18.29 (43) op(e1, e3) = all_52_2
% 117.27/18.29 (44) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.29 (45) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.29 (46) ~ (all_6_2 = e1)
% 117.27/18.29 (47) ~ (all_6_1 = e2)
% 117.27/18.29 (48) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.27/18.29
% 117.27/18.29 Begin of proof
% 117.27/18.29 |
% 117.27/18.29 | BETA: splitting (42) gives:
% 117.27/18.29 |
% 117.27/18.29 | Case 1:
% 117.27/18.29 | |
% 117.27/18.29 | | (49) ~ (all_56_4 = e2)
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (37), (49) imply:
% 117.27/18.29 | | (50) ~ (all_52_9 = e2)
% 117.27/18.29 | |
% 117.27/18.29 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 117.27/18.29 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 117.27/18.29 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 117.27/18.29 | | (36), (38), (39), (40), (41), (43), (44), (45), (46), (47), (48),
% 117.27/18.29 | | (50) are inconsistent by sub-proof #271.
% 117.27/18.29 | |
% 117.27/18.29 | Case 2:
% 117.27/18.29 | |
% 117.27/18.29 | | (51) ~ (all_56_15 = e1)
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (21), (51) imply:
% 117.27/18.29 | | (52) $false
% 117.27/18.29 | |
% 117.27/18.29 | | CLOSE: (52) is inconsistent.
% 117.27/18.29 | |
% 117.27/18.29 | End of split
% 117.27/18.29 |
% 117.27/18.29 End of proof
% 117.27/18.29
% 117.27/18.29 Sub-proof #271 shows that the following formulas are inconsistent:
% 117.27/18.29 ----------------------------------------------------------------
% 117.27/18.29 (1) ~ (all_52_6 = all_52_14)
% 117.27/18.29 (2) ~ (all_52_9 = e2)
% 117.27/18.29 (3) all_58_7 = all_52_6
% 117.27/18.29 (4) all_28_1 = all_6_1
% 117.27/18.29 (5) ~ (all_52_13 = all_52_14)
% 117.27/18.29 (6) all_56_14 = all_6_2
% 117.27/18.29 (7) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.27/18.29 (8) all_56_3 = all_52_1
% 117.27/18.29 (9) all_58_0 = all_10_2
% 117.27/18.29 (10) all_54_11 = all_52_14
% 117.27/18.29 (11) ~ (all_52_14 = all_6_2)
% 117.27/18.29 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.29 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.29 (14) ~ (all_52_2 = all_6_2)
% 117.27/18.29 (15) all_54_10 = all_6_2
% 117.27/18.29 (16) ~ (all_52_14 = e1)
% 117.27/18.29 (17) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.27/18.29 (18) all_58_3 = all_8_2
% 117.27/18.29 (19) all_58_11 = all_52_14
% 117.27/18.29 (20) all_28_2 = all_6_2
% 117.27/18.29 (21) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.29 (22) op(e1, e0) = all_52_14
% 117.27/18.29 (23) all_58_5 = all_52_9
% 117.27/18.29 (24) ~ (all_52_9 = all_52_13)
% 117.27/18.29 (25) op(e1, all_6_2) = all_6_1
% 117.27/18.29 (26) all_58_2 = all_52_1
% 117.27/18.29 (27) ~ (all_10_2 = e3)
% 117.27/18.29 (28) all_58_6 = all_52_2
% 117.27/18.29 (29) ~ (all_52_13 = e1)
% 117.27/18.29 (30) all_58_10 = all_52_13
% 117.27/18.29 (31) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.27/18.29 (32) ~ (all_8_2 = e2)
% 117.27/18.29 (33) ~ (all_6_2 = e2)
% 117.27/18.29 (34) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.29 (35) all_58_8 = all_6_2
% 117.27/18.29 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.27/18.29 (37) all_56_5 = all_52_13
% 117.27/18.29 (38) ~ (all_52_6 = all_6_2)
% 117.27/18.29 (39) all_56_6 = all_52_2
% 117.27/18.29 (40) ~ (all_52_2 = all_52_14)
% 117.27/18.29 (41) op(e1, e3) = all_52_2
% 117.27/18.29 (42) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.27/18.29 (43) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.29 (44) ~ (all_6_2 = e1)
% 117.27/18.29 (45) ~ (all_6_1 = e2)
% 117.27/18.29 (46) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.27/18.29
% 117.27/18.29 Begin of proof
% 117.27/18.29 |
% 117.27/18.29 | BETA: splitting (17) gives:
% 117.27/18.29 |
% 117.27/18.29 | Case 1:
% 117.27/18.29 | |
% 117.27/18.29 | | (47) ~ (all_56_6 = e1)
% 117.27/18.29 | |
% 117.27/18.29 | | REDUCE: (39), (47) imply:
% 117.27/18.29 | | (48) ~ (all_52_2 = e1)
% 117.27/18.29 | |
% 117.27/18.29 | | BETA: splitting (34) gives:
% 117.27/18.29 | |
% 117.27/18.29 | | Case 1:
% 117.27/18.29 | | |
% 117.27/18.29 | | | (49) all_58_6 = e1
% 117.27/18.29 | | |
% 117.27/18.29 | | | REF_CLOSE: (28), (48), (49) are inconsistent by sub-proof #452.
% 117.27/18.29 | | |
% 117.27/18.29 | | Case 2:
% 117.27/18.29 | | |
% 117.27/18.29 | | | (50) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.27/18.29 | | |
% 117.27/18.29 | | | BETA: splitting (50) gives:
% 117.27/18.29 | | |
% 117.27/18.29 | | | Case 1:
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | (51) all_58_7 = e1
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | COMBINE_EQS: (3), (51) imply:
% 117.27/18.29 | | | | (52) all_52_6 = e1
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | REDUCE: (1), (52) imply:
% 117.27/18.29 | | | | (53) ~ (all_52_14 = e1)
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | REDUCE: (38), (52) imply:
% 117.27/18.29 | | | | (54) ~ (all_6_2 = e1)
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | BETA: splitting (43) gives:
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | Case 1:
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | | (55) all_58_2 = e2
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 117.27/18.29 | | | | | (16), (20), (22), (25), (26), (27), (31), (33), (36), (42),
% 117.27/18.29 | | | | | (44), (45), (55) are inconsistent by sub-proof #276.
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | Case 2:
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | | (56) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | | REF_CLOSE: (2), (5), (6), (12), (13), (14), (15), (18), (19), (21),
% 117.27/18.29 | | | | | (23), (24), (25), (28), (29), (30), (32), (33), (35), (37),
% 117.27/18.29 | | | | | (41), (44), (45), (46), (51), (56) are inconsistent by
% 117.27/18.29 | | | | | sub-proof #272.
% 117.27/18.29 | | | | |
% 117.27/18.29 | | | | End of split
% 117.27/18.29 | | | |
% 117.27/18.29 | | | Case 2:
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | (57) all_58_8 = e1 | all_58_11 = e1
% 117.27/18.29 | | | |
% 117.27/18.29 | | | | REF_CLOSE: (16), (19), (35), (44), (57) are inconsistent by sub-proof
% 117.27/18.29 | | | | #445.
% 117.27/18.29 | | | |
% 117.27/18.29 | | | End of split
% 117.27/18.29 | | |
% 117.27/18.29 | | End of split
% 117.27/18.29 | |
% 117.27/18.29 | Case 2:
% 117.27/18.29 | |
% 117.27/18.30 | | (58) all_56_6 = e1
% 117.27/18.30 | | (59) ~ (all_56_14 = e3)
% 117.27/18.30 | |
% 117.27/18.30 | | COMBINE_EQS: (39), (58) imply:
% 117.27/18.30 | | (60) all_52_2 = e1
% 117.27/18.30 | |
% 117.27/18.30 | | REDUCE: (6), (59) imply:
% 117.27/18.30 | | (61) ~ (all_6_2 = e3)
% 117.27/18.30 | |
% 117.27/18.30 | | REDUCE: (40), (60) imply:
% 117.27/18.30 | | (62) ~ (all_52_14 = e1)
% 117.27/18.30 | |
% 117.27/18.30 | | REDUCE: (14), (60) imply:
% 117.27/18.30 | | (63) ~ (all_6_2 = e1)
% 117.27/18.30 | |
% 117.27/18.30 | | REF_CLOSE: (4), (7), (9), (10), (11), (12), (13), (15), (16), (20), (22),
% 117.27/18.30 | | (25), (27), (33), (36), (42), (44), (45), (61) are inconsistent
% 117.27/18.30 | | by sub-proof #277.
% 117.27/18.30 | |
% 117.27/18.30 | End of split
% 117.27/18.30 |
% 117.27/18.30 End of proof
% 117.27/18.30
% 117.27/18.30 Sub-proof #272 shows that the following formulas are inconsistent:
% 117.27/18.30 ----------------------------------------------------------------
% 117.27/18.30 (1) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.27/18.30 (2) ~ (all_52_9 = e2)
% 117.27/18.30 (3) ~ (all_52_13 = all_52_14)
% 117.27/18.30 (4) all_58_7 = e1
% 117.27/18.30 (5) all_56_14 = all_6_2
% 117.27/18.30 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.27/18.30 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.27/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.27/18.30 (8) ~ (all_52_2 = all_6_2)
% 117.27/18.30 (9) all_54_10 = all_6_2
% 117.27/18.30 (10) all_58_3 = all_8_2
% 117.27/18.30 (11) all_58_11 = all_52_14
% 117.27/18.30 (12) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.27/18.30 (13) all_58_5 = all_52_9
% 117.27/18.30 (14) ~ (all_52_9 = all_52_13)
% 117.27/18.30 (15) op(e1, all_6_2) = all_6_1
% 117.27/18.30 (16) all_58_6 = all_52_2
% 117.27/18.30 (17) ~ (all_52_13 = e1)
% 117.27/18.30 (18) all_58_10 = all_52_13
% 117.27/18.30 (19) ~ (all_8_2 = e2)
% 117.27/18.30 (20) ~ (all_6_2 = e2)
% 117.27/18.30 (21) all_58_8 = all_6_2
% 117.27/18.30 (22) all_56_5 = all_52_13
% 117.27/18.30 (23) op(e1, e3) = all_52_2
% 117.27/18.30 (24) ~ (all_6_2 = e1)
% 117.27/18.30 (25) ~ (all_6_1 = e2)
% 117.27/18.30 (26) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.27/18.30
% 117.27/18.30 Begin of proof
% 117.27/18.30 |
% 117.27/18.30 | BETA: splitting (1) gives:
% 117.27/18.30 |
% 117.27/18.30 | Case 1:
% 117.27/18.30 | |
% 117.27/18.30 | | (27) all_58_3 = e2
% 117.27/18.30 | |
% 117.27/18.30 | | COMBINE_EQS: (10), (27) imply:
% 117.27/18.30 | | (28) all_8_2 = e2
% 117.27/18.30 | |
% 117.27/18.30 | | REDUCE: (19), (28) imply:
% 117.27/18.30 | | (29) $false
% 117.27/18.30 | |
% 117.27/18.30 | | CLOSE: (29) is inconsistent.
% 117.27/18.30 | |
% 117.27/18.30 | Case 2:
% 117.27/18.30 | |
% 117.27/18.30 | | (30) all_58_5 = e2 | all_58_10 = e2
% 117.27/18.30 | |
% 117.27/18.30 | | BETA: splitting (30) gives:
% 117.27/18.30 | |
% 117.27/18.30 | | Case 1:
% 117.27/18.30 | | |
% 117.27/18.30 | | | (31) all_58_5 = e2
% 117.27/18.30 | | |
% 117.27/18.30 | | | COMBINE_EQS: (13), (31) imply:
% 117.27/18.30 | | | (32) all_52_9 = e2
% 117.27/18.30 | | |
% 117.27/18.30 | | | REDUCE: (2), (32) imply:
% 117.27/18.30 | | | (33) $false
% 117.27/18.30 | | |
% 117.27/18.30 | | | CLOSE: (33) is inconsistent.
% 117.27/18.30 | | |
% 117.27/18.30 | | Case 2:
% 117.27/18.30 | | |
% 117.27/18.30 | | | (34) all_58_10 = e2
% 117.27/18.30 | | |
% 117.27/18.30 | | | COMBINE_EQS: (18), (34) imply:
% 117.27/18.30 | | | (35) all_52_13 = e2
% 117.27/18.30 | | |
% 117.27/18.30 | | | COMBINE_EQS: (22), (35) imply:
% 117.27/18.30 | | | (36) all_56_5 = e2
% 117.27/18.30 | | |
% 117.27/18.30 | | | REDUCE: (3), (35) imply:
% 117.27/18.30 | | | (37) ~ (all_52_14 = e2)
% 117.27/18.30 | | |
% 117.27/18.30 | | | SIMP: (37) implies:
% 117.27/18.30 | | | (38) ~ (all_52_14 = e2)
% 117.27/18.30 | | |
% 117.27/18.30 | | | REDUCE: (17), (35) imply:
% 117.27/18.30 | | | (39) ~ (e2 = e1)
% 117.27/18.30 | | |
% 117.27/18.30 | | | BETA: splitting (26) gives:
% 117.27/18.30 | | |
% 117.27/18.30 | | | Case 1:
% 117.27/18.30 | | | |
% 117.27/18.30 | | | | (40) all_58_6 = e2
% 117.27/18.30 | | | |
% 117.27/18.30 | | | | COMBINE_EQS: (16), (40) imply:
% 117.54/18.30 | | | | (41) all_52_2 = e2
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | SIMP: (41) implies:
% 117.54/18.30 | | | | (42) all_52_2 = e2
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | REDUCE: (8), (42) imply:
% 117.54/18.30 | | | | (43) ~ (all_6_2 = e2)
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | REDUCE: (23), (42) imply:
% 117.54/18.30 | | | | (44) op(e1, e3) = e2
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | BETA: splitting (6) gives:
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | Case 1:
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | (45) all_54_10 = e3
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | COMBINE_EQS: (9), (45) imply:
% 117.54/18.30 | | | | | (46) all_6_2 = e3
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | SIMP: (46) implies:
% 117.54/18.30 | | | | | (47) all_6_2 = e3
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | REDUCE: (15), (47) imply:
% 117.54/18.30 | | | | | (48) op(e1, e3) = all_6_1
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | REF_CLOSE: (7), (25), (44), (48) are inconsistent by sub-proof #398.
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | Case 2:
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | (49) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | | REF_CLOSE: (2), (5), (9), (12), (13), (18), (20), (22), (24), (30),
% 117.54/18.30 | | | | | (49) are inconsistent by sub-proof #433.
% 117.54/18.30 | | | | |
% 117.54/18.30 | | | | End of split
% 117.54/18.30 | | | |
% 117.54/18.30 | | | Case 2:
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | (50) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.30 | | | |
% 117.54/18.30 | | | | REF_CLOSE: (4), (5), (6), (9), (11), (12), (20), (21), (24), (36), (38),
% 117.54/18.30 | | | | (39), (50) are inconsistent by sub-proof #273.
% 117.54/18.30 | | | |
% 117.54/18.30 | | | End of split
% 117.54/18.30 | | |
% 117.54/18.30 | | End of split
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #273 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_58_7 = e1
% 117.54/18.30 (2) all_56_14 = all_6_2
% 117.54/18.30 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 (4) all_54_10 = all_6_2
% 117.54/18.30 (5) ~ (e2 = e1)
% 117.54/18.30 (6) all_58_11 = all_52_14
% 117.54/18.30 (7) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.54/18.30 (8) all_56_5 = e2
% 117.54/18.30 (9) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.30 (10) ~ (all_52_14 = e2)
% 117.54/18.30 (11) ~ (all_6_2 = e2)
% 117.54/18.30 (12) all_58_8 = all_6_2
% 117.54/18.30 (13) ~ (all_6_2 = e1)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (7) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (14) ~ (all_56_5 = e2)
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (8), (14) imply:
% 117.54/18.30 | | (15) $false
% 117.54/18.30 | |
% 117.54/18.30 | | CLOSE: (15) is inconsistent.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (16) ~ (all_56_14 = e0)
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (2), (16) imply:
% 117.54/18.30 | | (17) ~ (all_6_2 = e0)
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (13), (17) are
% 117.54/18.30 | | inconsistent by sub-proof #274.
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #274 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_58_7 = e1
% 117.54/18.30 (2) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 (3) all_54_10 = all_6_2
% 117.54/18.30 (4) ~ (e2 = e1)
% 117.54/18.30 (5) all_58_11 = all_52_14
% 117.54/18.30 (6) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.30 (7) ~ (all_52_14 = e2)
% 117.54/18.30 (8) ~ (all_6_2 = e2)
% 117.54/18.30 (9) all_58_8 = all_6_2
% 117.54/18.30 (10) ~ (all_6_2 = e0)
% 117.54/18.30 (11) ~ (all_6_2 = e1)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (2) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (12) all_54_10 = e3
% 117.54/18.30 | |
% 117.54/18.30 | | COMBINE_EQS: (3), (12) imply:
% 117.54/18.30 | | (13) all_6_2 = e3
% 117.54/18.30 | |
% 117.54/18.30 | | SIMP: (13) implies:
% 117.54/18.30 | | (14) all_6_2 = e3
% 117.54/18.30 | |
% 117.54/18.30 | | COMBINE_EQS: (9), (14) imply:
% 117.54/18.30 | | (15) all_58_8 = e3
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (8), (14) imply:
% 117.54/18.30 | | (16) ~ (e3 = e2)
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (1), (4), (5), (6), (7), (15), (16) are inconsistent by sub-proof
% 117.54/18.30 | | #275.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (17) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (3), (8), (10), (11), (17) are inconsistent by sub-proof #435.
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #275 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_58_7 = e1
% 117.54/18.30 (2) ~ (e2 = e1)
% 117.54/18.30 (3) all_58_11 = all_52_14
% 117.54/18.30 (4) all_58_8 = e3
% 117.54/18.30 (5) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.30 (6) ~ (all_52_14 = e2)
% 117.54/18.30 (7) ~ (e3 = e2)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (5) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (8) all_58_7 = e2
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #346.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (9) all_58_8 = e2 | all_58_11 = e2
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (3), (4), (6), (7), (9) are inconsistent by sub-proof #345.
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #276 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_28_1 = all_6_1
% 117.54/18.30 (2) all_56_14 = all_6_2
% 117.54/18.30 (3) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.54/18.30 (4) all_56_3 = all_52_1
% 117.54/18.30 (5) all_58_0 = all_10_2
% 117.54/18.30 (6) all_54_11 = all_52_14
% 117.54/18.30 (7) ~ (all_52_14 = all_6_2)
% 117.54/18.30 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.30 (10) all_54_10 = all_6_2
% 117.54/18.30 (11) ~ (all_52_14 = e1)
% 117.54/18.30 (12) all_28_2 = all_6_2
% 117.54/18.30 (13) op(e1, e0) = all_52_14
% 117.54/18.30 (14) op(e1, all_6_2) = all_6_1
% 117.54/18.30 (15) all_58_2 = all_52_1
% 117.54/18.30 (16) ~ (all_10_2 = e3)
% 117.54/18.30 (17) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.54/18.30 (18) ~ (all_6_2 = e2)
% 117.54/18.30 (19) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.30 (20) all_58_2 = e2
% 117.54/18.30 (21) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.30 (22) ~ (all_6_2 = e1)
% 117.54/18.30 (23) ~ (all_6_1 = e2)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | COMBINE_EQS: (15), (20) imply:
% 117.54/18.30 | (24) all_52_1 = e2
% 117.54/18.30 |
% 117.54/18.30 | COMBINE_EQS: (4), (24) imply:
% 117.54/18.30 | (25) all_56_3 = e2
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (17) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (26) ~ (all_56_3 = e2)
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (25), (26) imply:
% 117.54/18.30 | | (27) $false
% 117.54/18.30 | |
% 117.54/18.30 | | CLOSE: (27) is inconsistent.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (28) ~ (all_56_14 = e3)
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (2), (28) imply:
% 117.54/18.30 | | (29) ~ (all_6_2 = e3)
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 117.54/18.30 | | (16), (18), (19), (21), (22), (23), (29) are inconsistent by
% 117.54/18.30 | | sub-proof #277.
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #277 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_28_1 = all_6_1
% 117.54/18.30 (2) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.54/18.30 (3) all_58_0 = all_10_2
% 117.54/18.30 (4) all_54_11 = all_52_14
% 117.54/18.30 (5) ~ (all_52_14 = all_6_2)
% 117.54/18.30 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.30 (8) all_54_10 = all_6_2
% 117.54/18.30 (9) ~ (all_52_14 = e1)
% 117.54/18.30 (10) all_28_2 = all_6_2
% 117.54/18.30 (11) op(e1, e0) = all_52_14
% 117.54/18.30 (12) op(e1, all_6_2) = all_6_1
% 117.54/18.30 (13) ~ (all_10_2 = e3)
% 117.54/18.30 (14) ~ (all_6_2 = e2)
% 117.54/18.30 (15) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.30 (16) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.30 (17) ~ (all_6_2 = e3)
% 117.54/18.30 (18) ~ (all_6_2 = e1)
% 117.54/18.30 (19) ~ (all_6_1 = e2)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (6) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (20) all_54_10 = e3
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (8), (17), (20) are inconsistent by sub-proof #352.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (21) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | BETA: splitting (21) gives:
% 117.54/18.30 | |
% 117.54/18.30 | | Case 1:
% 117.54/18.30 | | |
% 117.54/18.30 | | | (22) all_54_10 = e2
% 117.54/18.30 | | |
% 117.54/18.30 | | | REF_CLOSE: (8), (14), (22) are inconsistent by sub-proof #438.
% 117.54/18.30 | | |
% 117.54/18.30 | | Case 2:
% 117.54/18.30 | | |
% 117.54/18.30 | | | (23) all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 | | |
% 117.54/18.30 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 117.54/18.30 | | | (15), (16), (18), (19), (23) are inconsistent by sub-proof
% 117.54/18.30 | | | #278.
% 117.54/18.30 | | |
% 117.54/18.30 | | End of split
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #278 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_28_1 = all_6_1
% 117.54/18.30 (2) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.54/18.30 (3) all_58_0 = all_10_2
% 117.54/18.30 (4) all_54_11 = all_52_14
% 117.54/18.30 (5) ~ (all_52_14 = all_6_2)
% 117.54/18.30 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.30 (7) all_54_10 = all_6_2
% 117.54/18.30 (8) ~ (all_52_14 = e1)
% 117.54/18.30 (9) all_28_2 = all_6_2
% 117.54/18.30 (10) all_54_10 = e1 | all_54_10 = e0
% 117.54/18.30 (11) op(e1, e0) = all_52_14
% 117.54/18.30 (12) op(e1, all_6_2) = all_6_1
% 117.54/18.30 (13) ~ (all_10_2 = e3)
% 117.54/18.30 (14) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.30 (15) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.30 (16) ~ (all_6_2 = e1)
% 117.54/18.30 (17) ~ (all_6_1 = e2)
% 117.54/18.30
% 117.54/18.30 Begin of proof
% 117.54/18.30 |
% 117.54/18.30 | BETA: splitting (10) gives:
% 117.54/18.30 |
% 117.54/18.30 | Case 1:
% 117.54/18.30 | |
% 117.54/18.30 | | (18) all_54_10 = e1
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (7), (16), (18) are inconsistent by sub-proof #437.
% 117.54/18.30 | |
% 117.54/18.30 | Case 2:
% 117.54/18.30 | |
% 117.54/18.30 | | (19) all_54_10 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | COMBINE_EQS: (7), (19) imply:
% 117.54/18.30 | | (20) all_6_2 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | SIMP: (20) implies:
% 117.54/18.30 | | (21) all_6_2 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | COMBINE_EQS: (9), (21) imply:
% 117.54/18.30 | | (22) all_28_2 = e0
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (5), (21) imply:
% 117.54/18.30 | | (23) ~ (all_52_14 = e0)
% 117.54/18.30 | |
% 117.54/18.30 | | REDUCE: (12), (21) imply:
% 117.54/18.30 | | (24) op(e1, e0) = all_6_1
% 117.54/18.30 | |
% 117.54/18.30 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (11), (13), (14), (15), (17), (22),
% 117.54/18.30 | | (23), (24) are inconsistent by sub-proof #279.
% 117.54/18.30 | |
% 117.54/18.30 | End of split
% 117.54/18.30 |
% 117.54/18.30 End of proof
% 117.54/18.30
% 117.54/18.30 Sub-proof #279 shows that the following formulas are inconsistent:
% 117.54/18.30 ----------------------------------------------------------------
% 117.54/18.30 (1) all_28_1 = all_6_1
% 117.54/18.31 (2) ~ (all_28_1 = e3) | ~ (all_28_2 = e0)
% 117.54/18.31 (3) ~ (all_52_14 = e0)
% 117.54/18.31 (4) all_58_0 = all_10_2
% 117.54/18.31 (5) all_54_11 = all_52_14
% 117.54/18.31 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.31 (7) op(e1, e0) = all_6_1
% 117.54/18.31 (8) ~ (all_52_14 = e1)
% 117.54/18.31 (9) op(e1, e0) = all_52_14
% 117.54/18.31 (10) ~ (all_10_2 = e3)
% 117.54/18.31 (11) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.31 (12) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.31 (13) all_28_2 = e0
% 117.54/18.31 (14) ~ (all_6_1 = e2)
% 117.54/18.31
% 117.54/18.31 Begin of proof
% 117.54/18.31 |
% 117.54/18.31 | BETA: splitting (2) gives:
% 117.54/18.31 |
% 117.54/18.31 | Case 1:
% 117.54/18.31 | |
% 117.54/18.31 | | (15) ~ (all_28_1 = e3)
% 117.54/18.31 | |
% 117.54/18.31 | | REDUCE: (1), (15) imply:
% 117.54/18.31 | | (16) ~ (all_6_1 = e3)
% 117.54/18.31 | |
% 117.54/18.31 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), (16)
% 117.54/18.31 | | are inconsistent by sub-proof #415.
% 117.54/18.31 | |
% 117.54/18.31 | Case 2:
% 117.54/18.31 | |
% 117.54/18.31 | | (17) ~ (all_28_2 = e0)
% 117.54/18.31 | |
% 117.54/18.31 | | REDUCE: (13), (17) imply:
% 117.54/18.31 | | (18) $false
% 117.54/18.31 | |
% 117.54/18.31 | | CLOSE: (18) is inconsistent.
% 117.54/18.31 | |
% 117.54/18.31 | End of split
% 117.54/18.31 |
% 117.54/18.31 End of proof
% 117.54/18.31
% 117.54/18.31 Sub-proof #280 shows that the following formulas are inconsistent:
% 117.54/18.31 ----------------------------------------------------------------
% 117.54/18.31 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.31 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.54/18.31 (3) all_54_2 = all_52_8
% 117.54/18.31 (4) all_58_7 = all_52_6
% 117.54/18.31 (5) ~ (all_52_8 = all_52_11)
% 117.54/18.31 (6) ~ (all_52_9 = all_8_2)
% 117.54/18.31 (7) ~ (all_4_2 = e0)
% 117.54/18.31 (8) op(e3, e2) = all_52_4
% 117.54/18.31 (9) all_56_14 = all_6_2
% 117.54/18.31 (10) all_56_3 = all_52_1
% 117.54/18.31 (11) all_54_0 = all_10_2
% 117.54/18.31 (12) all_54_3 = all_52_12
% 117.54/18.31 (13) ~ (all_4_2 = e1)
% 117.54/18.31 (14) op(e0, e2) = all_52_7
% 117.54/18.31 (15) all_56_11 = all_52_11
% 117.54/18.31 (16) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 117.54/18.31 (17) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.31 (18) ~ (all_52_12 = all_10_2)
% 117.54/18.31 (19) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.54/18.31 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.31 (21) all_56_12 = all_10_2
% 117.54/18.31 (22) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.31 (23) all_54_14 = all_52_11
% 117.54/18.31 (24) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.31 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.31 (26) ~ (all_10_2 = e2)
% 117.54/18.31 (27) all_54_10 = all_6_2
% 117.54/18.31 (28) op(e3, e0) = all_52_12
% 117.54/18.31 (29) all_58_4 = all_52_8
% 117.54/18.31 (30) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.31 (31) ~ (all_52_4 = all_52_7)
% 117.54/18.31 (32) all_56_2 = all_52_12
% 117.54/18.31 (33) all_58_3 = all_8_2
% 117.54/18.31 (34) ~ (all_10_0 = e2)
% 117.54/18.31 (35) op(e3, e1) = all_52_8
% 117.54/18.31 (36) op(all_10_1, all_10_2) = all_10_0
% 117.54/18.31 (37) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.54/18.31 (38) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.54/18.31 (39) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.54/18.31 (40) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.54/18.31 (41) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.54/18.31 (42) all_58_5 = all_52_9
% 117.54/18.31 (43) all_56_9 = all_52_3
% 117.54/18.31 (44) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.31 (45) all_58_15 = all_4_2
% 117.54/18.31 (46) all_58_2 = all_52_1
% 117.54/18.31 (47) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.54/18.31 (48) ~ (all_10_2 = e3)
% 117.54/18.31 (49) all_58_13 = all_52_7
% 117.54/18.31 (50) ~ (all_52_1 = all_10_2)
% 117.54/18.31 (51) all_54_5 = all_8_2
% 117.54/18.31 (52) all_58_10 = all_52_13
% 117.54/18.31 (53) ~ (all_52_11 = all_4_2)
% 117.54/18.31 (54) op(e3, all_10_2) = all_10_1
% 117.54/18.31 (55) ~ (all_10_1 = e2)
% 117.54/18.31 (56) all_58_1 = all_52_4
% 117.54/18.31 (57) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.31 (58) ~ (all_52_9 = all_52_11)
% 117.54/18.31 (59) all_58_14 = all_52_11
% 117.54/18.31 (60) all_54_1 = all_52_4
% 117.54/18.31 (61) all_56_13 = all_8_2
% 117.54/18.31 (62) op(e0, e1) = all_52_11
% 117.54/18.31 (63) ~ (all_52_1 = all_8_2)
% 117.54/18.31 (64) ~ (all_8_2 = e2)
% 117.54/18.31 (65) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.54/18.31 (66) all_56_7 = all_52_6
% 117.54/18.31 (67) all_56_1 = all_52_8
% 117.54/18.31 (68) all_58_8 = all_6_2
% 117.54/18.31 (69) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.31 (70) ~ (all_10_0 = e1)
% 117.54/18.31 (71) all_56_4 = all_52_9
% 117.54/18.31 (72) all_56_5 = all_52_13
% 117.54/18.31 (73) ~ (all_52_6 = all_6_2)
% 117.54/18.31 (74) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.54/18.31 (75) ~ (all_52_13 = all_4_2)
% 117.54/18.31 (76) all_58_12 = all_52_3
% 117.54/18.31 (77) ~ (all_52_12 = all_4_2)
% 117.54/18.31 (78) ~ (all_52_8 = all_52_12)
% 117.54/18.31 (79) ~ (all_52_4 = all_10_2)
% 117.54/18.31 (80) ~ (all_10_1 = e1)
% 117.54/18.31 (81) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.31 (82) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.31 (83) all_56_0 = all_52_4
% 117.54/18.31 (84) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.54/18.31 (85) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.31 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.31 (86) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.54/18.31 (87) all_54_15 = all_4_2
% 117.54/18.31 (88) ~ (all_6_2 = e1)
% 117.54/18.31 (89) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.54/18.31
% 117.54/18.31 Begin of proof
% 117.54/18.31 |
% 117.54/18.31 | BETA: splitting (81) gives:
% 117.54/18.31 |
% 117.54/18.31 | Case 1:
% 117.54/18.31 | |
% 117.54/18.31 | | (90) ~ (all_56_12 = e1)
% 117.54/18.31 | |
% 117.54/18.31 | | REDUCE: (21), (90) imply:
% 117.54/18.31 | | (91) ~ (all_10_2 = e1)
% 117.54/18.31 | |
% 117.54/18.31 | | REF_CLOSE: (2), (4), (7), (8), (9), (11), (12), (14), (15), (17), (18),
% 117.54/18.31 | | (19), (21), (22), (24), (25), (26), (27), (28), (31), (32), (33),
% 117.54/18.31 | | (34), (36), (37), (38), (41), (42), (43), (44), (45), (46), (48),
% 117.54/18.31 | | (49), (50), (52), (54), (55), (56), (59), (60), (61), (64), (65),
% 117.54/18.31 | | (66), (69), (70), (71), (72), (73), (76), (79), (80), (82), (83),
% 117.54/18.31 | | (84), (85), (86), (88), (91) are inconsistent by sub-proof #355.
% 117.54/18.31 | |
% 117.54/18.31 | Case 2:
% 117.54/18.31 | |
% 117.54/18.31 | | (92) all_56_12 = e1
% 117.54/18.31 | |
% 117.54/18.31 | | REF_CLOSE: (1), (3), (5), (6), (7), (10), (12), (13), (16), (17), (18),
% 117.54/18.31 | | (20), (21), (23), (25), (29), (30), (32), (33), (34), (35), (36),
% 117.54/18.31 | | (39), (40), (42), (46), (47), (51), (52), (53), (54), (55), (57),
% 117.54/18.31 | | (58), (59), (61), (62), (63), (64), (67), (68), (70), (71), (74),
% 117.54/18.31 | | (75), (77), (78), (82), (87), (88), (89), (92) are inconsistent
% 117.54/18.31 | | by sub-proof #281.
% 117.54/18.31 | |
% 117.54/18.31 | End of split
% 117.54/18.31 |
% 117.54/18.31 End of proof
% 117.54/18.31
% 117.54/18.31 Sub-proof #281 shows that the following formulas are inconsistent:
% 117.54/18.31 ----------------------------------------------------------------
% 117.54/18.31 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.31 (2) all_54_2 = all_52_8
% 117.54/18.31 (3) ~ (all_52_8 = all_52_11)
% 117.54/18.31 (4) ~ (all_52_9 = all_8_2)
% 117.54/18.31 (5) ~ (all_4_2 = e0)
% 117.54/18.31 (6) all_56_3 = all_52_1
% 117.54/18.31 (7) all_54_3 = all_52_12
% 117.54/18.31 (8) ~ (all_4_2 = e1)
% 117.54/18.31 (9) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 117.54/18.31 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.31 (11) ~ (all_52_12 = all_10_2)
% 117.54/18.31 (12) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.31 (13) all_56_12 = all_10_2
% 117.54/18.31 (14) all_54_14 = all_52_11
% 117.54/18.31 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.31 (16) all_58_4 = all_52_8
% 117.54/18.31 (17) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.31 (18) all_56_2 = all_52_12
% 117.54/18.31 (19) all_58_3 = all_8_2
% 117.54/18.31 (20) ~ (all_10_0 = e2)
% 117.54/18.31 (21) op(e3, e1) = all_52_8
% 117.54/18.31 (22) op(all_10_1, all_10_2) = all_10_0
% 117.54/18.31 (23) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.54/18.31 (24) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.54/18.31 (25) all_58_5 = all_52_9
% 117.54/18.31 (26) all_58_2 = all_52_1
% 117.54/18.31 (27) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.54/18.31 (28) all_54_5 = all_8_2
% 117.54/18.31 (29) all_58_10 = all_52_13
% 117.54/18.31 (30) all_56_12 = e1
% 117.54/18.31 (31) ~ (all_52_11 = all_4_2)
% 117.54/18.31 (32) op(e3, all_10_2) = all_10_1
% 117.54/18.31 (33) ~ (all_10_1 = e2)
% 117.54/18.31 (34) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.31 (35) ~ (all_52_9 = all_52_11)
% 117.54/18.31 (36) all_58_14 = all_52_11
% 117.54/18.31 (37) all_56_13 = all_8_2
% 117.54/18.31 (38) op(e0, e1) = all_52_11
% 117.54/18.31 (39) ~ (all_52_1 = all_8_2)
% 117.54/18.31 (40) ~ (all_8_2 = e2)
% 117.54/18.31 (41) all_56_1 = all_52_8
% 117.54/18.31 (42) all_58_8 = all_6_2
% 117.54/18.31 (43) ~ (all_10_0 = e1)
% 117.54/18.31 (44) all_56_4 = all_52_9
% 117.54/18.31 (45) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.54/18.31 (46) ~ (all_52_13 = all_4_2)
% 117.54/18.31 (47) ~ (all_52_12 = all_4_2)
% 117.54/18.31 (48) ~ (all_52_8 = all_52_12)
% 117.54/18.31 (49) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.31 (50) all_54_15 = all_4_2
% 117.54/18.31 (51) ~ (all_6_2 = e1)
% 117.54/18.31 (52) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.54/18.31
% 117.54/18.31 Begin of proof
% 117.54/18.31 |
% 117.54/18.31 | COMBINE_EQS: (13), (30) imply:
% 117.54/18.31 | (53) all_10_2 = e1
% 117.54/18.31 |
% 117.54/18.31 | SIMP: (53) implies:
% 117.54/18.31 | (54) all_10_2 = e1
% 117.54/18.31 |
% 117.54/18.31 | REDUCE: (1), (54) imply:
% 117.54/18.31 | (55) ~ (all_52_8 = e1)
% 117.54/18.31 |
% 117.54/18.31 | REDUCE: (11), (54) imply:
% 117.54/18.31 | (56) ~ (all_52_12 = e1)
% 117.54/18.31 |
% 117.54/18.31 | REDUCE: (22), (54) imply:
% 117.54/18.31 | (57) op(all_10_1, e1) = all_10_0
% 117.54/18.31 |
% 117.54/18.31 | REDUCE: (32), (54) imply:
% 117.54/18.31 | (58) op(e3, e1) = all_10_1
% 117.54/18.31 |
% 117.54/18.31 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 117.54/18.31 | (16), (17), (18), (19), (20), (21), (23), (24), (25), (26), (27),
% 117.54/18.31 | (28), (29), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 117.54/18.31 | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 117.54/18.31 | (51), (52), (55), (56), (57), (58) are inconsistent by sub-proof
% 117.54/18.31 | #282.
% 117.54/18.31 |
% 117.54/18.31 End of proof
% 117.54/18.31
% 117.54/18.31 Sub-proof #282 shows that the following formulas are inconsistent:
% 117.54/18.31 ----------------------------------------------------------------
% 117.54/18.31 (1) all_54_2 = all_52_8
% 117.54/18.31 (2) ~ (all_52_8 = all_52_11)
% 117.54/18.31 (3) ~ (all_52_9 = all_8_2)
% 117.54/18.31 (4) ~ (all_4_2 = e0)
% 117.54/18.31 (5) all_56_3 = all_52_1
% 117.54/18.31 (6) all_54_3 = all_52_12
% 117.54/18.31 (7) ~ (all_4_2 = e1)
% 117.54/18.31 (8) ~ (all_52_8 = e1)
% 117.54/18.31 (9) ~ (all_56_3 = e2) | ~ (all_56_13 = e3)
% 117.54/18.31 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.31 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.31 (12) all_54_14 = all_52_11
% 117.54/18.31 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.31 (14) all_58_4 = all_52_8
% 117.54/18.31 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.31 (16) all_56_2 = all_52_12
% 117.54/18.31 (17) ~ (all_52_12 = e1)
% 117.54/18.31 (18) all_58_3 = all_8_2
% 117.54/18.31 (19) ~ (all_10_0 = e2)
% 117.54/18.31 (20) op(e3, e1) = all_52_8
% 117.54/18.31 (21) all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.54/18.31 (22) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.54/18.31 (23) all_58_5 = all_52_9
% 117.54/18.31 (24) all_58_2 = all_52_1
% 117.54/18.31 (25) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.54/18.31 (26) all_54_5 = all_8_2
% 117.54/18.31 (27) all_58_10 = all_52_13
% 117.54/18.31 (28) all_56_12 = e1
% 117.54/18.31 (29) ~ (all_52_11 = all_4_2)
% 117.54/18.31 (30) ~ (all_10_1 = e2)
% 117.54/18.31 (31) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.31 (32) ~ (all_52_9 = all_52_11)
% 117.54/18.31 (33) all_58_14 = all_52_11
% 117.54/18.31 (34) all_56_13 = all_8_2
% 117.54/18.31 (35) op(e0, e1) = all_52_11
% 117.54/18.31 (36) ~ (all_52_1 = all_8_2)
% 117.54/18.31 (37) ~ (all_8_2 = e2)
% 117.54/18.31 (38) all_56_1 = all_52_8
% 117.54/18.31 (39) all_58_8 = all_6_2
% 117.54/18.31 (40) ~ (all_10_0 = e1)
% 117.54/18.31 (41) all_56_4 = all_52_9
% 117.54/18.31 (42) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.54/18.31 (43) ~ (all_52_13 = all_4_2)
% 117.54/18.31 (44) ~ (all_52_12 = all_4_2)
% 117.54/18.31 (45) op(e3, e1) = all_10_1
% 117.54/18.31 (46) ~ (all_52_8 = all_52_12)
% 117.54/18.31 (47) op(all_10_1, e1) = all_10_0
% 117.54/18.31 (48) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.31 (49) all_54_15 = all_4_2
% 117.54/18.31 (50) ~ (all_6_2 = e1)
% 117.54/18.31 (51) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.54/18.31
% 117.54/18.31 Begin of proof
% 117.54/18.31 |
% 117.54/18.31 | BETA: splitting (25) gives:
% 117.54/18.31 |
% 117.54/18.31 | Case 1:
% 117.54/18.31 | |
% 117.54/18.31 | | (52) ~ (all_56_4 = e2)
% 117.54/18.31 | |
% 117.54/18.31 | | REDUCE: (41), (52) imply:
% 117.54/18.31 | | (53) ~ (all_52_9 = e2)
% 117.54/18.31 | |
% 117.54/18.31 | | BETA: splitting (22) gives:
% 117.54/18.31 | |
% 117.54/18.31 | | Case 1:
% 117.54/18.31 | | |
% 117.54/18.31 | | | (54) ~ (all_56_1 = e3)
% 117.54/18.31 | | |
% 117.54/18.31 | | | REDUCE: (38), (54) imply:
% 117.54/18.31 | | | (55) ~ (all_52_8 = e3)
% 117.54/18.31 | | |
% 117.54/18.32 | | | GROUND_INST: instantiating (13) with all_52_8, all_10_1, e1, e3,
% 117.54/18.32 | | | simplifying with (20), (45) gives:
% 117.54/18.32 | | | (56) all_52_8 = all_10_1
% 117.54/18.32 | | |
% 117.54/18.32 | | | COMBINE_EQS: (1), (56) imply:
% 117.54/18.32 | | | (57) all_54_2 = all_10_1
% 117.54/18.32 | | |
% 117.54/18.32 | | | COMBINE_EQS: (14), (56) imply:
% 117.54/18.32 | | | (58) all_58_4 = all_10_1
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (2), (56) imply:
% 117.54/18.32 | | | (59) ~ (all_52_11 = all_10_1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | SIMP: (59) implies:
% 117.54/18.32 | | | (60) ~ (all_52_11 = all_10_1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (46), (56) imply:
% 117.54/18.32 | | | (61) ~ (all_52_12 = all_10_1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | SIMP: (61) implies:
% 117.54/18.32 | | | (62) ~ (all_52_12 = all_10_1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (55), (56) imply:
% 117.54/18.32 | | | (63) ~ (all_10_1 = e3)
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (8), (56) imply:
% 117.54/18.32 | | | (64) ~ (all_10_1 = e1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | BETA: splitting (42) gives:
% 117.54/18.32 | | |
% 117.54/18.32 | | | Case 1:
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | (65) all_54_2 = e3
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | COMBINE_EQS: (57), (65) imply:
% 117.54/18.32 | | | | (66) all_10_1 = e3
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | REDUCE: (63), (66) imply:
% 117.54/18.32 | | | | (67) $false
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | CLOSE: (67) is inconsistent.
% 117.54/18.32 | | | |
% 117.54/18.32 | | | Case 2:
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | (68) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | BETA: splitting (68) gives:
% 117.54/18.32 | | | |
% 117.54/18.32 | | | | Case 1:
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | (69) all_54_2 = e2
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | COMBINE_EQS: (57), (69) imply:
% 117.54/18.32 | | | | | (70) all_10_1 = e2
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | REDUCE: (30), (70) imply:
% 117.54/18.32 | | | | | (71) $false
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | CLOSE: (71) is inconsistent.
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | Case 2:
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | (72) all_54_2 = e1 | all_54_2 = e0
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | BETA: splitting (72) gives:
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | | Case 1:
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | (73) all_54_2 = e1
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | COMBINE_EQS: (57), (73) imply:
% 117.54/18.32 | | | | | | (74) all_10_1 = e1
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (64), (74) imply:
% 117.54/18.32 | | | | | | (75) $false
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | CLOSE: (75) is inconsistent.
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | Case 2:
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | (76) all_54_2 = e0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | COMBINE_EQS: (57), (76) imply:
% 117.54/18.32 | | | | | | (77) all_10_1 = e0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | COMBINE_EQS: (58), (77) imply:
% 117.54/18.32 | | | | | | (78) all_58_4 = e0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (60), (77) imply:
% 117.54/18.32 | | | | | | (79) ~ (all_52_11 = e0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (62), (77) imply:
% 117.54/18.32 | | | | | | (80) ~ (all_52_12 = e0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (64), (77) imply:
% 117.54/18.32 | | | | | | (81) ~ (e1 = e0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | SIMP: (81) implies:
% 117.54/18.32 | | | | | | (82) ~ (e1 = e0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (47), (77) imply:
% 117.54/18.32 | | | | | | (83) op(e0, e1) = all_10_0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | GROUND_INST: instantiating (13) with all_52_11, all_10_0, e1, e0,
% 117.54/18.32 | | | | | | simplifying with (35), (83) gives:
% 117.54/18.32 | | | | | | (84) all_52_11 = all_10_0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | COMBINE_EQS: (12), (84) imply:
% 117.54/18.32 | | | | | | (85) all_54_14 = all_10_0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | COMBINE_EQS: (33), (84) imply:
% 117.54/18.32 | | | | | | (86) all_58_14 = all_10_0
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (32), (84) imply:
% 117.54/18.32 | | | | | | (87) ~ (all_52_9 = all_10_0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (29), (84) imply:
% 117.54/18.32 | | | | | | (88) ~ (all_10_0 = all_4_2)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | REDUCE: (79), (84) imply:
% 117.54/18.32 | | | | | | (89) ~ (all_10_0 = e0)
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | BETA: splitting (21) gives:
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | | Case 1:
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | (90) all_58_4 = e1
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | COMBINE_EQS: (78), (90) imply:
% 117.54/18.32 | | | | | | | (91) e1 = e0
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | SIMP: (91) implies:
% 117.54/18.32 | | | | | | | (92) e1 = e0
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | REDUCE: (82), (92) imply:
% 117.54/18.32 | | | | | | | (93) $false
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | CLOSE: (93) is inconsistent.
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | Case 2:
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | (94) all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | BETA: splitting (94) gives:
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | (95) all_58_5 = e1
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | COMBINE_EQS: (23), (95) imply:
% 117.54/18.32 | | | | | | | | (96) all_52_9 = e1
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | REDUCE: (87), (96) imply:
% 117.54/18.32 | | | | | | | | (97) ~ (all_10_0 = e1)
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | REDUCE: (3), (96) imply:
% 117.54/18.32 | | | | | | | | (98) ~ (all_8_2 = e1)
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | SIMP: (98) implies:
% 117.54/18.32 | | | | | | | | (99) ~ (all_8_2 = e1)
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | BETA: splitting (51) gives:
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | (100) all_54_14 = e3
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | COMBINE_EQS: (85), (100) imply:
% 117.54/18.32 | | | | | | | | | (101) all_10_0 = e3
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | SIMP: (101) implies:
% 117.54/18.32 | | | | | | | | | (102) all_10_0 = e3
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | REDUCE: (88), (102) imply:
% 117.54/18.32 | | | | | | | | | (103) ~ (all_4_2 = e3)
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | SIMP: (103) implies:
% 117.54/18.32 | | | | | | | | | (104) ~ (all_4_2 = e3)
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | BETA: splitting (15) gives:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | (105) all_54_15 = e3
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | REF_CLOSE: (49), (104), (105) are inconsistent by sub-proof
% 117.54/18.32 | | | | | | | | | | #312.
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | (106) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | BETA: splitting (106) gives:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | (107) all_54_15 = e2
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | COMBINE_EQS: (49), (107) imply:
% 117.54/18.32 | | | | | | | | | | | (108) all_4_2 = e2
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | SIMP: (108) implies:
% 117.54/18.32 | | | | | | | | | | | (109) all_4_2 = e2
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | REDUCE: (44), (109) imply:
% 117.54/18.32 | | | | | | | | | | | (110) ~ (all_52_12 = e2)
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | REDUCE: (43), (109) imply:
% 117.54/18.32 | | | | | | | | | | | (111) ~ (all_52_13 = e2)
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | BETA: splitting (48) gives:
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | (112) all_58_2 = e2
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | COMBINE_EQS: (24), (112) imply:
% 117.54/18.32 | | | | | | | | | | | | (113) all_52_1 = e2
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | COMBINE_EQS: (5), (113) imply:
% 117.54/18.32 | | | | | | | | | | | | (114) all_56_3 = e2
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | REDUCE: (36), (113) imply:
% 117.54/18.32 | | | | | | | | | | | | (115) ~ (all_8_2 = e2)
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | BETA: splitting (9) gives:
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | (116) ~ (all_56_3 = e2)
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | REDUCE: (114), (116) imply:
% 117.54/18.32 | | | | | | | | | | | | | (117) $false
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | CLOSE: (117) is inconsistent.
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | (118) ~ (all_56_13 = e3)
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | REDUCE: (34), (118) imply:
% 117.54/18.32 | | | | | | | | | | | | | (119) ~ (all_8_2 = e3)
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | BETA: splitting (11) gives:
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | (120) all_54_5 = e3
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | REF_CLOSE: (26), (119), (120) are inconsistent by sub-proof
% 117.54/18.32 | | | | | | | | | | | | | | #339.
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | (121) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | (122) all_54_3 = e3
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | COMBINE_EQS: (6), (122) imply:
% 117.54/18.32 | | | | | | | | | | | | | | | (123) all_52_12 = e3
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | SIMP: (123) implies:
% 117.54/18.32 | | | | | | | | | | | | | | | (124) all_52_12 = e3
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | COMBINE_EQS: (16), (124) imply:
% 117.54/18.32 | | | | | | | | | | | | | | | (125) all_56_2 = e3
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | REF_CLOSE: (26), (31), (34), (37), (99), (121), (125) are
% 117.54/18.32 | | | | | | | | | | | | | | | inconsistent by sub-proof #286.
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | (126) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (80), (110), (126) are inconsistent by
% 117.54/18.32 | | | | | | | | | | | | | | | sub-proof #283.
% 117.54/18.32 | | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | (127) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | | REF_CLOSE: (18), (23), (27), (37), (53), (111), (127) are
% 117.54/18.32 | | | | | | | | | | | | inconsistent by sub-proof #401.
% 117.54/18.32 | | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | (128) all_54_15 = e1 | all_54_15 = e0
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | REF_CLOSE: (4), (7), (49), (128) are inconsistent by
% 117.54/18.32 | | | | | | | | | | | sub-proof #418.
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | (129) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | BETA: splitting (129) gives:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | (130) all_54_14 = e2
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | COMBINE_EQS: (85), (130) imply:
% 117.54/18.32 | | | | | | | | | | (131) all_10_0 = e2
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | SIMP: (131) implies:
% 117.54/18.32 | | | | | | | | | | (132) all_10_0 = e2
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | REDUCE: (19), (132) imply:
% 117.54/18.32 | | | | | | | | | | (133) $false
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | CLOSE: (133) is inconsistent.
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | (134) all_54_14 = e1 | all_54_14 = e0
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | BETA: splitting (134) gives:
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | (135) all_54_14 = e1
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | COMBINE_EQS: (85), (135) imply:
% 117.54/18.32 | | | | | | | | | | | (136) all_10_0 = e1
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | SIMP: (136) implies:
% 117.54/18.32 | | | | | | | | | | | (137) all_10_0 = e1
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | REDUCE: (40), (137) imply:
% 117.54/18.32 | | | | | | | | | | | (138) $false
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | (139) all_54_14 = e0
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | COMBINE_EQS: (85), (139) imply:
% 117.54/18.32 | | | | | | | | | | | (140) all_10_0 = e0
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | SIMP: (140) implies:
% 117.54/18.32 | | | | | | | | | | | (141) all_10_0 = e0
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | REDUCE: (89), (141) imply:
% 117.54/18.32 | | | | | | | | | | | (142) $false
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 117.54/18.32 | | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | | |
% 117.54/18.32 | | | | | | | | | End of split
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | End of split
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | (143) all_58_8 = e1 | all_58_14 = e1
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | BETA: splitting (143) gives:
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | | Case 1:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | (144) all_58_8 = e1
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | COMBINE_EQS: (39), (144) imply:
% 117.54/18.32 | | | | | | | | | (145) all_6_2 = e1
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | REDUCE: (50), (145) imply:
% 117.54/18.32 | | | | | | | | | (146) $false
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | CLOSE: (146) is inconsistent.
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | Case 2:
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | (147) all_58_14 = e1
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | COMBINE_EQS: (86), (147) imply:
% 117.54/18.32 | | | | | | | | | (148) all_10_0 = e1
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | SIMP: (148) implies:
% 117.54/18.32 | | | | | | | | | (149) all_10_0 = e1
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | REDUCE: (40), (149) imply:
% 117.54/18.32 | | | | | | | | | (150) $false
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | | CLOSE: (150) is inconsistent.
% 117.54/18.32 | | | | | | | | |
% 117.54/18.32 | | | | | | | | End of split
% 117.54/18.32 | | | | | | | |
% 117.54/18.32 | | | | | | | End of split
% 117.54/18.32 | | | | | | |
% 117.54/18.32 | | | | | | End of split
% 117.54/18.32 | | | | | |
% 117.54/18.32 | | | | | End of split
% 117.54/18.32 | | | | |
% 117.54/18.32 | | | | End of split
% 117.54/18.32 | | | |
% 117.54/18.32 | | | End of split
% 117.54/18.32 | | |
% 117.54/18.32 | | Case 2:
% 117.54/18.32 | | |
% 117.54/18.32 | | | (151) ~ (all_56_12 = e1)
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (28), (151) imply:
% 117.54/18.32 | | | (152) $false
% 117.54/18.32 | | |
% 117.54/18.32 | | | CLOSE: (152) is inconsistent.
% 117.54/18.32 | | |
% 117.54/18.32 | | End of split
% 117.54/18.32 | |
% 117.54/18.32 | Case 2:
% 117.54/18.32 | |
% 117.54/18.32 | | (153) ~ (all_56_12 = e1)
% 117.54/18.32 | |
% 117.54/18.32 | | REDUCE: (28), (153) imply:
% 117.54/18.32 | | (154) $false
% 117.54/18.32 | |
% 117.54/18.32 | | CLOSE: (154) is inconsistent.
% 117.54/18.32 | |
% 117.54/18.32 | End of split
% 117.54/18.32 |
% 117.54/18.32 End of proof
% 117.54/18.32
% 117.54/18.32 Sub-proof #283 shows that the following formulas are inconsistent:
% 117.54/18.32 ----------------------------------------------------------------
% 117.54/18.32 (1) all_54_3 = all_52_12
% 117.54/18.32 (2) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.32 (3) ~ (all_52_12 = e1)
% 117.54/18.32 (4) ~ (all_52_12 = e0)
% 117.54/18.32 (5) ~ (all_52_12 = e2)
% 117.54/18.32
% 117.54/18.32 Begin of proof
% 117.54/18.32 |
% 117.54/18.32 | BETA: splitting (2) gives:
% 117.54/18.32 |
% 117.54/18.32 | Case 1:
% 117.54/18.32 | |
% 117.54/18.32 | | (6) all_54_3 = e2
% 117.54/18.32 | |
% 117.54/18.32 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #285.
% 117.54/18.32 | |
% 117.54/18.32 | Case 2:
% 117.54/18.32 | |
% 117.54/18.32 | | (7) all_54_3 = e1 | all_54_3 = e0
% 117.54/18.32 | |
% 117.54/18.32 | | BETA: splitting (7) gives:
% 117.54/18.32 | |
% 117.54/18.32 | | Case 1:
% 117.54/18.32 | | |
% 117.54/18.32 | | | (8) all_54_3 = e1
% 117.54/18.32 | | |
% 117.54/18.32 | | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #284.
% 117.54/18.32 | | |
% 117.54/18.32 | | Case 2:
% 117.54/18.32 | | |
% 117.54/18.32 | | | (9) all_54_3 = e0
% 117.54/18.32 | | |
% 117.54/18.32 | | | COMBINE_EQS: (1), (9) imply:
% 117.54/18.32 | | | (10) all_52_12 = e0
% 117.54/18.32 | | |
% 117.54/18.32 | | | SIMP: (10) implies:
% 117.54/18.32 | | | (11) all_52_12 = e0
% 117.54/18.32 | | |
% 117.54/18.32 | | | REDUCE: (4), (11) imply:
% 117.54/18.32 | | | (12) $false
% 117.54/18.32 | | |
% 117.54/18.32 | | | CLOSE: (12) is inconsistent.
% 117.54/18.32 | | |
% 117.54/18.32 | | End of split
% 117.54/18.32 | |
% 117.54/18.32 | End of split
% 117.54/18.32 |
% 117.54/18.32 End of proof
% 117.54/18.32
% 117.54/18.32 Sub-proof #284 shows that the following formulas are inconsistent:
% 117.54/18.32 ----------------------------------------------------------------
% 117.54/18.32 (1) all_54_3 = all_52_12
% 117.54/18.32 (2) all_54_3 = e1
% 117.54/18.32 (3) ~ (all_52_12 = e1)
% 117.54/18.32
% 117.54/18.32 Begin of proof
% 117.54/18.32 |
% 117.54/18.32 | COMBINE_EQS: (1), (2) imply:
% 117.54/18.32 | (4) all_52_12 = e1
% 117.54/18.32 |
% 117.54/18.32 | SIMP: (4) implies:
% 117.54/18.32 | (5) all_52_12 = e1
% 117.54/18.32 |
% 117.54/18.32 | REDUCE: (3), (5) imply:
% 117.54/18.32 | (6) $false
% 117.54/18.32 |
% 117.54/18.32 | CLOSE: (6) is inconsistent.
% 117.54/18.32 |
% 117.54/18.32 End of proof
% 117.54/18.32
% 117.54/18.32 Sub-proof #285 shows that the following formulas are inconsistent:
% 117.54/18.32 ----------------------------------------------------------------
% 117.54/18.32 (1) all_54_3 = all_52_12
% 117.54/18.32 (2) all_54_3 = e2
% 117.54/18.32 (3) ~ (all_52_12 = e2)
% 117.54/18.32
% 117.54/18.32 Begin of proof
% 117.54/18.32 |
% 117.54/18.32 | COMBINE_EQS: (1), (2) imply:
% 117.54/18.32 | (4) all_52_12 = e2
% 117.54/18.32 |
% 117.54/18.32 | SIMP: (4) implies:
% 117.54/18.32 | (5) all_52_12 = e2
% 117.54/18.32 |
% 117.54/18.32 | REDUCE: (3), (5) imply:
% 117.54/18.32 | (6) $false
% 117.54/18.32 |
% 117.54/18.32 | CLOSE: (6) is inconsistent.
% 117.54/18.32 |
% 117.54/18.32 End of proof
% 117.54/18.32
% 117.54/18.32 Sub-proof #286 shows that the following formulas are inconsistent:
% 117.54/18.32 ----------------------------------------------------------------
% 117.54/18.32 (1) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.32 (2) all_54_5 = all_8_2
% 117.54/18.32 (3) all_56_2 = e3
% 117.54/18.32 (4) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.32 (5) ~ (all_8_2 = e1)
% 117.54/18.32 (6) all_56_13 = all_8_2
% 117.54/18.32 (7) ~ (all_8_2 = e2)
% 117.54/18.32
% 117.54/18.32 Begin of proof
% 117.54/18.32 |
% 117.54/18.32 | BETA: splitting (4) gives:
% 117.54/18.32 |
% 117.54/18.32 | Case 1:
% 117.54/18.32 | |
% 117.54/18.32 | | (8) ~ (all_56_2 = e3)
% 117.54/18.32 | |
% 117.54/18.32 | | REDUCE: (3), (8) imply:
% 117.54/18.32 | | (9) $false
% 117.54/18.32 | |
% 117.54/18.32 | | CLOSE: (9) is inconsistent.
% 117.54/18.32 | |
% 117.54/18.32 | Case 2:
% 117.54/18.32 | |
% 117.54/18.32 | | (10) ~ (all_56_13 = e0)
% 117.54/18.32 | |
% 117.54/18.32 | | REDUCE: (6), (10) imply:
% 117.54/18.32 | | (11) ~ (all_8_2 = e0)
% 117.54/18.32 | |
% 117.54/18.32 | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #310.
% 117.54/18.32 | |
% 117.54/18.32 | End of split
% 117.54/18.32 |
% 117.54/18.32 End of proof
% 117.54/18.32
% 117.54/18.32 Sub-proof #287 shows that the following formulas are inconsistent:
% 117.54/18.32 ----------------------------------------------------------------
% 117.54/18.32 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.32 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.54/18.32 (3) ~ (all_52_2 = all_10_2)
% 117.54/18.32 (4) ~ (all_52_6 = all_52_14)
% 117.54/18.32 (5) all_58_7 = all_52_6
% 117.54/18.32 (6) all_36_2 = all_6_2
% 117.54/18.32 (7) ~ (all_32_0 = e0) | ~ (all_32_1 = e1) | ~ (all_32_2 = e2)
% 117.54/18.32 (8) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.32 (9) ~ (all_52_13 = all_52_14)
% 117.54/18.32 (10) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.54/18.32 (11) ~ (all_4_2 = e0)
% 117.54/18.32 (12) op(e3, e2) = all_52_4
% 117.54/18.32 (13) all_56_14 = all_6_2
% 117.54/18.32 (14) all_56_3 = all_52_1
% 117.54/18.32 (15) all_38_1 = all_10_1
% 117.54/18.32 (16) all_54_0 = all_10_2
% 117.54/18.32 (17) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.54/18.32 (18) all_54_3 = all_52_12
% 117.54/18.32 (19) ~ (all_52_2 = all_52_6)
% 117.54/18.32 (20) op(e0, e2) = all_52_7
% 117.54/18.32 (21) ~ (all_52_7 = all_4_2)
% 117.54/18.32 (22) all_56_11 = all_52_11
% 117.54/18.32 (23) ~ (all_4_0 = e1)
% 117.54/18.32 (24) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.54/18.32 (25) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.32 (26) ~ (all_52_4 = all_52_8)
% 117.54/18.32 (27) ~ (all_52_12 = all_10_2)
% 117.54/18.32 (28) ~ (e3 = e1)
% 117.54/18.32 (29) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.54/18.33 (30) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.54/18.33 (31) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.33 (32) all_56_12 = all_10_2
% 117.54/18.33 (33) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.54/18.33 (34) all_58_0 = all_10_2
% 117.54/18.33 (35) op(all_6_1, all_6_2) = all_6_0
% 117.54/18.33 (36) all_54_11 = all_52_14
% 117.54/18.33 (37) all_54_13 = all_52_7
% 117.54/18.33 (38) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.33 (39) all_36_1 = all_6_1
% 117.54/18.33 (40) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.54/18.33 (41) ~ (all_52_14 = all_6_2)
% 117.54/18.33 (42) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.54/18.33 (43) all_56_10 = all_52_7
% 117.54/18.33 (44) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.33 (45) op(all_4_1, all_4_2) = all_4_0
% 117.54/18.33 (46) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.33 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.33 (48) all_54_8 = all_52_2
% 117.54/18.33 (49) ~ (all_52_2 = all_6_2)
% 117.54/18.33 (50) all_32_2 = all_10_2
% 117.54/18.33 (51) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.54/18.33 (52) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.54/18.33 (53) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 117.54/18.33 (54) all_54_10 = all_6_2
% 117.54/18.33 (55) ~ (e2 = e1)
% 117.54/18.33 (56) all_36_0 = all_6_0
% 117.54/18.33 (57) op(e3, e0) = all_52_12
% 117.54/18.33 (58) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 117.54/18.33 (59) all_38_0 = all_10_0
% 117.54/18.33 (60) ~ (all_52_8 = all_6_2)
% 117.54/18.33 (61) all_58_4 = all_52_8
% 117.54/18.33 (62) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.33 (63) ~ (all_52_4 = all_52_7)
% 117.54/18.33 (64) all_56_2 = all_52_12
% 117.54/18.33 (65) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.33 (66) all_58_3 = all_8_2
% 117.54/18.33 (67) all_54_6 = all_52_9
% 117.54/18.33 (68) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.54/18.33 (69) ~ (all_10_0 = e2)
% 117.54/18.33 (70) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.33 (71) all_58_11 = all_52_14
% 117.54/18.33 (72) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 117.54/18.33 (73) all_54_9 = all_52_6
% 117.54/18.33 (74) op(e3, e1) = all_52_8
% 117.54/18.33 (75) all_54_7 = all_52_13
% 117.54/18.33 (76) op(all_10_1, all_10_2) = all_10_0
% 117.54/18.33 (77) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.54/18.33 (78) ~ (all_52_11 = all_6_2)
% 117.54/18.33 (79) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.54/18.33 (80) op(e2, e3) = all_52_1
% 117.54/18.33 (81) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.54/18.33 (82) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.54/18.33 (83) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.54/18.33 (84) ~ (all_52_7 = all_8_2)
% 117.54/18.33 (85) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.33 (86) ~ (all_52_4 = all_8_2)
% 117.54/18.33 (87) op(e1, e0) = all_52_14
% 117.54/18.33 (88) all_58_5 = all_52_9
% 117.54/18.33 (89) all_40_0 = all_6_0
% 117.54/18.33 (90) ~ (all_4_0 = e3)
% 117.54/18.33 (91) all_56_9 = all_52_3
% 117.54/18.33 (92) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 117.54/18.33 (93) op(e1, all_6_2) = all_6_1
% 117.54/18.33 (94) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.54/18.33 (95) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.33 (96) all_32_0 = all_10_0
% 117.54/18.33 (97) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.54/18.33 (98) all_58_15 = all_4_2
% 117.54/18.33 (99) all_58_2 = all_52_1
% 117.54/18.33 (100) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.54/18.33 (101) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.54/18.33 (102) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.54/18.33 (103) op(e0, e3) = all_52_3
% 117.54/18.33 (104) ~ (all_10_2 = e3)
% 117.54/18.33 (105) ~ (all_52_12 = all_52_13)
% 117.54/18.33 (106) all_58_13 = all_52_7
% 117.54/18.33 (107) all_32_1 = all_10_1
% 117.54/18.33 (108) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.33 (109) all_40_1 = all_6_1
% 117.54/18.33 (110) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 117.54/18.33 (111) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.54/18.33 (112) ~ (all_52_14 = all_4_2)
% 117.54/18.33 (113) all_58_6 = all_52_2
% 117.54/18.33 (114) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 117.54/18.33 (115) ~ (all_52_1 = all_10_2)
% 117.54/18.33 (116) all_54_5 = all_8_2
% 117.54/18.33 (117) all_56_15 = all_4_2
% 117.54/18.33 (118) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.54/18.33 (119) all_58_10 = all_52_13
% 117.54/18.33 (120) ~ (all_52_11 = all_4_2)
% 117.54/18.33 (121) op(e3, all_10_2) = all_10_1
% 117.54/18.33 (122) ~ (all_52_6 = all_8_2)
% 117.54/18.33 (123) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.54/18.33 (124) ~ (all_6_0 = e2)
% 117.54/18.33 (125) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.54/18.33 (126) all_38_2 = all_10_2
% 117.54/18.33 (127) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 117.54/18.33 (128) all_58_1 = all_52_4
% 117.54/18.33 (129) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.33 (130) all_58_14 = all_52_11
% 117.54/18.33 (131) all_54_1 = all_52_4
% 117.54/18.33 (132) all_56_13 = all_8_2
% 117.54/18.33 (133) ~ (all_52_1 = all_8_2)
% 117.54/18.33 (134) ~ (all_8_2 = e2)
% 117.54/18.33 (135) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.54/18.33 (136) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 117.54/18.33 (137) ~ (all_52_7 = all_52_11)
% 117.54/18.33 (138) op(e1, e2) = all_52_6
% 117.54/18.33 (139) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.33 (140) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.54/18.33 (141) all_56_7 = all_52_6
% 117.54/18.33 (142) ~ (all_52_9 = all_6_2)
% 117.54/18.33 (143) all_56_1 = all_52_8
% 117.54/18.33 (144) op(e0, all_4_2) = all_4_1
% 117.54/18.33 (145) all_58_8 = all_6_2
% 117.54/18.33 (146) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.33 (147) ~ (all_10_0 = e1)
% 117.54/18.33 (148) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 117.54/18.33 (149) all_40_2 = all_6_2
% 117.54/18.33 (150) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.33 (151) all_56_4 = all_52_9
% 117.54/18.33 (152) all_58_9 = all_52_12
% 117.54/18.33 (153) all_56_5 = all_52_13
% 117.54/18.33 (154) op(e2, e1) = all_52_9
% 117.54/18.33 (155) ~ (all_52_3 = all_4_2)
% 117.54/18.33 (156) ~ (all_52_6 = all_6_2)
% 117.54/18.33 (157) all_56_6 = all_52_2
% 117.54/18.33 (158) ~ (all_52_13 = all_4_2)
% 117.54/18.33 (159) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.54/18.33 (160) all_58_12 = all_52_3
% 117.54/18.33 (161) ~ (all_52_2 = all_52_14)
% 117.54/18.33 (162) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.33 (163) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.54/18.33 (164) op(e2, e0) = all_52_13
% 117.54/18.33 (165) ~ (all_52_12 = all_4_2)
% 117.54/18.33 (166) ~ (all_52_3 = all_10_2)
% 117.54/18.33 (167) op(e1, e3) = all_52_2
% 117.54/18.33 (168) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.54/18.33 (169) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 117.54/18.33 (170) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.33 (171) all_56_8 = all_52_14
% 117.54/18.33 (172) ~ (all_52_4 = all_10_2)
% 117.54/18.33 (173) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.33 (174) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.33 (175) all_56_0 = all_52_4
% 117.54/18.33 (176) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.54/18.33 (177) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.33 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.33 (178) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.54/18.33 (179) all_54_4 = all_52_1
% 117.54/18.33 (180) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.54/18.33 (181) all_54_15 = all_4_2
% 117.54/18.33 (182) ~ (all_6_2 = e1)
% 117.54/18.33 (183) ~ (all_6_1 = e2)
% 117.54/18.33 (184) ~ (all_52_6 = all_52_7)
% 117.54/18.33 (185) ~ (all_52_3 = all_52_11)
% 117.54/18.33 (186) all_54_12 = all_52_3
% 117.54/18.33 (187) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.33 (188) ~ (all_52_3 = all_52_7)
% 117.54/18.33
% 117.54/18.33 Begin of proof
% 117.54/18.33 |
% 117.54/18.33 | BETA: splitting (7) gives:
% 117.54/18.33 |
% 117.54/18.33 | Case 1:
% 117.54/18.33 | |
% 117.54/18.33 | | (189) ~ (all_32_1 = e1)
% 117.54/18.33 | |
% 117.54/18.33 | | REDUCE: (107), (189) imply:
% 117.54/18.33 | | (190) ~ (all_10_1 = e1)
% 117.54/18.33 | |
% 117.54/18.33 | | BETA: splitting (127) gives:
% 117.54/18.33 | |
% 117.54/18.33 | | Case 1:
% 117.54/18.33 | | |
% 117.54/18.33 | | | (191) ~ (all_36_1 = e3)
% 117.54/18.33 | | |
% 117.54/18.33 | | | REDUCE: (39), (191) imply:
% 117.54/18.33 | | | (192) ~ (all_6_1 = e3)
% 117.54/18.33 | | |
% 117.54/18.33 | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (13), (14),
% 117.54/18.33 | | | (15), (16), (17), (18), (19), (20), (22), (24), (25), (27),
% 117.54/18.33 | | | (28), (30), (32), (34), (35), (36), (37), (38), (41), (42),
% 117.54/18.33 | | | (44), (46), (47), (48), (49), (52), (53), (54), (57), (59),
% 117.54/18.33 | | | (60), (61), (62), (63), (64), (65), (66), (67), (69), (70),
% 117.54/18.33 | | | (71), (73), (74), (76), (77), (79), (83), (85), (87), (88),
% 117.54/18.33 | | | (89), (91), (92), (93), (94), (95), (97), (98), (99), (100),
% 117.54/18.33 | | | (101), (102), (104), (106), (109), (110), (112), (113), (115),
% 117.54/18.33 | | | (117), (119), (120), (121), (123), (124), (125), (126), (128),
% 117.54/18.33 | | | (130), (131), (132), (134), (135), (138), (139), (140), (141),
% 117.54/18.33 | | | (142), (145), (146), (147), (148), (149), (150), (151), (152),
% 117.54/18.33 | | | (153), (154), (155), (156), (157), (159), (160), (161), (162),
% 117.54/18.33 | | | (163), (164), (165), (166), (167), (168), (170), (171), (172),
% 117.54/18.33 | | | (173), (174), (175), (176), (177), (178), (180), (181), (182),
% 117.54/18.33 | | | (183), (184), (185), (186), (190), (192) are inconsistent by
% 117.54/18.33 | | | sub-proof #363.
% 117.54/18.33 | | |
% 117.54/18.33 | | Case 2:
% 117.54/18.33 | | |
% 117.54/18.33 | | | (193) all_36_1 = e3
% 117.54/18.33 | | | (194) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 117.54/18.33 | | |
% 117.54/18.33 | | | COMBINE_EQS: (39), (193) imply:
% 117.54/18.33 | | | (195) all_6_1 = e3
% 117.54/18.33 | | |
% 117.54/18.33 | | | SIMP: (195) implies:
% 117.54/18.33 | | | (196) all_6_1 = e3
% 117.54/18.33 | | |
% 117.54/18.33 | | | REDUCE: (35), (196) imply:
% 117.54/18.33 | | | (197) op(e3, all_6_2) = all_6_0
% 117.54/18.33 | | |
% 117.54/18.33 | | | REDUCE: (93), (196) imply:
% 117.54/18.33 | | | (198) op(e1, all_6_2) = e3
% 117.54/18.33 | | |
% 117.54/18.33 | | | BETA: splitting (53) gives:
% 117.54/18.33 | | |
% 117.54/18.33 | | | Case 1:
% 117.54/18.33 | | | |
% 117.54/18.33 | | | | (199) ~ (all_38_1 = e2)
% 117.54/18.33 | | | |
% 117.54/18.33 | | | | REDUCE: (15), (199) imply:
% 117.54/18.33 | | | | (200) ~ (all_10_1 = e2)
% 117.54/18.33 | | | |
% 117.54/18.33 | | | | BETA: splitting (110) gives:
% 117.54/18.33 | | | |
% 117.54/18.33 | | | | Case 1:
% 117.54/18.33 | | | | |
% 117.54/18.33 | | | | | (201) ~ (all_56_14 = e2)
% 117.54/18.33 | | | | |
% 117.54/18.33 | | | | | REDUCE: (13), (201) imply:
% 117.54/18.33 | | | | | (202) ~ (all_6_2 = e2)
% 117.54/18.33 | | | | |
% 117.54/18.33 | | | | | BETA: splitting (111) gives:
% 117.54/18.33 | | | | |
% 117.54/18.33 | | | | | Case 1:
% 117.54/18.33 | | | | | |
% 117.54/18.33 | | | | | | (203) ~ (all_56_12 = e2)
% 117.54/18.33 | | | | | |
% 117.54/18.33 | | | | | | REDUCE: (32), (203) imply:
% 117.54/18.33 | | | | | | (204) ~ (all_10_2 = e2)
% 117.54/18.33 | | | | | |
% 117.54/18.33 | | | | | | BETA: splitting (148) gives:
% 117.54/18.33 | | | | | |
% 117.54/18.33 | | | | | | Case 1:
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | (205) ~ (all_56_15 = e3)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (117), (205) imply:
% 117.54/18.33 | | | | | | | (206) ~ (all_4_2 = e3)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REF_CLOSE: (2), (3), (5), (9), (11), (12), (13), (14), (16), (18),
% 117.54/18.33 | | | | | | | (20), (22), (24), (25), (27), (28), (30), (32), (33),
% 117.54/18.33 | | | | | | | (38), (43), (46), (47), (49), (54), (57), (62), (63),
% 117.54/18.33 | | | | | | | (64), (65), (66), (68), (69), (71), (75), (76), (77),
% 117.54/18.33 | | | | | | | (79), (83), (87), (88), (91), (94), (95), (98), (99),
% 117.54/18.33 | | | | | | | (104), (105), (106), (112), (113), (115), (117), (118),
% 117.54/18.33 | | | | | | | (119), (121), (123), (124), (128), (130), (131), (132),
% 117.54/18.33 | | | | | | | (134), (139), (140), (141), (145), (146), (147), (151),
% 117.54/18.33 | | | | | | | (153), (156), (157), (158), (160), (162), (165), (167),
% 117.54/18.33 | | | | | | | (168), (171), (172), (173), (174), (175), (176), (177),
% 117.54/18.33 | | | | | | | (180), (181), (182), (187), (190), (197), (198), (200),
% 117.54/18.33 | | | | | | | (202), (204), (206) are inconsistent by sub-proof #340.
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | Case 2:
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | (207) all_56_15 = e3
% 117.54/18.33 | | | | | | | (208) ~ (all_56_9 = e0)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | COMBINE_EQS: (117), (207) imply:
% 117.54/18.33 | | | | | | | (209) all_4_2 = e3
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | SIMP: (209) implies:
% 117.54/18.33 | | | | | | | (210) all_4_2 = e3
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | COMBINE_EQS: (98), (210) imply:
% 117.54/18.33 | | | | | | | (211) all_58_15 = e3
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (91), (208) imply:
% 117.54/18.33 | | | | | | | (212) ~ (all_52_3 = e0)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (155), (210) imply:
% 117.54/18.33 | | | | | | | (213) ~ (all_52_3 = e3)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (21), (210) imply:
% 117.54/18.33 | | | | | | | (214) ~ (all_52_7 = e3)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (165), (210) imply:
% 117.54/18.33 | | | | | | | (215) ~ (all_52_12 = e3)
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (45), (210) imply:
% 117.54/18.33 | | | | | | | (216) op(all_4_1, e3) = all_4_0
% 117.54/18.33 | | | | | | |
% 117.54/18.33 | | | | | | | REDUCE: (144), (210) imply:
% 117.54/18.33 | | | | | | | (217) op(e0, e3) = all_4_1
% 117.54/18.33 | | | | | | |
% 117.54/18.34 | | | | | | | REF_CLOSE: (1), (5), (8), (10), (13), (14), (16), (17), (23),
% 117.54/18.34 | | | | | | | (24), (26), (29), (31), (32), (34), (37), (40), (41),
% 117.54/18.34 | | | | | | | (46), (47), (49), (51), (54), (58), (61), (63), (66),
% 117.54/18.34 | | | | | | | (71), (78), (80), (81), (82), (84), (86), (90), (94),
% 117.54/18.34 | | | | | | | (99), (103), (104), (106), (113), (115), (116), (122),
% 117.54/18.34 | | | | | | | (128), (130), (133), (134), (135), (137), (139), (143),
% 117.54/18.34 | | | | | | | (145), (146), (152), (156), (157), (160), (163), (166),
% 117.54/18.34 | | | | | | | (167), (170), (171), (177), (179), (182), (184), (186),
% 117.54/18.34 | | | | | | | (188), (198), (202), (204), (207), (211), (212), (213),
% 117.54/18.34 | | | | | | | (214), (215), (216), (217) are inconsistent by
% 117.54/18.34 | | | | | | | sub-proof #313.
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | End of split
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | Case 2:
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | (218) all_56_12 = e2
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | COMBINE_EQS: (32), (218) imply:
% 117.54/18.34 | | | | | | (219) all_10_2 = e2
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | SIMP: (219) implies:
% 117.54/18.34 | | | | | | (220) all_10_2 = e2
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | REF_CLOSE: (5), (11), (12), (13), (20), (22), (30), (38), (46),
% 117.54/18.34 | | | | | | (47), (54), (63), (66), (69), (76), (77), (79), (83),
% 117.54/18.34 | | | | | | (88), (91), (95), (98), (99), (106), (115), (119), (121),
% 117.54/18.34 | | | | | | (128), (130), (131), (132), (134), (140), (141), (147),
% 117.54/18.34 | | | | | | (151), (153), (156), (160), (172), (174), (175), (176),
% 117.54/18.34 | | | | | | (177), (180), (182), (190), (218), (220) are inconsistent
% 117.54/18.34 | | | | | | by sub-proof #425.
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | End of split
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | Case 2:
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | (221) all_56_14 = e2
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (17), (21), (31), (34), (37),
% 117.54/18.34 | | | | | (47), (51), (56), (61), (62), (63), (64), (66), (72), (84),
% 117.54/18.34 | | | | | (86), (88), (99), (104), (114), (116), (117), (119), (122),
% 117.54/18.34 | | | | | (124), (128), (129), (131), (132), (134), (136), (138),
% 117.54/18.34 | | | | | (140), (142), (143), (152), (153), (170), (174), (175),
% 117.54/18.34 | | | | | (178), (181), (184), (194), (197), (198), (221) are
% 117.54/18.34 | | | | | inconsistent by sub-proof #306.
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | End of split
% 117.54/18.34 | | | |
% 117.54/18.34 | | | Case 2:
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | (222) all_38_1 = e2
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | COMBINE_EQS: (15), (222) imply:
% 117.54/18.34 | | | | (223) all_10_1 = e2
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | SIMP: (223) implies:
% 117.54/18.34 | | | | (224) all_10_1 = e2
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | REDUCE: (121), (224) imply:
% 117.54/18.34 | | | | (225) op(e3, all_10_2) = e2
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | BETA: splitting (110) gives:
% 117.54/18.34 | | | |
% 117.54/18.34 | | | | Case 1:
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | (226) ~ (all_56_14 = e2)
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | REDUCE: (13), (226) imply:
% 117.54/18.34 | | | | | (227) ~ (all_6_2 = e2)
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | BETA: splitting (111) gives:
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | Case 1:
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | (228) ~ (all_56_12 = e2)
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | REDUCE: (32), (228) imply:
% 117.54/18.34 | | | | | | (229) ~ (all_10_2 = e2)
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | BETA: splitting (148) gives:
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | Case 1:
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | (230) ~ (all_56_15 = e3)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (117), (230) imply:
% 117.54/18.34 | | | | | | | (231) ~ (all_4_2 = e3)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (16), (18), (22),
% 117.54/18.34 | | | | | | | (24), (25), (28), (32), (33), (43), (46), (47), (49),
% 117.54/18.34 | | | | | | | (54), (57), (62), (64), (65), (66), (68), (71), (75),
% 117.54/18.34 | | | | | | | (77), (78), (83), (87), (88), (91), (94), (98), (99),
% 117.54/18.34 | | | | | | | (104), (105), (106), (112), (113), (117), (118), (119),
% 117.54/18.34 | | | | | | | (123), (124), (130), (134), (139), (141), (145), (146),
% 117.54/18.34 | | | | | | | (151), (153), (156), (157), (158), (160), (161), (162),
% 117.54/18.34 | | | | | | | (165), (166), (167), (168), (171), (173), (174), (177),
% 117.54/18.34 | | | | | | | (181), (182), (187), (197), (198), (227), (229), (231)
% 117.54/18.34 | | | | | | | are inconsistent by sub-proof #302.
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | Case 2:
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | (232) all_56_15 = e3
% 117.54/18.34 | | | | | | | (233) ~ (all_56_9 = e0)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | COMBINE_EQS: (117), (232) imply:
% 117.54/18.34 | | | | | | | (234) all_4_2 = e3
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | SIMP: (234) implies:
% 117.54/18.34 | | | | | | | (235) all_4_2 = e3
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | COMBINE_EQS: (98), (235) imply:
% 117.54/18.34 | | | | | | | (236) all_58_15 = e3
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (91), (233) imply:
% 117.54/18.34 | | | | | | | (237) ~ (all_52_3 = e0)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (155), (235) imply:
% 117.54/18.34 | | | | | | | (238) ~ (all_52_3 = e3)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (21), (235) imply:
% 117.54/18.34 | | | | | | | (239) ~ (all_52_7 = e3)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (165), (235) imply:
% 117.54/18.34 | | | | | | | (240) ~ (all_52_12 = e3)
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (45), (235) imply:
% 117.54/18.34 | | | | | | | (241) op(all_4_1, e3) = all_4_0
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REDUCE: (144), (235) imply:
% 117.54/18.34 | | | | | | | (242) op(e0, e3) = all_4_1
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | | REF_CLOSE: (1), (5), (8), (10), (13), (14), (16), (17), (23),
% 117.54/18.34 | | | | | | | (24), (26), (29), (31), (32), (34), (37), (40), (41),
% 117.54/18.34 | | | | | | | (46), (47), (49), (51), (54), (58), (61), (63), (66),
% 117.54/18.34 | | | | | | | (71), (78), (80), (81), (82), (84), (86), (90), (94),
% 117.54/18.34 | | | | | | | (99), (103), (104), (106), (113), (115), (116), (122),
% 117.54/18.34 | | | | | | | (128), (130), (133), (134), (135), (137), (139), (143),
% 117.54/18.34 | | | | | | | (145), (146), (152), (156), (157), (160), (163), (166),
% 117.54/18.34 | | | | | | | (167), (170), (171), (177), (179), (182), (184), (186),
% 117.54/18.34 | | | | | | | (188), (198), (227), (229), (232), (236), (237), (238),
% 117.54/18.34 | | | | | | | (239), (240), (241), (242) are inconsistent by
% 117.54/18.34 | | | | | | | sub-proof #313.
% 117.54/18.34 | | | | | | |
% 117.54/18.34 | | | | | | End of split
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | Case 2:
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | (243) all_56_12 = e2
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | | REF_CLOSE: (12), (32), (47), (172), (225), (243) are inconsistent by
% 117.54/18.34 | | | | | | sub-proof #300.
% 117.54/18.34 | | | | | |
% 117.54/18.34 | | | | | End of split
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | Case 2:
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | (244) all_56_14 = e2
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (17), (21), (31), (34), (37),
% 117.54/18.34 | | | | | (47), (51), (56), (61), (62), (63), (64), (66), (72), (84),
% 117.54/18.34 | | | | | (86), (88), (99), (104), (114), (116), (117), (119), (122),
% 117.54/18.34 | | | | | (124), (128), (129), (131), (132), (134), (136), (138),
% 117.54/18.34 | | | | | (140), (142), (143), (152), (153), (170), (174), (175),
% 117.54/18.34 | | | | | (178), (181), (184), (194), (197), (198), (244) are
% 117.54/18.34 | | | | | inconsistent by sub-proof #306.
% 117.54/18.34 | | | | |
% 117.54/18.34 | | | | End of split
% 117.54/18.34 | | | |
% 117.54/18.34 | | | End of split
% 117.54/18.34 | | |
% 117.54/18.34 | | End of split
% 117.54/18.34 | |
% 117.54/18.34 | Case 2:
% 117.54/18.34 | |
% 117.54/18.34 | | (245) all_32_1 = e1
% 117.54/18.34 | | (246) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.34 | |
% 117.54/18.34 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13), (14), (16),
% 117.54/18.34 | | (17), (19), (20), (21), (22), (24), (28), (31), (32), (33), (34),
% 117.54/18.34 | | (35), (36), (37), (38), (39), (41), (42), (43), (44), (46), (47),
% 117.54/18.34 | | (48), (49), (50), (51), (52), (54), (55), (56), (57), (60), (61),
% 117.54/18.34 | | (62), (63), (64), (65), (66), (69), (70), (71), (72), (73), (74),
% 117.54/18.34 | | (76), (78), (84), (85), (86), (87), (88), (89), (91), (93), (94),
% 117.54/18.34 | | (95), (96), (97), (98), (99), (102), (104), (106), (107), (108),
% 117.54/18.34 | | (109), (110), (111), (113), (114), (116), (117), (119), (121),
% 117.54/18.34 | | (122), (124), (125), (127), (128), (129), (130), (131), (132),
% 117.54/18.34 | | (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 117.54/18.34 | | (143), (145), (146), (149), (150), (151), (152), (153), (156),
% 117.54/18.34 | | (157), (160), (161), (162), (166), (168), (169), (170), (171),
% 117.54/18.34 | | (172), (173), (174), (175), (176), (177), (178), (181), (182),
% 117.54/18.34 | | (183), (184), (245), (246) are inconsistent by sub-proof #288.
% 117.54/18.34 | |
% 117.54/18.34 | End of split
% 117.54/18.34 |
% 117.54/18.34 End of proof
% 117.54/18.34
% 117.54/18.34 Sub-proof #288 shows that the following formulas are inconsistent:
% 117.54/18.34 ----------------------------------------------------------------
% 117.54/18.34 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.34 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.54/18.34 (3) ~ (all_52_2 = all_10_2)
% 117.54/18.34 (4) ~ (all_52_6 = all_52_14)
% 117.54/18.34 (5) all_58_7 = all_52_6
% 117.54/18.34 (6) all_36_2 = all_6_2
% 117.54/18.34 (7) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.34 (8) ~ (all_4_2 = e0)
% 117.54/18.34 (9) op(e3, e2) = all_52_4
% 117.54/18.34 (10) all_56_14 = all_6_2
% 117.54/18.34 (11) all_56_3 = all_52_1
% 117.54/18.34 (12) all_54_0 = all_10_2
% 117.54/18.34 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.54/18.34 (14) ~ (all_52_2 = all_52_6)
% 117.54/18.34 (15) op(e0, e2) = all_52_7
% 117.54/18.34 (16) ~ (all_52_7 = all_4_2)
% 117.54/18.34 (17) all_56_11 = all_52_11
% 117.54/18.34 (18) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.54/18.34 (19) ~ (e3 = e1)
% 117.54/18.34 (20) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.54/18.34 (21) all_56_12 = all_10_2
% 117.54/18.34 (22) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.54/18.34 (23) all_58_0 = all_10_2
% 117.54/18.34 (24) op(all_6_1, all_6_2) = all_6_0
% 117.54/18.34 (25) all_54_11 = all_52_14
% 117.54/18.34 (26) all_54_13 = all_52_7
% 117.54/18.34 (27) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.34 (28) all_36_1 = all_6_1
% 117.54/18.34 (29) ~ (all_52_14 = all_6_2)
% 117.54/18.34 (30) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.54/18.34 (31) all_56_10 = all_52_7
% 117.54/18.34 (32) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.34 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.34 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.34 (35) all_54_8 = all_52_2
% 117.54/18.34 (36) ~ (all_52_2 = all_6_2)
% 117.54/18.34 (37) all_32_2 = all_10_2
% 117.54/18.34 (38) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.54/18.34 (39) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.54/18.34 (40) all_54_10 = all_6_2
% 117.54/18.34 (41) ~ (e2 = e1)
% 117.54/18.34 (42) all_36_0 = all_6_0
% 117.54/18.34 (43) op(e3, e0) = all_52_12
% 117.54/18.34 (44) all_32_1 = e1
% 117.54/18.34 (45) ~ (all_52_8 = all_6_2)
% 117.54/18.34 (46) all_58_4 = all_52_8
% 117.54/18.34 (47) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.34 (48) ~ (all_52_4 = all_52_7)
% 117.54/18.34 (49) all_56_2 = all_52_12
% 117.54/18.34 (50) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.34 (51) all_58_3 = all_8_2
% 117.54/18.34 (52) ~ (all_10_0 = e2)
% 117.54/18.34 (53) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.34 (54) all_58_11 = all_52_14
% 117.54/18.34 (55) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 117.54/18.34 (56) all_54_9 = all_52_6
% 117.54/18.34 (57) op(e3, e1) = all_52_8
% 117.54/18.34 (58) op(all_10_1, all_10_2) = all_10_0
% 117.54/18.34 (59) ~ (all_52_11 = all_6_2)
% 117.54/18.34 (60) ~ (all_52_7 = all_8_2)
% 117.54/18.34 (61) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.34 (62) ~ (all_52_4 = all_8_2)
% 117.54/18.34 (63) op(e1, e0) = all_52_14
% 117.54/18.34 (64) all_58_5 = all_52_9
% 117.54/18.34 (65) all_40_0 = all_6_0
% 117.54/18.34 (66) all_56_9 = all_52_3
% 117.54/18.34 (67) op(e1, all_6_2) = all_6_1
% 117.54/18.34 (68) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.54/18.34 (69) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.34 (70) all_32_0 = all_10_0
% 117.54/18.34 (71) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.54/18.34 (72) all_58_15 = all_4_2
% 117.54/18.34 (73) all_58_2 = all_52_1
% 117.54/18.34 (74) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.54/18.34 (75) ~ (all_10_2 = e3)
% 117.54/18.34 (76) all_58_13 = all_52_7
% 117.54/18.34 (77) all_32_1 = all_10_1
% 117.54/18.34 (78) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.34 (79) all_40_1 = all_6_1
% 117.54/18.34 (80) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 117.54/18.34 (81) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.54/18.34 (82) all_58_6 = all_52_2
% 117.54/18.34 (83) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 117.54/18.34 (84) all_54_5 = all_8_2
% 117.54/18.34 (85) all_56_15 = all_4_2
% 117.54/18.34 (86) all_58_10 = all_52_13
% 117.54/18.34 (87) op(e3, all_10_2) = all_10_1
% 117.54/18.34 (88) ~ (all_52_6 = all_8_2)
% 117.54/18.34 (89) ~ (all_6_0 = e2)
% 117.54/18.34 (90) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.54/18.34 (91) ~ (all_36_0 = e0) | ~ (all_36_1 = e3) | ~ (all_36_2 = e2)
% 117.54/18.34 (92) all_58_1 = all_52_4
% 117.54/18.34 (93) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.54/18.34 (94) all_58_14 = all_52_11
% 117.54/18.34 (95) all_54_1 = all_52_4
% 117.54/18.34 (96) all_56_13 = all_8_2
% 117.54/18.34 (97) ~ (all_8_2 = e2)
% 117.54/18.34 (98) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.54/18.34 (99) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 117.54/18.34 (100) ~ (all_52_7 = all_52_11)
% 117.54/18.34 (101) op(e1, e2) = all_52_6
% 117.54/18.34 (102) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.34 (103) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.54/18.34 (104) all_56_7 = all_52_6
% 117.54/18.34 (105) ~ (all_52_9 = all_6_2)
% 117.54/18.34 (106) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.34 (107) all_56_1 = all_52_8
% 117.54/18.34 (108) all_58_8 = all_6_2
% 117.54/18.35 (109) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.35 (110) all_40_2 = all_6_2
% 117.54/18.35 (111) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.35 (112) all_56_4 = all_52_9
% 117.54/18.35 (113) all_58_9 = all_52_12
% 117.54/18.35 (114) all_56_5 = all_52_13
% 117.54/18.35 (115) ~ (all_52_6 = all_6_2)
% 117.54/18.35 (116) all_56_6 = all_52_2
% 117.54/18.35 (117) all_58_12 = all_52_3
% 117.54/18.35 (118) ~ (all_52_2 = all_52_14)
% 117.54/18.35 (119) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.35 (120) ~ (all_52_3 = all_10_2)
% 117.54/18.35 (121) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.54/18.35 (122) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 117.54/18.35 (123) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.35 (124) all_56_8 = all_52_14
% 117.54/18.35 (125) ~ (all_52_4 = all_10_2)
% 117.54/18.35 (126) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.35 (127) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.35 (128) all_56_0 = all_52_4
% 117.54/18.35 (129) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.54/18.35 (130) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.35 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.35 (131) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.54/18.35 (132) all_54_15 = all_4_2
% 117.54/18.35 (133) ~ (all_6_2 = e1)
% 117.54/18.35 (134) ~ (all_6_1 = e2)
% 117.54/18.35 (135) ~ (all_52_6 = all_52_7)
% 117.54/18.35
% 117.54/18.35 Begin of proof
% 117.54/18.35 |
% 117.54/18.35 | COMBINE_EQS: (44), (77) imply:
% 117.54/18.35 | (136) all_10_1 = e1
% 117.54/18.35 |
% 117.54/18.35 | REDUCE: (58), (136) imply:
% 117.54/18.35 | (137) op(e1, all_10_2) = all_10_0
% 117.54/18.35 |
% 117.54/18.35 | REDUCE: (87), (136) imply:
% 117.54/18.35 | (138) op(e3, all_10_2) = e1
% 117.54/18.35 |
% 117.54/18.35 | BETA: splitting (91) gives:
% 117.54/18.35 |
% 117.54/18.35 | Case 1:
% 117.54/18.35 | |
% 117.54/18.35 | | (139) ~ (all_36_1 = e3)
% 117.54/18.35 | |
% 117.54/18.35 | | REDUCE: (28), (139) imply:
% 117.54/18.35 | | (140) ~ (all_6_1 = e3)
% 117.54/18.35 | |
% 117.54/18.35 | | BETA: splitting (39) gives:
% 117.54/18.35 | |
% 117.54/18.35 | | Case 1:
% 117.54/18.35 | | |
% 117.54/18.35 | | | (141) ~ (all_40_0 = e3)
% 117.54/18.35 | | |
% 117.54/18.35 | | | REDUCE: (65), (141) imply:
% 117.54/18.35 | | | (142) ~ (all_6_0 = e3)
% 117.54/18.35 | | |
% 117.54/18.35 | | | BETA: splitting (80) gives:
% 117.54/18.35 | | |
% 117.54/18.35 | | | Case 1:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (143) ~ (all_56_14 = e2)
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REDUCE: (10), (143) imply:
% 117.54/18.35 | | | | (144) ~ (all_6_2 = e2)
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (12), (14), (16),
% 117.54/18.35 | | | | (18), (21), (23), (25), (27), (29), (32), (33), (34), (35),
% 117.54/18.35 | | | | (36), (37), (40), (41), (43), (45), (46), (47), (49), (51),
% 117.54/18.35 | | | | (52), (53), (54), (56), (57), (61), (63), (64), (67), (69),
% 117.54/18.35 | | | | (70), (72), (75), (76), (78), (81), (85), (86), (90), (92),
% 117.54/18.35 | | | | (94), (97), (100), (101), (104), (105), (106), (108), (109),
% 117.54/18.35 | | | | (111), (112), (113), (114), (115), (116), (119), (122),
% 117.54/18.35 | | | | (123), (124), (125), (126), (128), (132), (133), (134),
% 117.54/18.35 | | | | (135), (137), (138), (140), (144) are inconsistent by
% 117.54/18.35 | | | | sub-proof #290.
% 117.54/18.35 | | | |
% 117.54/18.35 | | | Case 2:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (145) all_56_14 = e2
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REF_CLOSE: (3), (4), (5), (8), (10), (12), (13), (14), (15), (17), (19),
% 117.54/18.35 | | | | (21), (24), (25), (26), (27), (29), (30), (34), (35), (36),
% 117.54/18.35 | | | | (48), (51), (53), (56), (61), (66), (67), (68), (71), (72),
% 117.54/18.35 | | | | (74), (76), (89), (92), (94), (96), (97), (98), (101), (104),
% 117.54/18.35 | | | | (109), (111), (115), (116), (117), (118), (124), (125),
% 117.54/18.35 | | | | (126), (128), (129), (130), (131), (133), (135), (140),
% 117.54/18.35 | | | | (142), (145) are inconsistent by sub-proof #374.
% 117.54/18.35 | | | |
% 117.54/18.35 | | | End of split
% 117.54/18.35 | | |
% 117.54/18.35 | | Case 2:
% 117.54/18.35 | | |
% 117.54/18.35 | | | (146) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.54/18.35 | | |
% 117.54/18.35 | | | BETA: splitting (80) gives:
% 117.54/18.35 | | |
% 117.54/18.35 | | | Case 1:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (147) ~ (all_56_14 = e2)
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REDUCE: (10), (147) imply:
% 117.54/18.35 | | | | (148) ~ (all_6_2 = e2)
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (12), (14), (16),
% 117.54/18.35 | | | | (18), (21), (23), (25), (27), (29), (32), (33), (34), (35),
% 117.54/18.35 | | | | (36), (37), (40), (41), (43), (45), (46), (47), (49), (51),
% 117.54/18.35 | | | | (52), (53), (54), (56), (57), (61), (63), (64), (67), (69),
% 117.54/18.35 | | | | (70), (72), (75), (76), (78), (81), (85), (86), (90), (92),
% 117.54/18.35 | | | | (94), (97), (100), (101), (104), (105), (106), (108), (109),
% 117.54/18.35 | | | | (111), (112), (113), (114), (115), (116), (119), (122),
% 117.54/18.35 | | | | (123), (124), (125), (126), (128), (132), (133), (134),
% 117.54/18.35 | | | | (135), (137), (138), (140), (148) are inconsistent by
% 117.54/18.35 | | | | sub-proof #290.
% 117.54/18.35 | | | |
% 117.54/18.35 | | | Case 2:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (149) all_56_14 = e2
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REF_CLOSE: (10), (30), (34), (53), (56), (67), (79), (101), (104),
% 117.54/18.35 | | | | (110), (115), (140), (146), (149) are inconsistent by
% 117.54/18.35 | | | | sub-proof #372.
% 117.54/18.35 | | | |
% 117.54/18.35 | | | End of split
% 117.54/18.35 | | |
% 117.54/18.35 | | End of split
% 117.54/18.35 | |
% 117.54/18.35 | Case 2:
% 117.54/18.35 | |
% 117.54/18.35 | | (150) all_36_1 = e3
% 117.54/18.35 | | (151) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 117.54/18.35 | |
% 117.54/18.35 | | COMBINE_EQS: (28), (150) imply:
% 117.54/18.35 | | (152) all_6_1 = e3
% 117.54/18.35 | |
% 117.54/18.35 | | SIMP: (152) implies:
% 117.54/18.35 | | (153) all_6_1 = e3
% 117.54/18.35 | |
% 117.54/18.35 | | REDUCE: (24), (153) imply:
% 117.54/18.35 | | (154) op(e3, all_6_2) = all_6_0
% 117.54/18.35 | |
% 117.54/18.35 | | REDUCE: (67), (153) imply:
% 117.54/18.35 | | (155) op(e1, all_6_2) = e3
% 117.54/18.35 | |
% 117.54/18.35 | | BETA: splitting (80) gives:
% 117.54/18.35 | |
% 117.54/18.35 | | Case 1:
% 117.54/18.35 | | |
% 117.54/18.35 | | | (156) ~ (all_56_14 = e2)
% 117.54/18.35 | | |
% 117.54/18.35 | | | REDUCE: (10), (156) imply:
% 117.54/18.35 | | | (157) ~ (all_6_2 = e2)
% 117.54/18.35 | | |
% 117.54/18.35 | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (12), (14), (16), (21),
% 117.54/18.35 | | | (22), (27), (31), (32), (33), (34), (35), (36), (37), (40),
% 117.54/18.35 | | | (41), (43), (46), (47), (50), (51), (52), (53), (54), (56),
% 117.54/18.35 | | | (57), (59), (61), (63), (64), (68), (69), (70), (72), (75),
% 117.54/18.35 | | | (76), (78), (81), (82), (85), (86), (92), (94), (97), (100),
% 117.54/18.35 | | | (101), (102), (104), (105), (106), (108), (109), (112), (113),
% 117.54/18.35 | | | (114), (115), (116), (117), (119), (120), (121), (122), (124),
% 117.54/18.35 | | | (125), (126), (130), (132), (133), (135), (137), (138), (157)
% 117.54/18.35 | | | are inconsistent by sub-proof #289.
% 117.54/18.35 | | |
% 117.54/18.35 | | Case 2:
% 117.54/18.35 | | |
% 117.54/18.35 | | | (158) all_56_14 = e2
% 117.54/18.35 | | |
% 117.54/18.35 | | | REF_CLOSE: (6), (8), (9), (10), (11), (13), (16), (20), (23), (26), (34),
% 117.54/18.35 | | | (38), (42), (46), (47), (48), (49), (51), (55), (60), (62),
% 117.54/18.35 | | | (64), (73), (75), (83), (84), (85), (86), (88), (89), (92),
% 117.54/18.35 | | | (93), (95), (96), (97), (99), (101), (103), (105), (107),
% 117.54/18.35 | | | (113), (114), (123), (127), (128), (131), (132), (135), (151),
% 117.54/18.35 | | | (154), (155), (158) are inconsistent by sub-proof #306.
% 117.54/18.35 | | |
% 117.54/18.35 | | End of split
% 117.54/18.35 | |
% 117.54/18.35 | End of split
% 117.54/18.35 |
% 117.54/18.35 End of proof
% 117.54/18.35
% 117.54/18.35 Sub-proof #289 shows that the following formulas are inconsistent:
% 117.54/18.35 ----------------------------------------------------------------
% 117.54/18.35 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.35 (2) ~ (all_52_2 = all_10_2)
% 117.54/18.35 (3) all_58_7 = all_52_6
% 117.54/18.35 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.35 (5) ~ (all_4_2 = e0)
% 117.54/18.35 (6) op(e3, e2) = all_52_4
% 117.54/18.35 (7) all_56_14 = all_6_2
% 117.54/18.35 (8) all_54_0 = all_10_2
% 117.54/18.35 (9) ~ (all_52_2 = all_52_6)
% 117.54/18.35 (10) ~ (all_52_7 = all_4_2)
% 117.54/18.35 (11) op(e3, all_10_2) = e1
% 117.54/18.35 (12) all_56_12 = all_10_2
% 117.54/18.35 (13) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.54/18.35 (14) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.35 (15) all_56_10 = all_52_7
% 117.54/18.35 (16) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.35 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.35 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.35 (19) all_54_8 = all_52_2
% 117.54/18.35 (20) ~ (all_52_2 = all_6_2)
% 117.54/18.35 (21) all_32_2 = all_10_2
% 117.54/18.35 (22) all_54_10 = all_6_2
% 117.54/18.35 (23) ~ (e2 = e1)
% 117.54/18.35 (24) op(e3, e0) = all_52_12
% 117.54/18.35 (25) all_58_4 = all_52_8
% 117.54/18.35 (26) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.35 (27) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.35 (28) all_58_3 = all_8_2
% 117.54/18.35 (29) ~ (all_10_0 = e2)
% 117.54/18.35 (30) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.35 (31) all_58_11 = all_52_14
% 117.54/18.35 (32) all_54_9 = all_52_6
% 117.54/18.35 (33) op(e3, e1) = all_52_8
% 117.54/18.35 (34) ~ (all_52_11 = all_6_2)
% 117.54/18.35 (35) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.35 (36) op(e1, e0) = all_52_14
% 117.54/18.35 (37) all_58_5 = all_52_9
% 117.54/18.35 (38) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.54/18.35 (39) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.35 (40) all_32_0 = all_10_0
% 117.54/18.35 (41) all_58_15 = all_4_2
% 117.54/18.35 (42) ~ (all_10_2 = e3)
% 117.54/18.35 (43) all_58_13 = all_52_7
% 117.54/18.35 (44) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.35 (45) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.54/18.35 (46) all_58_6 = all_52_2
% 117.54/18.35 (47) all_56_15 = all_4_2
% 117.54/18.35 (48) all_58_10 = all_52_13
% 117.54/18.35 (49) all_58_1 = all_52_4
% 117.54/18.35 (50) all_58_14 = all_52_11
% 117.54/18.35 (51) ~ (all_8_2 = e2)
% 117.54/18.35 (52) ~ (all_6_2 = e2)
% 117.54/18.35 (53) ~ (all_52_7 = all_52_11)
% 117.54/18.35 (54) op(e1, e2) = all_52_6
% 117.54/18.35 (55) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.35 (56) all_56_7 = all_52_6
% 117.54/18.35 (57) ~ (all_52_9 = all_6_2)
% 117.54/18.35 (58) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.35 (59) all_58_8 = all_6_2
% 117.54/18.35 (60) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.35 (61) all_56_4 = all_52_9
% 117.54/18.35 (62) all_58_9 = all_52_12
% 117.54/18.35 (63) all_56_5 = all_52_13
% 117.54/18.35 (64) op(e1, all_10_2) = all_10_0
% 117.54/18.35 (65) ~ (all_52_6 = all_6_2)
% 117.54/18.35 (66) all_56_6 = all_52_2
% 117.54/18.35 (67) all_58_12 = all_52_3
% 117.54/18.35 (68) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.35 (69) ~ (all_52_3 = all_10_2)
% 117.54/18.35 (70) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.54/18.35 (71) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 117.54/18.35 (72) all_56_8 = all_52_14
% 117.54/18.35 (73) ~ (all_52_4 = all_10_2)
% 117.54/18.35 (74) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.35 (75) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.35 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.35 (76) all_54_15 = all_4_2
% 117.54/18.35 (77) ~ (all_6_2 = e1)
% 117.54/18.35 (78) ~ (all_52_6 = all_52_7)
% 117.54/18.35
% 117.54/18.35 Begin of proof
% 117.54/18.35 |
% 117.54/18.35 | BETA: splitting (45) gives:
% 117.54/18.35 |
% 117.54/18.35 | Case 1:
% 117.54/18.35 | |
% 117.54/18.35 | | (79) ~ (all_56_12 = e2)
% 117.54/18.35 | |
% 117.54/18.35 | | REDUCE: (12), (79) imply:
% 117.54/18.35 | | (80) ~ (all_10_2 = e2)
% 117.54/18.35 | |
% 117.54/18.35 | | BETA: splitting (74) gives:
% 117.54/18.35 | |
% 117.54/18.35 | | Case 1:
% 117.54/18.35 | | |
% 117.54/18.35 | | | (81) ~ (all_56_12 = e1)
% 117.54/18.35 | | |
% 117.54/18.35 | | | REDUCE: (12), (81) imply:
% 117.54/18.35 | | | (82) ~ (all_10_2 = e1)
% 117.54/18.35 | | |
% 117.54/18.35 | | | BETA: splitting (60) gives:
% 117.54/18.35 | | |
% 117.54/18.35 | | | Case 1:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (83) all_54_0 = e3
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | REF_CLOSE: (8), (42), (83) are inconsistent by sub-proof #451.
% 117.54/18.35 | | | |
% 117.54/18.35 | | | Case 2:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | (84) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | BETA: splitting (84) gives:
% 117.54/18.35 | | | |
% 117.54/18.35 | | | | Case 1:
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | | (85) all_54_0 = e2
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | | REF_CLOSE: (8), (80), (85) are inconsistent by sub-proof #450.
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | Case 2:
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | | (86) ~ (all_54_0 = e2)
% 117.54/18.35 | | | | | (87) all_54_0 = e1 | all_54_0 = e0
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | | BETA: splitting (87) gives:
% 117.54/18.35 | | | | |
% 117.54/18.35 | | | | | Case 1:
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | (88) all_54_0 = e1
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | REF_CLOSE: (8), (82), (88) are inconsistent by sub-proof #449.
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | Case 2:
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | (89) all_54_0 = e0
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | COMBINE_EQS: (8), (89) imply:
% 117.54/18.35 | | | | | | (90) all_10_2 = e0
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | SIMP: (90) implies:
% 117.54/18.35 | | | | | | (91) all_10_2 = e0
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | COMBINE_EQS: (12), (91) imply:
% 117.54/18.35 | | | | | | (92) all_56_12 = e0
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | REDUCE: (69), (91) imply:
% 117.54/18.35 | | | | | | (93) ~ (all_52_3 = e0)
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | REDUCE: (11), (91) imply:
% 117.54/18.35 | | | | | | (94) op(e3, e0) = e1
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | REDUCE: (64), (91) imply:
% 117.54/18.35 | | | | | | (95) op(e1, e0) = all_10_0
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | BETA: splitting (38) gives:
% 117.54/18.35 | | | | | |
% 117.54/18.35 | | | | | | Case 1:
% 117.54/18.35 | | | | | | |
% 117.54/18.35 | | | | | | | (96) ~ (all_56_8 = e1)
% 117.54/18.35 | | | | | | |
% 117.54/18.35 | | | | | | | REDUCE: (72), (96) imply:
% 117.54/18.35 | | | | | | | (97) ~ (all_52_14 = e1)
% 117.54/18.35 | | | | | | |
% 117.54/18.35 | | | | | | | BETA: splitting (71) gives:
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | (98) ~ (all_56_5 = e2)
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | REDUCE: (63), (98) imply:
% 117.54/18.36 | | | | | | | | (99) ~ (all_52_13 = e2)
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | GROUND_INST: instantiating (18) with all_52_14, all_10_0, e0,
% 117.54/18.36 | | | | | | | | e1, simplifying with (36), (95) gives:
% 117.54/18.36 | | | | | | | | (100) all_52_14 = all_10_0
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | GROUND_INST: instantiating (18) with all_52_12, e1, e0, e3,
% 117.54/18.36 | | | | | | | | simplifying with (24), (94) gives:
% 117.54/18.36 | | | | | | | | (101) all_52_12 = e1
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | COMBINE_EQS: (31), (100) imply:
% 117.54/18.36 | | | | | | | | (102) all_58_11 = all_10_0
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | COMBINE_EQS: (62), (101) imply:
% 117.54/18.36 | | | | | | | | (103) all_58_9 = e1
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | BETA: splitting (44) gives:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | (104) all_58_9 = e2
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | REF_CLOSE: (23), (103), (104) are inconsistent by sub-proof
% 117.54/18.36 | | | | | | | | | #370.
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | (105) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | BETA: splitting (105) gives:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | (106) all_58_10 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | COMBINE_EQS: (48), (106) imply:
% 117.54/18.36 | | | | | | | | | | (107) all_52_13 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | REDUCE: (99), (107) imply:
% 117.54/18.36 | | | | | | | | | | (108) $false
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | CLOSE: (108) is inconsistent.
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | (109) all_58_11 = e2 | all_58_15 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | BETA: splitting (109) gives:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | (110) all_58_11 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (102), (110) imply:
% 117.54/18.36 | | | | | | | | | | | (111) all_10_0 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | REDUCE: (29), (111) imply:
% 117.54/18.36 | | | | | | | | | | | (112) $false
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | (113) all_58_15 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (41), (113) imply:
% 117.54/18.36 | | | | | | | | | | | (114) all_4_2 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (47), (114) imply:
% 117.54/18.36 | | | | | | | | | | | (115) all_56_15 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | REDUCE: (5), (114) imply:
% 117.54/18.36 | | | | | | | | | | | (116) ~ (e2 = e0)
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | REF_CLOSE: (3), (7), (13), (15), (17), (20), (22), (27),
% 117.54/18.36 | | | | | | | | | | | (31), (34), (43), (46), (50), (52), (55), (56),
% 117.54/18.36 | | | | | | | | | | | (59), (66), (67), (70), (75), (77), (93), (97),
% 117.54/18.36 | | | | | | | | | | | (113), (115), (116) are inconsistent by sub-proof
% 117.54/18.36 | | | | | | | | | | | #303.
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | End of split
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | End of split
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | End of split
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | (117) ~ (all_56_12 = e0)
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | REDUCE: (92), (117) imply:
% 117.54/18.36 | | | | | | | | (118) $false
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | CLOSE: (118) is inconsistent.
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | End of split
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | Case 2:
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | (119) all_56_8 = e1
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | REF_CLOSE: (8), (12), (38), (80), (82), (84), (119) are
% 117.54/18.36 | | | | | | | inconsistent by sub-proof #385.
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | End of split
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | End of split
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | End of split
% 117.54/18.36 | | | |
% 117.54/18.36 | | | End of split
% 117.54/18.36 | | |
% 117.54/18.36 | | Case 2:
% 117.54/18.36 | | |
% 117.54/18.36 | | | (120) all_56_12 = e1
% 117.54/18.36 | | |
% 117.54/18.36 | | | COMBINE_EQS: (12), (120) imply:
% 117.54/18.36 | | | (121) all_10_2 = e1
% 117.54/18.36 | | |
% 117.54/18.36 | | | REF_CLOSE: (1), (11), (18), (33), (121) are inconsistent by sub-proof
% 117.54/18.36 | | | #299.
% 117.54/18.36 | | |
% 117.54/18.36 | | End of split
% 117.54/18.36 | |
% 117.54/18.36 | Case 2:
% 117.54/18.36 | |
% 117.54/18.36 | | (122) all_56_12 = e2
% 117.54/18.36 | |
% 117.54/18.36 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (14), (16),
% 117.54/18.36 | | (17), (18), (19), (20), (21), (22), (25), (26), (28), (29), (30),
% 117.54/18.36 | | (32), (35), (37), (39), (40), (43), (47), (49), (50), (51), (52),
% 117.54/18.36 | | (53), (54), (56), (57), (58), (59), (61), (64), (65), (66), (68),
% 117.54/18.36 | | (73), (76), (77), (78), (122) are inconsistent by sub-proof #291.
% 117.54/18.36 | |
% 117.54/18.36 | End of split
% 117.54/18.36 |
% 117.54/18.36 End of proof
% 117.54/18.36
% 117.54/18.36 Sub-proof #290 shows that the following formulas are inconsistent:
% 117.54/18.36 ----------------------------------------------------------------
% 117.54/18.36 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.36 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.54/18.36 (3) ~ (all_52_2 = all_10_2)
% 117.54/18.36 (4) all_58_7 = all_52_6
% 117.54/18.36 (5) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.36 (6) ~ (all_4_2 = e0)
% 117.54/18.36 (7) op(e3, e2) = all_52_4
% 117.54/18.36 (8) all_56_14 = all_6_2
% 117.54/18.36 (9) all_54_0 = all_10_2
% 117.54/18.36 (10) ~ (all_52_2 = all_52_6)
% 117.54/18.36 (11) ~ (all_52_7 = all_4_2)
% 117.54/18.36 (12) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.54/18.36 (13) ~ (all_6_1 = e3)
% 117.54/18.36 (14) op(e3, all_10_2) = e1
% 117.54/18.36 (15) all_56_12 = all_10_2
% 117.54/18.36 (16) all_58_0 = all_10_2
% 117.54/18.36 (17) all_54_11 = all_52_14
% 117.54/18.36 (18) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.36 (19) ~ (all_52_14 = all_6_2)
% 117.54/18.36 (20) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.36 (21) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.36 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.36 (23) all_54_8 = all_52_2
% 117.54/18.36 (24) ~ (all_52_2 = all_6_2)
% 117.54/18.36 (25) all_32_2 = all_10_2
% 117.54/18.36 (26) all_54_10 = all_6_2
% 117.54/18.36 (27) ~ (e2 = e1)
% 117.54/18.36 (28) op(e3, e0) = all_52_12
% 117.54/18.36 (29) ~ (all_52_8 = all_6_2)
% 117.54/18.36 (30) all_58_4 = all_52_8
% 117.54/18.36 (31) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.36 (32) all_56_2 = all_52_12
% 117.54/18.36 (33) all_58_3 = all_8_2
% 117.54/18.36 (34) ~ (all_10_0 = e2)
% 117.54/18.36 (35) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.36 (36) all_58_11 = all_52_14
% 117.54/18.36 (37) all_54_9 = all_52_6
% 117.54/18.36 (38) op(e3, e1) = all_52_8
% 117.54/18.36 (39) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.36 (40) op(e1, e0) = all_52_14
% 117.54/18.36 (41) all_58_5 = all_52_9
% 117.54/18.36 (42) op(e1, all_6_2) = all_6_1
% 117.54/18.36 (43) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.36 (44) all_32_0 = all_10_0
% 117.54/18.36 (45) all_58_15 = all_4_2
% 117.54/18.36 (46) ~ (all_10_2 = e3)
% 117.54/18.36 (47) all_58_13 = all_52_7
% 117.54/18.36 (48) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.36 (49) ~ (all_56_10 = e0) | ~ (all_56_12 = e2)
% 117.54/18.36 (50) all_56_15 = all_4_2
% 117.54/18.36 (51) all_58_10 = all_52_13
% 117.54/18.36 (52) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.54/18.36 (53) all_58_1 = all_52_4
% 117.54/18.36 (54) all_58_14 = all_52_11
% 117.54/18.36 (55) ~ (all_8_2 = e2)
% 117.54/18.36 (56) ~ (all_6_2 = e2)
% 117.54/18.36 (57) ~ (all_52_7 = all_52_11)
% 117.54/18.36 (58) op(e1, e2) = all_52_6
% 117.54/18.36 (59) all_56_7 = all_52_6
% 117.54/18.36 (60) ~ (all_52_9 = all_6_2)
% 117.54/18.36 (61) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.36 (62) all_58_8 = all_6_2
% 117.54/18.36 (63) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.36 (64) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.54/18.36 (65) all_56_4 = all_52_9
% 117.54/18.36 (66) all_58_9 = all_52_12
% 117.54/18.36 (67) all_56_5 = all_52_13
% 117.54/18.36 (68) op(e1, all_10_2) = all_10_0
% 117.54/18.36 (69) ~ (all_52_6 = all_6_2)
% 117.54/18.36 (70) all_56_6 = all_52_2
% 117.54/18.36 (71) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.36 (72) ~ (all_56_5 = e2) | ~ (all_56_12 = e0)
% 117.54/18.36 (73) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.54/18.36 (74) all_56_8 = all_52_14
% 117.54/18.36 (75) ~ (all_52_4 = all_10_2)
% 117.54/18.36 (76) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.36 (77) all_56_0 = all_52_4
% 117.54/18.36 (78) all_54_15 = all_4_2
% 117.54/18.36 (79) ~ (all_6_2 = e1)
% 117.54/18.36 (80) ~ (all_6_1 = e2)
% 117.54/18.36 (81) ~ (all_52_6 = all_52_7)
% 117.54/18.36
% 117.54/18.36 Begin of proof
% 117.54/18.36 |
% 117.54/18.36 | BETA: splitting (49) gives:
% 117.54/18.36 |
% 117.54/18.36 | Case 1:
% 117.54/18.36 | |
% 117.54/18.36 | | (82) ~ (all_56_12 = e2)
% 117.54/18.36 | |
% 117.54/18.36 | | REDUCE: (15), (82) imply:
% 117.54/18.36 | | (83) ~ (all_10_2 = e2)
% 117.54/18.36 | |
% 117.54/18.36 | | BETA: splitting (76) gives:
% 117.54/18.36 | |
% 117.54/18.36 | | Case 1:
% 117.54/18.36 | | |
% 117.54/18.36 | | | (84) ~ (all_56_12 = e1)
% 117.54/18.36 | | |
% 117.54/18.36 | | | REDUCE: (15), (84) imply:
% 117.54/18.36 | | | (85) ~ (all_10_2 = e1)
% 117.54/18.36 | | |
% 117.54/18.36 | | | BETA: splitting (63) gives:
% 117.54/18.36 | | |
% 117.54/18.36 | | | Case 1:
% 117.54/18.36 | | | |
% 117.54/18.36 | | | | (86) all_54_0 = e3
% 117.54/18.36 | | | |
% 117.54/18.36 | | | | REF_CLOSE: (9), (46), (86) are inconsistent by sub-proof #451.
% 117.54/18.36 | | | |
% 117.54/18.36 | | | Case 2:
% 117.54/18.36 | | | |
% 117.54/18.36 | | | | (87) ~ (all_54_0 = e3)
% 117.54/18.36 | | | | (88) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.36 | | | |
% 117.54/18.36 | | | | BETA: splitting (88) gives:
% 117.54/18.36 | | | |
% 117.54/18.36 | | | | Case 1:
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | | (89) all_54_0 = e2
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | | REF_CLOSE: (9), (83), (89) are inconsistent by sub-proof #450.
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | Case 2:
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | | (90) ~ (all_54_0 = e2)
% 117.54/18.36 | | | | | (91) all_54_0 = e1 | all_54_0 = e0
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | | BETA: splitting (91) gives:
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | | Case 1:
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | (92) all_54_0 = e1
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | REF_CLOSE: (9), (85), (92) are inconsistent by sub-proof #449.
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | Case 2:
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | (93) all_54_0 = e0
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | COMBINE_EQS: (9), (93) imply:
% 117.54/18.36 | | | | | | (94) all_10_2 = e0
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | SIMP: (94) implies:
% 117.54/18.36 | | | | | | (95) all_10_2 = e0
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | COMBINE_EQS: (15), (95) imply:
% 117.54/18.36 | | | | | | (96) all_56_12 = e0
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | REDUCE: (14), (95) imply:
% 117.54/18.36 | | | | | | (97) op(e3, e0) = e1
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | REDUCE: (68), (95) imply:
% 117.54/18.36 | | | | | | (98) op(e1, e0) = all_10_0
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | BETA: splitting (72) gives:
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | | Case 1:
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | (99) ~ (all_56_5 = e2)
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | REDUCE: (67), (99) imply:
% 117.54/18.36 | | | | | | | (100) ~ (all_52_13 = e2)
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | BETA: splitting (2) gives:
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | (101) ~ (all_56_2 = e3)
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | REDUCE: (32), (101) imply:
% 117.54/18.36 | | | | | | | | (102) ~ (all_52_12 = e3)
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | GROUND_INST: instantiating (22) with all_52_14, all_10_0, e0,
% 117.54/18.36 | | | | | | | | e1, simplifying with (40), (98) gives:
% 117.54/18.36 | | | | | | | | (103) all_52_14 = all_10_0
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | GROUND_INST: instantiating (22) with all_52_12, e1, e0, e3,
% 117.54/18.36 | | | | | | | | simplifying with (28), (97) gives:
% 117.54/18.36 | | | | | | | | (104) all_52_12 = e1
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | COMBINE_EQS: (36), (103) imply:
% 117.54/18.36 | | | | | | | | (105) all_58_11 = all_10_0
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | COMBINE_EQS: (66), (104) imply:
% 117.54/18.36 | | | | | | | | (106) all_58_9 = e1
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | BETA: splitting (48) gives:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | (107) all_58_9 = e2
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | REF_CLOSE: (27), (106), (107) are inconsistent by sub-proof
% 117.54/18.36 | | | | | | | | | #370.
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | (108) all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | BETA: splitting (108) gives:
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | (109) all_58_10 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | COMBINE_EQS: (51), (109) imply:
% 117.54/18.36 | | | | | | | | | | (110) all_52_13 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | REDUCE: (100), (110) imply:
% 117.54/18.36 | | | | | | | | | | (111) $false
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | CLOSE: (111) is inconsistent.
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | (112) all_58_11 = e2 | all_58_15 = e2
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | BETA: splitting (112) gives:
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | (113) all_58_11 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (105), (113) imply:
% 117.54/18.36 | | | | | | | | | | | (114) all_10_0 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | REDUCE: (34), (114) imply:
% 117.54/18.36 | | | | | | | | | | | (115) $false
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | (116) all_58_15 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (45), (116) imply:
% 117.54/18.36 | | | | | | | | | | | (117) all_4_2 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | COMBINE_EQS: (50), (117) imply:
% 117.54/18.36 | | | | | | | | | | | (118) all_56_15 = e2
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | BETA: splitting (52) gives:
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | Case 1:
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | (119) ~ (all_56_0 = e3)
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | REDUCE: (77), (119) imply:
% 117.54/18.36 | | | | | | | | | | | | (120) ~ (all_52_4 = e3)
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | REF_CLOSE: (1), (8), (12), (13), (16), (17), (19), (21),
% 117.54/18.36 | | | | | | | | | | | | (22), (26), (29), (30), (40), (42), (46), (53),
% 117.54/18.36 | | | | | | | | | | | | (56), (64), (66), (73), (74), (79), (80), (102),
% 117.54/18.36 | | | | | | | | | | | | (120) are inconsistent by sub-proof #411.
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | (121) ~ (all_56_15 = e2)
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | REDUCE: (118), (121) imply:
% 117.54/18.36 | | | | | | | | | | | | (122) $false
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 117.54/18.36 | | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | | End of split
% 117.54/18.36 | | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | | End of split
% 117.54/18.36 | | | | | | | | | |
% 117.54/18.36 | | | | | | | | | End of split
% 117.54/18.36 | | | | | | | | |
% 117.54/18.36 | | | | | | | | End of split
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | Case 2:
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | (123) all_56_2 = e3
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | | REF_CLOSE: (1), (2), (9), (14), (15), (22), (38), (46), (63),
% 117.54/18.36 | | | | | | | | (83), (123) are inconsistent by sub-proof #297.
% 117.54/18.36 | | | | | | | |
% 117.54/18.36 | | | | | | | End of split
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | Case 2:
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | (124) ~ (all_56_12 = e0)
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | REDUCE: (96), (124) imply:
% 117.54/18.36 | | | | | | | (125) $false
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | | CLOSE: (125) is inconsistent.
% 117.54/18.36 | | | | | | |
% 117.54/18.36 | | | | | | End of split
% 117.54/18.36 | | | | | |
% 117.54/18.36 | | | | | End of split
% 117.54/18.36 | | | | |
% 117.54/18.36 | | | | End of split
% 117.54/18.36 | | | |
% 117.54/18.36 | | | End of split
% 117.54/18.36 | | |
% 117.54/18.36 | | Case 2:
% 117.54/18.36 | | |
% 117.54/18.36 | | | (126) all_56_12 = e1
% 117.54/18.36 | | |
% 117.54/18.36 | | | COMBINE_EQS: (15), (126) imply:
% 117.54/18.36 | | | (127) all_10_2 = e1
% 117.54/18.36 | | |
% 117.54/18.36 | | | REF_CLOSE: (1), (14), (22), (38), (127) are inconsistent by sub-proof
% 117.54/18.36 | | | #299.
% 117.54/18.36 | | |
% 117.54/18.36 | | End of split
% 117.54/18.36 | |
% 117.54/18.36 | Case 2:
% 117.54/18.36 | |
% 117.54/18.36 | | (128) all_56_12 = e2
% 117.54/18.36 | |
% 117.54/18.36 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (14), (15), (18), (20),
% 117.54/18.36 | | (21), (22), (23), (24), (25), (26), (30), (31), (33), (34), (35),
% 117.54/18.36 | | (37), (39), (41), (43), (44), (47), (50), (53), (54), (55), (56),
% 117.54/18.36 | | (57), (58), (59), (60), (61), (62), (65), (68), (69), (70), (71),
% 117.54/18.36 | | (75), (78), (79), (81), (128) are inconsistent by sub-proof #291.
% 117.54/18.36 | |
% 117.54/18.36 | End of split
% 117.54/18.36 |
% 117.54/18.36 End of proof
% 117.54/18.36
% 117.54/18.36 Sub-proof #291 shows that the following formulas are inconsistent:
% 117.54/18.36 ----------------------------------------------------------------
% 117.54/18.36 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.36 (2) ~ (all_52_2 = all_10_2)
% 117.54/18.36 (3) all_58_7 = all_52_6
% 117.54/18.36 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.36 (5) ~ (all_4_2 = e0)
% 117.54/18.36 (6) op(e3, e2) = all_52_4
% 117.54/18.37 (7) ~ (all_52_2 = all_52_6)
% 117.54/18.37 (8) ~ (all_52_7 = all_4_2)
% 117.54/18.37 (9) op(e3, all_10_2) = e1
% 117.54/18.37 (10) all_56_12 = all_10_2
% 117.54/18.37 (11) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.37 (12) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.37 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.37 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.37 (15) all_54_8 = all_52_2
% 117.54/18.37 (16) ~ (all_52_2 = all_6_2)
% 117.54/18.37 (17) all_32_2 = all_10_2
% 117.54/18.37 (18) all_54_10 = all_6_2
% 117.54/18.37 (19) all_58_4 = all_52_8
% 117.54/18.37 (20) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.37 (21) all_56_12 = e2
% 117.54/18.37 (22) all_58_3 = all_8_2
% 117.54/18.37 (23) ~ (all_10_0 = e2)
% 117.54/18.37 (24) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.37 (25) all_54_9 = all_52_6
% 117.54/18.37 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.37 (27) all_58_5 = all_52_9
% 117.54/18.37 (28) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.37 (29) all_32_0 = all_10_0
% 117.54/18.37 (30) all_58_13 = all_52_7
% 117.54/18.37 (31) all_56_15 = all_4_2
% 117.54/18.37 (32) all_58_1 = all_52_4
% 117.54/18.37 (33) all_58_14 = all_52_11
% 117.54/18.37 (34) ~ (all_8_2 = e2)
% 117.54/18.37 (35) ~ (all_6_2 = e2)
% 117.54/18.37 (36) ~ (all_52_7 = all_52_11)
% 117.54/18.37 (37) op(e1, e2) = all_52_6
% 117.54/18.37 (38) all_56_7 = all_52_6
% 117.54/18.37 (39) ~ (all_52_9 = all_6_2)
% 117.54/18.37 (40) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.37 (41) all_58_8 = all_6_2
% 117.54/18.37 (42) all_56_4 = all_52_9
% 117.54/18.37 (43) op(e1, all_10_2) = all_10_0
% 117.54/18.37 (44) ~ (all_52_6 = all_6_2)
% 117.54/18.37 (45) all_56_6 = all_52_2
% 117.54/18.37 (46) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.37 (47) ~ (all_52_4 = all_10_2)
% 117.54/18.37 (48) all_54_15 = all_4_2
% 117.54/18.37 (49) ~ (all_6_2 = e1)
% 117.54/18.37 (50) ~ (all_52_6 = all_52_7)
% 117.54/18.37
% 117.54/18.37 Begin of proof
% 117.54/18.37 |
% 117.54/18.37 | COMBINE_EQS: (10), (21) imply:
% 117.54/18.37 | (51) all_10_2 = e2
% 117.54/18.37 |
% 117.54/18.37 | SIMP: (51) implies:
% 117.54/18.37 | (52) all_10_2 = e2
% 117.54/18.37 |
% 117.54/18.37 | COMBINE_EQS: (17), (52) imply:
% 117.54/18.37 | (53) all_32_2 = e2
% 117.54/18.37 |
% 117.54/18.37 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 117.54/18.37 | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 117.54/18.37 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 117.54/18.37 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 117.54/18.37 | (48), (49), (50), (52), (53) are inconsistent by sub-proof #292.
% 117.54/18.37 |
% 117.54/18.37 End of proof
% 117.54/18.37
% 117.54/18.37 Sub-proof #292 shows that the following formulas are inconsistent:
% 117.54/18.37 ----------------------------------------------------------------
% 117.54/18.37 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.37 (2) ~ (all_52_2 = all_10_2)
% 117.54/18.37 (3) all_58_7 = all_52_6
% 117.54/18.37 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.37 (5) ~ (all_4_2 = e0)
% 117.54/18.37 (6) op(e3, e2) = all_52_4
% 117.54/18.37 (7) ~ (all_52_2 = all_52_6)
% 117.54/18.37 (8) ~ (all_52_7 = all_4_2)
% 117.54/18.37 (9) op(e3, all_10_2) = e1
% 117.54/18.37 (10) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.37 (11) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.37 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.37 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.37 (14) all_54_8 = all_52_2
% 117.54/18.37 (15) ~ (all_52_2 = all_6_2)
% 117.54/18.37 (16) all_10_2 = e2
% 117.54/18.37 (17) all_54_10 = all_6_2
% 117.54/18.37 (18) all_58_4 = all_52_8
% 117.54/18.37 (19) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.37 (20) all_56_12 = e2
% 117.54/18.37 (21) all_58_3 = all_8_2
% 117.54/18.37 (22) ~ (all_10_0 = e2)
% 117.54/18.37 (23) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.37 (24) all_54_9 = all_52_6
% 117.54/18.37 (25) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.37 (26) all_58_5 = all_52_9
% 117.54/18.37 (27) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.37 (28) all_32_0 = all_10_0
% 117.54/18.37 (29) all_58_13 = all_52_7
% 117.54/18.37 (30) all_56_15 = all_4_2
% 117.54/18.37 (31) all_58_1 = all_52_4
% 117.54/18.37 (32) all_58_14 = all_52_11
% 117.54/18.37 (33) ~ (all_8_2 = e2)
% 117.54/18.37 (34) ~ (all_6_2 = e2)
% 117.54/18.37 (35) ~ (all_52_7 = all_52_11)
% 117.54/18.37 (36) op(e1, e2) = all_52_6
% 117.54/18.37 (37) all_56_7 = all_52_6
% 117.54/18.37 (38) ~ (all_52_9 = all_6_2)
% 117.54/18.37 (39) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.37 (40) all_58_8 = all_6_2
% 117.54/18.37 (41) all_32_2 = e2
% 117.54/18.37 (42) all_56_4 = all_52_9
% 117.54/18.37 (43) op(e1, all_10_2) = all_10_0
% 117.54/18.37 (44) ~ (all_52_6 = all_6_2)
% 117.54/18.37 (45) all_56_6 = all_52_2
% 117.54/18.37 (46) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.37 (47) ~ (all_52_4 = all_10_2)
% 117.54/18.37 (48) all_54_15 = all_4_2
% 117.54/18.37 (49) ~ (all_6_2 = e1)
% 117.54/18.37 (50) ~ (all_52_6 = all_52_7)
% 117.54/18.37
% 117.54/18.37 Begin of proof
% 117.54/18.37 |
% 117.54/18.37 | REDUCE: (2), (16) imply:
% 117.54/18.37 | (51) ~ (all_52_2 = e2)
% 117.54/18.37 |
% 117.54/18.37 | REDUCE: (16), (47) imply:
% 117.54/18.37 | (52) ~ (all_52_4 = e2)
% 117.54/18.37 |
% 117.54/18.37 | REDUCE: (1), (16) imply:
% 117.54/18.37 | (53) ~ (all_52_8 = e2)
% 117.54/18.37 |
% 117.54/18.37 | REDUCE: (9), (16) imply:
% 117.54/18.37 | (54) op(e3, e2) = e1
% 117.54/18.37 |
% 117.54/18.37 | REDUCE: (16), (43) imply:
% 117.54/18.37 | (55) op(e1, e2) = all_10_0
% 117.54/18.37 |
% 117.54/18.37 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 117.54/18.37 | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 117.54/18.37 | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 117.54/18.37 | (39), (40), (41), (42), (44), (45), (46), (48), (49), (50), (51),
% 117.54/18.37 | (52), (53), (54), (55) are inconsistent by sub-proof #293.
% 117.54/18.37 |
% 117.54/18.37 End of proof
% 117.54/18.37
% 117.54/18.37 Sub-proof #293 shows that the following formulas are inconsistent:
% 117.54/18.37 ----------------------------------------------------------------
% 117.54/18.37 (1) all_58_7 = all_52_6
% 117.54/18.37 (2) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.54/18.37 (3) ~ (all_4_2 = e0)
% 117.54/18.37 (4) op(e3, e2) = all_52_4
% 117.54/18.37 (5) ~ (all_52_2 = all_52_6)
% 117.54/18.37 (6) ~ (all_52_7 = all_4_2)
% 117.54/18.37 (7) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.37 (8) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.37 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.37 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.37 (11) all_54_8 = all_52_2
% 117.54/18.37 (12) ~ (all_52_2 = all_6_2)
% 117.54/18.37 (13) all_54_10 = all_6_2
% 117.54/18.37 (14) all_58_4 = all_52_8
% 117.54/18.37 (15) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.37 (16) all_56_12 = e2
% 117.54/18.37 (17) all_58_3 = all_8_2
% 117.54/18.37 (18) ~ (all_10_0 = e2)
% 117.54/18.37 (19) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.37 (20) all_54_9 = all_52_6
% 117.54/18.37 (21) op(e3, e2) = e1
% 117.54/18.37 (22) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.37 (23) all_58_5 = all_52_9
% 117.54/18.37 (24) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.54/18.37 (25) all_32_0 = all_10_0
% 117.54/18.37 (26) all_58_13 = all_52_7
% 117.54/18.37 (27) all_56_15 = all_4_2
% 117.54/18.37 (28) op(e1, e2) = all_10_0
% 117.54/18.37 (29) all_58_1 = all_52_4
% 117.54/18.37 (30) all_58_14 = all_52_11
% 117.54/18.37 (31) ~ (all_52_8 = e2)
% 117.54/18.37 (32) ~ (all_8_2 = e2)
% 117.54/18.37 (33) ~ (all_6_2 = e2)
% 117.54/18.37 (34) ~ (all_52_7 = all_52_11)
% 117.54/18.37 (35) op(e1, e2) = all_52_6
% 117.54/18.37 (36) all_56_7 = all_52_6
% 117.54/18.37 (37) ~ (all_52_9 = all_6_2)
% 117.54/18.37 (38) ~ (all_32_0 = e0) | ~ (all_32_2 = e2)
% 117.54/18.37 (39) all_58_8 = all_6_2
% 117.54/18.37 (40) all_32_2 = e2
% 117.54/18.37 (41) all_56_4 = all_52_9
% 117.54/18.37 (42) ~ (all_52_6 = all_6_2)
% 117.54/18.37 (43) all_56_6 = all_52_2
% 117.54/18.37 (44) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.37 (45) ~ (all_52_2 = e2)
% 117.54/18.37 (46) all_54_15 = all_4_2
% 117.54/18.37 (47) ~ (all_6_2 = e1)
% 117.54/18.37 (48) ~ (all_52_6 = all_52_7)
% 117.54/18.37 (49) ~ (all_52_4 = e2)
% 117.54/18.37
% 117.54/18.37 Begin of proof
% 117.54/18.37 |
% 117.54/18.37 | BETA: splitting (38) gives:
% 117.54/18.37 |
% 117.54/18.37 | Case 1:
% 117.54/18.37 | |
% 117.54/18.37 | | (50) ~ (all_32_2 = e2)
% 117.54/18.37 | |
% 117.54/18.37 | | REDUCE: (40), (50) imply:
% 117.54/18.37 | | (51) $false
% 117.54/18.37 | |
% 117.54/18.37 | | CLOSE: (51) is inconsistent.
% 117.54/18.37 | |
% 117.54/18.37 | Case 2:
% 117.54/18.37 | |
% 117.54/18.37 | | (52) ~ (all_32_0 = e0)
% 117.54/18.37 | |
% 117.54/18.37 | | REDUCE: (25), (52) imply:
% 117.54/18.37 | | (53) ~ (all_10_0 = e0)
% 117.54/18.37 | |
% 117.54/18.37 | | BETA: splitting (24) gives:
% 117.54/18.37 | |
% 117.54/18.37 | | Case 1:
% 117.54/18.37 | | |
% 117.54/18.37 | | | (54) ~ (all_56_7 = e1)
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (36), (54) imply:
% 117.54/18.37 | | | (55) ~ (all_52_6 = e1)
% 117.54/18.37 | | |
% 117.54/18.37 | | | GROUND_INST: instantiating (10) with all_52_6, all_10_0, e2, e1,
% 117.54/18.37 | | | simplifying with (28), (35) gives:
% 117.54/18.37 | | | (56) all_52_6 = all_10_0
% 117.54/18.37 | | |
% 117.54/18.37 | | | GROUND_INST: instantiating (10) with all_52_4, e1, e2, e3, simplifying
% 117.54/18.37 | | | with (4), (21) gives:
% 117.54/18.37 | | | (57) all_52_4 = e1
% 117.54/18.37 | | |
% 117.54/18.37 | | | COMBINE_EQS: (20), (56) imply:
% 117.54/18.37 | | | (58) all_54_9 = all_10_0
% 117.54/18.37 | | |
% 117.54/18.37 | | | COMBINE_EQS: (1), (56) imply:
% 117.54/18.37 | | | (59) all_58_7 = all_10_0
% 117.54/18.37 | | |
% 117.54/18.37 | | | COMBINE_EQS: (29), (57) imply:
% 117.54/18.37 | | | (60) all_58_1 = e1
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (5), (56) imply:
% 117.54/18.37 | | | (61) ~ (all_52_2 = all_10_0)
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (49), (57) imply:
% 117.54/18.37 | | | (62) ~ (e2 = e1)
% 117.54/18.37 | | |
% 117.54/18.37 | | | SIMP: (62) implies:
% 117.54/18.37 | | | (63) ~ (e2 = e1)
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (48), (56) imply:
% 117.54/18.37 | | | (64) ~ (all_52_7 = all_10_0)
% 117.54/18.37 | | |
% 117.54/18.37 | | | SIMP: (64) implies:
% 117.54/18.37 | | | (65) ~ (all_52_7 = all_10_0)
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (42), (56) imply:
% 117.54/18.37 | | | (66) ~ (all_10_0 = all_6_2)
% 117.54/18.37 | | |
% 117.54/18.37 | | | REDUCE: (55), (56) imply:
% 117.54/18.37 | | | (67) ~ (all_10_0 = e1)
% 117.54/18.37 | | |
% 117.54/18.37 | | | BETA: splitting (7) gives:
% 117.54/18.37 | | |
% 117.54/18.37 | | | Case 1:
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | (68) all_58_1 = e2
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | COMBINE_EQS: (60), (68) imply:
% 117.54/18.37 | | | | (69) e2 = e1
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | SIMP: (69) implies:
% 117.54/18.37 | | | | (70) e2 = e1
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | REDUCE: (63), (70) imply:
% 117.54/18.37 | | | | (71) $false
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | CLOSE: (71) is inconsistent.
% 117.54/18.37 | | | |
% 117.54/18.37 | | | Case 2:
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | (72) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | BETA: splitting (72) gives:
% 117.54/18.37 | | | |
% 117.54/18.37 | | | | Case 1:
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | (73) all_58_3 = e2
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | COMBINE_EQS: (17), (73) imply:
% 117.54/18.37 | | | | | (74) all_8_2 = e2
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | REDUCE: (32), (74) imply:
% 117.54/18.37 | | | | | (75) $false
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | CLOSE: (75) is inconsistent.
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | Case 2:
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | (76) all_58_7 = e2 | all_58_13 = e2
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | BETA: splitting (76) gives:
% 117.54/18.37 | | | | |
% 117.54/18.37 | | | | | Case 1:
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | (77) all_58_7 = e2
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | COMBINE_EQS: (59), (77) imply:
% 117.54/18.37 | | | | | | (78) all_10_0 = e2
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | REDUCE: (18), (78) imply:
% 117.54/18.37 | | | | | | (79) $false
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | CLOSE: (79) is inconsistent.
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | Case 2:
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | (80) all_58_13 = e2
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | COMBINE_EQS: (26), (80) imply:
% 117.54/18.37 | | | | | | (81) all_52_7 = e2
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | SIMP: (81) implies:
% 117.54/18.37 | | | | | | (82) all_52_7 = e2
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | REDUCE: (34), (82) imply:
% 117.54/18.37 | | | | | | (83) ~ (all_52_11 = e2)
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | SIMP: (83) implies:
% 117.54/18.37 | | | | | | (84) ~ (all_52_11 = e2)
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | REDUCE: (65), (82) imply:
% 117.54/18.37 | | | | | | (85) ~ (all_10_0 = e2)
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | REDUCE: (6), (82) imply:
% 117.54/18.37 | | | | | | (86) ~ (all_4_2 = e2)
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | SIMP: (86) implies:
% 117.54/18.37 | | | | | | (87) ~ (all_4_2 = e2)
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | BETA: splitting (8) gives:
% 117.54/18.37 | | | | | |
% 117.54/18.37 | | | | | | Case 1:
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | (88) all_58_4 = e2
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | COMBINE_EQS: (14), (88) imply:
% 117.54/18.37 | | | | | | | (89) all_52_8 = e2
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | REDUCE: (31), (89) imply:
% 117.54/18.37 | | | | | | | (90) $false
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | CLOSE: (90) is inconsistent.
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | Case 2:
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | (91) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | BETA: splitting (91) gives:
% 117.54/18.37 | | | | | | |
% 117.54/18.37 | | | | | | | Case 1:
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | (92) all_58_5 = e2
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | COMBINE_EQS: (23), (92) imply:
% 117.54/18.37 | | | | | | | | (93) all_52_9 = e2
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | COMBINE_EQS: (41), (93) imply:
% 117.54/18.37 | | | | | | | | (94) all_56_4 = e2
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | REDUCE: (37), (93) imply:
% 117.54/18.37 | | | | | | | | (95) ~ (all_6_2 = e2)
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | BETA: splitting (19) gives:
% 117.54/18.37 | | | | | | | |
% 117.54/18.37 | | | | | | | | Case 1:
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | (96) all_54_9 = e3
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | COMBINE_EQS: (58), (96) imply:
% 117.54/18.37 | | | | | | | | | (97) all_10_0 = e3
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | REDUCE: (61), (97) imply:
% 117.54/18.37 | | | | | | | | | (98) ~ (all_52_2 = e3)
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | REDUCE: (66), (97) imply:
% 117.54/18.37 | | | | | | | | | (99) ~ (all_6_2 = e3)
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | SIMP: (99) implies:
% 117.54/18.37 | | | | | | | | | (100) ~ (all_6_2 = e3)
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | BETA: splitting (9) gives:
% 117.54/18.37 | | | | | | | | |
% 117.54/18.37 | | | | | | | | | Case 1:
% 117.54/18.37 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | (101) all_54_10 = e3
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | COMBINE_EQS: (13), (101) imply:
% 117.54/18.38 | | | | | | | | | | (102) all_6_2 = e3
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | REDUCE: (100), (102) imply:
% 117.54/18.38 | | | | | | | | | | (103) $false
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | CLOSE: (103) is inconsistent.
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | (104) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | BETA: splitting (44) gives:
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | Case 1:
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | (105) ~ (all_56_4 = e2)
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | REDUCE: (94), (105) imply:
% 117.54/18.38 | | | | | | | | | | | (106) $false
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | CLOSE: (106) is inconsistent.
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | (107) ~ (all_56_15 = e1)
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | REDUCE: (27), (107) imply:
% 117.54/18.38 | | | | | | | | | | | (108) ~ (all_4_2 = e1)
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | BETA: splitting (15) gives:
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | Case 1:
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | (109) all_54_15 = e3
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | COMBINE_EQS: (46), (109) imply:
% 117.54/18.38 | | | | | | | | | | | | (110) all_4_2 = e3
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | COMBINE_EQS: (27), (110) imply:
% 117.54/18.38 | | | | | | | | | | | | (111) all_56_15 = e3
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | BETA: splitting (2) gives:
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | Case 1:
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | (112) ~ (all_56_6 = e1)
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | REDUCE: (43), (112) imply:
% 117.54/18.38 | | | | | | | | | | | | | (113) ~ (all_52_2 = e1)
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (22), (33), (45), (47), (98),
% 117.54/18.38 | | | | | | | | | | | | | (104), (113) are inconsistent by sub-proof #296.
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | (114) ~ (all_56_15 = e3)
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | REDUCE: (111), (114) imply:
% 117.54/18.38 | | | | | | | | | | | | | (115) $false
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 117.54/18.38 | | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | (116) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | | REF_CLOSE: (3), (46), (87), (108), (116) are inconsistent by
% 117.54/18.38 | | | | | | | | | | | | sub-proof #417.
% 117.54/18.38 | | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | |
% 117.54/18.38 | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | |
% 117.54/18.38 | | | | | | | | | (117) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.54/18.38 | | | | | | | | |
% 117.54/18.38 | | | | | | | | | BETA: splitting (117) gives:
% 117.54/18.38 | | | | | | | | |
% 117.54/18.38 | | | | | | | | | Case 1:
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | (118) all_54_9 = e2
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | COMBINE_EQS: (58), (118) imply:
% 117.54/18.38 | | | | | | | | | | (119) all_10_0 = e2
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | REDUCE: (18), (119) imply:
% 117.54/18.38 | | | | | | | | | | (120) $false
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | CLOSE: (120) is inconsistent.
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | (121) all_54_9 = e1 | all_54_9 = e0
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | BETA: splitting (121) gives:
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | Case 1:
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | (122) all_54_9 = e1
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | COMBINE_EQS: (58), (122) imply:
% 117.54/18.38 | | | | | | | | | | | (123) all_10_0 = e1
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | REDUCE: (67), (123) imply:
% 117.54/18.38 | | | | | | | | | | | (124) $false
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | (125) all_54_9 = e0
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | COMBINE_EQS: (58), (125) imply:
% 117.54/18.38 | | | | | | | | | | | (126) all_10_0 = e0
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | REDUCE: (53), (126) imply:
% 117.54/18.38 | | | | | | | | | | | (127) $false
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 117.54/18.38 | | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | | |
% 117.54/18.38 | | | | | | | | | End of split
% 117.54/18.38 | | | | | | | | |
% 117.54/18.38 | | | | | | | | End of split
% 117.54/18.38 | | | | | | | |
% 117.54/18.38 | | | | | | | Case 2:
% 117.54/18.38 | | | | | | | |
% 117.54/18.38 | | | | | | | | (128) all_58_8 = e2 | all_58_14 = e2
% 117.54/18.38 | | | | | | | |
% 117.54/18.38 | | | | | | | | REF_CLOSE: (30), (33), (39), (84), (128) are inconsistent by
% 117.54/18.38 | | | | | | | | sub-proof #294.
% 117.54/18.38 | | | | | | | |
% 117.54/18.38 | | | | | | | End of split
% 117.54/18.38 | | | | | | |
% 117.54/18.38 | | | | | | End of split
% 117.54/18.38 | | | | | |
% 117.54/18.38 | | | | | End of split
% 117.54/18.38 | | | | |
% 117.54/18.38 | | | | End of split
% 117.54/18.38 | | | |
% 117.54/18.38 | | | End of split
% 117.54/18.38 | | |
% 117.54/18.38 | | Case 2:
% 117.54/18.38 | | |
% 117.54/18.38 | | | (129) ~ (all_56_12 = e2)
% 117.54/18.38 | | |
% 117.54/18.38 | | | REDUCE: (16), (129) imply:
% 117.54/18.38 | | | (130) $false
% 117.54/18.38 | | |
% 117.54/18.38 | | | CLOSE: (130) is inconsistent.
% 117.54/18.38 | | |
% 117.54/18.38 | | End of split
% 117.54/18.38 | |
% 117.54/18.38 | End of split
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #294 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) all_58_8 = e2 | all_58_14 = e2
% 117.54/18.38 (2) ~ (all_52_11 = e2)
% 117.54/18.38 (3) all_58_14 = all_52_11
% 117.54/18.38 (4) ~ (all_6_2 = e2)
% 117.54/18.38 (5) all_58_8 = all_6_2
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | BETA: splitting (1) gives:
% 117.54/18.38 |
% 117.54/18.38 | Case 1:
% 117.54/18.38 | |
% 117.54/18.38 | | (6) all_58_8 = e2
% 117.54/18.38 | |
% 117.54/18.38 | | COMBINE_EQS: (5), (6) imply:
% 117.54/18.38 | | (7) all_6_2 = e2
% 117.54/18.38 | |
% 117.54/18.38 | | REDUCE: (4), (7) imply:
% 117.54/18.38 | | (8) $false
% 117.54/18.38 | |
% 117.54/18.38 | | CLOSE: (8) is inconsistent.
% 117.54/18.38 | |
% 117.54/18.38 | Case 2:
% 117.54/18.38 | |
% 117.54/18.38 | | (9) all_58_14 = e2
% 117.54/18.38 | |
% 117.54/18.38 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #295.
% 117.54/18.38 | |
% 117.54/18.38 | End of split
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #295 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) all_58_14 = all_52_11
% 117.54/18.38 (2) all_58_14 = e2
% 117.54/18.38 (3) ~ (all_52_11 = e2)
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | COMBINE_EQS: (1), (2) imply:
% 117.54/18.38 | (4) all_52_11 = e2
% 117.54/18.38 |
% 117.54/18.38 | SIMP: (4) implies:
% 117.54/18.38 | (5) all_52_11 = e2
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (3), (5) imply:
% 117.54/18.38 | (6) $false
% 117.54/18.38 |
% 117.54/18.38 | CLOSE: (6) is inconsistent.
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #296 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) all_54_8 = all_52_2
% 117.54/18.38 (2) ~ (all_52_2 = all_6_2)
% 117.54/18.38 (3) all_54_10 = all_6_2
% 117.54/18.38 (4) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.38 (5) ~ (all_52_2 = e3)
% 117.54/18.38 (6) ~ (all_52_2 = e1)
% 117.54/18.38 (7) ~ (all_6_2 = e2)
% 117.54/18.38 (8) ~ (all_52_2 = e2)
% 117.54/18.38 (9) ~ (all_6_2 = e1)
% 117.54/18.38 (10) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | BETA: splitting (4) gives:
% 117.54/18.38 |
% 117.54/18.38 | Case 1:
% 117.54/18.38 | |
% 117.54/18.38 | | (11) all_54_8 = e3
% 117.54/18.38 | |
% 117.54/18.38 | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #399.
% 117.54/18.38 | |
% 117.54/18.38 | Case 2:
% 117.54/18.38 | |
% 117.54/18.38 | | (12) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.54/18.38 | |
% 117.54/18.38 | | BETA: splitting (12) gives:
% 117.54/18.38 | |
% 117.54/18.38 | | Case 1:
% 117.54/18.38 | | |
% 117.54/18.38 | | | (13) all_54_8 = e2
% 117.54/18.38 | | |
% 117.54/18.38 | | | REF_CLOSE: (1), (8), (13) are inconsistent by sub-proof #382.
% 117.54/18.38 | | |
% 117.54/18.38 | | Case 2:
% 117.54/18.38 | | |
% 117.54/18.38 | | | (14) all_54_8 = e1 | all_54_8 = e0
% 117.54/18.38 | | |
% 117.54/18.38 | | | BETA: splitting (14) gives:
% 117.54/18.38 | | |
% 117.54/18.38 | | | Case 1:
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | (15) all_54_8 = e1
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | REF_CLOSE: (1), (6), (15) are inconsistent by sub-proof #397.
% 117.54/18.38 | | | |
% 117.54/18.38 | | | Case 2:
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | (16) all_54_8 = e0
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | COMBINE_EQS: (1), (16) imply:
% 117.54/18.38 | | | | (17) all_52_2 = e0
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | SIMP: (17) implies:
% 117.54/18.38 | | | | (18) all_52_2 = e0
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | REDUCE: (2), (18) imply:
% 117.54/18.38 | | | | (19) ~ (all_6_2 = e0)
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | SIMP: (19) implies:
% 117.54/18.38 | | | | (20) ~ (all_6_2 = e0)
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | REF_CLOSE: (3), (7), (9), (10), (20) are inconsistent by sub-proof #435.
% 117.54/18.38 | | | |
% 117.54/18.38 | | | End of split
% 117.54/18.38 | | |
% 117.54/18.38 | | End of split
% 117.54/18.38 | |
% 117.54/18.38 | End of split
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #297 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.38 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.54/18.38 (3) all_54_0 = all_10_2
% 117.54/18.38 (4) op(e3, all_10_2) = e1
% 117.54/18.38 (5) all_56_12 = all_10_2
% 117.54/18.38 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (7) ~ (all_10_2 = e2)
% 117.54/18.38 (8) op(e3, e1) = all_52_8
% 117.54/18.38 (9) ~ (all_10_2 = e3)
% 117.54/18.38 (10) all_56_2 = e3
% 117.54/18.38 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | BETA: splitting (2) gives:
% 117.54/18.38 |
% 117.54/18.38 | Case 1:
% 117.54/18.38 | |
% 117.54/18.38 | | (12) ~ (all_56_2 = e3)
% 117.54/18.38 | |
% 117.54/18.38 | | REDUCE: (10), (12) imply:
% 117.54/18.38 | | (13) $false
% 117.54/18.38 | |
% 117.54/18.38 | | CLOSE: (13) is inconsistent.
% 117.54/18.38 | |
% 117.54/18.38 | Case 2:
% 117.54/18.38 | |
% 117.54/18.38 | | (14) ~ (all_56_12 = e0)
% 117.54/18.38 | |
% 117.54/18.38 | | REDUCE: (5), (14) imply:
% 117.54/18.38 | | (15) ~ (all_10_2 = e0)
% 117.54/18.38 | |
% 117.54/18.38 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (11), (15) are inconsistent by
% 117.54/18.38 | | sub-proof #298.
% 117.54/18.38 | |
% 117.54/18.38 | End of split
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #298 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.38 (2) all_54_0 = all_10_2
% 117.54/18.38 (3) op(e3, all_10_2) = e1
% 117.54/18.38 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (5) ~ (all_10_2 = e2)
% 117.54/18.38 (6) op(e3, e1) = all_52_8
% 117.54/18.38 (7) ~ (all_10_2 = e3)
% 117.54/18.38 (8) ~ (all_10_2 = e0)
% 117.54/18.38 (9) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | BETA: splitting (9) gives:
% 117.54/18.38 |
% 117.54/18.38 | Case 1:
% 117.54/18.38 | |
% 117.54/18.38 | | (10) all_54_0 = e3
% 117.54/18.38 | |
% 117.54/18.38 | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #451.
% 117.54/18.38 | |
% 117.54/18.38 | Case 2:
% 117.54/18.38 | |
% 117.54/18.38 | | (11) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.38 | |
% 117.54/18.38 | | BETA: splitting (11) gives:
% 117.54/18.38 | |
% 117.54/18.38 | | Case 1:
% 117.54/18.38 | | |
% 117.54/18.38 | | | (12) all_54_0 = e2
% 117.54/18.38 | | |
% 117.54/18.38 | | | REF_CLOSE: (2), (5), (12) are inconsistent by sub-proof #450.
% 117.54/18.38 | | |
% 117.54/18.38 | | Case 2:
% 117.54/18.38 | | |
% 117.54/18.38 | | | (13) all_54_0 = e1 | all_54_0 = e0
% 117.54/18.38 | | |
% 117.54/18.38 | | | BETA: splitting (13) gives:
% 117.54/18.38 | | |
% 117.54/18.38 | | | Case 1:
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | (14) all_54_0 = e1
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | COMBINE_EQS: (2), (14) imply:
% 117.54/18.38 | | | | (15) all_10_2 = e1
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | REF_CLOSE: (1), (3), (4), (6), (15) are inconsistent by sub-proof #299.
% 117.54/18.38 | | | |
% 117.54/18.38 | | | Case 2:
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | (16) all_54_0 = e0
% 117.54/18.38 | | | |
% 117.54/18.38 | | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #424.
% 117.54/18.38 | | | |
% 117.54/18.38 | | | End of split
% 117.54/18.38 | | |
% 117.54/18.38 | | End of split
% 117.54/18.38 | |
% 117.54/18.38 | End of split
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #299 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) ~ (all_52_8 = all_10_2)
% 117.54/18.38 (2) op(e3, all_10_2) = e1
% 117.54/18.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (4) op(e3, e1) = all_52_8
% 117.54/18.38 (5) all_10_2 = e1
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | SIMP: (5) implies:
% 117.54/18.38 | (6) all_10_2 = e1
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (1), (6) imply:
% 117.54/18.38 | (7) ~ (all_52_8 = e1)
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (2), (6) imply:
% 117.54/18.38 | (8) op(e3, e1) = e1
% 117.54/18.38 |
% 117.54/18.38 | GROUND_INST: instantiating (3) with all_52_8, e1, e1, e3, simplifying with
% 117.54/18.38 | (4), (8) gives:
% 117.54/18.38 | (9) all_52_8 = e1
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (7), (9) imply:
% 117.54/18.38 | (10) $false
% 117.54/18.38 |
% 117.54/18.38 | CLOSE: (10) is inconsistent.
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #300 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) op(e3, e2) = all_52_4
% 117.54/18.38 (2) all_56_12 = all_10_2
% 117.54/18.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (4) all_56_12 = e2
% 117.54/18.38 (5) op(e3, all_10_2) = e2
% 117.54/18.38 (6) ~ (all_52_4 = all_10_2)
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | COMBINE_EQS: (2), (4) imply:
% 117.54/18.38 | (7) all_10_2 = e2
% 117.54/18.38 |
% 117.54/18.38 | SIMP: (7) implies:
% 117.54/18.38 | (8) all_10_2 = e2
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (6), (8) imply:
% 117.54/18.38 | (9) ~ (all_52_4 = e2)
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (5), (8) imply:
% 117.54/18.38 | (10) op(e3, e2) = e2
% 117.54/18.38 |
% 117.54/18.38 | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #301.
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #301 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (2) op(e3, e2) = all_52_4
% 117.54/18.38 (3) op(e3, e2) = e2
% 117.54/18.38 (4) ~ (all_52_4 = e2)
% 117.54/18.38
% 117.54/18.38 Begin of proof
% 117.54/18.38 |
% 117.54/18.38 | GROUND_INST: instantiating (1) with all_52_4, e2, e2, e3, simplifying with
% 117.54/18.38 | (2), (3) gives:
% 117.54/18.38 | (5) all_52_4 = e2
% 117.54/18.38 |
% 117.54/18.38 | REDUCE: (4), (5) imply:
% 117.54/18.38 | (6) $false
% 117.54/18.38 |
% 117.54/18.38 | CLOSE: (6) is inconsistent.
% 117.54/18.38 |
% 117.54/18.38 End of proof
% 117.54/18.38
% 117.54/18.38 Sub-proof #302 shows that the following formulas are inconsistent:
% 117.54/18.38 ----------------------------------------------------------------
% 117.54/18.38 (1) ~ (all_52_2 = all_10_2)
% 117.54/18.38 (2) all_58_7 = all_52_6
% 117.54/18.38 (3) ~ (all_52_13 = all_52_14)
% 117.54/18.38 (4) ~ (all_4_2 = e0)
% 117.54/18.38 (5) all_56_14 = all_6_2
% 117.54/18.38 (6) all_56_3 = all_52_1
% 117.54/18.38 (7) all_54_0 = all_10_2
% 117.54/18.38 (8) all_54_3 = all_52_12
% 117.54/18.38 (9) all_56_11 = all_52_11
% 117.54/18.38 (10) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.54/18.38 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.54/18.38 (12) ~ (e3 = e1)
% 117.54/18.38 (13) all_56_12 = all_10_2
% 117.54/18.38 (14) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.54/18.38 (15) all_56_10 = all_52_7
% 117.54/18.38 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.38 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.54/18.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.54/18.38 (18) ~ (all_52_2 = all_6_2)
% 117.54/18.38 (19) ~ (all_10_2 = e2)
% 117.54/18.38 (20) all_54_10 = all_6_2
% 117.54/18.38 (21) op(e3, e0) = all_52_12
% 117.54/18.38 (22) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.54/18.38 (23) all_56_2 = all_52_12
% 117.54/18.38 (24) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.38 (25) all_58_3 = all_8_2
% 117.54/18.38 (26) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.54/18.38 (27) all_58_11 = all_52_14
% 117.54/18.38 (28) op(e3, all_6_2) = all_6_0
% 117.54/18.38 (29) all_54_7 = all_52_13
% 117.54/18.38 (30) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.54/18.38 (31) ~ (all_52_11 = all_6_2)
% 117.54/18.38 (32) ~ (all_4_2 = e3)
% 117.54/18.38 (33) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.54/18.38 (34) op(e1, e0) = all_52_14
% 117.54/18.38 (35) all_58_5 = all_52_9
% 117.54/18.38 (36) all_56_9 = all_52_3
% 117.54/18.38 (37) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.54/18.38 (38) all_58_15 = all_4_2
% 117.54/18.38 (39) all_58_2 = all_52_1
% 117.54/18.38 (40) ~ (all_10_2 = e3)
% 117.54/18.38 (41) ~ (all_52_12 = all_52_13)
% 117.54/18.38 (42) all_58_13 = all_52_7
% 117.54/18.38 (43) ~ (all_52_14 = all_4_2)
% 117.54/18.38 (44) all_58_6 = all_52_2
% 117.54/18.38 (45) all_56_15 = all_4_2
% 117.54/18.38 (46) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.54/18.38 (47) all_58_10 = all_52_13
% 117.54/18.38 (48) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.54/18.39 (49) ~ (all_6_0 = e2)
% 117.54/18.39 (50) all_58_14 = all_52_11
% 117.54/18.39 (51) op(e1, all_6_2) = e3
% 117.54/18.39 (52) ~ (all_8_2 = e2)
% 117.54/18.39 (53) ~ (all_6_2 = e2)
% 117.54/18.39 (54) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.39 (55) all_56_7 = all_52_6
% 117.54/18.39 (56) all_58_8 = all_6_2
% 117.54/18.39 (57) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.39 (58) all_56_4 = all_52_9
% 117.54/18.39 (59) all_56_5 = all_52_13
% 117.54/18.39 (60) ~ (all_52_6 = all_6_2)
% 117.54/18.39 (61) all_56_6 = all_52_2
% 117.54/18.39 (62) ~ (all_52_13 = all_4_2)
% 117.54/18.39 (63) all_58_12 = all_52_3
% 117.54/18.39 (64) ~ (all_52_2 = all_52_14)
% 117.54/18.39 (65) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.54/18.39 (66) ~ (all_52_12 = all_4_2)
% 117.54/18.39 (67) ~ (all_52_3 = all_10_2)
% 117.54/18.39 (68) op(e1, e3) = all_52_2
% 117.54/18.39 (69) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.54/18.39 (70) all_56_8 = all_52_14
% 117.54/18.39 (71) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.54/18.39 (72) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.54/18.39 (73) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.39 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.39 (74) all_54_15 = all_4_2
% 117.54/18.39 (75) ~ (all_6_2 = e1)
% 117.54/18.39 (76) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.54/18.39
% 117.54/18.39 Begin of proof
% 117.54/18.39 |
% 117.54/18.39 | BETA: splitting (14) gives:
% 117.54/18.39 |
% 117.54/18.39 | Case 1:
% 117.54/18.39 | |
% 117.54/18.39 | | (77) ~ (all_56_7 = e1)
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (55), (77) imply:
% 117.54/18.39 | | (78) ~ (all_52_6 = e1)
% 117.54/18.39 | |
% 117.54/18.39 | | BETA: splitting (16) gives:
% 117.54/18.39 | |
% 117.54/18.39 | | Case 1:
% 117.54/18.39 | | |
% 117.54/18.39 | | | (79) all_54_10 = e3
% 117.54/18.39 | | |
% 117.54/18.39 | | | COMBINE_EQS: (20), (79) imply:
% 117.54/18.39 | | | (80) all_6_2 = e3
% 117.54/18.39 | | |
% 117.54/18.39 | | | SIMP: (80) implies:
% 117.54/18.39 | | | (81) all_6_2 = e3
% 117.54/18.39 | | |
% 117.54/18.39 | | | REF_CLOSE: (2), (4), (5), (7), (9), (12), (13), (15), (19), (22), (24),
% 117.54/18.39 | | | (27), (30), (32), (36), (37), (38), (40), (42), (43), (44),
% 117.54/18.39 | | | (45), (50), (54), (56), (57), (61), (63), (69), (70), (71),
% 117.54/18.39 | | | (73), (74), (78), (81) are inconsistent by sub-proof #357.
% 117.54/18.39 | | |
% 117.54/18.39 | | Case 2:
% 117.54/18.39 | | |
% 117.54/18.39 | | | (82) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.39 | | |
% 117.54/18.39 | | | BETA: splitting (82) gives:
% 117.54/18.39 | | |
% 117.54/18.39 | | | Case 1:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | (83) all_54_10 = e2
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | REF_CLOSE: (20), (53), (83) are inconsistent by sub-proof #438.
% 117.54/18.39 | | | |
% 117.54/18.39 | | | Case 2:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | (84) ~ (all_54_10 = e2)
% 117.54/18.39 | | | | (85) all_54_10 = e1 | all_54_10 = e0
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | BETA: splitting (85) gives:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | Case 1:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | (86) all_54_10 = e1
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | REF_CLOSE: (20), (75), (86) are inconsistent by sub-proof #437.
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | Case 2:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | (87) all_54_10 = e0
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | COMBINE_EQS: (20), (87) imply:
% 117.54/18.39 | | | | | (88) all_6_2 = e0
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | SIMP: (88) implies:
% 117.54/18.39 | | | | | (89) all_6_2 = e0
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | COMBINE_EQS: (5), (89) imply:
% 117.54/18.39 | | | | | (90) all_56_14 = e0
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | BETA: splitting (10) gives:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | Case 1:
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | (91) ~ (all_56_8 = e1)
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | REDUCE: (70), (91) imply:
% 117.54/18.39 | | | | | | (92) ~ (all_52_14 = e1)
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | BETA: splitting (54) gives:
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | Case 1:
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | (93) all_58_6 = e1
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | COMBINE_EQS: (44), (93) imply:
% 117.54/18.39 | | | | | | | (94) all_52_2 = e1
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | SIMP: (94) implies:
% 117.54/18.39 | | | | | | | (95) all_52_2 = e1
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | REDUCE: (64), (95) imply:
% 117.54/18.39 | | | | | | | (96) ~ (all_52_14 = e1)
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | REDUCE: (1), (95) imply:
% 117.54/18.39 | | | | | | | (97) ~ (all_10_2 = e1)
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | SIMP: (97) implies:
% 117.54/18.39 | | | | | | | (98) ~ (all_10_2 = e1)
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | BETA: splitting (57) gives:
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | Case 1:
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | | (99) all_54_0 = e3
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | | REF_CLOSE: (7), (40), (99) are inconsistent by sub-proof #451.
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | Case 2:
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | | (100) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | | BETA: splitting (100) gives:
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | | Case 1:
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | | (101) all_54_0 = e2
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | | REF_CLOSE: (7), (19), (101) are inconsistent by sub-proof
% 117.54/18.39 | | | | | | | | | #450.
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | Case 2:
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | | (102) ~ (all_54_0 = e2)
% 117.54/18.39 | | | | | | | | | (103) all_54_0 = e1 | all_54_0 = e0
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | | BETA: splitting (103) gives:
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | | Case 1:
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | (104) all_54_0 = e1
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | REF_CLOSE: (7), (98), (104) are inconsistent by sub-proof
% 117.54/18.39 | | | | | | | | | | #449.
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | Case 2:
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | (105) all_54_0 = e0
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | COMBINE_EQS: (7), (105) imply:
% 117.54/18.39 | | | | | | | | | | (106) all_10_2 = e0
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | SIMP: (106) implies:
% 117.54/18.39 | | | | | | | | | | (107) all_10_2 = e0
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | REDUCE: (67), (107) imply:
% 117.54/18.39 | | | | | | | | | | (108) ~ (all_52_3 = e0)
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | REDUCE: (19), (107) imply:
% 117.54/18.39 | | | | | | | | | | (109) ~ (e2 = e0)
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | SIMP: (109) implies:
% 117.54/18.39 | | | | | | | | | | (110) ~ (e2 = e0)
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | BETA: splitting (69) gives:
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | Case 1:
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | (111) ~ (all_56_15 = e2)
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | REDUCE: (45), (111) imply:
% 117.54/18.39 | | | | | | | | | | | (112) ~ (all_4_2 = e2)
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (16), (17),
% 117.54/18.39 | | | | | | | | | | | (18), (20), (21), (22), (23), (24), (25), (26),
% 117.54/18.39 | | | | | | | | | | | (27), (28), (29), (32), (33), (34), (35), (39),
% 117.54/18.39 | | | | | | | | | | | (41), (43), (44), (45), (46), (47), (48), (49),
% 117.54/18.39 | | | | | | | | | | | (51), (52), (53), (54), (56), (58), (59), (61),
% 117.54/18.39 | | | | | | | | | | | (62), (65), (66), (68), (72), (74), (75), (76),
% 117.54/18.39 | | | | | | | | | | | (112) are inconsistent by sub-proof #342.
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | Case 2:
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | (113) all_56_15 = e2
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | COMBINE_EQS: (45), (113) imply:
% 117.54/18.39 | | | | | | | | | | | (114) all_4_2 = e2
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | SIMP: (114) implies:
% 117.54/18.39 | | | | | | | | | | | (115) all_4_2 = e2
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | COMBINE_EQS: (38), (115) imply:
% 117.54/18.39 | | | | | | | | | | | (116) all_58_15 = e2
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | | REF_CLOSE: (2), (5), (14), (15), (16), (18), (20), (24),
% 117.54/18.39 | | | | | | | | | | | (27), (31), (42), (44), (50), (53), (54), (55),
% 117.54/18.39 | | | | | | | | | | | (56), (61), (63), (69), (73), (75), (92), (108),
% 117.54/18.39 | | | | | | | | | | | (110), (113), (116) are inconsistent by sub-proof
% 117.54/18.39 | | | | | | | | | | | #303.
% 117.54/18.39 | | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | | End of split
% 117.54/18.39 | | | | | | | | | |
% 117.54/18.39 | | | | | | | | | End of split
% 117.54/18.39 | | | | | | | | |
% 117.54/18.39 | | | | | | | | End of split
% 117.54/18.39 | | | | | | | |
% 117.54/18.39 | | | | | | | End of split
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | Case 2:
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | (117) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | | REF_CLOSE: (2), (27), (56), (75), (78), (92), (117) are
% 117.54/18.39 | | | | | | | inconsistent by sub-proof #354.
% 117.54/18.39 | | | | | | |
% 117.54/18.39 | | | | | | End of split
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | Case 2:
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | (118) ~ (all_56_14 = e0)
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | REDUCE: (90), (118) imply:
% 117.54/18.39 | | | | | | (119) $false
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | CLOSE: (119) is inconsistent.
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | End of split
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | End of split
% 117.54/18.39 | | | |
% 117.54/18.39 | | | End of split
% 117.54/18.39 | | |
% 117.54/18.39 | | End of split
% 117.54/18.39 | |
% 117.54/18.39 | Case 2:
% 117.54/18.39 | |
% 117.54/18.39 | | (120) all_56_7 = e1
% 117.54/18.39 | | (121) ~ (all_56_15 = e2)
% 117.54/18.39 | |
% 117.54/18.39 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (16), (17), (18), (20), (21),
% 117.54/18.39 | | (22), (23), (24), (25), (26), (27), (28), (29), (32), (33), (34),
% 117.54/18.39 | | (35), (39), (41), (43), (44), (45), (46), (47), (48), (49), (51),
% 117.54/18.39 | | (52), (53), (54), (55), (56), (58), (59), (60), (61), (62), (65),
% 117.54/18.39 | | (66), (68), (72), (74), (76), (120), (121) are inconsistent by
% 117.54/18.39 | | sub-proof #341.
% 117.54/18.39 | |
% 117.54/18.39 | End of split
% 117.54/18.39 |
% 117.54/18.39 End of proof
% 117.54/18.39
% 117.54/18.39 Sub-proof #303 shows that the following formulas are inconsistent:
% 117.54/18.39 ----------------------------------------------------------------
% 117.54/18.39 (1) ~ (all_52_3 = e0)
% 117.54/18.39 (2) all_58_7 = all_52_6
% 117.54/18.39 (3) all_56_14 = all_6_2
% 117.54/18.39 (4) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.54/18.39 (5) all_56_10 = all_52_7
% 117.54/18.39 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.39 (7) ~ (all_52_2 = all_6_2)
% 117.54/18.39 (8) all_54_10 = all_6_2
% 117.54/18.39 (9) ~ (all_52_14 = e1)
% 117.54/18.39 (10) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.39 (11) all_58_11 = all_52_14
% 117.54/18.39 (12) ~ (all_52_11 = all_6_2)
% 117.54/18.39 (13) all_58_13 = all_52_7
% 117.54/18.39 (14) all_58_6 = all_52_2
% 117.54/18.39 (15) all_58_14 = all_52_11
% 117.54/18.39 (16) ~ (all_6_2 = e2)
% 117.54/18.39 (17) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.39 (18) all_56_7 = all_52_6
% 117.54/18.39 (19) all_58_15 = e2
% 117.54/18.39 (20) all_58_8 = all_6_2
% 117.54/18.39 (21) all_56_6 = all_52_2
% 117.54/18.39 (22) ~ (e2 = e0)
% 117.54/18.39 (23) all_58_12 = all_52_3
% 117.54/18.39 (24) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.54/18.39 (25) all_56_15 = e2
% 117.54/18.39 (26) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.54/18.39 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.54/18.39 (27) ~ (all_6_2 = e1)
% 117.54/18.39
% 117.54/18.39 Begin of proof
% 117.54/18.39 |
% 117.54/18.39 | BETA: splitting (24) gives:
% 117.54/18.39 |
% 117.54/18.39 | Case 1:
% 117.54/18.39 | |
% 117.54/18.39 | | (28) ~ (all_56_15 = e2)
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (25), (28) imply:
% 117.54/18.39 | | (29) $false
% 117.54/18.39 | |
% 117.54/18.39 | | CLOSE: (29) is inconsistent.
% 117.54/18.39 | |
% 117.54/18.39 | Case 2:
% 117.54/18.39 | |
% 117.54/18.39 | | (30) ~ (all_56_10 = e0)
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (5), (30) imply:
% 117.54/18.39 | | (31) ~ (all_52_7 = e0)
% 117.54/18.39 | |
% 117.54/18.39 | | BETA: splitting (4) gives:
% 117.54/18.39 | |
% 117.54/18.39 | | Case 1:
% 117.54/18.39 | | |
% 117.54/18.39 | | | (32) ~ (all_56_7 = e1)
% 117.54/18.39 | | |
% 117.54/18.39 | | | REDUCE: (18), (32) imply:
% 117.54/18.39 | | | (33) ~ (all_52_6 = e1)
% 117.54/18.39 | | |
% 117.54/18.39 | | | BETA: splitting (26) gives:
% 117.54/18.39 | | |
% 117.54/18.39 | | | Case 1:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | (34) all_58_15 = e0
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | COMBINE_EQS: (19), (34) imply:
% 117.54/18.39 | | | | (35) e2 = e0
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | REDUCE: (22), (35) imply:
% 117.54/18.39 | | | | (36) $false
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | CLOSE: (36) is inconsistent.
% 117.54/18.39 | | | |
% 117.54/18.39 | | | Case 2:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | (37) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 117.54/18.39 | | | | e0 | all_58_13 = e0 | all_58_14 = e0)
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | ALPHA: (37) implies:
% 117.54/18.39 | | | | (38) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | BETA: splitting (17) gives:
% 117.54/18.39 | | | |
% 117.54/18.39 | | | | Case 1:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | (39) all_58_6 = e1
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | COMBINE_EQS: (14), (39) imply:
% 117.54/18.39 | | | | | (40) all_52_2 = e1
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | COMBINE_EQS: (21), (40) imply:
% 117.54/18.39 | | | | | (41) all_56_6 = e1
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | REDUCE: (7), (40) imply:
% 117.54/18.39 | | | | | (42) ~ (all_6_2 = e1)
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | BETA: splitting (38) gives:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | Case 1:
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | (43) all_58_12 = e0
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | COMBINE_EQS: (23), (43) imply:
% 117.54/18.39 | | | | | | (44) all_52_3 = e0
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | REDUCE: (1), (44) imply:
% 117.54/18.39 | | | | | | (45) $false
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | CLOSE: (45) is inconsistent.
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | Case 2:
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | (46) all_58_13 = e0 | all_58_14 = e0
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | | REF_CLOSE: (3), (6), (8), (10), (12), (13), (15), (16), (27), (31),
% 117.54/18.39 | | | | | | (41), (46) are inconsistent by sub-proof #304.
% 117.54/18.39 | | | | | |
% 117.54/18.39 | | | | | End of split
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | Case 2:
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | (47) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | | REF_CLOSE: (2), (9), (11), (20), (27), (33), (47) are inconsistent by
% 117.54/18.39 | | | | | sub-proof #354.
% 117.54/18.39 | | | | |
% 117.54/18.39 | | | | End of split
% 117.54/18.39 | | | |
% 117.54/18.39 | | | End of split
% 117.54/18.39 | | |
% 117.54/18.39 | | Case 2:
% 117.54/18.39 | | |
% 117.54/18.39 | | | (48) ~ (all_56_15 = e2)
% 117.54/18.39 | | |
% 117.54/18.39 | | | REDUCE: (25), (48) imply:
% 117.54/18.39 | | | (49) $false
% 117.54/18.39 | | |
% 117.54/18.39 | | | CLOSE: (49) is inconsistent.
% 117.54/18.39 | | |
% 117.54/18.39 | | End of split
% 117.54/18.39 | |
% 117.54/18.39 | End of split
% 117.54/18.39 |
% 117.54/18.39 End of proof
% 117.54/18.39
% 117.54/18.39 Sub-proof #304 shows that the following formulas are inconsistent:
% 117.54/18.39 ----------------------------------------------------------------
% 117.54/18.39 (1) all_56_14 = all_6_2
% 117.54/18.39 (2) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.39 (3) all_54_10 = all_6_2
% 117.54/18.39 (4) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.39 (5) all_56_6 = e1
% 117.54/18.39 (6) ~ (all_52_11 = all_6_2)
% 117.54/18.39 (7) all_58_13 = all_52_7
% 117.54/18.39 (8) ~ (all_52_7 = e0)
% 117.54/18.39 (9) all_58_14 = all_52_11
% 117.54/18.39 (10) ~ (all_6_2 = e2)
% 117.54/18.39 (11) all_58_13 = e0 | all_58_14 = e0
% 117.54/18.39 (12) ~ (all_6_2 = e1)
% 117.54/18.39
% 117.54/18.39 Begin of proof
% 117.54/18.39 |
% 117.54/18.39 | BETA: splitting (11) gives:
% 117.54/18.39 |
% 117.54/18.39 | Case 1:
% 117.54/18.39 | |
% 117.54/18.39 | | (13) all_58_13 = e0
% 117.54/18.39 | |
% 117.54/18.39 | | COMBINE_EQS: (7), (13) imply:
% 117.54/18.39 | | (14) all_52_7 = e0
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (8), (14) imply:
% 117.54/18.39 | | (15) $false
% 117.54/18.39 | |
% 117.54/18.39 | | CLOSE: (15) is inconsistent.
% 117.54/18.39 | |
% 117.54/18.39 | Case 2:
% 117.54/18.39 | |
% 117.54/18.39 | | (16) all_58_14 = e0
% 117.54/18.39 | |
% 117.54/18.39 | | COMBINE_EQS: (9), (16) imply:
% 117.54/18.39 | | (17) all_52_11 = e0
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (6), (17) imply:
% 117.54/18.39 | | (18) ~ (all_6_2 = e0)
% 117.54/18.39 | |
% 117.54/18.39 | | SIMP: (18) implies:
% 117.54/18.39 | | (19) ~ (all_6_2 = e0)
% 117.54/18.39 | |
% 117.54/18.39 | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (12), (19) are inconsistent by
% 117.54/18.39 | | sub-proof #305.
% 117.54/18.39 | |
% 117.54/18.39 | End of split
% 117.54/18.39 |
% 117.54/18.39 End of proof
% 117.54/18.39
% 117.54/18.39 Sub-proof #305 shows that the following formulas are inconsistent:
% 117.54/18.39 ----------------------------------------------------------------
% 117.54/18.39 (1) all_56_14 = all_6_2
% 117.54/18.39 (2) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.54/18.39 (3) all_54_10 = all_6_2
% 117.54/18.39 (4) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.54/18.39 (5) all_56_6 = e1
% 117.54/18.39 (6) ~ (all_6_2 = e2)
% 117.54/18.39 (7) ~ (all_6_2 = e0)
% 117.54/18.39 (8) ~ (all_6_2 = e1)
% 117.54/18.39
% 117.54/18.39 Begin of proof
% 117.54/18.39 |
% 117.54/18.39 | BETA: splitting (4) gives:
% 117.54/18.39 |
% 117.54/18.39 | Case 1:
% 117.54/18.39 | |
% 117.54/18.39 | | (9) ~ (all_56_6 = e1)
% 117.54/18.39 | |
% 117.54/18.39 | | REDUCE: (5), (9) imply:
% 117.54/18.39 | | (10) $false
% 117.54/18.39 | |
% 117.54/18.39 | | CLOSE: (10) is inconsistent.
% 117.54/18.39 | |
% 117.54/18.39 | Case 2:
% 117.54/18.39 | |
% 117.54/18.39 | | (11) ~ (all_56_14 = e3)
% 117.74/18.39 | |
% 117.74/18.39 | | REDUCE: (1), (11) imply:
% 117.74/18.39 | | (12) ~ (all_6_2 = e3)
% 117.74/18.39 | |
% 117.74/18.39 | | BETA: splitting (2) gives:
% 117.74/18.39 | |
% 117.74/18.39 | | Case 1:
% 117.74/18.39 | | |
% 117.74/18.39 | | | (13) all_54_10 = e3
% 117.74/18.39 | | |
% 117.74/18.39 | | | REF_CLOSE: (3), (12), (13) are inconsistent by sub-proof #352.
% 117.74/18.39 | | |
% 117.74/18.39 | | Case 2:
% 117.74/18.39 | | |
% 117.74/18.39 | | | (14) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.39 | | |
% 117.74/18.39 | | | REF_CLOSE: (3), (6), (7), (8), (14) are inconsistent by sub-proof #435.
% 117.74/18.39 | | |
% 117.74/18.39 | | End of split
% 117.74/18.39 | |
% 117.74/18.39 | End of split
% 117.74/18.39 |
% 117.74/18.39 End of proof
% 117.74/18.39
% 117.74/18.39 Sub-proof #306 shows that the following formulas are inconsistent:
% 117.74/18.39 ----------------------------------------------------------------
% 117.74/18.39 (1) all_36_2 = all_6_2
% 117.74/18.39 (2) ~ (all_4_2 = e0)
% 117.74/18.39 (3) op(e3, e2) = all_52_4
% 117.74/18.39 (4) all_56_14 = all_6_2
% 117.74/18.40 (5) all_56_3 = all_52_1
% 117.74/18.40 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.40 (7) ~ (all_52_7 = all_4_2)
% 117.74/18.40 (8) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.40 (9) all_56_14 = e2
% 117.74/18.40 (10) all_58_0 = all_10_2
% 117.74/18.40 (11) all_54_13 = all_52_7
% 117.74/18.40 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.40 (13) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.74/18.40 (14) all_36_0 = all_6_0
% 117.74/18.40 (15) all_58_4 = all_52_8
% 117.74/18.40 (16) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.40 (17) ~ (all_52_4 = all_52_7)
% 117.74/18.40 (18) all_56_2 = all_52_12
% 117.74/18.40 (19) all_58_3 = all_8_2
% 117.74/18.40 (20) ~ (all_56_5 = e2) | ~ (all_56_13 = e0)
% 117.74/18.40 (21) op(e3, all_6_2) = all_6_0
% 117.74/18.40 (22) ~ (all_36_0 = e0) | ~ (all_36_2 = e2)
% 117.74/18.40 (23) ~ (all_52_7 = all_8_2)
% 117.74/18.40 (24) ~ (all_52_4 = all_8_2)
% 117.74/18.40 (25) all_58_5 = all_52_9
% 117.74/18.40 (26) all_58_2 = all_52_1
% 117.74/18.40 (27) ~ (all_10_2 = e3)
% 117.74/18.40 (28) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 117.74/18.40 (29) all_54_5 = all_8_2
% 117.74/18.40 (30) all_56_15 = all_4_2
% 117.74/18.40 (31) all_58_10 = all_52_13
% 117.74/18.40 (32) ~ (all_52_6 = all_8_2)
% 117.74/18.40 (33) ~ (all_6_0 = e2)
% 117.74/18.40 (34) all_58_1 = all_52_4
% 117.74/18.40 (35) ~ (all_56_2 = e3) | ~ (all_56_13 = e0)
% 117.74/18.40 (36) all_54_1 = all_52_4
% 117.74/18.40 (37) all_56_13 = all_8_2
% 117.74/18.40 (38) op(e1, all_6_2) = e3
% 117.74/18.40 (39) ~ (all_8_2 = e2)
% 117.74/18.40 (40) all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 117.74/18.40 (41) op(e1, e2) = all_52_6
% 117.74/18.40 (42) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.40 (43) ~ (all_52_9 = all_6_2)
% 117.74/18.40 (44) all_56_1 = all_52_8
% 117.74/18.40 (45) all_58_9 = all_52_12
% 117.74/18.40 (46) all_56_5 = all_52_13
% 117.74/18.40 (47) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.40 (48) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.40 (49) all_56_0 = all_52_4
% 117.74/18.40 (50) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.74/18.40 (51) all_54_15 = all_4_2
% 117.74/18.40 (52) ~ (all_52_6 = all_52_7)
% 117.74/18.40
% 117.74/18.40 Begin of proof
% 117.74/18.40 |
% 117.74/18.40 | COMBINE_EQS: (4), (9) imply:
% 117.74/18.40 | (53) all_6_2 = e2
% 117.74/18.40 |
% 117.74/18.40 | SIMP: (53) implies:
% 117.74/18.40 | (54) all_6_2 = e2
% 117.74/18.40 |
% 117.74/18.40 | COMBINE_EQS: (1), (54) imply:
% 117.74/18.40 | (55) all_36_2 = e2
% 117.74/18.40 |
% 117.74/18.40 | REDUCE: (43), (54) imply:
% 117.74/18.40 | (56) ~ (all_52_9 = e2)
% 117.74/18.40 |
% 117.74/18.40 | REDUCE: (21), (54) imply:
% 117.74/18.40 | (57) op(e3, e2) = all_6_0
% 117.74/18.40 |
% 117.74/18.40 | REDUCE: (38), (54) imply:
% 117.74/18.40 | (58) op(e1, e2) = e3
% 117.74/18.40 |
% 117.74/18.40 | BETA: splitting (22) gives:
% 117.74/18.40 |
% 117.74/18.40 | Case 1:
% 117.74/18.40 | |
% 117.74/18.40 | | (59) ~ (all_36_2 = e2)
% 117.74/18.40 | |
% 117.74/18.40 | | REDUCE: (55), (59) imply:
% 117.74/18.40 | | (60) $false
% 117.74/18.40 | |
% 117.74/18.40 | | CLOSE: (60) is inconsistent.
% 117.74/18.40 | |
% 117.74/18.40 | Case 2:
% 117.74/18.40 | |
% 117.74/18.40 | | (61) ~ (all_36_0 = e0)
% 117.74/18.40 | |
% 117.74/18.40 | | REDUCE: (14), (61) imply:
% 117.74/18.40 | | (62) ~ (all_6_0 = e0)
% 117.74/18.40 | |
% 117.74/18.40 | | BETA: splitting (50) gives:
% 117.74/18.40 | |
% 117.74/18.40 | | Case 1:
% 117.74/18.40 | | |
% 117.74/18.40 | | | (63) ~ (all_56_0 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (49), (63) imply:
% 117.74/18.40 | | | (64) ~ (all_52_4 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | GROUND_INST: instantiating (12) with all_52_6, e3, e2, e1, simplifying
% 117.74/18.40 | | | with (41), (58) gives:
% 117.74/18.40 | | | (65) all_52_6 = e3
% 117.74/18.40 | | |
% 117.74/18.40 | | | GROUND_INST: instantiating (12) with all_52_4, all_6_0, e2, e3,
% 117.74/18.40 | | | simplifying with (3), (57) gives:
% 117.74/18.40 | | | (66) all_52_4 = all_6_0
% 117.74/18.40 | | |
% 117.74/18.40 | | | COMBINE_EQS: (36), (66) imply:
% 117.74/18.40 | | | (67) all_54_1 = all_6_0
% 117.74/18.40 | | |
% 117.74/18.40 | | | COMBINE_EQS: (34), (66) imply:
% 117.74/18.40 | | | (68) all_58_1 = all_6_0
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (17), (66) imply:
% 117.74/18.40 | | | (69) ~ (all_52_7 = all_6_0)
% 117.74/18.40 | | |
% 117.74/18.40 | | | SIMP: (69) implies:
% 117.74/18.40 | | | (70) ~ (all_52_7 = all_6_0)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (24), (66) imply:
% 117.74/18.40 | | | (71) ~ (all_8_2 = all_6_0)
% 117.74/18.40 | | |
% 117.74/18.40 | | | SIMP: (71) implies:
% 117.74/18.40 | | | (72) ~ (all_8_2 = all_6_0)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (64), (66) imply:
% 117.74/18.40 | | | (73) ~ (all_6_0 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (52), (65) imply:
% 117.74/18.40 | | | (74) ~ (all_52_7 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | SIMP: (74) implies:
% 117.74/18.40 | | | (75) ~ (all_52_7 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (32), (65) imply:
% 117.74/18.40 | | | (76) ~ (all_8_2 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | SIMP: (76) implies:
% 117.74/18.40 | | | (77) ~ (all_8_2 = e3)
% 117.74/18.40 | | |
% 117.74/18.40 | | | BETA: splitting (42) gives:
% 117.74/18.40 | | |
% 117.74/18.40 | | | Case 1:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | (78) all_54_1 = e3
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | COMBINE_EQS: (67), (78) imply:
% 117.74/18.40 | | | | (79) all_6_0 = e3
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | SIMP: (79) implies:
% 117.74/18.40 | | | | (80) all_6_0 = e3
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | REDUCE: (73), (80) imply:
% 117.74/18.40 | | | | (81) $false
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | CLOSE: (81) is inconsistent.
% 117.74/18.40 | | | |
% 117.74/18.40 | | | Case 2:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | (82) ~ (all_54_1 = e3)
% 117.74/18.40 | | | | (83) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | BETA: splitting (83) gives:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | Case 1:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | (84) all_54_1 = e2
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | COMBINE_EQS: (67), (84) imply:
% 117.74/18.40 | | | | | (85) all_6_0 = e2
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | SIMP: (85) implies:
% 117.74/18.40 | | | | | (86) all_6_0 = e2
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | REDUCE: (33), (86) imply:
% 117.74/18.40 | | | | | (87) $false
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | CLOSE: (87) is inconsistent.
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | Case 2:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | (88) all_54_1 = e1 | all_54_1 = e0
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | BETA: splitting (88) gives:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | Case 1:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | (89) all_54_1 = e1
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | COMBINE_EQS: (67), (89) imply:
% 117.74/18.40 | | | | | | (90) all_6_0 = e1
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | SIMP: (90) implies:
% 117.74/18.40 | | | | | | (91) all_6_0 = e1
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | COMBINE_EQS: (68), (91) imply:
% 117.74/18.40 | | | | | | (92) all_58_1 = e1
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REDUCE: (70), (91) imply:
% 117.74/18.40 | | | | | | (93) ~ (all_52_7 = e1)
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REDUCE: (72), (91) imply:
% 117.74/18.40 | | | | | | (94) ~ (all_8_2 = e1)
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REDUCE: (73), (91) imply:
% 117.74/18.40 | | | | | | (95) ~ (e3 = e1)
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | SIMP: (95) implies:
% 117.74/18.40 | | | | | | (96) ~ (e3 = e1)
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REDUCE: (62), (91) imply:
% 117.74/18.40 | | | | | | (97) ~ (e1 = e0)
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | BETA: splitting (8) gives:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | Case 1:
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | (98) all_54_5 = e3
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | REF_CLOSE: (29), (77), (98) are inconsistent by sub-proof #339.
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | Case 2:
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | (99) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | BETA: splitting (6) gives:
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | (100) all_54_13 = e3
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | COMBINE_EQS: (11), (100) imply:
% 117.74/18.40 | | | | | | | | (101) all_52_7 = e3
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | REDUCE: (75), (101) imply:
% 117.74/18.40 | | | | | | | | (102) $false
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | CLOSE: (102) is inconsistent.
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | (103) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | BETA: splitting (40) gives:
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | (104) all_58_1 = e0
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | COMBINE_EQS: (92), (104) imply:
% 117.74/18.40 | | | | | | | | | (105) e1 = e0
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | REDUCE: (97), (105) imply:
% 117.74/18.40 | | | | | | | | | (106) $false
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | CLOSE: (106) is inconsistent.
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | (107) all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | BETA: splitting (107) gives:
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | (108) all_58_3 = e0
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | COMBINE_EQS: (19), (108) imply:
% 117.74/18.40 | | | | | | | | | | (109) all_8_2 = e0
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | COMBINE_EQS: (37), (109) imply:
% 117.74/18.40 | | | | | | | | | | (110) all_56_13 = e0
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | BETA: splitting (35) gives:
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | (111) ~ (all_56_2 = e3)
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | REDUCE: (18), (111) imply:
% 117.74/18.40 | | | | | | | | | | | (112) ~ (all_52_12 = e3)
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | BETA: splitting (20) gives:
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | (113) ~ (all_56_5 = e2)
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | REDUCE: (46), (113) imply:
% 117.74/18.40 | | | | | | | | | | | | (114) ~ (all_52_13 = e2)
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | BETA: splitting (48) gives:
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | (115) all_58_2 = e2
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | COMBINE_EQS: (26), (115) imply:
% 117.74/18.40 | | | | | | | | | | | | | (116) all_52_1 = e2
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | COMBINE_EQS: (5), (116) imply:
% 117.74/18.40 | | | | | | | | | | | | | (117) all_56_3 = e2
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | BETA: splitting (47) gives:
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | Case 1:
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | (118) all_58_0 = e3
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | COMBINE_EQS: (10), (118) imply:
% 117.74/18.40 | | | | | | | | | | | | | | (119) all_10_2 = e3
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | REDUCE: (27), (119) imply:
% 117.74/18.40 | | | | | | | | | | | | | | (120) $false
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | CLOSE: (120) is inconsistent.
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | (121) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (11), (13), (15), (16), (23), (28),
% 117.74/18.40 | | | | | | | | | | | | | | (29), (30), (39), (44), (45), (51), (92), (93),
% 117.74/18.40 | | | | | | | | | | | | | | (94), (96), (99), (103), (112), (117), (121) are
% 117.74/18.40 | | | | | | | | | | | | | | inconsistent by sub-proof #307.
% 117.74/18.40 | | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | End of split
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | (122) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | | REF_CLOSE: (19), (25), (31), (39), (56), (114), (122) are
% 117.74/18.40 | | | | | | | | | | | | | inconsistent by sub-proof #401.
% 117.74/18.40 | | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | End of split
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | (123) ~ (all_56_13 = e0)
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | REDUCE: (110), (123) imply:
% 117.74/18.40 | | | | | | | | | | | | (124) $false
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 117.74/18.40 | | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | End of split
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | (125) ~ (all_56_13 = e0)
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | REDUCE: (110), (125) imply:
% 117.74/18.40 | | | | | | | | | | | (126) $false
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 117.74/18.40 | | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | End of split
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | Case 2:
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | (127) ~ (all_58_3 = e0)
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | REDUCE: (19), (127) imply:
% 117.74/18.40 | | | | | | | | | | (128) ~ (all_8_2 = e0)
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | | REF_CLOSE: (29), (39), (94), (99), (128) are inconsistent by
% 117.74/18.40 | | | | | | | | | | sub-proof #310.
% 117.74/18.40 | | | | | | | | | |
% 117.74/18.40 | | | | | | | | | End of split
% 117.74/18.40 | | | | | | | | |
% 117.74/18.40 | | | | | | | | End of split
% 117.74/18.40 | | | | | | | |
% 117.74/18.40 | | | | | | | End of split
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | End of split
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | Case 2:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | (129) all_54_1 = e0
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | COMBINE_EQS: (67), (129) imply:
% 117.74/18.40 | | | | | | (130) all_6_0 = e0
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | SIMP: (130) implies:
% 117.74/18.40 | | | | | | (131) all_6_0 = e0
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REDUCE: (62), (131) imply:
% 117.74/18.40 | | | | | | (132) $false
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | CLOSE: (132) is inconsistent.
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | End of split
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | End of split
% 117.74/18.40 | | | |
% 117.74/18.40 | | | End of split
% 117.74/18.40 | | |
% 117.74/18.40 | | Case 2:
% 117.74/18.40 | | |
% 117.74/18.40 | | | (133) ~ (all_56_14 = e2)
% 117.74/18.40 | | |
% 117.74/18.40 | | | REDUCE: (9), (133) imply:
% 117.74/18.40 | | | (134) $false
% 117.74/18.40 | | |
% 117.74/18.40 | | | CLOSE: (134) is inconsistent.
% 117.74/18.40 | | |
% 117.74/18.40 | | End of split
% 117.74/18.40 | |
% 117.74/18.40 | End of split
% 117.74/18.40 |
% 117.74/18.40 End of proof
% 117.74/18.40
% 117.74/18.40 Sub-proof #307 shows that the following formulas are inconsistent:
% 117.74/18.40 ----------------------------------------------------------------
% 117.74/18.40 (1) ~ (all_4_2 = e0)
% 117.74/18.40 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.40 (3) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.40 (4) ~ (all_52_7 = all_4_2)
% 117.74/18.40 (5) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.40 (6) ~ (e3 = e1)
% 117.74/18.40 (7) all_54_13 = all_52_7
% 117.74/18.40 (8) all_56_3 = e2
% 117.74/18.40 (9) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.74/18.40 (10) all_58_4 = all_52_8
% 117.74/18.40 (11) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.40 (12) ~ (all_52_7 = all_8_2)
% 117.74/18.40 (13) ~ (all_56_1 = e3) | ~ (all_56_15 = e1)
% 117.74/18.40 (14) all_58_1 = e1
% 117.74/18.40 (15) all_54_5 = all_8_2
% 117.74/18.40 (16) ~ (all_52_12 = e3)
% 117.74/18.40 (17) all_56_15 = all_4_2
% 117.74/18.40 (18) ~ (all_8_2 = e1)
% 117.74/18.40 (19) ~ (all_8_2 = e2)
% 117.74/18.40 (20) all_56_1 = all_52_8
% 117.74/18.40 (21) all_58_9 = all_52_12
% 117.74/18.40 (22) ~ (all_52_7 = e1)
% 117.74/18.40 (23) all_54_15 = all_4_2
% 117.74/18.40
% 117.74/18.40 Begin of proof
% 117.74/18.40 |
% 117.74/18.40 | BETA: splitting (3) gives:
% 117.74/18.40 |
% 117.74/18.40 | Case 1:
% 117.74/18.40 | |
% 117.74/18.40 | | (24) all_58_1 = e3
% 117.74/18.40 | |
% 117.74/18.40 | | COMBINE_EQS: (14), (24) imply:
% 117.74/18.40 | | (25) e3 = e1
% 117.74/18.40 | |
% 117.74/18.40 | | SIMP: (25) implies:
% 117.74/18.40 | | (26) e3 = e1
% 117.74/18.40 | |
% 117.74/18.40 | | REDUCE: (6), (26) imply:
% 117.74/18.40 | | (27) $false
% 117.74/18.40 | |
% 117.74/18.40 | | CLOSE: (27) is inconsistent.
% 117.74/18.40 | |
% 117.74/18.40 | Case 2:
% 117.74/18.40 | |
% 117.74/18.40 | | (28) all_58_4 = e3 | all_58_9 = e3
% 117.74/18.40 | |
% 117.74/18.40 | | BETA: splitting (28) gives:
% 117.74/18.40 | |
% 117.74/18.40 | | Case 1:
% 117.74/18.40 | | |
% 117.74/18.40 | | | (29) all_58_4 = e3
% 117.74/18.40 | | |
% 117.74/18.40 | | | COMBINE_EQS: (10), (29) imply:
% 117.74/18.40 | | | (30) all_52_8 = e3
% 117.74/18.40 | | |
% 117.74/18.40 | | | COMBINE_EQS: (20), (30) imply:
% 117.74/18.40 | | | (31) all_56_1 = e3
% 117.74/18.40 | | |
% 117.74/18.40 | | | BETA: splitting (13) gives:
% 117.74/18.40 | | |
% 117.74/18.40 | | | Case 1:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | (32) ~ (all_56_1 = e3)
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | REDUCE: (31), (32) imply:
% 117.74/18.40 | | | | (33) $false
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | CLOSE: (33) is inconsistent.
% 117.74/18.40 | | | |
% 117.74/18.40 | | | Case 2:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | (34) ~ (all_56_15 = e1)
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | REDUCE: (17), (34) imply:
% 117.74/18.40 | | | | (35) ~ (all_4_2 = e1)
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | BETA: splitting (9) gives:
% 117.74/18.40 | | | |
% 117.74/18.40 | | | | Case 1:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | (36) ~ (all_56_3 = e2)
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | REDUCE: (8), (36) imply:
% 117.74/18.40 | | | | | (37) $false
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | CLOSE: (37) is inconsistent.
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | Case 2:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | (38) ~ (all_56_15 = e3)
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | REDUCE: (17), (38) imply:
% 117.74/18.40 | | | | | (39) ~ (all_4_2 = e3)
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | BETA: splitting (11) gives:
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | | Case 1:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | (40) all_54_15 = e3
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | REF_CLOSE: (23), (39), (40) are inconsistent by sub-proof #312.
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | Case 2:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | (41) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | BETA: splitting (41) gives:
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | | Case 1:
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | (42) all_54_15 = e2
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | COMBINE_EQS: (23), (42) imply:
% 117.74/18.40 | | | | | | | (43) all_4_2 = e2
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | SIMP: (43) implies:
% 117.74/18.40 | | | | | | | (44) all_4_2 = e2
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | REDUCE: (4), (44) imply:
% 117.74/18.40 | | | | | | | (45) ~ (all_52_7 = e2)
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | REF_CLOSE: (2), (5), (7), (12), (15), (18), (19), (22), (45) are
% 117.74/18.40 | | | | | | | inconsistent by sub-proof #308.
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | Case 2:
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | (46) all_54_15 = e1 | all_54_15 = e0
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | | REF_CLOSE: (1), (23), (35), (46) are inconsistent by sub-proof
% 117.74/18.40 | | | | | | | #418.
% 117.74/18.40 | | | | | | |
% 117.74/18.40 | | | | | | End of split
% 117.74/18.40 | | | | | |
% 117.74/18.40 | | | | | End of split
% 117.74/18.40 | | | | |
% 117.74/18.40 | | | | End of split
% 117.74/18.40 | | | |
% 117.74/18.40 | | | End of split
% 117.74/18.40 | | |
% 117.74/18.40 | | Case 2:
% 117.74/18.40 | | |
% 117.74/18.40 | | | (47) all_58_9 = e3
% 117.74/18.41 | | |
% 117.74/18.41 | | | COMBINE_EQS: (21), (47) imply:
% 117.74/18.41 | | | (48) all_52_12 = e3
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (16), (48) imply:
% 117.74/18.41 | | | (49) $false
% 117.74/18.41 | | |
% 117.74/18.41 | | | CLOSE: (49) is inconsistent.
% 117.74/18.41 | | |
% 117.74/18.41 | | End of split
% 117.74/18.41 | |
% 117.74/18.41 | End of split
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #308 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.41 (2) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.41 (3) all_54_13 = all_52_7
% 117.74/18.41 (4) ~ (all_52_7 = all_8_2)
% 117.74/18.41 (5) all_54_5 = all_8_2
% 117.74/18.41 (6) ~ (all_52_7 = e2)
% 117.74/18.41 (7) ~ (all_8_2 = e1)
% 117.74/18.41 (8) ~ (all_8_2 = e2)
% 117.74/18.41 (9) ~ (all_52_7 = e1)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | BETA: splitting (2) gives:
% 117.74/18.41 |
% 117.74/18.41 | Case 1:
% 117.74/18.41 | |
% 117.74/18.41 | | (10) all_54_13 = e2
% 117.74/18.41 | |
% 117.74/18.41 | | COMBINE_EQS: (3), (10) imply:
% 117.74/18.41 | | (11) all_52_7 = e2
% 117.74/18.41 | |
% 117.74/18.41 | | REDUCE: (6), (11) imply:
% 117.74/18.41 | | (12) $false
% 117.74/18.41 | |
% 117.74/18.41 | | CLOSE: (12) is inconsistent.
% 117.74/18.41 | |
% 117.74/18.41 | Case 2:
% 117.74/18.41 | |
% 117.74/18.41 | | (13) all_54_13 = e1 | all_54_13 = e0
% 117.74/18.41 | |
% 117.74/18.41 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (13) are inconsistent by
% 117.74/18.41 | | sub-proof #309.
% 117.74/18.41 | |
% 117.74/18.41 | End of split
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #309 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.41 (2) all_54_13 = e1 | all_54_13 = e0
% 117.74/18.41 (3) all_54_13 = all_52_7
% 117.74/18.41 (4) ~ (all_52_7 = all_8_2)
% 117.74/18.41 (5) all_54_5 = all_8_2
% 117.74/18.41 (6) ~ (all_8_2 = e1)
% 117.74/18.41 (7) ~ (all_8_2 = e2)
% 117.74/18.41 (8) ~ (all_52_7 = e1)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | BETA: splitting (2) gives:
% 117.74/18.41 |
% 117.74/18.41 | Case 1:
% 117.74/18.41 | |
% 117.74/18.41 | | (9) all_54_13 = e1
% 117.74/18.41 | |
% 117.74/18.41 | | COMBINE_EQS: (3), (9) imply:
% 117.74/18.41 | | (10) all_52_7 = e1
% 117.74/18.41 | |
% 117.74/18.41 | | REDUCE: (8), (10) imply:
% 117.74/18.41 | | (11) $false
% 117.74/18.41 | |
% 117.74/18.41 | | CLOSE: (11) is inconsistent.
% 117.74/18.41 | |
% 117.74/18.41 | Case 2:
% 117.74/18.41 | |
% 117.74/18.41 | | (12) all_54_13 = e0
% 117.74/18.41 | |
% 117.74/18.41 | | COMBINE_EQS: (3), (12) imply:
% 117.74/18.41 | | (13) all_52_7 = e0
% 117.74/18.41 | |
% 117.74/18.41 | | REDUCE: (4), (13) imply:
% 117.74/18.41 | | (14) ~ (all_8_2 = e0)
% 117.74/18.41 | |
% 117.74/18.41 | | SIMP: (14) implies:
% 117.74/18.41 | | (15) ~ (all_8_2 = e0)
% 117.74/18.41 | |
% 117.74/18.41 | | REF_CLOSE: (1), (5), (6), (7), (15) are inconsistent by sub-proof #310.
% 117.74/18.41 | |
% 117.74/18.41 | End of split
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #310 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.41 (2) ~ (all_8_2 = e0)
% 117.74/18.41 (3) all_54_5 = all_8_2
% 117.74/18.41 (4) ~ (all_8_2 = e1)
% 117.74/18.41 (5) ~ (all_8_2 = e2)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | BETA: splitting (1) gives:
% 117.74/18.41 |
% 117.74/18.41 | Case 1:
% 117.74/18.41 | |
% 117.74/18.41 | | (6) all_54_5 = e2
% 117.74/18.41 | |
% 117.74/18.41 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #338.
% 117.74/18.41 | |
% 117.74/18.41 | Case 2:
% 117.74/18.41 | |
% 117.74/18.41 | | (7) all_54_5 = e1 | all_54_5 = e0
% 117.74/18.41 | |
% 117.74/18.41 | | BETA: splitting (7) gives:
% 117.74/18.41 | |
% 117.74/18.41 | | Case 1:
% 117.74/18.41 | | |
% 117.74/18.41 | | | (8) all_54_5 = e1
% 117.74/18.41 | | |
% 117.74/18.41 | | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #337.
% 117.74/18.41 | | |
% 117.74/18.41 | | Case 2:
% 117.74/18.41 | | |
% 117.74/18.41 | | | (9) all_54_5 = e0
% 117.74/18.41 | | |
% 117.74/18.41 | | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #311.
% 117.74/18.41 | | |
% 117.74/18.41 | | End of split
% 117.74/18.41 | |
% 117.74/18.41 | End of split
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #311 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_5 = all_8_2
% 117.74/18.41 (2) all_54_5 = e0
% 117.74/18.41 (3) ~ (all_8_2 = e0)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.41 | (4) all_8_2 = e0
% 117.74/18.41 |
% 117.74/18.41 | SIMP: (4) implies:
% 117.74/18.41 | (5) all_8_2 = e0
% 117.74/18.41 |
% 117.74/18.41 | REDUCE: (3), (5) imply:
% 117.74/18.41 | (6) $false
% 117.74/18.41 |
% 117.74/18.41 | CLOSE: (6) is inconsistent.
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #312 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_15 = all_4_2
% 117.74/18.41 (2) all_54_15 = e3
% 117.74/18.41 (3) ~ (all_4_2 = e3)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.41 | (4) all_4_2 = e3
% 117.74/18.41 |
% 117.74/18.41 | SIMP: (4) implies:
% 117.74/18.41 | (5) all_4_2 = e3
% 117.74/18.41 |
% 117.74/18.41 | REDUCE: (3), (5) imply:
% 117.74/18.41 | (6) $false
% 117.74/18.41 |
% 117.74/18.41 | CLOSE: (6) is inconsistent.
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #313 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) ~ (all_52_8 = all_10_2)
% 117.74/18.41 (2) ~ (all_52_3 = e0)
% 117.74/18.41 (3) all_58_7 = all_52_6
% 117.74/18.41 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.74/18.41 (5) ~ (all_52_3 = e3)
% 117.74/18.41 (6) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.41 (7) all_56_14 = all_6_2
% 117.74/18.41 (8) all_56_3 = all_52_1
% 117.74/18.41 (9) all_54_0 = all_10_2
% 117.74/18.41 (10) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.41 (11) ~ (all_4_0 = e1)
% 117.74/18.41 (12) all_58_15 = e3
% 117.74/18.41 (13) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.74/18.41 (14) ~ (all_52_4 = all_52_8)
% 117.74/18.41 (15) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.41 (16) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.41 (17) all_56_12 = all_10_2
% 117.74/18.41 (18) all_58_0 = all_10_2
% 117.74/18.41 (19) all_54_13 = all_52_7
% 117.74/18.41 (20) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.74/18.41 (21) ~ (all_52_14 = all_6_2)
% 117.74/18.41 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.41 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.41 (24) ~ (all_52_2 = all_6_2)
% 117.74/18.41 (25) op(e0, e3) = all_4_1
% 117.74/18.41 (26) ~ (all_56_3 = e2) | ~ (all_56_15 = e3)
% 117.74/18.41 (27) ~ (all_52_7 = e3)
% 117.74/18.41 (28) ~ (all_10_2 = e2)
% 117.74/18.41 (29) all_54_10 = all_6_2
% 117.74/18.41 (30) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 117.74/18.41 (31) all_58_4 = all_52_8
% 117.74/18.41 (32) ~ (all_52_4 = all_52_7)
% 117.74/18.41 (33) all_58_3 = all_8_2
% 117.74/18.41 (34) all_58_11 = all_52_14
% 117.74/18.41 (35) ~ (all_52_11 = all_6_2)
% 117.74/18.41 (36) op(e2, e3) = all_52_1
% 117.74/18.41 (37) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.74/18.41 (38) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.74/18.41 (39) ~ (all_52_7 = all_8_2)
% 117.74/18.41 (40) ~ (all_52_4 = all_8_2)
% 117.74/18.41 (41) ~ (all_4_0 = e3)
% 117.74/18.41 (42) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.41 (43) all_58_2 = all_52_1
% 117.74/18.41 (44) op(e0, e3) = all_52_3
% 117.74/18.41 (45) ~ (all_10_2 = e3)
% 117.74/18.41 (46) all_58_13 = all_52_7
% 117.74/18.41 (47) all_58_6 = all_52_2
% 117.74/18.41 (48) ~ (all_52_1 = all_10_2)
% 117.74/18.41 (49) all_54_5 = all_8_2
% 117.74/18.41 (50) ~ (all_52_12 = e3)
% 117.74/18.41 (51) ~ (all_52_6 = all_8_2)
% 117.74/18.41 (52) all_58_1 = all_52_4
% 117.74/18.41 (53) all_58_14 = all_52_11
% 117.74/18.41 (54) ~ (all_52_1 = all_8_2)
% 117.74/18.41 (55) op(e1, all_6_2) = e3
% 117.74/18.41 (56) ~ (all_8_2 = e2)
% 117.74/18.41 (57) op(all_4_1, e3) = all_4_0
% 117.74/18.41 (58) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.74/18.41 (59) ~ (all_6_2 = e2)
% 117.74/18.41 (60) ~ (all_52_7 = all_52_11)
% 117.74/18.41 (61) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.41 (62) all_56_1 = all_52_8
% 117.74/18.41 (63) all_58_8 = all_6_2
% 117.74/18.41 (64) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.41 (65) all_58_9 = all_52_12
% 117.74/18.41 (66) ~ (all_52_6 = all_6_2)
% 117.74/18.41 (67) all_56_6 = all_52_2
% 117.74/18.41 (68) all_58_12 = all_52_3
% 117.74/18.41 (69) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.74/18.41 (70) ~ (all_52_3 = all_10_2)
% 117.74/18.41 (71) all_56_15 = e3
% 117.74/18.41 (72) op(e1, e3) = all_52_2
% 117.74/18.41 (73) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.41 (74) all_56_8 = all_52_14
% 117.74/18.41 (75) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.41 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.41 (76) all_54_4 = all_52_1
% 117.74/18.41 (77) ~ (all_6_2 = e1)
% 117.74/18.41 (78) ~ (all_52_6 = all_52_7)
% 117.74/18.41 (79) all_54_12 = all_52_3
% 117.74/18.41 (80) ~ (all_52_3 = all_52_7)
% 117.74/18.41
% 117.74/18.41 Begin of proof
% 117.74/18.41 |
% 117.74/18.41 | BETA: splitting (26) gives:
% 117.74/18.41 |
% 117.74/18.41 | Case 1:
% 117.74/18.41 | |
% 117.74/18.41 | | (81) ~ (all_56_3 = e2)
% 117.74/18.41 | |
% 117.74/18.41 | | REDUCE: (8), (81) imply:
% 117.74/18.41 | | (82) ~ (all_52_1 = e2)
% 117.74/18.41 | |
% 117.74/18.41 | | BETA: splitting (4) gives:
% 117.74/18.41 | |
% 117.74/18.41 | | Case 1:
% 117.74/18.41 | | |
% 117.74/18.41 | | | (83) ~ (all_56_6 = e1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (67), (83) imply:
% 117.74/18.41 | | | (84) ~ (all_52_2 = e1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | GROUND_INST: instantiating (23) with all_52_3, all_4_1, e3, e0,
% 117.74/18.41 | | | simplifying with (25), (44) gives:
% 117.74/18.41 | | | (85) all_52_3 = all_4_1
% 117.74/18.41 | | |
% 117.74/18.41 | | | COMBINE_EQS: (79), (85) imply:
% 117.74/18.41 | | | (86) all_54_12 = all_4_1
% 117.74/18.41 | | |
% 117.74/18.41 | | | COMBINE_EQS: (68), (85) imply:
% 117.74/18.41 | | | (87) all_58_12 = all_4_1
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (80), (85) imply:
% 117.74/18.41 | | | (88) ~ (all_52_7 = all_4_1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | SIMP: (88) implies:
% 117.74/18.41 | | | (89) ~ (all_52_7 = all_4_1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (70), (85) imply:
% 117.74/18.41 | | | (90) ~ (all_10_2 = all_4_1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | SIMP: (90) implies:
% 117.74/18.41 | | | (91) ~ (all_10_2 = all_4_1)
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (5), (85) imply:
% 117.74/18.41 | | | (92) ~ (all_4_1 = e3)
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (2), (85) imply:
% 117.74/18.41 | | | (93) ~ (all_4_1 = e0)
% 117.74/18.41 | | |
% 117.74/18.41 | | | BETA: splitting (42) gives:
% 117.74/18.41 | | |
% 117.74/18.41 | | | Case 1:
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | (94) ~ (all_56_8 = e1)
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | REDUCE: (74), (94) imply:
% 117.74/18.41 | | | | (95) ~ (all_52_14 = e1)
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (12), (14), (15), (16), (17),
% 117.74/18.41 | | | | (18), (19), (20), (22), (23), (24), (27), (28), (29), (30),
% 117.74/18.41 | | | | (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 117.74/18.41 | | | | (43), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 117.74/18.41 | | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 117.74/18.41 | | | | (64), (65), (66), (72), (73), (75), (76), (77), (78), (82),
% 117.74/18.41 | | | | (84), (87), (89), (92), (93), (95) are inconsistent by
% 117.74/18.41 | | | | sub-proof #320.
% 117.74/18.41 | | | |
% 117.74/18.41 | | | Case 2:
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | (96) all_56_8 = e1
% 117.74/18.41 | | | | (97) ~ (all_56_12 = e0)
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | COMBINE_EQS: (74), (96) imply:
% 117.74/18.41 | | | | (98) all_52_14 = e1
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | REDUCE: (17), (97) imply:
% 117.74/18.41 | | | | (99) ~ (all_10_2 = e0)
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | REDUCE: (21), (98) imply:
% 117.74/18.41 | | | | (100) ~ (all_6_2 = e1)
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | BETA: splitting (64) gives:
% 117.74/18.41 | | | |
% 117.74/18.41 | | | | Case 1:
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | | (101) all_54_0 = e3
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | | REF_CLOSE: (9), (45), (101) are inconsistent by sub-proof #451.
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | Case 2:
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | | (102) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | | BETA: splitting (13) gives:
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | | Case 1:
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | (103) ~ (all_56_8 = e1)
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | REDUCE: (96), (103) imply:
% 117.74/18.41 | | | | | | (104) $false
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | CLOSE: (104) is inconsistent.
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | Case 2:
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | (105) ~ (all_56_14 = e0)
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | REDUCE: (7), (105) imply:
% 117.74/18.41 | | | | | | (106) ~ (all_6_2 = e0)
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | BETA: splitting (102) gives:
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | | Case 1:
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | | (107) all_54_0 = e2
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | | REF_CLOSE: (9), (28), (107) are inconsistent by sub-proof #450.
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | Case 2:
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | | (108) all_54_0 = e1 | all_54_0 = e0
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | | REF_CLOSE: (9), (15), (18), (22), (23), (24), (29), (36), (41),
% 117.74/18.41 | | | | | | | (43), (47), (57), (59), (69), (77), (86), (87), (91),
% 117.74/18.41 | | | | | | | (92), (93), (99), (106), (108) are inconsistent by
% 117.74/18.41 | | | | | | | sub-proof #314.
% 117.74/18.41 | | | | | | |
% 117.74/18.41 | | | | | | End of split
% 117.74/18.41 | | | | | |
% 117.74/18.41 | | | | | End of split
% 117.74/18.41 | | | | |
% 117.74/18.41 | | | | End of split
% 117.74/18.41 | | | |
% 117.74/18.41 | | | End of split
% 117.74/18.41 | | |
% 117.74/18.41 | | Case 2:
% 117.74/18.41 | | |
% 117.74/18.41 | | | (109) ~ (all_56_15 = e3)
% 117.74/18.41 | | |
% 117.74/18.41 | | | REDUCE: (71), (109) imply:
% 117.74/18.41 | | | (110) $false
% 117.74/18.41 | | |
% 117.74/18.41 | | | CLOSE: (110) is inconsistent.
% 117.74/18.41 | | |
% 117.74/18.41 | | End of split
% 117.74/18.41 | |
% 117.74/18.41 | Case 2:
% 117.74/18.41 | |
% 117.74/18.41 | | (111) ~ (all_56_15 = e3)
% 117.74/18.41 | |
% 117.74/18.41 | | REDUCE: (71), (111) imply:
% 117.74/18.41 | | (112) $false
% 117.74/18.41 | |
% 117.74/18.41 | | CLOSE: (112) is inconsistent.
% 117.74/18.41 | |
% 117.74/18.41 | End of split
% 117.74/18.41 |
% 117.74/18.41 End of proof
% 117.74/18.41
% 117.74/18.41 Sub-proof #314 shows that the following formulas are inconsistent:
% 117.74/18.41 ----------------------------------------------------------------
% 117.74/18.41 (1) all_54_0 = all_10_2
% 117.74/18.41 (2) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.41 (3) all_58_0 = all_10_2
% 117.74/18.41 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.41 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.41 (6) ~ (all_52_2 = all_6_2)
% 117.74/18.41 (7) ~ (all_10_2 = all_4_1)
% 117.74/18.41 (8) all_54_10 = all_6_2
% 117.74/18.41 (9) op(e2, e3) = all_52_1
% 117.74/18.41 (10) all_54_0 = e1 | all_54_0 = e0
% 117.74/18.41 (11) ~ (all_4_0 = e3)
% 117.74/18.41 (12) all_58_2 = all_52_1
% 117.74/18.41 (13) ~ (all_4_1 = e0)
% 117.74/18.41 (14) all_58_6 = all_52_2
% 117.74/18.41 (15) all_58_12 = all_4_1
% 117.74/18.41 (16) op(all_4_1, e3) = all_4_0
% 117.74/18.42 (17) ~ (all_6_2 = e2)
% 117.74/18.42 (18) ~ (all_10_2 = e0)
% 117.74/18.42 (19) ~ (all_6_2 = e0)
% 117.74/18.42 (20) all_54_12 = all_4_1
% 117.74/18.42 (21) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.74/18.42 (22) ~ (all_4_1 = e3)
% 117.74/18.42 (23) ~ (all_6_2 = e1)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | BETA: splitting (10) gives:
% 117.74/18.42 |
% 117.74/18.42 | Case 1:
% 117.74/18.42 | |
% 117.74/18.42 | | (24) all_54_0 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (1), (24) imply:
% 117.74/18.42 | | (25) all_10_2 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | SIMP: (25) implies:
% 117.74/18.42 | | (26) all_10_2 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (3), (26) imply:
% 117.74/18.42 | | (27) all_58_0 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (7), (26) imply:
% 117.74/18.42 | | (28) ~ (all_4_1 = e1)
% 117.74/18.42 | |
% 117.74/18.42 | | SIMP: (28) implies:
% 117.74/18.42 | | (29) ~ (all_4_1 = e1)
% 117.74/18.42 | |
% 117.74/18.42 | | BETA: splitting (21) gives:
% 117.74/18.42 | |
% 117.74/18.42 | | Case 1:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (30) all_54_12 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | COMBINE_EQS: (20), (30) imply:
% 117.74/18.42 | | | (31) all_4_1 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | REDUCE: (22), (31) imply:
% 117.74/18.42 | | | (32) $false
% 117.74/18.42 | | |
% 117.74/18.42 | | | CLOSE: (32) is inconsistent.
% 117.74/18.42 | | |
% 117.74/18.42 | | Case 2:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (33) ~ (all_54_12 = e3)
% 117.74/18.42 | | | (34) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.74/18.42 | | |
% 117.74/18.42 | | | BETA: splitting (34) gives:
% 117.74/18.42 | | |
% 117.74/18.42 | | | Case 1:
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | (35) all_54_12 = e2
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | COMBINE_EQS: (20), (35) imply:
% 117.74/18.42 | | | | (36) all_4_1 = e2
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | REDUCE: (16), (36) imply:
% 117.74/18.42 | | | | (37) op(e2, e3) = all_4_0
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (14), (15), (17),
% 117.74/18.42 | | | | (19), (22), (23), (27), (37) are inconsistent by sub-proof
% 117.74/18.42 | | | | #316.
% 117.74/18.42 | | | |
% 117.74/18.42 | | | Case 2:
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | (38) all_54_12 = e1 | all_54_12 = e0
% 117.74/18.42 | | | |
% 117.74/18.42 | | | | REF_CLOSE: (13), (20), (29), (38) are inconsistent by sub-proof #315.
% 117.74/18.42 | | | |
% 117.74/18.42 | | | End of split
% 117.74/18.42 | | |
% 117.74/18.42 | | End of split
% 117.74/18.42 | |
% 117.74/18.42 | Case 2:
% 117.74/18.42 | |
% 117.74/18.42 | | (39) all_54_0 = e0
% 117.74/18.42 | |
% 117.74/18.42 | | REF_CLOSE: (1), (18), (39) are inconsistent by sub-proof #424.
% 117.74/18.42 | |
% 117.74/18.42 | End of split
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #315 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) all_54_12 = e1 | all_54_12 = e0
% 117.74/18.42 (2) all_54_12 = all_4_1
% 117.74/18.42 (3) ~ (all_4_1 = e1)
% 117.74/18.42 (4) ~ (all_4_1 = e0)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | BETA: splitting (1) gives:
% 117.74/18.42 |
% 117.74/18.42 | Case 1:
% 117.74/18.42 | |
% 117.74/18.42 | | (5) all_54_12 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (2), (5) imply:
% 117.74/18.42 | | (6) all_4_1 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (3), (6) imply:
% 117.74/18.42 | | (7) $false
% 117.74/18.42 | |
% 117.74/18.42 | | CLOSE: (7) is inconsistent.
% 117.74/18.42 | |
% 117.74/18.42 | Case 2:
% 117.74/18.42 | |
% 117.74/18.42 | | (8) all_54_12 = e0
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (2), (8) imply:
% 117.74/18.42 | | (9) all_4_1 = e0
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (4), (9) imply:
% 117.74/18.42 | | (10) $false
% 117.74/18.42 | |
% 117.74/18.42 | | CLOSE: (10) is inconsistent.
% 117.74/18.42 | |
% 117.74/18.42 | End of split
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #316 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42 (2) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.42 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.42 (4) ~ (all_52_2 = all_6_2)
% 117.74/18.42 (5) all_54_10 = all_6_2
% 117.74/18.42 (6) all_58_0 = e1
% 117.74/18.42 (7) op(e2, e3) = all_52_1
% 117.74/18.42 (8) ~ (all_4_0 = e3)
% 117.74/18.42 (9) all_58_2 = all_52_1
% 117.74/18.42 (10) all_58_6 = all_52_2
% 117.74/18.42 (11) all_58_12 = all_4_1
% 117.74/18.42 (12) ~ (all_6_2 = e2)
% 117.74/18.42 (13) ~ (all_6_2 = e0)
% 117.74/18.42 (14) op(e2, e3) = all_4_0
% 117.74/18.42 (15) ~ (all_4_1 = e3)
% 117.74/18.42 (16) ~ (all_6_2 = e1)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | BETA: splitting (2) gives:
% 117.74/18.42 |
% 117.74/18.42 | Case 1:
% 117.74/18.42 | |
% 117.74/18.42 | | (17) all_54_10 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (5), (17) imply:
% 117.74/18.42 | | (18) all_6_2 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (4), (18) imply:
% 117.74/18.42 | | (19) ~ (all_52_2 = e3)
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (16), (18) imply:
% 117.74/18.42 | | (20) ~ (e3 = e1)
% 117.74/18.42 | |
% 117.74/18.42 | | BETA: splitting (1) gives:
% 117.74/18.42 | |
% 117.74/18.42 | | Case 1:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (21) all_58_0 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (6), (20), (21) are inconsistent by sub-proof #319.
% 117.74/18.42 | | |
% 117.74/18.42 | | Case 2:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (22) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (3), (7), (8), (9), (10), (11), (14), (15), (19), (22) are
% 117.74/18.42 | | | inconsistent by sub-proof #317.
% 117.74/18.42 | | |
% 117.74/18.42 | | End of split
% 117.74/18.42 | |
% 117.74/18.42 | Case 2:
% 117.74/18.42 | |
% 117.74/18.42 | | (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.42 | |
% 117.74/18.42 | | REF_CLOSE: (5), (12), (13), (16), (23) are inconsistent by sub-proof #435.
% 117.74/18.42 | |
% 117.74/18.42 | End of split
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #317 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.42 (2) op(e2, e3) = all_52_1
% 117.74/18.42 (3) ~ (all_4_0 = e3)
% 117.74/18.42 (4) all_58_2 = all_52_1
% 117.74/18.42 (5) ~ (all_52_2 = e3)
% 117.74/18.42 (6) all_58_6 = all_52_2
% 117.74/18.42 (7) all_58_12 = all_4_1
% 117.74/18.42 (8) op(e2, e3) = all_4_0
% 117.74/18.42 (9) ~ (all_4_1 = e3)
% 117.74/18.42 (10) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | BETA: splitting (10) gives:
% 117.74/18.42 |
% 117.74/18.42 | Case 1:
% 117.74/18.42 | |
% 117.74/18.42 | | (11) all_58_2 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | COMBINE_EQS: (4), (11) imply:
% 117.74/18.42 | | (12) all_52_1 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (2), (12) imply:
% 117.74/18.42 | | (13) op(e2, e3) = e3
% 117.74/18.42 | |
% 117.74/18.42 | | GROUND_INST: instantiating (1) with e3, all_4_0, e3, e2, simplifying with
% 117.74/18.42 | | (8), (13) gives:
% 117.74/18.42 | | (14) all_4_0 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | REDUCE: (3), (14) imply:
% 117.74/18.42 | | (15) $false
% 117.74/18.42 | |
% 117.74/18.42 | | CLOSE: (15) is inconsistent.
% 117.74/18.42 | |
% 117.74/18.42 | Case 2:
% 117.74/18.42 | |
% 117.74/18.42 | | (16) all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42 | |
% 117.74/18.42 | | BETA: splitting (16) gives:
% 117.74/18.42 | |
% 117.74/18.42 | | Case 1:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (17) all_58_6 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #318.
% 117.74/18.42 | | |
% 117.74/18.42 | | Case 2:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (18) all_58_12 = e3
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (7), (9), (18) are inconsistent by sub-proof #324.
% 117.74/18.42 | | |
% 117.74/18.42 | | End of split
% 117.74/18.42 | |
% 117.74/18.42 | End of split
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #318 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) all_58_6 = all_52_2
% 117.74/18.42 (2) all_58_6 = e3
% 117.74/18.42 (3) ~ (all_52_2 = e3)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.42 | (4) all_52_2 = e3
% 117.74/18.42 |
% 117.74/18.42 | SIMP: (4) implies:
% 117.74/18.42 | (5) all_52_2 = e3
% 117.74/18.42 |
% 117.74/18.42 | REDUCE: (3), (5) imply:
% 117.74/18.42 | (6) $false
% 117.74/18.42 |
% 117.74/18.42 | CLOSE: (6) is inconsistent.
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #319 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) all_58_0 = e3
% 117.74/18.42 (2) all_58_0 = e1
% 117.74/18.42 (3) ~ (e3 = e1)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.42 | (4) e3 = e1
% 117.74/18.42 |
% 117.74/18.42 | SIMP: (4) implies:
% 117.74/18.42 | (5) e3 = e1
% 117.74/18.42 |
% 117.74/18.42 | REDUCE: (3), (5) imply:
% 117.74/18.42 | (6) $false
% 117.74/18.42 |
% 117.74/18.42 | CLOSE: (6) is inconsistent.
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #320 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) ~ (all_52_8 = all_10_2)
% 117.74/18.42 (2) all_58_7 = all_52_6
% 117.74/18.42 (3) ~ (all_52_1 = e2)
% 117.74/18.42 (4) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.42 (5) all_54_0 = all_10_2
% 117.74/18.42 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.42 (7) ~ (all_4_0 = e1)
% 117.74/18.42 (8) all_58_15 = e3
% 117.74/18.42 (9) ~ (all_52_4 = all_52_8)
% 117.74/18.42 (10) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.42 (12) all_56_12 = all_10_2
% 117.74/18.42 (13) all_58_0 = all_10_2
% 117.74/18.42 (14) all_54_13 = all_52_7
% 117.74/18.42 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.74/18.42 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.42 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.42 (18) ~ (all_52_2 = all_6_2)
% 117.74/18.42 (19) ~ (all_52_7 = e3)
% 117.74/18.42 (20) ~ (all_10_2 = e2)
% 117.74/18.42 (21) all_54_10 = all_6_2
% 117.74/18.42 (22) ~ (all_52_14 = e1)
% 117.74/18.42 (23) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 117.74/18.42 (24) all_58_4 = all_52_8
% 117.74/18.42 (25) ~ (all_52_4 = all_52_7)
% 117.74/18.42 (26) all_58_3 = all_8_2
% 117.74/18.42 (27) all_58_11 = all_52_14
% 117.74/18.42 (28) ~ (all_52_11 = all_6_2)
% 117.74/18.42 (29) ~ (all_52_7 = all_4_1)
% 117.74/18.42 (30) op(e2, e3) = all_52_1
% 117.74/18.42 (31) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.74/18.42 (32) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.74/18.42 (33) ~ (all_52_7 = all_8_2)
% 117.74/18.42 (34) ~ (all_52_4 = all_8_2)
% 117.74/18.42 (35) all_58_2 = all_52_1
% 117.74/18.42 (36) ~ (all_10_2 = e3)
% 117.74/18.42 (37) ~ (all_4_1 = e0)
% 117.74/18.42 (38) all_58_13 = all_52_7
% 117.74/18.42 (39) all_58_6 = all_52_2
% 117.74/18.42 (40) ~ (all_52_2 = e1)
% 117.74/18.42 (41) ~ (all_52_1 = all_10_2)
% 117.74/18.42 (42) all_54_5 = all_8_2
% 117.74/18.42 (43) ~ (all_52_12 = e3)
% 117.74/18.42 (44) all_58_12 = all_4_1
% 117.74/18.42 (45) ~ (all_52_6 = all_8_2)
% 117.74/18.42 (46) all_58_1 = all_52_4
% 117.74/18.42 (47) all_58_14 = all_52_11
% 117.74/18.42 (48) ~ (all_52_1 = all_8_2)
% 117.74/18.42 (49) op(e1, all_6_2) = e3
% 117.74/18.42 (50) ~ (all_8_2 = e2)
% 117.74/18.42 (51) op(all_4_1, e3) = all_4_0
% 117.74/18.42 (52) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.74/18.42 (53) ~ (all_6_2 = e2)
% 117.74/18.42 (54) ~ (all_52_7 = all_52_11)
% 117.74/18.42 (55) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.42 (56) all_56_1 = all_52_8
% 117.74/18.42 (57) all_58_8 = all_6_2
% 117.74/18.42 (58) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.42 (59) all_58_9 = all_52_12
% 117.74/18.42 (60) ~ (all_52_6 = all_6_2)
% 117.74/18.42 (61) op(e1, e3) = all_52_2
% 117.74/18.42 (62) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.42 (63) ~ (all_4_1 = e3)
% 117.74/18.42 (64) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.42 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.42 (65) all_54_4 = all_52_1
% 117.74/18.42 (66) ~ (all_6_2 = e1)
% 117.74/18.42 (67) ~ (all_52_6 = all_52_7)
% 117.74/18.42
% 117.74/18.42 Begin of proof
% 117.74/18.42 |
% 117.74/18.42 | BETA: splitting (55) gives:
% 117.74/18.42 |
% 117.74/18.42 | Case 1:
% 117.74/18.42 | |
% 117.74/18.42 | | (68) all_58_6 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | REF_CLOSE: (39), (40), (68) are inconsistent by sub-proof #452.
% 117.74/18.42 | |
% 117.74/18.42 | Case 2:
% 117.74/18.42 | |
% 117.74/18.42 | | (69) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.42 | |
% 117.74/18.42 | | BETA: splitting (69) gives:
% 117.74/18.42 | |
% 117.74/18.42 | | Case 1:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (70) all_58_7 = e1
% 117.74/18.42 | | |
% 117.74/18.42 | | | COMBINE_EQS: (2), (70) imply:
% 117.74/18.42 | | | (71) all_52_6 = e1
% 117.74/18.42 | | |
% 117.74/18.42 | | | REDUCE: (67), (71) imply:
% 117.74/18.42 | | | (72) ~ (all_52_7 = e1)
% 117.74/18.42 | | |
% 117.74/18.42 | | | SIMP: (72) implies:
% 117.74/18.42 | | | (73) ~ (all_52_7 = e1)
% 117.74/18.42 | | |
% 117.74/18.42 | | | REDUCE: (45), (71) imply:
% 117.74/18.42 | | | (74) ~ (all_8_2 = e1)
% 117.74/18.42 | | |
% 117.74/18.42 | | | SIMP: (74) implies:
% 117.74/18.42 | | | (75) ~ (all_8_2 = e1)
% 117.74/18.42 | | |
% 117.74/18.42 | | | REDUCE: (60), (71) imply:
% 117.74/18.42 | | | (76) ~ (all_6_2 = e1)
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.74/18.42 | | | (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 117.74/18.42 | | | (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 117.74/18.42 | | | (36), (37), (38), (39), (41), (42), (43), (44), (46), (47),
% 117.74/18.42 | | | (48), (49), (50), (51), (52), (53), (54), (56), (58), (59),
% 117.74/18.42 | | | (61), (62), (63), (64), (65), (66), (73), (75) are inconsistent
% 117.74/18.42 | | | by sub-proof #321.
% 117.74/18.42 | | |
% 117.74/18.42 | | Case 2:
% 117.74/18.42 | | |
% 117.74/18.42 | | | (77) all_58_8 = e1 | all_58_11 = e1
% 117.74/18.42 | | |
% 117.74/18.42 | | | REF_CLOSE: (22), (27), (57), (66), (77) are inconsistent by sub-proof
% 117.74/18.42 | | | #445.
% 117.74/18.42 | | |
% 117.74/18.42 | | End of split
% 117.74/18.42 | |
% 117.74/18.42 | End of split
% 117.74/18.42 |
% 117.74/18.42 End of proof
% 117.74/18.42
% 117.74/18.42 Sub-proof #321 shows that the following formulas are inconsistent:
% 117.74/18.42 ----------------------------------------------------------------
% 117.74/18.42 (1) ~ (all_52_8 = all_10_2)
% 117.74/18.42 (2) ~ (all_52_1 = e2)
% 117.74/18.42 (3) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.42 (4) all_54_0 = all_10_2
% 117.74/18.42 (5) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.42 (6) ~ (all_4_0 = e1)
% 117.74/18.42 (7) all_58_15 = e3
% 117.74/18.42 (8) ~ (all_52_4 = all_52_8)
% 117.74/18.42 (9) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.42 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.42 (11) all_56_12 = all_10_2
% 117.74/18.42 (12) all_58_0 = all_10_2
% 117.74/18.42 (13) all_54_13 = all_52_7
% 117.74/18.42 (14) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.74/18.42 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.42 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.42 (17) ~ (all_52_2 = all_6_2)
% 117.74/18.42 (18) ~ (all_52_7 = e3)
% 117.74/18.42 (19) ~ (all_10_2 = e2)
% 117.74/18.42 (20) all_54_10 = all_6_2
% 117.74/18.42 (21) all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 117.74/18.42 (22) all_58_4 = all_52_8
% 117.74/18.42 (23) ~ (all_52_4 = all_52_7)
% 117.74/18.42 (24) all_58_3 = all_8_2
% 117.74/18.42 (25) ~ (all_52_11 = all_6_2)
% 117.74/18.42 (26) ~ (all_52_7 = all_4_1)
% 117.74/18.42 (27) op(e2, e3) = all_52_1
% 117.74/18.43 (28) ~ (all_56_1 = e3) | ~ (all_56_12 = e1)
% 117.74/18.43 (29) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.74/18.43 (30) ~ (all_52_7 = all_8_2)
% 117.74/18.43 (31) ~ (all_52_4 = all_8_2)
% 117.74/18.43 (32) all_58_2 = all_52_1
% 117.74/18.43 (33) ~ (all_10_2 = e3)
% 117.74/18.43 (34) ~ (all_4_1 = e0)
% 117.74/18.43 (35) all_58_13 = all_52_7
% 117.74/18.43 (36) all_58_6 = all_52_2
% 117.74/18.43 (37) ~ (all_52_1 = all_10_2)
% 117.74/18.43 (38) all_54_5 = all_8_2
% 117.74/18.43 (39) ~ (all_52_12 = e3)
% 117.74/18.43 (40) all_58_12 = all_4_1
% 117.74/18.43 (41) all_58_1 = all_52_4
% 117.74/18.43 (42) ~ (all_8_2 = e1)
% 117.74/18.43 (43) all_58_14 = all_52_11
% 117.74/18.43 (44) ~ (all_52_1 = all_8_2)
% 117.74/18.43 (45) op(e1, all_6_2) = e3
% 117.74/18.43 (46) ~ (all_8_2 = e2)
% 117.74/18.43 (47) op(all_4_1, e3) = all_4_0
% 117.74/18.43 (48) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.74/18.43 (49) ~ (all_6_2 = e2)
% 117.74/18.43 (50) ~ (all_52_7 = all_52_11)
% 117.74/18.43 (51) all_56_1 = all_52_8
% 117.74/18.43 (52) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.43 (53) all_58_9 = all_52_12
% 117.74/18.43 (54) op(e1, e3) = all_52_2
% 117.74/18.43 (55) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.43 (56) ~ (all_52_7 = e1)
% 117.74/18.43 (57) ~ (all_4_1 = e3)
% 117.74/18.43 (58) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.43 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.43 (59) all_54_4 = all_52_1
% 117.74/18.43 (60) ~ (all_6_2 = e1)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | BETA: splitting (28) gives:
% 117.74/18.43 |
% 117.74/18.43 | Case 1:
% 117.74/18.43 | |
% 117.74/18.43 | | (61) ~ (all_56_1 = e3)
% 117.74/18.43 | |
% 117.74/18.43 | | REDUCE: (51), (61) imply:
% 117.74/18.43 | | (62) ~ (all_52_8 = e3)
% 117.74/18.43 | |
% 117.74/18.43 | | BETA: splitting (55) gives:
% 117.74/18.43 | |
% 117.74/18.43 | | Case 1:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (63) all_58_0 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | COMBINE_EQS: (12), (63) imply:
% 117.74/18.43 | | | (64) all_10_2 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | REDUCE: (33), (64) imply:
% 117.74/18.43 | | | (65) $false
% 117.74/18.43 | | |
% 117.74/18.43 | | | CLOSE: (65) is inconsistent.
% 117.74/18.43 | | |
% 117.74/18.43 | | Case 2:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (66) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | BETA: splitting (66) gives:
% 117.74/18.43 | | |
% 117.74/18.43 | | | Case 1:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (67) all_58_1 = e3
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | COMBINE_EQS: (41), (67) imply:
% 117.74/18.43 | | | | (68) all_52_4 = e3
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REDUCE: (23), (68) imply:
% 117.74/18.43 | | | | (69) ~ (all_52_7 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REDUCE: (31), (68) imply:
% 117.74/18.43 | | | | (70) ~ (all_8_2 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | SIMP: (70) implies:
% 117.74/18.43 | | | | (71) ~ (all_8_2 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REF_CLOSE: (2), (3), (5), (7), (10), (12), (13), (15), (16), (17), (18),
% 117.74/18.43 | | | | (19), (20), (25), (26), (29), (30), (32), (34), (35), (36),
% 117.74/18.43 | | | | (38), (40), (42), (43), (45), (46), (47), (49), (50), (54),
% 117.74/18.43 | | | | (56), (58), (60), (71) are inconsistent by sub-proof #332.
% 117.74/18.43 | | | |
% 117.74/18.43 | | | Case 2:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (72) all_58_4 = e3 | all_58_9 = e3
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | BETA: splitting (72) gives:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | Case 1:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (73) all_58_4 = e3
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REF_CLOSE: (22), (62), (73) are inconsistent by sub-proof #331.
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | Case 2:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (74) all_58_9 = e3
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REF_CLOSE: (39), (53), (74) are inconsistent by sub-proof #330.
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | End of split
% 117.74/18.43 | | | |
% 117.74/18.43 | | | End of split
% 117.74/18.43 | | |
% 117.74/18.43 | | End of split
% 117.74/18.43 | |
% 117.74/18.43 | Case 2:
% 117.74/18.43 | |
% 117.74/18.43 | | (75) all_56_1 = e3
% 117.74/18.43 | | (76) ~ (all_56_12 = e1)
% 117.74/18.43 | |
% 117.74/18.43 | | COMBINE_EQS: (51), (75) imply:
% 117.74/18.43 | | (77) all_52_8 = e3
% 117.74/18.43 | |
% 117.74/18.43 | | REDUCE: (11), (76) imply:
% 117.74/18.43 | | (78) ~ (all_10_2 = e1)
% 117.74/18.43 | |
% 117.74/18.43 | | REDUCE: (8), (77) imply:
% 117.74/18.43 | | (79) ~ (all_52_4 = e3)
% 117.74/18.43 | |
% 117.74/18.43 | | REDUCE: (1), (77) imply:
% 117.74/18.43 | | (80) ~ (all_10_2 = e3)
% 117.74/18.43 | |
% 117.74/18.43 | | BETA: splitting (48) gives:
% 117.74/18.43 | |
% 117.74/18.43 | | Case 1:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (81) all_58_1 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | COMBINE_EQS: (41), (81) imply:
% 117.74/18.43 | | | (82) all_52_4 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | REDUCE: (79), (82) imply:
% 117.74/18.43 | | | (83) $false
% 117.74/18.43 | | |
% 117.74/18.43 | | | CLOSE: (83) is inconsistent.
% 117.74/18.43 | | |
% 117.74/18.43 | | Case 2:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (84) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | BETA: splitting (84) gives:
% 117.74/18.43 | | |
% 117.74/18.43 | | | Case 1:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (85) all_58_3 = e3
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | COMBINE_EQS: (24), (85) imply:
% 117.74/18.43 | | | | (86) all_8_2 = e3
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REDUCE: (44), (86) imply:
% 117.74/18.43 | | | | (87) ~ (all_52_1 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REDUCE: (46), (86) imply:
% 117.74/18.43 | | | | (88) ~ (e3 = e2)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | BETA: splitting (52) gives:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | Case 1:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (89) all_54_0 = e3
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REF_CLOSE: (4), (33), (89) are inconsistent by sub-proof #451.
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | Case 2:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (90) ~ (all_54_0 = e3)
% 117.74/18.43 | | | | | (91) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | BETA: splitting (21) gives:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | Case 1:
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | (92) all_58_0 = e0
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | COMBINE_EQS: (12), (92) imply:
% 117.74/18.43 | | | | | | (93) all_10_2 = e0
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REDUCE: (37), (93) imply:
% 117.74/18.43 | | | | | | (94) ~ (all_52_1 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REDUCE: (33), (93) imply:
% 117.74/18.43 | | | | | | (95) ~ (e3 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | SIMP: (95) implies:
% 117.74/18.43 | | | | | | (96) ~ (e3 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REDUCE: (19), (93) imply:
% 117.74/18.43 | | | | | | (97) ~ (e2 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | SIMP: (97) implies:
% 117.74/18.43 | | | | | | (98) ~ (e2 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REF_CLOSE: (2), (3), (6), (9), (14), (16), (27), (32), (40), (47),
% 117.74/18.43 | | | | | | (57), (59), (87), (88), (92), (94), (96), (98) are
% 117.74/18.43 | | | | | | inconsistent by sub-proof #322.
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | Case 2:
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | (99) ~ (all_58_0 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REDUCE: (12), (99) imply:
% 117.74/18.43 | | | | | | (100) ~ (all_10_2 = e0)
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REF_CLOSE: (4), (19), (78), (91), (100) are inconsistent by
% 117.74/18.43 | | | | | | sub-proof #386.
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | End of split
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | End of split
% 117.74/18.43 | | | |
% 117.74/18.43 | | | Case 2:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (101) ~ (all_58_3 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REDUCE: (24), (101) imply:
% 117.74/18.43 | | | | (102) ~ (all_8_2 = e3)
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REF_CLOSE: (2), (3), (5), (7), (10), (12), (13), (15), (16), (17), (18),
% 117.74/18.43 | | | | (19), (20), (25), (26), (29), (30), (32), (34), (35), (36),
% 117.74/18.43 | | | | (38), (40), (42), (43), (45), (46), (47), (49), (50), (54),
% 117.74/18.43 | | | | (56), (58), (60), (102) are inconsistent by sub-proof #332.
% 117.74/18.43 | | | |
% 117.74/18.43 | | | End of split
% 117.74/18.43 | | |
% 117.74/18.43 | | End of split
% 117.74/18.43 | |
% 117.74/18.43 | End of split
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #322 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) ~ (all_52_1 = e2)
% 117.74/18.43 (2) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.43 (3) ~ (all_4_0 = e1)
% 117.74/18.43 (4) all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.43 (5) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.74/18.43 (6) ~ (all_52_1 = e3)
% 117.74/18.43 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.43 (8) op(e2, e3) = all_52_1
% 117.74/18.43 (9) ~ (e3 = e0)
% 117.74/18.43 (10) all_58_2 = all_52_1
% 117.74/18.43 (11) all_58_12 = all_4_1
% 117.74/18.43 (12) ~ (all_52_1 = e0)
% 117.74/18.43 (13) op(all_4_1, e3) = all_4_0
% 117.74/18.43 (14) all_58_0 = e0
% 117.74/18.43 (15) ~ (e2 = e0)
% 117.74/18.43 (16) ~ (e3 = e2)
% 117.74/18.43 (17) ~ (all_4_1 = e3)
% 117.74/18.43 (18) all_54_4 = all_52_1
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | BETA: splitting (4) gives:
% 117.74/18.43 |
% 117.74/18.43 | Case 1:
% 117.74/18.43 | |
% 117.74/18.43 | | (19) all_58_0 = e3
% 117.74/18.43 | |
% 117.74/18.43 | | COMBINE_EQS: (14), (19) imply:
% 117.74/18.43 | | (20) e3 = e0
% 117.74/18.43 | |
% 117.74/18.43 | | SIMP: (20) implies:
% 117.74/18.43 | | (21) e3 = e0
% 117.74/18.43 | |
% 117.74/18.43 | | REDUCE: (9), (21) imply:
% 117.74/18.43 | | (22) $false
% 117.74/18.43 | |
% 117.74/18.43 | | CLOSE: (22) is inconsistent.
% 117.74/18.43 | |
% 117.74/18.43 | Case 2:
% 117.74/18.43 | |
% 117.74/18.43 | | (23) all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 117.74/18.43 | |
% 117.74/18.43 | | BETA: splitting (5) gives:
% 117.74/18.43 | |
% 117.74/18.43 | | Case 1:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (24) all_54_4 = e3
% 117.74/18.43 | | |
% 117.74/18.43 | | | REF_CLOSE: (6), (18), (24) are inconsistent by sub-proof #329.
% 117.74/18.43 | | |
% 117.74/18.43 | | Case 2:
% 117.74/18.43 | | |
% 117.74/18.43 | | | (25) ~ (all_54_4 = e3)
% 117.74/18.43 | | | (26) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 117.74/18.43 | | |
% 117.74/18.43 | | | BETA: splitting (26) gives:
% 117.74/18.43 | | |
% 117.74/18.43 | | | Case 1:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (27) all_54_4 = e2
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | REF_CLOSE: (1), (18), (27) are inconsistent by sub-proof #328.
% 117.74/18.43 | | | |
% 117.74/18.43 | | | Case 2:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | (28) ~ (all_54_4 = e2)
% 117.74/18.43 | | | | (29) all_54_4 = e1 | all_54_4 = e0
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | BETA: splitting (29) gives:
% 117.74/18.43 | | | |
% 117.74/18.43 | | | | Case 1:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (30) all_54_4 = e1
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | COMBINE_EQS: (18), (30) imply:
% 117.74/18.43 | | | | | (31) all_52_1 = e1
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | SIMP: (31) implies:
% 117.74/18.43 | | | | | (32) all_52_1 = e1
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | COMBINE_EQS: (10), (32) imply:
% 117.74/18.43 | | | | | (33) all_58_2 = e1
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REDUCE: (6), (32) imply:
% 117.74/18.43 | | | | | (34) ~ (e3 = e1)
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | SIMP: (34) implies:
% 117.74/18.43 | | | | | (35) ~ (e3 = e1)
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REDUCE: (1), (32) imply:
% 117.74/18.43 | | | | | (36) ~ (e2 = e1)
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | SIMP: (36) implies:
% 117.74/18.43 | | | | | (37) ~ (e2 = e1)
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REDUCE: (8), (32) imply:
% 117.74/18.43 | | | | | (38) op(e2, e3) = e1
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | BETA: splitting (23) gives:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | Case 1:
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | (39) all_58_2 = e3
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | COMBINE_EQS: (33), (39) imply:
% 117.74/18.43 | | | | | | (40) e3 = e1
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | SIMP: (40) implies:
% 117.74/18.43 | | | | | | (41) e3 = e1
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | REDUCE: (35), (41) imply:
% 117.74/18.43 | | | | | | (42) $false
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | CLOSE: (42) is inconsistent.
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | Case 2:
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | (43) all_58_6 = e3 | all_58_12 = e3
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | BETA: splitting (43) gives:
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | | Case 1:
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | | (44) all_58_6 = e3
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | | BETA: splitting (2) gives:
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | | Case 1:
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | | (45) all_58_0 = e2
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | | REF_CLOSE: (14), (15), (45) are inconsistent by sub-proof #327.
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | Case 2:
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | | (46) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | | BETA: splitting (46) gives:
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | | Case 1:
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | | (47) all_58_2 = e2
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | | REF_CLOSE: (33), (37), (47) are inconsistent by sub-proof
% 117.74/18.43 | | | | | | | | | #326.
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | Case 2:
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | | (48) all_58_6 = e2 | all_58_12 = e2
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | | BETA: splitting (48) gives:
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | | Case 1:
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | (49) all_58_6 = e2
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | COMBINE_EQS: (44), (49) imply:
% 117.74/18.43 | | | | | | | | | | (50) e3 = e2
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | SIMP: (50) implies:
% 117.74/18.43 | | | | | | | | | | (51) e3 = e2
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | REDUCE: (16), (51) imply:
% 117.74/18.43 | | | | | | | | | | (52) $false
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | CLOSE: (52) is inconsistent.
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | Case 2:
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | (53) all_58_12 = e2
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | COMBINE_EQS: (11), (53) imply:
% 117.74/18.43 | | | | | | | | | | (54) all_4_1 = e2
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | REDUCE: (13), (54) imply:
% 117.74/18.43 | | | | | | | | | | (55) op(e2, e3) = all_4_0
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | | REF_CLOSE: (3), (7), (38), (55) are inconsistent by sub-proof
% 117.74/18.43 | | | | | | | | | | #325.
% 117.74/18.43 | | | | | | | | | |
% 117.74/18.43 | | | | | | | | | End of split
% 117.74/18.43 | | | | | | | | |
% 117.74/18.43 | | | | | | | | End of split
% 117.74/18.43 | | | | | | | |
% 117.74/18.43 | | | | | | | End of split
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | Case 2:
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | | (56) all_58_12 = e3
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | | REF_CLOSE: (11), (17), (56) are inconsistent by sub-proof #324.
% 117.74/18.43 | | | | | | |
% 117.74/18.43 | | | | | | End of split
% 117.74/18.43 | | | | | |
% 117.74/18.43 | | | | | End of split
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | Case 2:
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | (57) all_54_4 = e0
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | | REF_CLOSE: (12), (18), (57) are inconsistent by sub-proof #323.
% 117.74/18.43 | | | | |
% 117.74/18.43 | | | | End of split
% 117.74/18.43 | | | |
% 117.74/18.43 | | | End of split
% 117.74/18.43 | | |
% 117.74/18.43 | | End of split
% 117.74/18.43 | |
% 117.74/18.43 | End of split
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #323 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) all_54_4 = all_52_1
% 117.74/18.43 (2) all_54_4 = e0
% 117.74/18.43 (3) ~ (all_52_1 = e0)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.43 | (4) all_52_1 = e0
% 117.74/18.43 |
% 117.74/18.43 | SIMP: (4) implies:
% 117.74/18.43 | (5) all_52_1 = e0
% 117.74/18.43 |
% 117.74/18.43 | REDUCE: (3), (5) imply:
% 117.74/18.43 | (6) $false
% 117.74/18.43 |
% 117.74/18.43 | CLOSE: (6) is inconsistent.
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #324 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) all_58_12 = all_4_1
% 117.74/18.43 (2) all_58_12 = e3
% 117.74/18.43 (3) ~ (all_4_1 = e3)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.43 | (4) all_4_1 = e3
% 117.74/18.43 |
% 117.74/18.43 | SIMP: (4) implies:
% 117.74/18.43 | (5) all_4_1 = e3
% 117.74/18.43 |
% 117.74/18.43 | REDUCE: (3), (5) imply:
% 117.74/18.43 | (6) $false
% 117.74/18.43 |
% 117.74/18.43 | CLOSE: (6) is inconsistent.
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #325 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.43 (2) op(e2, e3) = all_4_0
% 117.74/18.43 (3) op(e2, e3) = e1
% 117.74/18.43 (4) ~ (all_4_0 = e1)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | GROUND_INST: instantiating (1) with e1, all_4_0, e3, e2, simplifying with (2),
% 117.74/18.43 | (3) gives:
% 117.74/18.43 | (5) all_4_0 = e1
% 117.74/18.43 |
% 117.74/18.43 | REDUCE: (4), (5) imply:
% 117.74/18.43 | (6) $false
% 117.74/18.43 |
% 117.74/18.43 | CLOSE: (6) is inconsistent.
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #326 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) all_58_2 = e2
% 117.74/18.43 (2) all_58_2 = e1
% 117.74/18.43 (3) ~ (e2 = e1)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.43 | (4) e2 = e1
% 117.74/18.43 |
% 117.74/18.43 | SIMP: (4) implies:
% 117.74/18.43 | (5) e2 = e1
% 117.74/18.43 |
% 117.74/18.43 | REDUCE: (3), (5) imply:
% 117.74/18.43 | (6) $false
% 117.74/18.43 |
% 117.74/18.43 | CLOSE: (6) is inconsistent.
% 117.74/18.43 |
% 117.74/18.43 End of proof
% 117.74/18.43
% 117.74/18.43 Sub-proof #327 shows that the following formulas are inconsistent:
% 117.74/18.43 ----------------------------------------------------------------
% 117.74/18.43 (1) all_58_0 = e2
% 117.74/18.43 (2) all_58_0 = e0
% 117.74/18.43 (3) ~ (e2 = e0)
% 117.74/18.43
% 117.74/18.43 Begin of proof
% 117.74/18.43 |
% 117.74/18.43 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.43 | (4) e2 = e0
% 117.74/18.43 |
% 117.74/18.43 | SIMP: (4) implies:
% 117.74/18.44 | (5) e2 = e0
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #328 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_54_4 = all_52_1
% 117.74/18.44 (2) all_54_4 = e2
% 117.74/18.44 (3) ~ (all_52_1 = e2)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_1 = e2
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_1 = e2
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #329 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_54_4 = all_52_1
% 117.74/18.44 (2) all_54_4 = e3
% 117.74/18.44 (3) ~ (all_52_1 = e3)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_1 = e3
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_1 = e3
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #330 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_58_9 = all_52_12
% 117.74/18.44 (2) all_58_9 = e3
% 117.74/18.44 (3) ~ (all_52_12 = e3)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_12 = e3
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_12 = e3
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #331 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_58_4 = all_52_8
% 117.74/18.44 (2) all_58_4 = e3
% 117.74/18.44 (3) ~ (all_52_8 = e3)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_8 = e3
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_8 = e3
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #332 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) ~ (all_52_1 = e2)
% 117.74/18.44 (2) all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.44 (3) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.44 (4) all_58_15 = e3
% 117.74/18.44 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.44 (6) all_58_0 = all_10_2
% 117.74/18.44 (7) all_54_13 = all_52_7
% 117.74/18.44 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.44 (10) ~ (all_52_2 = all_6_2)
% 117.74/18.44 (11) ~ (all_52_7 = e3)
% 117.74/18.44 (12) ~ (all_10_2 = e2)
% 117.74/18.44 (13) all_54_10 = all_6_2
% 117.74/18.44 (14) ~ (all_8_2 = e3)
% 117.74/18.44 (15) ~ (all_52_11 = all_6_2)
% 117.74/18.44 (16) ~ (all_52_7 = all_4_1)
% 117.74/18.44 (17) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.74/18.44 (18) ~ (all_52_7 = all_8_2)
% 117.74/18.44 (19) all_58_2 = all_52_1
% 117.74/18.44 (20) ~ (all_4_1 = e0)
% 117.74/18.44 (21) all_58_13 = all_52_7
% 117.74/18.44 (22) all_58_6 = all_52_2
% 117.74/18.44 (23) all_54_5 = all_8_2
% 117.74/18.44 (24) all_58_12 = all_4_1
% 117.74/18.44 (25) ~ (all_8_2 = e1)
% 117.74/18.44 (26) all_58_14 = all_52_11
% 117.74/18.44 (27) op(e1, all_6_2) = e3
% 117.74/18.44 (28) ~ (all_8_2 = e2)
% 117.74/18.44 (29) op(all_4_1, e3) = all_4_0
% 117.74/18.44 (30) ~ (all_6_2 = e2)
% 117.74/18.44 (31) ~ (all_52_7 = all_52_11)
% 117.74/18.44 (32) op(e1, e3) = all_52_2
% 117.74/18.44 (33) ~ (all_52_7 = e1)
% 117.74/18.44 (34) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.44 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.44 (35) ~ (all_6_2 = e1)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | BETA: splitting (5) gives:
% 117.74/18.44 |
% 117.74/18.44 | Case 1:
% 117.74/18.44 | |
% 117.74/18.44 | | (36) all_54_5 = e3
% 117.74/18.44 | |
% 117.74/18.44 | | REF_CLOSE: (14), (23), (36) are inconsistent by sub-proof #339.
% 117.74/18.44 | |
% 117.74/18.44 | Case 2:
% 117.74/18.44 | |
% 117.74/18.44 | | (37) ~ (all_54_5 = e3)
% 117.74/18.44 | | (38) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 117.74/18.44 | |
% 117.74/18.44 | | BETA: splitting (38) gives:
% 117.74/18.44 | |
% 117.74/18.44 | | Case 1:
% 117.74/18.44 | | |
% 117.74/18.44 | | | (39) all_54_5 = e2
% 117.74/18.44 | | |
% 117.74/18.44 | | | REF_CLOSE: (23), (28), (39) are inconsistent by sub-proof #338.
% 117.74/18.44 | | |
% 117.74/18.44 | | Case 2:
% 117.74/18.44 | | |
% 117.74/18.44 | | | (40) all_54_5 = e1 | all_54_5 = e0
% 117.74/18.44 | | |
% 117.74/18.44 | | | BETA: splitting (40) gives:
% 117.74/18.44 | | |
% 117.74/18.44 | | | Case 1:
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | (41) all_54_5 = e1
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | REF_CLOSE: (23), (25), (41) are inconsistent by sub-proof #337.
% 117.74/18.44 | | | |
% 117.74/18.44 | | | Case 2:
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | (42) all_54_5 = e0
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | COMBINE_EQS: (23), (42) imply:
% 117.74/18.44 | | | | (43) all_8_2 = e0
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | SIMP: (43) implies:
% 117.74/18.44 | | | | (44) all_8_2 = e0
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | REDUCE: (18), (44) imply:
% 117.74/18.44 | | | | (45) ~ (all_52_7 = e0)
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | REDUCE: (14), (44) imply:
% 117.74/18.44 | | | | (46) ~ (e3 = e0)
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | SIMP: (46) implies:
% 117.74/18.44 | | | | (47) ~ (e3 = e0)
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | REDUCE: (25), (44) imply:
% 117.74/18.44 | | | | (48) ~ (e1 = e0)
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | SIMP: (48) implies:
% 117.74/18.44 | | | | (49) ~ (e1 = e0)
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | BETA: splitting (3) gives:
% 117.74/18.44 | | | |
% 117.74/18.44 | | | | Case 1:
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | | (50) all_54_13 = e3
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | | REF_CLOSE: (7), (11), (50) are inconsistent by sub-proof #336.
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | Case 2:
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | | (51) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | | BETA: splitting (34) gives:
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | | Case 1:
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | (52) all_58_15 = e0
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | COMBINE_EQS: (4), (52) imply:
% 117.74/18.44 | | | | | | (53) e3 = e0
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | REDUCE: (47), (53) imply:
% 117.74/18.44 | | | | | | (54) $false
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | CLOSE: (54) is inconsistent.
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | Case 2:
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | (55) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.44 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | ALPHA: (55) implies:
% 117.74/18.44 | | | | | | (56) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | BETA: splitting (56) gives:
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | | Case 1:
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | (57) all_58_12 = e0
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | COMBINE_EQS: (24), (57) imply:
% 117.74/18.44 | | | | | | | (58) all_4_1 = e0
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | SIMP: (58) implies:
% 117.74/18.44 | | | | | | | (59) all_4_1 = e0
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | REDUCE: (20), (59) imply:
% 117.74/18.44 | | | | | | | (60) $false
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | CLOSE: (60) is inconsistent.
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | Case 2:
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | (61) all_58_13 = e0 | all_58_14 = e0
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | BETA: splitting (61) gives:
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | (62) all_58_13 = e0
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | REF_CLOSE: (21), (45), (62) are inconsistent by sub-proof #430.
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | (63) all_58_14 = e0
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | COMBINE_EQS: (26), (63) imply:
% 117.74/18.44 | | | | | | | | (64) all_52_11 = e0
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | SIMP: (64) implies:
% 117.74/18.44 | | | | | | | | (65) all_52_11 = e0
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | REDUCE: (15), (65) imply:
% 117.74/18.44 | | | | | | | | (66) ~ (all_6_2 = e0)
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | SIMP: (66) implies:
% 117.74/18.44 | | | | | | | | (67) ~ (all_6_2 = e0)
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | BETA: splitting (8) gives:
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | (68) all_54_10 = e3
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | COMBINE_EQS: (13), (68) imply:
% 117.74/18.44 | | | | | | | | | (69) all_6_2 = e3
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | SIMP: (69) implies:
% 117.74/18.44 | | | | | | | | | (70) all_6_2 = e3
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | REDUCE: (10), (70) imply:
% 117.74/18.44 | | | | | | | | | (71) ~ (all_52_2 = e3)
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | REDUCE: (35), (70) imply:
% 117.74/18.44 | | | | | | | | | (72) ~ (e3 = e1)
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | REDUCE: (27), (70) imply:
% 117.74/18.44 | | | | | | | | | (73) op(e1, e3) = e3
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | BETA: splitting (51) gives:
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | (74) all_54_13 = e2
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | COMBINE_EQS: (7), (74) imply:
% 117.74/18.44 | | | | | | | | | | (75) all_52_7 = e2
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | COMBINE_EQS: (21), (75) imply:
% 117.74/18.44 | | | | | | | | | | (76) all_58_13 = e2
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | REDUCE: (16), (75) imply:
% 117.74/18.44 | | | | | | | | | | (77) ~ (all_4_1 = e2)
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | SIMP: (77) implies:
% 117.74/18.44 | | | | | | | | | | (78) ~ (all_4_1 = e2)
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | REDUCE: (33), (75) imply:
% 117.74/18.44 | | | | | | | | | | (79) ~ (e2 = e1)
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | BETA: splitting (2) gives:
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | (80) all_58_0 = e2
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | COMBINE_EQS: (6), (80) imply:
% 117.74/18.44 | | | | | | | | | | | (81) all_10_2 = e2
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | REDUCE: (12), (81) imply:
% 117.74/18.44 | | | | | | | | | | | (82) $false
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | CLOSE: (82) is inconsistent.
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | (83) all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | BETA: splitting (83) gives:
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | (84) all_58_2 = e2
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | REF_CLOSE: (1), (19), (84) are inconsistent by sub-proof
% 117.74/18.44 | | | | | | | | | | | | #335.
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | (85) all_58_6 = e2 | all_58_12 = e2
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | BETA: splitting (17) gives:
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | (86) all_58_12 = e1
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | COMBINE_EQS: (24), (86) imply:
% 117.74/18.44 | | | | | | | | | | | | | (87) all_4_1 = e1
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | SIMP: (87) implies:
% 117.74/18.44 | | | | | | | | | | | | | (88) all_4_1 = e1
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | REDUCE: (78), (88) imply:
% 117.74/18.44 | | | | | | | | | | | | | (89) ~ (e2 = e1)
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | REDUCE: (29), (88) imply:
% 117.74/18.44 | | | | | | | | | | | | | (90) op(e1, e3) = all_4_0
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | (91) all_58_6 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | COMBINE_EQS: (22), (91) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (92) all_52_2 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | SIMP: (92) implies:
% 117.74/18.44 | | | | | | | | | | | | | | (93) all_52_2 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | REDUCE: (71), (93) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (94) ~ (e3 = e2)
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | SIMP: (94) implies:
% 117.74/18.44 | | | | | | | | | | | | | | (95) ~ (e3 = e2)
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | REDUCE: (32), (93) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (96) op(e1, e3) = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e3, all_4_0, e3, e1,
% 117.74/18.44 | | | | | | | | | | | | | | simplifying with (73), (90) gives:
% 117.74/18.44 | | | | | | | | | | | | | | (97) all_4_0 = e3
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e2, all_4_0, e3, e1,
% 117.74/18.44 | | | | | | | | | | | | | | simplifying with (90), (96) gives:
% 117.74/18.44 | | | | | | | | | | | | | | (98) all_4_0 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | COMBINE_EQS: (97), (98) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (99) e3 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | REDUCE: (95), (99) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (100) $false
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | CLOSE: (100) is inconsistent.
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | (101) all_58_12 = e2
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | COMBINE_EQS: (86), (101) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (102) e2 = e1
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | REDUCE: (79), (102) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (103) $false
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | (104) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | BETA: splitting (104) gives:
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | (105) all_58_13 = e1
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | COMBINE_EQS: (76), (105) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (106) e2 = e1
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | SIMP: (106) implies:
% 117.74/18.44 | | | | | | | | | | | | | | (107) e2 = e1
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | REDUCE: (79), (107) imply:
% 117.74/18.44 | | | | | | | | | | | | | | (108) $false
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | CLOSE: (108) is inconsistent.
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | (109) all_58_14 = e1 | all_58_15 = e1
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | Case 1:
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | (110) all_58_14 = e1
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | COMBINE_EQS: (63), (110) imply:
% 117.74/18.44 | | | | | | | | | | | | | | | (111) e1 = e0
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | REDUCE: (49), (111) imply:
% 117.74/18.44 | | | | | | | | | | | | | | | (112) $false
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | (113) all_58_15 = e1
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | COMBINE_EQS: (4), (113) imply:
% 117.74/18.44 | | | | | | | | | | | | | | | (114) e3 = e1
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | REDUCE: (72), (114) imply:
% 117.74/18.44 | | | | | | | | | | | | | | | (115) $false
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 117.74/18.44 | | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | (116) all_54_13 = e1 | all_54_13 = e0
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | | REF_CLOSE: (7), (33), (45), (116) are inconsistent by
% 117.74/18.44 | | | | | | | | | | sub-proof #333.
% 117.74/18.44 | | | | | | | | | |
% 117.74/18.44 | | | | | | | | | End of split
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | Case 2:
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | (117) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | | REF_CLOSE: (13), (30), (35), (67), (117) are inconsistent by
% 117.74/18.44 | | | | | | | | | sub-proof #435.
% 117.74/18.44 | | | | | | | | |
% 117.74/18.44 | | | | | | | | End of split
% 117.74/18.44 | | | | | | | |
% 117.74/18.44 | | | | | | | End of split
% 117.74/18.44 | | | | | | |
% 117.74/18.44 | | | | | | End of split
% 117.74/18.44 | | | | | |
% 117.74/18.44 | | | | | End of split
% 117.74/18.44 | | | | |
% 117.74/18.44 | | | | End of split
% 117.74/18.44 | | | |
% 117.74/18.44 | | | End of split
% 117.74/18.44 | | |
% 117.74/18.44 | | End of split
% 117.74/18.44 | |
% 117.74/18.44 | End of split
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #333 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_54_13 = e1 | all_54_13 = e0
% 117.74/18.44 (2) all_54_13 = all_52_7
% 117.74/18.44 (3) ~ (all_52_7 = e1)
% 117.74/18.44 (4) ~ (all_52_7 = e0)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | BETA: splitting (1) gives:
% 117.74/18.44 |
% 117.74/18.44 | Case 1:
% 117.74/18.44 | |
% 117.74/18.44 | | (5) all_54_13 = e1
% 117.74/18.44 | |
% 117.74/18.44 | | COMBINE_EQS: (2), (5) imply:
% 117.74/18.44 | | (6) all_52_7 = e1
% 117.74/18.44 | |
% 117.74/18.44 | | SIMP: (6) implies:
% 117.74/18.44 | | (7) all_52_7 = e1
% 117.74/18.44 | |
% 117.74/18.44 | | REDUCE: (3), (7) imply:
% 117.74/18.44 | | (8) $false
% 117.74/18.44 | |
% 117.74/18.44 | | CLOSE: (8) is inconsistent.
% 117.74/18.44 | |
% 117.74/18.44 | Case 2:
% 117.74/18.44 | |
% 117.74/18.44 | | (9) all_54_13 = e0
% 117.74/18.44 | |
% 117.74/18.44 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #334.
% 117.74/18.44 | |
% 117.74/18.44 | End of split
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #334 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_54_13 = all_52_7
% 117.74/18.44 (2) all_54_13 = e0
% 117.74/18.44 (3) ~ (all_52_7 = e0)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_7 = e0
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_7 = e0
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #335 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_58_2 = all_52_1
% 117.74/18.44 (2) all_58_2 = e2
% 117.74/18.44 (3) ~ (all_52_1 = e2)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_1 = e2
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_1 = e2
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #336 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.44 (1) all_54_13 = all_52_7
% 117.74/18.44 (2) all_54_13 = e3
% 117.74/18.44 (3) ~ (all_52_7 = e3)
% 117.74/18.44
% 117.74/18.44 Begin of proof
% 117.74/18.44 |
% 117.74/18.44 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.44 | (4) all_52_7 = e3
% 117.74/18.44 |
% 117.74/18.44 | SIMP: (4) implies:
% 117.74/18.44 | (5) all_52_7 = e3
% 117.74/18.44 |
% 117.74/18.44 | REDUCE: (3), (5) imply:
% 117.74/18.44 | (6) $false
% 117.74/18.44 |
% 117.74/18.44 | CLOSE: (6) is inconsistent.
% 117.74/18.44 |
% 117.74/18.44 End of proof
% 117.74/18.44
% 117.74/18.44 Sub-proof #337 shows that the following formulas are inconsistent:
% 117.74/18.44 ----------------------------------------------------------------
% 117.74/18.45 (1) all_54_5 = all_8_2
% 117.74/18.45 (2) all_54_5 = e1
% 117.74/18.45 (3) ~ (all_8_2 = e1)
% 117.74/18.45
% 117.74/18.45 Begin of proof
% 117.74/18.45 |
% 117.74/18.45 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.45 | (4) all_8_2 = e1
% 117.74/18.45 |
% 117.74/18.45 | SIMP: (4) implies:
% 117.74/18.45 | (5) all_8_2 = e1
% 117.74/18.45 |
% 117.74/18.45 | REDUCE: (3), (5) imply:
% 117.74/18.45 | (6) $false
% 117.74/18.45 |
% 117.74/18.45 | CLOSE: (6) is inconsistent.
% 117.74/18.45 |
% 117.74/18.45 End of proof
% 117.74/18.45
% 117.74/18.45 Sub-proof #338 shows that the following formulas are inconsistent:
% 117.74/18.45 ----------------------------------------------------------------
% 117.74/18.45 (1) all_54_5 = all_8_2
% 117.74/18.45 (2) all_54_5 = e2
% 117.74/18.45 (3) ~ (all_8_2 = e2)
% 117.74/18.45
% 117.74/18.45 Begin of proof
% 117.74/18.45 |
% 117.74/18.45 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.45 | (4) all_8_2 = e2
% 117.74/18.45 |
% 117.74/18.45 | SIMP: (4) implies:
% 117.74/18.45 | (5) all_8_2 = e2
% 117.74/18.45 |
% 117.74/18.45 | REDUCE: (3), (5) imply:
% 117.74/18.45 | (6) $false
% 117.74/18.45 |
% 117.74/18.45 | CLOSE: (6) is inconsistent.
% 117.74/18.45 |
% 117.74/18.45 End of proof
% 117.74/18.45
% 117.74/18.45 Sub-proof #339 shows that the following formulas are inconsistent:
% 117.74/18.45 ----------------------------------------------------------------
% 117.74/18.45 (1) all_54_5 = all_8_2
% 117.74/18.45 (2) all_54_5 = e3
% 117.74/18.45 (3) ~ (all_8_2 = e3)
% 117.74/18.45
% 117.74/18.45 Begin of proof
% 117.74/18.45 |
% 117.74/18.45 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.45 | (4) all_8_2 = e3
% 117.74/18.45 |
% 117.74/18.45 | SIMP: (4) implies:
% 117.74/18.45 | (5) all_8_2 = e3
% 117.74/18.45 |
% 117.74/18.45 | REDUCE: (3), (5) imply:
% 117.74/18.45 | (6) $false
% 117.74/18.45 |
% 117.74/18.45 | CLOSE: (6) is inconsistent.
% 117.74/18.45 |
% 117.74/18.45 End of proof
% 117.74/18.45
% 117.74/18.45 Sub-proof #340 shows that the following formulas are inconsistent:
% 117.74/18.45 ----------------------------------------------------------------
% 117.74/18.45 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.74/18.45 (2) ~ (all_52_2 = all_10_2)
% 117.74/18.45 (3) all_58_7 = all_52_6
% 117.74/18.45 (4) ~ (all_52_13 = all_52_14)
% 117.74/18.45 (5) ~ (all_4_2 = e0)
% 117.74/18.45 (6) op(e3, e2) = all_52_4
% 117.74/18.45 (7) all_56_14 = all_6_2
% 117.74/18.45 (8) all_56_3 = all_52_1
% 117.74/18.45 (9) all_54_0 = all_10_2
% 117.74/18.45 (10) all_54_3 = all_52_12
% 117.74/18.45 (11) op(e0, e2) = all_52_7
% 117.74/18.45 (12) all_56_11 = all_52_11
% 117.74/18.45 (13) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.74/18.45 (14) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.45 (15) ~ (all_52_12 = all_10_2)
% 117.74/18.45 (16) ~ (e3 = e1)
% 117.74/18.45 (17) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.74/18.45 (18) all_56_12 = all_10_2
% 117.74/18.45 (19) ~ (all_56_7 = e1) | ~ (all_56_15 = e2)
% 117.74/18.45 (20) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.74/18.45 (21) all_56_10 = all_52_7
% 117.74/18.45 (22) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.45 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.45 (24) ~ (all_52_2 = all_6_2)
% 117.74/18.45 (25) ~ (all_10_2 = e2)
% 117.74/18.45 (26) all_54_10 = all_6_2
% 117.74/18.45 (27) op(e3, e0) = all_52_12
% 117.74/18.45 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.45 (29) ~ (all_52_4 = all_52_7)
% 117.74/18.45 (30) all_56_2 = all_52_12
% 117.74/18.45 (31) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.45 (32) all_58_3 = all_8_2
% 117.74/18.45 (33) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.45 (34) ~ (all_10_0 = e2)
% 117.74/18.45 (35) all_58_11 = all_52_14
% 117.74/18.45 (36) op(e3, all_6_2) = all_6_0
% 117.74/18.45 (37) all_54_7 = all_52_13
% 117.74/18.45 (38) op(all_10_1, all_10_2) = all_10_0
% 117.74/18.45 (39) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.45 (40) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.74/18.45 (41) ~ (all_4_2 = e3)
% 117.74/18.45 (42) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.45 (43) op(e1, e0) = all_52_14
% 117.74/18.45 (44) all_58_5 = all_52_9
% 117.74/18.45 (45) all_56_9 = all_52_3
% 117.74/18.45 (46) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.45 (47) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.74/18.45 (48) all_58_15 = all_4_2
% 117.74/18.45 (49) all_58_2 = all_52_1
% 117.74/18.45 (50) ~ (all_10_2 = e3)
% 117.74/18.45 (51) ~ (all_52_12 = all_52_13)
% 117.74/18.45 (52) all_58_13 = all_52_7
% 117.74/18.45 (53) ~ (all_52_14 = all_4_2)
% 117.74/18.45 (54) all_58_6 = all_52_2
% 117.74/18.45 (55) ~ (all_52_1 = all_10_2)
% 117.74/18.45 (56) all_56_15 = all_4_2
% 117.74/18.45 (57) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.45 (58) all_58_10 = all_52_13
% 117.74/18.45 (59) op(e3, all_10_2) = all_10_1
% 117.74/18.45 (60) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.45 (61) ~ (all_6_0 = e2)
% 117.74/18.45 (62) ~ (all_10_1 = e2)
% 117.74/18.45 (63) all_58_1 = all_52_4
% 117.74/18.45 (64) all_58_14 = all_52_11
% 117.74/18.45 (65) all_54_1 = all_52_4
% 117.74/18.45 (66) all_56_13 = all_8_2
% 117.74/18.45 (67) op(e1, all_6_2) = e3
% 117.74/18.45 (68) ~ (all_8_2 = e2)
% 117.74/18.45 (69) ~ (all_6_2 = e2)
% 117.74/18.45 (70) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.45 (71) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.45 (72) all_56_7 = all_52_6
% 117.74/18.45 (73) all_58_8 = all_6_2
% 117.74/18.45 (74) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.45 (75) ~ (all_10_0 = e1)
% 117.74/18.45 (76) all_56_4 = all_52_9
% 117.74/18.45 (77) all_56_5 = all_52_13
% 117.74/18.45 (78) ~ (all_52_6 = all_6_2)
% 117.74/18.45 (79) all_56_6 = all_52_2
% 117.74/18.45 (80) ~ (all_52_13 = all_4_2)
% 117.74/18.45 (81) all_58_12 = all_52_3
% 117.74/18.45 (82) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.74/18.45 (83) ~ (all_52_12 = all_4_2)
% 117.74/18.45 (84) op(e1, e3) = all_52_2
% 117.74/18.45 (85) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.74/18.45 (86) all_56_8 = all_52_14
% 117.74/18.45 (87) ~ (all_52_4 = all_10_2)
% 117.74/18.45 (88) ~ (all_10_1 = e1)
% 117.74/18.45 (89) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.74/18.45 (90) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.45 (91) all_56_0 = all_52_4
% 117.74/18.45 (92) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.74/18.45 (93) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.45 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.45 (94) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.74/18.45 (95) all_54_15 = all_4_2
% 117.74/18.45 (96) ~ (all_6_2 = e1)
% 117.74/18.45 (97) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.45
% 117.74/18.45 Begin of proof
% 117.74/18.45 |
% 117.74/18.45 | BETA: splitting (19) gives:
% 117.74/18.45 |
% 117.74/18.45 | Case 1:
% 117.74/18.45 | |
% 117.74/18.45 | | (98) ~ (all_56_7 = e1)
% 117.74/18.45 | |
% 117.74/18.45 | | REDUCE: (72), (98) imply:
% 117.74/18.45 | | (99) ~ (all_52_6 = e1)
% 117.74/18.45 | |
% 117.74/18.45 | | BETA: splitting (22) gives:
% 117.74/18.45 | |
% 117.74/18.45 | | Case 1:
% 117.74/18.45 | | |
% 117.74/18.45 | | | (100) all_54_10 = e3
% 117.74/18.45 | | |
% 117.74/18.45 | | | COMBINE_EQS: (26), (100) imply:
% 117.74/18.45 | | | (101) all_6_2 = e3
% 117.74/18.45 | | |
% 117.74/18.45 | | | REF_CLOSE: (3), (5), (7), (9), (12), (16), (18), (21), (25), (28), (31),
% 117.74/18.45 | | | (35), (39), (41), (45), (46), (48), (50), (52), (53), (54),
% 117.74/18.45 | | | (56), (64), (70), (73), (74), (79), (81), (85), (86), (89),
% 117.74/18.45 | | | (93), (95), (99), (101) are inconsistent by sub-proof #357.
% 117.74/18.45 | | |
% 117.74/18.45 | | Case 2:
% 117.74/18.45 | | |
% 117.74/18.45 | | | (102) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.45 | | |
% 117.74/18.45 | | | BETA: splitting (102) gives:
% 117.74/18.45 | | |
% 117.74/18.45 | | | Case 1:
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | (103) all_54_10 = e2
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | COMBINE_EQS: (26), (103) imply:
% 117.74/18.45 | | | | (104) all_6_2 = e2
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | REDUCE: (69), (104) imply:
% 117.74/18.45 | | | | (105) $false
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | CLOSE: (105) is inconsistent.
% 117.74/18.45 | | | |
% 117.74/18.45 | | | Case 2:
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | (106) all_54_10 = e1 | all_54_10 = e0
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | BETA: splitting (106) gives:
% 117.74/18.45 | | | |
% 117.74/18.45 | | | | Case 1:
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | (107) all_54_10 = e1
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | COMBINE_EQS: (26), (107) imply:
% 117.74/18.45 | | | | | (108) all_6_2 = e1
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | REDUCE: (96), (108) imply:
% 117.74/18.45 | | | | | (109) $false
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | CLOSE: (109) is inconsistent.
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | Case 2:
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | (110) all_54_10 = e0
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | COMBINE_EQS: (26), (110) imply:
% 117.74/18.45 | | | | | (111) all_6_2 = e0
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | COMBINE_EQS: (7), (111) imply:
% 117.74/18.45 | | | | | (112) all_56_14 = e0
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | BETA: splitting (13) gives:
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | | Case 1:
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | (113) ~ (all_56_8 = e1)
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | REDUCE: (86), (113) imply:
% 117.74/18.45 | | | | | | (114) ~ (all_52_14 = e1)
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12),
% 117.74/18.45 | | | | | | (14), (15), (17), (18), (20), (22), (23), (24), (25),
% 117.74/18.45 | | | | | | (26), (27), (29), (30), (32), (34), (35), (38), (39),
% 117.74/18.45 | | | | | | (40), (42), (44), (45), (47), (48), (49), (50), (52),
% 117.74/18.45 | | | | | | (54), (55), (58), (59), (62), (63), (64), (65), (66),
% 117.74/18.45 | | | | | | (68), (70), (71), (72), (73), (74), (75), (76), (77),
% 117.74/18.45 | | | | | | (78), (81), (87), (88), (90), (91), (92), (93), (94),
% 117.74/18.45 | | | | | | (96), (99), (114) are inconsistent by sub-proof #353.
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | Case 2:
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | (115) ~ (all_56_14 = e0)
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | REDUCE: (112), (115) imply:
% 117.74/18.45 | | | | | | (116) $false
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | | CLOSE: (116) is inconsistent.
% 117.74/18.45 | | | | | |
% 117.74/18.45 | | | | | End of split
% 117.74/18.45 | | | | |
% 117.74/18.45 | | | | End of split
% 117.74/18.45 | | | |
% 117.74/18.45 | | | End of split
% 117.74/18.45 | | |
% 117.74/18.45 | | End of split
% 117.74/18.45 | |
% 117.74/18.45 | Case 2:
% 117.74/18.45 | |
% 117.74/18.45 | | (117) all_56_7 = e1
% 117.74/18.45 | | (118) ~ (all_56_15 = e2)
% 117.74/18.45 | |
% 117.74/18.45 | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (14), (22), (23), (24), (26),
% 117.74/18.45 | | (27), (28), (30), (31), (32), (33), (35), (36), (37), (41), (42),
% 117.74/18.45 | | (43), (44), (49), (51), (53), (54), (56), (57), (58), (60), (61),
% 117.74/18.45 | | (67), (68), (69), (70), (72), (73), (76), (77), (78), (79), (80),
% 117.74/18.45 | | (82), (83), (84), (90), (95), (97), (117), (118) are inconsistent
% 117.74/18.45 | | by sub-proof #341.
% 117.74/18.45 | |
% 117.74/18.45 | End of split
% 117.74/18.45 |
% 117.74/18.45 End of proof
% 117.74/18.45
% 117.74/18.45 Sub-proof #341 shows that the following formulas are inconsistent:
% 117.74/18.45 ----------------------------------------------------------------
% 117.74/18.45 (1) all_58_7 = all_52_6
% 117.74/18.45 (2) ~ (all_52_13 = all_52_14)
% 117.74/18.45 (3) ~ (all_4_2 = e0)
% 117.74/18.45 (4) all_56_14 = all_6_2
% 117.74/18.45 (5) all_56_3 = all_52_1
% 117.74/18.45 (6) all_54_3 = all_52_12
% 117.74/18.45 (7) all_56_7 = e1
% 117.74/18.45 (8) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.45 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.45 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.45 (11) ~ (all_52_2 = all_6_2)
% 117.74/18.45 (12) all_54_10 = all_6_2
% 117.74/18.45 (13) op(e3, e0) = all_52_12
% 117.74/18.45 (14) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.45 (15) all_56_2 = all_52_12
% 117.74/18.45 (16) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.45 (17) all_58_3 = all_8_2
% 117.74/18.45 (18) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.45 (19) all_58_11 = all_52_14
% 117.74/18.45 (20) op(e3, all_6_2) = all_6_0
% 117.74/18.45 (21) all_54_7 = all_52_13
% 117.74/18.45 (22) ~ (all_4_2 = e3)
% 117.74/18.45 (23) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.45 (24) op(e1, e0) = all_52_14
% 117.74/18.45 (25) all_58_5 = all_52_9
% 117.74/18.45 (26) all_58_2 = all_52_1
% 117.74/18.45 (27) ~ (all_52_12 = all_52_13)
% 117.74/18.45 (28) ~ (all_52_14 = all_4_2)
% 117.74/18.45 (29) all_58_6 = all_52_2
% 117.74/18.45 (30) all_56_15 = all_4_2
% 117.74/18.45 (31) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.45 (32) all_58_10 = all_52_13
% 117.74/18.45 (33) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.45 (34) ~ (all_6_0 = e2)
% 117.74/18.45 (35) op(e1, all_6_2) = e3
% 117.74/18.45 (36) ~ (all_8_2 = e2)
% 117.74/18.45 (37) ~ (all_6_2 = e2)
% 117.74/18.45 (38) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.45 (39) all_56_7 = all_52_6
% 117.74/18.45 (40) all_58_8 = all_6_2
% 117.74/18.45 (41) all_56_4 = all_52_9
% 117.74/18.45 (42) all_56_5 = all_52_13
% 117.74/18.45 (43) ~ (all_52_6 = all_6_2)
% 117.74/18.45 (44) all_56_6 = all_52_2
% 117.74/18.45 (45) ~ (all_52_13 = all_4_2)
% 117.74/18.45 (46) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.74/18.45 (47) ~ (all_52_12 = all_4_2)
% 117.74/18.45 (48) op(e1, e3) = all_52_2
% 117.74/18.45 (49) ~ (all_56_15 = e2)
% 117.74/18.45 (50) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.45 (51) all_54_15 = all_4_2
% 117.74/18.45 (52) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.45
% 117.74/18.45 Begin of proof
% 117.74/18.45 |
% 117.74/18.45 | COMBINE_EQS: (7), (39) imply:
% 117.74/18.45 | (53) all_52_6 = e1
% 117.74/18.45 |
% 117.74/18.45 | REDUCE: (30), (49) imply:
% 117.74/18.45 | (54) ~ (all_4_2 = e2)
% 117.74/18.45 |
% 117.74/18.45 | REDUCE: (43), (53) imply:
% 117.74/18.45 | (55) ~ (all_6_2 = e1)
% 117.74/18.45 |
% 117.74/18.45 | SIMP: (55) implies:
% 117.74/18.45 | (56) ~ (all_6_2 = e1)
% 117.74/18.45 |
% 117.74/18.45 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 117.74/18.45 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 117.74/18.45 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 117.74/18.45 | (36), (37), (38), (40), (41), (42), (44), (45), (46), (47), (48),
% 117.74/18.45 | (50), (51), (52), (54), (56) are inconsistent by sub-proof #342.
% 117.74/18.45 |
% 117.74/18.45 End of proof
% 117.74/18.45
% 117.74/18.45 Sub-proof #342 shows that the following formulas are inconsistent:
% 117.74/18.45 ----------------------------------------------------------------
% 117.74/18.45 (1) all_58_7 = all_52_6
% 117.74/18.45 (2) ~ (all_52_13 = all_52_14)
% 117.74/18.45 (3) ~ (all_4_2 = e0)
% 117.74/18.45 (4) all_56_14 = all_6_2
% 117.74/18.45 (5) all_56_3 = all_52_1
% 117.74/18.45 (6) all_54_3 = all_52_12
% 117.74/18.45 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.45 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.45 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.45 (10) ~ (all_52_2 = all_6_2)
% 117.74/18.45 (11) all_54_10 = all_6_2
% 117.74/18.45 (12) op(e3, e0) = all_52_12
% 117.74/18.45 (13) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.45 (14) all_56_2 = all_52_12
% 117.74/18.45 (15) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.46 (16) all_58_3 = all_8_2
% 117.74/18.46 (17) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.46 (18) all_58_11 = all_52_14
% 117.74/18.46 (19) op(e3, all_6_2) = all_6_0
% 117.74/18.46 (20) all_54_7 = all_52_13
% 117.74/18.46 (21) ~ (all_4_2 = e3)
% 117.74/18.46 (22) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.46 (23) op(e1, e0) = all_52_14
% 117.74/18.46 (24) all_58_5 = all_52_9
% 117.74/18.46 (25) all_58_2 = all_52_1
% 117.74/18.46 (26) ~ (all_52_12 = all_52_13)
% 117.74/18.46 (27) ~ (all_52_14 = all_4_2)
% 117.74/18.46 (28) all_58_6 = all_52_2
% 117.74/18.46 (29) all_56_15 = all_4_2
% 117.74/18.46 (30) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.46 (31) all_58_10 = all_52_13
% 117.74/18.46 (32) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.46 (33) ~ (all_6_0 = e2)
% 117.74/18.46 (34) op(e1, all_6_2) = e3
% 117.74/18.46 (35) ~ (all_8_2 = e2)
% 117.74/18.46 (36) ~ (all_6_2 = e2)
% 117.74/18.46 (37) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.46 (38) all_58_8 = all_6_2
% 117.74/18.46 (39) all_56_4 = all_52_9
% 117.74/18.46 (40) all_56_5 = all_52_13
% 117.74/18.46 (41) all_56_6 = all_52_2
% 117.74/18.46 (42) ~ (all_52_13 = all_4_2)
% 117.74/18.46 (43) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.74/18.46 (44) ~ (all_52_12 = all_4_2)
% 117.74/18.46 (45) op(e1, e3) = all_52_2
% 117.74/18.46 (46) ~ (all_4_2 = e2)
% 117.74/18.46 (47) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.46 (48) all_54_15 = all_4_2
% 117.74/18.46 (49) ~ (all_6_2 = e1)
% 117.74/18.46 (50) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.46
% 117.74/18.46 Begin of proof
% 117.74/18.46 |
% 117.74/18.46 | BETA: splitting (13) gives:
% 117.74/18.46 |
% 117.74/18.46 | Case 1:
% 117.74/18.46 | |
% 117.74/18.46 | | (51) all_54_15 = e3
% 117.74/18.46 | |
% 117.74/18.46 | | COMBINE_EQS: (48), (51) imply:
% 117.74/18.46 | | (52) all_4_2 = e3
% 117.74/18.46 | |
% 117.74/18.46 | | REDUCE: (21), (52) imply:
% 117.74/18.46 | | (53) $false
% 117.74/18.46 | |
% 117.74/18.46 | | CLOSE: (53) is inconsistent.
% 117.74/18.46 | |
% 117.74/18.46 | Case 2:
% 117.74/18.46 | |
% 117.74/18.46 | | (54) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.46 | |
% 117.74/18.46 | | BETA: splitting (54) gives:
% 117.74/18.46 | |
% 117.74/18.46 | | Case 1:
% 117.74/18.46 | | |
% 117.74/18.46 | | | (55) all_54_15 = e2
% 117.74/18.46 | | |
% 117.74/18.46 | | | COMBINE_EQS: (48), (55) imply:
% 117.74/18.46 | | | (56) all_4_2 = e2
% 117.74/18.46 | | |
% 117.74/18.46 | | | REDUCE: (46), (56) imply:
% 117.74/18.46 | | | (57) $false
% 117.74/18.46 | | |
% 117.74/18.46 | | | CLOSE: (57) is inconsistent.
% 117.74/18.46 | | |
% 117.74/18.46 | | Case 2:
% 117.74/18.46 | | |
% 117.74/18.46 | | | (58) all_54_15 = e1 | all_54_15 = e0
% 117.74/18.46 | | |
% 117.74/18.46 | | | BETA: splitting (58) gives:
% 117.74/18.46 | | |
% 117.74/18.46 | | | Case 1:
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | (59) all_54_15 = e1
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (48), (59) imply:
% 117.74/18.46 | | | | (60) all_4_2 = e1
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (29), (60) imply:
% 117.74/18.46 | | | | (61) all_56_15 = e1
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 117.74/18.46 | | | | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 117.74/18.46 | | | | (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 117.74/18.46 | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 117.74/18.46 | | | | (47), (49), (50), (60), (61) are inconsistent by sub-proof
% 117.74/18.46 | | | | #343.
% 117.74/18.46 | | | |
% 117.74/18.46 | | | Case 2:
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | (62) all_54_15 = e0
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (48), (62) imply:
% 117.74/18.46 | | | | (63) all_4_2 = e0
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | REDUCE: (3), (63) imply:
% 117.74/18.46 | | | | (64) $false
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | CLOSE: (64) is inconsistent.
% 117.74/18.46 | | | |
% 117.74/18.46 | | | End of split
% 117.74/18.46 | | |
% 117.74/18.46 | | End of split
% 117.74/18.46 | |
% 117.74/18.46 | End of split
% 117.74/18.46 |
% 117.74/18.46 End of proof
% 117.74/18.46
% 117.74/18.46 Sub-proof #343 shows that the following formulas are inconsistent:
% 117.74/18.46 ----------------------------------------------------------------
% 117.74/18.46 (1) all_58_7 = all_52_6
% 117.74/18.46 (2) ~ (all_52_13 = all_52_14)
% 117.74/18.46 (3) all_56_14 = all_6_2
% 117.74/18.46 (4) all_56_3 = all_52_1
% 117.74/18.46 (5) all_54_3 = all_52_12
% 117.74/18.46 (6) all_4_2 = e1
% 117.74/18.46 (7) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.46 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.46 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.46 (10) ~ (all_52_2 = all_6_2)
% 117.74/18.46 (11) all_54_10 = all_6_2
% 117.74/18.46 (12) op(e3, e0) = all_52_12
% 117.74/18.46 (13) all_56_2 = all_52_12
% 117.74/18.46 (14) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.46 (15) all_58_3 = all_8_2
% 117.74/18.46 (16) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.46 (17) all_58_11 = all_52_14
% 117.74/18.46 (18) op(e3, all_6_2) = all_6_0
% 117.74/18.46 (19) all_54_7 = all_52_13
% 117.74/18.46 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.46 (21) all_56_15 = e1
% 117.74/18.46 (22) op(e1, e0) = all_52_14
% 117.74/18.46 (23) all_58_5 = all_52_9
% 117.74/18.46 (24) all_58_2 = all_52_1
% 117.74/18.46 (25) ~ (all_52_12 = all_52_13)
% 117.74/18.46 (26) ~ (all_52_14 = all_4_2)
% 117.74/18.46 (27) all_58_6 = all_52_2
% 117.74/18.46 (28) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.46 (29) all_58_10 = all_52_13
% 117.74/18.46 (30) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.46 (31) ~ (all_6_0 = e2)
% 117.74/18.46 (32) op(e1, all_6_2) = e3
% 117.74/18.46 (33) ~ (all_8_2 = e2)
% 117.74/18.46 (34) ~ (all_6_2 = e2)
% 117.74/18.46 (35) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.46 (36) all_58_8 = all_6_2
% 117.74/18.46 (37) all_56_4 = all_52_9
% 117.74/18.46 (38) all_56_5 = all_52_13
% 117.74/18.46 (39) all_56_6 = all_52_2
% 117.74/18.46 (40) ~ (all_52_13 = all_4_2)
% 117.74/18.46 (41) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.74/18.46 (42) ~ (all_52_12 = all_4_2)
% 117.74/18.46 (43) op(e1, e3) = all_52_2
% 117.74/18.46 (44) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.46 (45) ~ (all_6_2 = e1)
% 117.74/18.46 (46) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.46
% 117.74/18.46 Begin of proof
% 117.74/18.46 |
% 117.74/18.46 | REDUCE: (6), (42) imply:
% 117.74/18.46 | (47) ~ (all_52_12 = e1)
% 117.74/18.46 |
% 117.74/18.46 | REDUCE: (6), (40) imply:
% 117.74/18.46 | (48) ~ (all_52_13 = e1)
% 117.74/18.46 |
% 117.74/18.46 | REDUCE: (6), (26) imply:
% 117.74/18.46 | (49) ~ (all_52_14 = e1)
% 117.74/18.46 |
% 117.74/18.46 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 117.74/18.46 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 117.74/18.46 | (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 117.74/18.46 | (37), (38), (39), (41), (43), (44), (45), (46), (47), (48), (49)
% 117.74/18.46 | are inconsistent by sub-proof #344.
% 117.74/18.46 |
% 117.74/18.46 End of proof
% 117.74/18.46
% 117.74/18.46 Sub-proof #344 shows that the following formulas are inconsistent:
% 117.74/18.46 ----------------------------------------------------------------
% 117.74/18.46 (1) all_58_7 = all_52_6
% 117.74/18.46 (2) ~ (all_52_13 = all_52_14)
% 117.74/18.46 (3) all_56_14 = all_6_2
% 117.74/18.46 (4) all_56_3 = all_52_1
% 117.74/18.46 (5) all_54_3 = all_52_12
% 117.74/18.46 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.46 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.46 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.46 (9) ~ (all_52_2 = all_6_2)
% 117.74/18.46 (10) all_54_10 = all_6_2
% 117.74/18.46 (11) ~ (all_52_14 = e1)
% 117.74/18.46 (12) op(e3, e0) = all_52_12
% 117.74/18.46 (13) all_56_2 = all_52_12
% 117.74/18.46 (14) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.46 (15) ~ (all_52_12 = e1)
% 117.74/18.46 (16) all_58_3 = all_8_2
% 117.74/18.46 (17) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.46 (18) all_58_11 = all_52_14
% 117.74/18.46 (19) op(e3, all_6_2) = all_6_0
% 117.74/18.46 (20) all_54_7 = all_52_13
% 117.74/18.46 (21) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.46 (22) all_56_15 = e1
% 117.74/18.46 (23) op(e1, e0) = all_52_14
% 117.74/18.46 (24) all_58_5 = all_52_9
% 117.74/18.46 (25) all_58_2 = all_52_1
% 117.74/18.46 (26) ~ (all_52_12 = all_52_13)
% 117.74/18.46 (27) all_58_6 = all_52_2
% 117.74/18.46 (28) ~ (all_52_13 = e1)
% 117.74/18.46 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.46 (30) all_58_10 = all_52_13
% 117.74/18.46 (31) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.46 (32) ~ (all_6_0 = e2)
% 117.74/18.46 (33) op(e1, all_6_2) = e3
% 117.74/18.46 (34) ~ (all_8_2 = e2)
% 117.74/18.46 (35) ~ (all_6_2 = e2)
% 117.74/18.46 (36) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.46 (37) all_58_8 = all_6_2
% 117.74/18.46 (38) all_56_4 = all_52_9
% 117.74/18.46 (39) all_56_5 = all_52_13
% 117.74/18.46 (40) all_56_6 = all_52_2
% 117.74/18.46 (41) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.74/18.46 (42) op(e1, e3) = all_52_2
% 117.74/18.46 (43) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.46 (44) ~ (all_6_2 = e1)
% 117.74/18.46 (45) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.46
% 117.74/18.46 Begin of proof
% 117.74/18.46 |
% 117.74/18.46 | BETA: splitting (41) gives:
% 117.74/18.46 |
% 117.74/18.46 | Case 1:
% 117.74/18.46 | |
% 117.74/18.46 | | (46) ~ (all_56_4 = e2)
% 117.74/18.46 | |
% 117.74/18.46 | | REDUCE: (38), (46) imply:
% 117.74/18.46 | | (47) ~ (all_52_9 = e2)
% 117.74/18.46 | |
% 117.74/18.46 | | BETA: splitting (21) gives:
% 117.74/18.46 | |
% 117.74/18.46 | | Case 1:
% 117.74/18.46 | | |
% 117.74/18.46 | | | (48) ~ (all_56_5 = e2)
% 117.74/18.46 | | |
% 117.74/18.46 | | | REDUCE: (39), (48) imply:
% 117.74/18.46 | | | (49) ~ (all_52_13 = e2)
% 117.74/18.46 | | |
% 117.74/18.46 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (15),
% 117.74/18.46 | | | (16), (17), (19), (20), (21), (23), (24), (25), (26), (28),
% 117.74/18.46 | | | (29), (30), (31), (32), (33), (34), (35), (39), (43), (44),
% 117.74/18.46 | | | (47), (49) are inconsistent by sub-proof #347.
% 117.74/18.46 | | |
% 117.74/18.46 | | Case 2:
% 117.74/18.46 | | |
% 117.74/18.46 | | | (50) all_56_5 = e2
% 117.74/18.46 | | | (51) ~ (all_56_14 = e0)
% 117.74/18.46 | | |
% 117.74/18.46 | | | COMBINE_EQS: (39), (50) imply:
% 117.74/18.46 | | | (52) all_52_13 = e2
% 117.74/18.46 | | |
% 117.74/18.46 | | | REDUCE: (3), (51) imply:
% 117.74/18.46 | | | (53) ~ (all_6_2 = e0)
% 117.74/18.46 | | |
% 117.74/18.46 | | | REDUCE: (2), (52) imply:
% 117.74/18.46 | | | (54) ~ (all_52_14 = e2)
% 117.74/18.46 | | |
% 117.74/18.46 | | | SIMP: (54) implies:
% 117.74/18.46 | | | (55) ~ (all_52_14 = e2)
% 117.74/18.46 | | |
% 117.74/18.46 | | | REDUCE: (28), (52) imply:
% 117.74/18.46 | | | (56) ~ (e2 = e1)
% 117.74/18.46 | | |
% 117.74/18.46 | | | BETA: splitting (7) gives:
% 117.74/18.46 | | |
% 117.74/18.46 | | | Case 1:
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | (57) all_54_10 = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (10), (57) imply:
% 117.74/18.46 | | | | (58) all_6_2 = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | SIMP: (58) implies:
% 117.74/18.46 | | | | (59) all_6_2 = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (3), (59) imply:
% 117.74/18.46 | | | | (60) all_56_14 = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | COMBINE_EQS: (37), (59) imply:
% 117.74/18.46 | | | | (61) all_58_8 = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | REDUCE: (9), (59) imply:
% 117.74/18.46 | | | | (62) ~ (all_52_2 = e3)
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | REDUCE: (35), (59) imply:
% 117.74/18.46 | | | | (63) ~ (e3 = e2)
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | REDUCE: (33), (59) imply:
% 117.74/18.46 | | | | (64) op(e1, e3) = e3
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | BETA: splitting (14) gives:
% 117.74/18.46 | | | |
% 117.74/18.46 | | | | Case 1:
% 117.74/18.46 | | | | |
% 117.74/18.46 | | | | | (65) ~ (all_56_6 = e1)
% 117.74/18.46 | | | | |
% 117.74/18.46 | | | | | REDUCE: (40), (65) imply:
% 117.74/18.46 | | | | | (66) ~ (all_52_2 = e1)
% 117.74/18.46 | | | | |
% 117.74/18.46 | | | | | BETA: splitting (36) gives:
% 117.74/18.46 | | | | |
% 117.74/18.46 | | | | | Case 1:
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | | (67) all_58_6 = e1
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | | REF_CLOSE: (27), (66), (67) are inconsistent by sub-proof #452.
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | Case 2:
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | | (68) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | | BETA: splitting (68) gives:
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | | Case 1:
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | (69) all_58_7 = e1
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | COMBINE_EQS: (1), (69) imply:
% 117.74/18.46 | | | | | | | (70) all_52_6 = e1
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | BETA: splitting (45) gives:
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | Case 1:
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | (71) all_58_6 = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | COMBINE_EQS: (27), (71) imply:
% 117.74/18.46 | | | | | | | | (72) all_52_2 = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | SIMP: (72) implies:
% 117.74/18.46 | | | | | | | | (73) all_52_2 = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | REDUCE: (62), (73) imply:
% 117.74/18.46 | | | | | | | | (74) ~ (e3 = e2)
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | REDUCE: (42), (73) imply:
% 117.74/18.46 | | | | | | | | (75) op(e1, e3) = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | GROUND_INST: instantiating (8) with e2, e3, e3, e1, simplifying
% 117.74/18.46 | | | | | | | | with (64), (75) gives:
% 117.74/18.46 | | | | | | | | (76) e3 = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | REDUCE: (63), (76) imply:
% 117.74/18.46 | | | | | | | | (77) $false
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | CLOSE: (77) is inconsistent.
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | Case 2:
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | (78) all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | BETA: splitting (78) gives:
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | | Case 1:
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | | (79) all_58_7 = e2
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | | REF_CLOSE: (56), (69), (79) are inconsistent by sub-proof
% 117.74/18.46 | | | | | | | | | #346.
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | Case 2:
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | | (80) all_58_8 = e2 | all_58_11 = e2
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | | REF_CLOSE: (18), (55), (61), (63), (80) are inconsistent by
% 117.74/18.46 | | | | | | | | | sub-proof #345.
% 117.74/18.46 | | | | | | | | |
% 117.74/18.46 | | | | | | | | End of split
% 117.74/18.46 | | | | | | | |
% 117.74/18.46 | | | | | | | End of split
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | Case 2:
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | (81) all_58_8 = e1 | all_58_11 = e1
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | | REF_CLOSE: (11), (18), (37), (44), (81) are inconsistent by
% 117.74/18.46 | | | | | | | sub-proof #445.
% 117.74/18.46 | | | | | | |
% 117.74/18.46 | | | | | | End of split
% 117.74/18.46 | | | | | |
% 117.74/18.46 | | | | | End of split
% 117.74/18.46 | | | | |
% 117.74/18.46 | | | | Case 2:
% 117.74/18.46 | | | | |
% 117.74/18.47 | | | | | (82) ~ (all_56_14 = e3)
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | REDUCE: (60), (82) imply:
% 117.74/18.47 | | | | | (83) $false
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | CLOSE: (83) is inconsistent.
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | End of split
% 117.74/18.47 | | | |
% 117.74/18.47 | | | Case 2:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | (84) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | REF_CLOSE: (10), (35), (44), (53), (84) are inconsistent by sub-proof
% 117.74/18.47 | | | | #435.
% 117.74/18.47 | | | |
% 117.74/18.47 | | | End of split
% 117.74/18.47 | | |
% 117.74/18.47 | | End of split
% 117.74/18.47 | |
% 117.74/18.47 | Case 2:
% 117.74/18.47 | |
% 117.74/18.47 | | (85) ~ (all_56_15 = e1)
% 117.74/18.47 | |
% 117.74/18.47 | | REDUCE: (22), (85) imply:
% 117.74/18.47 | | (86) $false
% 117.74/18.47 | |
% 117.74/18.47 | | CLOSE: (86) is inconsistent.
% 117.74/18.47 | |
% 117.74/18.47 | End of split
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #345 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_58_11 = all_52_14
% 117.74/18.47 (2) all_58_8 = e3
% 117.74/18.47 (3) all_58_8 = e2 | all_58_11 = e2
% 117.74/18.47 (4) ~ (all_52_14 = e2)
% 117.74/18.47 (5) ~ (e3 = e2)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | BETA: splitting (3) gives:
% 117.74/18.47 |
% 117.74/18.47 | Case 1:
% 117.74/18.47 | |
% 117.74/18.47 | | (6) all_58_8 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | COMBINE_EQS: (2), (6) imply:
% 117.74/18.47 | | (7) e3 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | REDUCE: (5), (7) imply:
% 117.74/18.47 | | (8) $false
% 117.74/18.47 | |
% 117.74/18.47 | | CLOSE: (8) is inconsistent.
% 117.74/18.47 | |
% 117.74/18.47 | Case 2:
% 117.74/18.47 | |
% 117.74/18.47 | | (9) all_58_11 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | COMBINE_EQS: (1), (9) imply:
% 117.74/18.47 | | (10) all_52_14 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | REDUCE: (4), (10) imply:
% 117.74/18.47 | | (11) $false
% 117.74/18.47 | |
% 117.74/18.47 | | CLOSE: (11) is inconsistent.
% 117.74/18.47 | |
% 117.74/18.47 | End of split
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #346 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_58_7 = e2
% 117.74/18.47 (2) all_58_7 = e1
% 117.74/18.47 (3) ~ (e2 = e1)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.47 | (4) e2 = e1
% 117.74/18.47 |
% 117.74/18.47 | SIMP: (4) implies:
% 117.74/18.47 | (5) e2 = e1
% 117.74/18.47 |
% 117.74/18.47 | REDUCE: (3), (5) imply:
% 117.74/18.47 | (6) $false
% 117.74/18.47 |
% 117.74/18.47 | CLOSE: (6) is inconsistent.
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #347 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) ~ (all_52_9 = e2)
% 117.74/18.47 (2) ~ (all_52_13 = all_52_14)
% 117.74/18.47 (3) all_56_14 = all_6_2
% 117.74/18.47 (4) all_56_3 = all_52_1
% 117.74/18.47 (5) all_54_3 = all_52_12
% 117.74/18.47 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.47 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.47 (9) all_54_10 = all_6_2
% 117.74/18.47 (10) op(e3, e0) = all_52_12
% 117.74/18.47 (11) all_56_2 = all_52_12
% 117.74/18.47 (12) ~ (all_52_12 = e1)
% 117.74/18.47 (13) all_58_3 = all_8_2
% 117.74/18.47 (14) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.47 (15) op(e3, all_6_2) = all_6_0
% 117.74/18.47 (16) all_54_7 = all_52_13
% 117.74/18.47 (17) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.47 (18) op(e1, e0) = all_52_14
% 117.74/18.47 (19) all_58_5 = all_52_9
% 117.74/18.47 (20) all_58_2 = all_52_1
% 117.74/18.47 (21) ~ (all_52_12 = all_52_13)
% 117.74/18.47 (22) ~ (all_52_13 = e1)
% 117.74/18.47 (23) ~ (all_52_13 = e2)
% 117.74/18.47 (24) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.47 (25) all_58_10 = all_52_13
% 117.74/18.47 (26) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.74/18.47 (27) ~ (all_6_0 = e2)
% 117.74/18.47 (28) op(e1, all_6_2) = e3
% 117.74/18.47 (29) ~ (all_8_2 = e2)
% 117.74/18.47 (30) ~ (all_6_2 = e2)
% 117.74/18.47 (31) all_56_5 = all_52_13
% 117.74/18.47 (32) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.47 (33) ~ (all_6_2 = e1)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | BETA: splitting (32) gives:
% 117.74/18.47 |
% 117.74/18.47 | Case 1:
% 117.74/18.47 | |
% 117.74/18.47 | | (34) all_58_2 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | COMBINE_EQS: (20), (34) imply:
% 117.74/18.47 | | (35) all_52_1 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | SIMP: (35) implies:
% 117.74/18.47 | | (36) all_52_1 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | COMBINE_EQS: (4), (36) imply:
% 117.74/18.47 | | (37) all_56_3 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | BETA: splitting (26) gives:
% 117.74/18.47 | |
% 117.74/18.47 | | Case 1:
% 117.74/18.47 | | |
% 117.74/18.47 | | | (38) ~ (all_56_3 = e2)
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (37), (38) imply:
% 117.74/18.47 | | | (39) $false
% 117.74/18.47 | | |
% 117.74/18.47 | | | CLOSE: (39) is inconsistent.
% 117.74/18.47 | | |
% 117.74/18.47 | | Case 2:
% 117.74/18.47 | | |
% 117.74/18.47 | | | (40) ~ (all_56_14 = e3)
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (3), (40) imply:
% 117.74/18.47 | | | (41) ~ (all_6_2 = e3)
% 117.74/18.47 | | |
% 117.74/18.47 | | | BETA: splitting (7) gives:
% 117.74/18.47 | | |
% 117.74/18.47 | | | Case 1:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | (42) all_54_10 = e3
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | REF_CLOSE: (9), (41), (42) are inconsistent by sub-proof #352.
% 117.74/18.47 | | | |
% 117.74/18.47 | | | Case 2:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | (43) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 117.74/18.47 | | | | (16), (17), (18), (21), (22), (24), (27), (28), (30), (31),
% 117.74/18.47 | | | | (33), (43) are inconsistent by sub-proof #348.
% 117.74/18.47 | | | |
% 117.74/18.47 | | | End of split
% 117.74/18.47 | | |
% 117.74/18.47 | | End of split
% 117.74/18.47 | |
% 117.74/18.47 | Case 2:
% 117.74/18.47 | |
% 117.74/18.47 | | (44) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | REF_CLOSE: (1), (13), (19), (23), (25), (29), (44) are inconsistent by
% 117.74/18.47 | | sub-proof #401.
% 117.74/18.47 | |
% 117.74/18.47 | End of split
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #348 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) ~ (all_52_13 = all_52_14)
% 117.74/18.47 (2) all_56_14 = all_6_2
% 117.74/18.47 (3) all_54_3 = all_52_12
% 117.74/18.47 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.47 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.47 (6) all_54_10 = all_6_2
% 117.74/18.47 (7) op(e3, e0) = all_52_12
% 117.74/18.47 (8) all_56_2 = all_52_12
% 117.74/18.47 (9) ~ (all_52_12 = e1)
% 117.74/18.47 (10) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.47 (11) op(e3, all_6_2) = all_6_0
% 117.74/18.47 (12) all_54_7 = all_52_13
% 117.74/18.47 (13) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.47 (14) op(e1, e0) = all_52_14
% 117.74/18.47 (15) ~ (all_52_12 = all_52_13)
% 117.74/18.47 (16) ~ (all_52_13 = e1)
% 117.74/18.47 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.47 (18) ~ (all_6_0 = e2)
% 117.74/18.47 (19) op(e1, all_6_2) = e3
% 117.74/18.47 (20) ~ (all_6_2 = e2)
% 117.74/18.47 (21) all_56_5 = all_52_13
% 117.74/18.47 (22) ~ (all_6_2 = e1)
% 117.74/18.47 (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | BETA: splitting (23) gives:
% 117.74/18.47 |
% 117.74/18.47 | Case 1:
% 117.74/18.47 | |
% 117.74/18.47 | | (24) all_54_10 = e2
% 117.74/18.47 | |
% 117.74/18.47 | | REF_CLOSE: (6), (20), (24) are inconsistent by sub-proof #438.
% 117.74/18.47 | |
% 117.74/18.47 | Case 2:
% 117.74/18.47 | |
% 117.74/18.47 | | (25) ~ (all_54_10 = e2)
% 117.74/18.47 | | (26) all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47 | |
% 117.74/18.47 | | BETA: splitting (26) gives:
% 117.74/18.47 | |
% 117.74/18.47 | | Case 1:
% 117.74/18.47 | | |
% 117.74/18.47 | | | (27) all_54_10 = e1
% 117.74/18.47 | | |
% 117.74/18.47 | | | REF_CLOSE: (6), (22), (27) are inconsistent by sub-proof #437.
% 117.74/18.47 | | |
% 117.74/18.47 | | Case 2:
% 117.74/18.47 | | |
% 117.74/18.47 | | | (28) all_54_10 = e0
% 117.74/18.47 | | |
% 117.74/18.47 | | | COMBINE_EQS: (6), (28) imply:
% 117.74/18.47 | | | (29) all_6_2 = e0
% 117.74/18.47 | | |
% 117.74/18.47 | | | SIMP: (29) implies:
% 117.74/18.47 | | | (30) all_6_2 = e0
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (11), (30) imply:
% 117.74/18.47 | | | (31) op(e3, e0) = all_6_0
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (19), (30) imply:
% 117.74/18.47 | | | (32) op(e1, e0) = e3
% 117.74/18.47 | | |
% 117.74/18.47 | | | GROUND_INST: instantiating (5) with all_52_14, e3, e0, e1, simplifying
% 117.74/18.47 | | | with (14), (32) gives:
% 117.74/18.47 | | | (33) all_52_14 = e3
% 117.74/18.47 | | |
% 117.74/18.47 | | | GROUND_INST: instantiating (5) with all_52_12, all_6_0, e0, e3,
% 117.74/18.47 | | | simplifying with (7), (31) gives:
% 117.74/18.47 | | | (34) all_52_12 = all_6_0
% 117.74/18.47 | | |
% 117.74/18.47 | | | COMBINE_EQS: (3), (34) imply:
% 117.74/18.47 | | | (35) all_54_3 = all_6_0
% 117.74/18.47 | | |
% 117.74/18.47 | | | COMBINE_EQS: (8), (34) imply:
% 117.74/18.47 | | | (36) all_56_2 = all_6_0
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (15), (34) imply:
% 117.74/18.47 | | | (37) ~ (all_52_13 = all_6_0)
% 117.74/18.47 | | |
% 117.74/18.47 | | | SIMP: (37) implies:
% 117.74/18.47 | | | (38) ~ (all_52_13 = all_6_0)
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (9), (34) imply:
% 117.74/18.47 | | | (39) ~ (all_6_0 = e1)
% 117.74/18.47 | | |
% 117.74/18.47 | | | REDUCE: (1), (33) imply:
% 117.74/18.47 | | | (40) ~ (all_52_13 = e3)
% 117.74/18.47 | | |
% 117.74/18.47 | | | BETA: splitting (4) gives:
% 117.74/18.47 | | |
% 117.74/18.47 | | | Case 1:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | (41) all_54_3 = e3
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | COMBINE_EQS: (35), (41) imply:
% 117.74/18.47 | | | | (42) all_6_0 = e3
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | SIMP: (42) implies:
% 117.74/18.47 | | | | (43) all_6_0 = e3
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | COMBINE_EQS: (36), (43) imply:
% 117.74/18.47 | | | | (44) all_56_2 = e3
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | REF_CLOSE: (2), (6), (10), (20), (22), (23), (44) are inconsistent by
% 117.74/18.47 | | | | sub-proof #351.
% 117.74/18.47 | | | |
% 117.74/18.47 | | | Case 2:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | (45) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | BETA: splitting (17) gives:
% 117.74/18.47 | | | |
% 117.74/18.47 | | | | Case 1:
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | (46) all_54_7 = e3
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | REF_CLOSE: (12), (40), (46) are inconsistent by sub-proof #350.
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | Case 2:
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | (47) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | BETA: splitting (47) gives:
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | | Case 1:
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | (48) all_54_7 = e2
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | COMBINE_EQS: (12), (48) imply:
% 117.74/18.47 | | | | | | (49) all_52_13 = e2
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | SIMP: (49) implies:
% 117.74/18.47 | | | | | | (50) all_52_13 = e2
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | COMBINE_EQS: (21), (50) imply:
% 117.74/18.47 | | | | | | (51) all_56_5 = e2
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | REF_CLOSE: (2), (6), (13), (20), (22), (23), (51) are inconsistent
% 117.74/18.47 | | | | | | by sub-proof #434.
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | Case 2:
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | (52) all_54_7 = e1 | all_54_7 = e0
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | BETA: splitting (45) gives:
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | | Case 1:
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | (53) all_54_3 = e2
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | COMBINE_EQS: (35), (53) imply:
% 117.74/18.47 | | | | | | | (54) all_6_0 = e2
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | SIMP: (54) implies:
% 117.74/18.47 | | | | | | | (55) all_6_0 = e2
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | REDUCE: (18), (55) imply:
% 117.74/18.47 | | | | | | | (56) $false
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | CLOSE: (56) is inconsistent.
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | Case 2:
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | (57) all_54_3 = e1 | all_54_3 = e0
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | BETA: splitting (52) gives:
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | | Case 1:
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | (58) all_54_7 = e1
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | REF_CLOSE: (12), (16), (58) are inconsistent by sub-proof #349.
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | Case 2:
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | (59) all_54_7 = e0
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | COMBINE_EQS: (12), (59) imply:
% 117.74/18.47 | | | | | | | | (60) all_52_13 = e0
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | SIMP: (60) implies:
% 117.74/18.47 | | | | | | | | (61) all_52_13 = e0
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | REDUCE: (38), (61) imply:
% 117.74/18.47 | | | | | | | | (62) ~ (all_6_0 = e0)
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | SIMP: (62) implies:
% 117.74/18.47 | | | | | | | | (63) ~ (all_6_0 = e0)
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | BETA: splitting (57) gives:
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | | Case 1:
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | (64) all_54_3 = e1
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | COMBINE_EQS: (35), (64) imply:
% 117.74/18.47 | | | | | | | | | (65) all_6_0 = e1
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | SIMP: (65) implies:
% 117.74/18.47 | | | | | | | | | (66) all_6_0 = e1
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | REDUCE: (39), (66) imply:
% 117.74/18.47 | | | | | | | | | (67) $false
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | CLOSE: (67) is inconsistent.
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | Case 2:
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | (68) all_54_3 = e0
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | COMBINE_EQS: (35), (68) imply:
% 117.74/18.47 | | | | | | | | | (69) all_6_0 = e0
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | SIMP: (69) implies:
% 117.74/18.47 | | | | | | | | | (70) all_6_0 = e0
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | REDUCE: (63), (70) imply:
% 117.74/18.47 | | | | | | | | | (71) $false
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | | CLOSE: (71) is inconsistent.
% 117.74/18.47 | | | | | | | | |
% 117.74/18.47 | | | | | | | | End of split
% 117.74/18.47 | | | | | | | |
% 117.74/18.47 | | | | | | | End of split
% 117.74/18.47 | | | | | | |
% 117.74/18.47 | | | | | | End of split
% 117.74/18.47 | | | | | |
% 117.74/18.47 | | | | | End of split
% 117.74/18.47 | | | | |
% 117.74/18.47 | | | | End of split
% 117.74/18.47 | | | |
% 117.74/18.47 | | | End of split
% 117.74/18.47 | | |
% 117.74/18.47 | | End of split
% 117.74/18.47 | |
% 117.74/18.47 | End of split
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #349 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_54_7 = all_52_13
% 117.74/18.47 (2) all_54_7 = e1
% 117.74/18.47 (3) ~ (all_52_13 = e1)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.47 | (4) all_52_13 = e1
% 117.74/18.47 |
% 117.74/18.47 | SIMP: (4) implies:
% 117.74/18.47 | (5) all_52_13 = e1
% 117.74/18.47 |
% 117.74/18.47 | REDUCE: (3), (5) imply:
% 117.74/18.47 | (6) $false
% 117.74/18.47 |
% 117.74/18.47 | CLOSE: (6) is inconsistent.
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #350 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_54_7 = all_52_13
% 117.74/18.47 (2) all_54_7 = e3
% 117.74/18.47 (3) ~ (all_52_13 = e3)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.47 | (4) all_52_13 = e3
% 117.74/18.47 |
% 117.74/18.47 | SIMP: (4) implies:
% 117.74/18.47 | (5) all_52_13 = e3
% 117.74/18.47 |
% 117.74/18.47 | REDUCE: (3), (5) imply:
% 117.74/18.47 | (6) $false
% 117.74/18.47 |
% 117.74/18.47 | CLOSE: (6) is inconsistent.
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #351 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_56_14 = all_6_2
% 117.74/18.47 (2) all_54_10 = all_6_2
% 117.74/18.47 (3) ~ (all_56_2 = e3) | ~ (all_56_14 = e0)
% 117.74/18.47 (4) all_56_2 = e3
% 117.74/18.47 (5) ~ (all_6_2 = e2)
% 117.74/18.47 (6) ~ (all_6_2 = e1)
% 117.74/18.47 (7) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | BETA: splitting (3) gives:
% 117.74/18.47 |
% 117.74/18.47 | Case 1:
% 117.74/18.47 | |
% 117.74/18.47 | | (8) ~ (all_56_2 = e3)
% 117.74/18.47 | |
% 117.74/18.47 | | REDUCE: (4), (8) imply:
% 117.74/18.47 | | (9) $false
% 117.74/18.47 | |
% 117.74/18.47 | | CLOSE: (9) is inconsistent.
% 117.74/18.47 | |
% 117.74/18.47 | Case 2:
% 117.74/18.47 | |
% 117.74/18.47 | | (10) ~ (all_56_14 = e0)
% 117.74/18.47 | |
% 117.74/18.47 | | REDUCE: (1), (10) imply:
% 117.74/18.47 | | (11) ~ (all_6_2 = e0)
% 117.74/18.47 | |
% 117.74/18.47 | | REF_CLOSE: (2), (5), (6), (7), (11) are inconsistent by sub-proof #435.
% 117.74/18.47 | |
% 117.74/18.47 | End of split
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #352 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) all_54_10 = all_6_2
% 117.74/18.47 (2) all_54_10 = e3
% 117.74/18.47 (3) ~ (all_6_2 = e3)
% 117.74/18.47
% 117.74/18.47 Begin of proof
% 117.74/18.47 |
% 117.74/18.47 | COMBINE_EQS: (1), (2) imply:
% 117.74/18.47 | (4) all_6_2 = e3
% 117.74/18.47 |
% 117.74/18.47 | SIMP: (4) implies:
% 117.74/18.47 | (5) all_6_2 = e3
% 117.74/18.47 |
% 117.74/18.47 | REDUCE: (3), (5) imply:
% 117.74/18.47 | (6) $false
% 117.74/18.47 |
% 117.74/18.47 | CLOSE: (6) is inconsistent.
% 117.74/18.47 |
% 117.74/18.47 End of proof
% 117.74/18.47
% 117.74/18.47 Sub-proof #353 shows that the following formulas are inconsistent:
% 117.74/18.47 ----------------------------------------------------------------
% 117.74/18.47 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.74/18.47 (2) ~ (all_52_2 = all_10_2)
% 117.74/18.47 (3) all_58_7 = all_52_6
% 117.74/18.47 (4) ~ (all_4_2 = e0)
% 117.74/18.47 (5) op(e3, e2) = all_52_4
% 117.74/18.47 (6) all_56_14 = all_6_2
% 117.74/18.47 (7) all_54_0 = all_10_2
% 117.74/18.47 (8) all_54_3 = all_52_12
% 117.74/18.47 (9) op(e0, e2) = all_52_7
% 117.74/18.47 (10) all_56_11 = all_52_11
% 117.74/18.47 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.47 (12) ~ (all_52_12 = all_10_2)
% 117.74/18.47 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.74/18.47 (14) all_56_12 = all_10_2
% 117.74/18.47 (15) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.74/18.47 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.48 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.48 (18) ~ (all_52_2 = all_6_2)
% 117.74/18.48 (19) ~ (all_10_2 = e2)
% 117.74/18.48 (20) all_54_10 = all_6_2
% 117.74/18.48 (21) ~ (all_52_14 = e1)
% 117.74/18.48 (22) op(e3, e0) = all_52_12
% 117.74/18.48 (23) ~ (all_52_4 = all_52_7)
% 117.74/18.48 (24) all_56_2 = all_52_12
% 117.74/18.48 (25) all_58_3 = all_8_2
% 117.74/18.48 (26) ~ (all_10_0 = e2)
% 117.74/18.48 (27) all_58_11 = all_52_14
% 117.74/18.48 (28) op(all_10_1, all_10_2) = all_10_0
% 117.74/18.48 (29) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.48 (30) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.74/18.48 (31) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.48 (32) all_58_5 = all_52_9
% 117.74/18.48 (33) all_56_9 = all_52_3
% 117.74/18.48 (34) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.74/18.48 (35) all_58_15 = all_4_2
% 117.74/18.48 (36) all_58_2 = all_52_1
% 117.74/18.48 (37) ~ (all_10_2 = e3)
% 117.74/18.48 (38) all_58_13 = all_52_7
% 117.74/18.48 (39) all_58_6 = all_52_2
% 117.74/18.48 (40) ~ (all_52_1 = all_10_2)
% 117.74/18.48 (41) all_58_10 = all_52_13
% 117.74/18.48 (42) op(e3, all_10_2) = all_10_1
% 117.74/18.48 (43) ~ (all_10_1 = e2)
% 117.74/18.48 (44) all_58_1 = all_52_4
% 117.74/18.48 (45) all_58_14 = all_52_11
% 117.74/18.48 (46) all_54_1 = all_52_4
% 117.74/18.48 (47) all_56_13 = all_8_2
% 117.74/18.48 (48) ~ (all_8_2 = e2)
% 117.74/18.48 (49) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.48 (50) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.48 (51) all_56_7 = all_52_6
% 117.74/18.48 (52) all_58_8 = all_6_2
% 117.74/18.48 (53) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.48 (54) ~ (all_10_0 = e1)
% 117.74/18.48 (55) all_56_4 = all_52_9
% 117.74/18.48 (56) all_56_5 = all_52_13
% 117.74/18.48 (57) ~ (all_52_6 = all_6_2)
% 117.74/18.48 (58) all_58_12 = all_52_3
% 117.74/18.48 (59) ~ (all_52_4 = all_10_2)
% 117.74/18.48 (60) ~ (all_10_1 = e1)
% 117.74/18.48 (61) ~ (all_52_6 = e1)
% 117.74/18.48 (62) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.48 (63) all_56_0 = all_52_4
% 117.74/18.48 (64) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.74/18.48 (65) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.48 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.48 (66) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.74/18.48 (67) ~ (all_6_2 = e1)
% 117.74/18.48
% 117.74/18.48 Begin of proof
% 117.74/18.48 |
% 117.74/18.48 | BETA: splitting (49) gives:
% 117.74/18.48 |
% 117.74/18.48 | Case 1:
% 117.74/18.48 | |
% 117.74/18.48 | | (68) all_58_6 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | COMBINE_EQS: (39), (68) imply:
% 117.74/18.48 | | (69) all_52_2 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | SIMP: (69) implies:
% 117.74/18.48 | | (70) all_52_2 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | REDUCE: (2), (70) imply:
% 117.74/18.48 | | (71) ~ (all_10_2 = e1)
% 117.74/18.48 | |
% 117.74/18.48 | | SIMP: (71) implies:
% 117.74/18.48 | | (72) ~ (all_10_2 = e1)
% 117.74/18.48 | |
% 117.74/18.48 | | REDUCE: (18), (70) imply:
% 117.74/18.48 | | (73) ~ (all_6_2 = e1)
% 117.74/18.48 | |
% 117.74/18.48 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.74/18.48 | | (14), (15), (16), (17), (19), (20), (22), (23), (24), (25), (26),
% 117.74/18.48 | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 117.74/18.48 | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 117.74/18.48 | | (53), (54), (55), (56), (57), (58), (59), (60), (62), (63), (64),
% 117.74/18.48 | | (65), (66), (67), (72) are inconsistent by sub-proof #355.
% 117.74/18.48 | |
% 117.74/18.48 | Case 2:
% 117.74/18.48 | |
% 117.74/18.48 | | (74) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | REF_CLOSE: (3), (21), (27), (52), (61), (67), (74) are inconsistent by
% 117.74/18.48 | | sub-proof #354.
% 117.74/18.48 | |
% 117.74/18.48 | End of split
% 117.74/18.48 |
% 117.74/18.48 End of proof
% 117.74/18.48
% 117.74/18.48 Sub-proof #354 shows that the following formulas are inconsistent:
% 117.74/18.48 ----------------------------------------------------------------
% 117.74/18.48 (1) all_58_7 = all_52_6
% 117.74/18.48 (2) ~ (all_52_14 = e1)
% 117.74/18.48 (3) all_58_11 = all_52_14
% 117.74/18.48 (4) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.48 (5) all_58_8 = all_6_2
% 117.74/18.48 (6) ~ (all_52_6 = e1)
% 117.74/18.48 (7) ~ (all_6_2 = e1)
% 117.74/18.48
% 117.74/18.48 Begin of proof
% 117.74/18.48 |
% 117.74/18.48 | BETA: splitting (4) gives:
% 117.74/18.48 |
% 117.74/18.48 | Case 1:
% 117.74/18.48 | |
% 117.74/18.48 | | (8) all_58_7 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | COMBINE_EQS: (1), (8) imply:
% 117.74/18.48 | | (9) all_52_6 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | REDUCE: (6), (9) imply:
% 117.74/18.48 | | (10) $false
% 117.74/18.48 | |
% 117.74/18.48 | | CLOSE: (10) is inconsistent.
% 117.74/18.48 | |
% 117.74/18.48 | Case 2:
% 117.74/18.48 | |
% 117.74/18.48 | | (11) all_58_8 = e1 | all_58_11 = e1
% 117.74/18.48 | |
% 117.74/18.48 | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #445.
% 117.74/18.48 | |
% 117.74/18.48 | End of split
% 117.74/18.48 |
% 117.74/18.48 End of proof
% 117.74/18.48
% 117.74/18.48 Sub-proof #355 shows that the following formulas are inconsistent:
% 117.74/18.48 ----------------------------------------------------------------
% 117.74/18.48 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.74/18.48 (2) all_58_7 = all_52_6
% 117.74/18.48 (3) ~ (all_4_2 = e0)
% 117.74/18.48 (4) op(e3, e2) = all_52_4
% 117.74/18.48 (5) all_56_14 = all_6_2
% 117.74/18.48 (6) all_54_0 = all_10_2
% 117.74/18.48 (7) all_54_3 = all_52_12
% 117.74/18.48 (8) op(e0, e2) = all_52_7
% 117.74/18.48 (9) all_56_11 = all_52_11
% 117.74/18.48 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.74/18.48 (11) ~ (all_52_12 = all_10_2)
% 117.74/18.48 (12) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.74/18.48 (13) all_56_12 = all_10_2
% 117.74/18.48 (14) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.74/18.48 (15) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.48 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.48 (17) ~ (all_10_2 = e2)
% 117.74/18.48 (18) all_54_10 = all_6_2
% 117.74/18.48 (19) op(e3, e0) = all_52_12
% 117.74/18.48 (20) ~ (all_52_4 = all_52_7)
% 117.74/18.48 (21) all_56_2 = all_52_12
% 117.74/18.48 (22) all_58_3 = all_8_2
% 117.74/18.48 (23) ~ (all_10_0 = e2)
% 117.74/18.48 (24) op(all_10_1, all_10_2) = all_10_0
% 117.74/18.48 (25) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.48 (26) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.74/18.48 (27) ~ (all_10_2 = e1)
% 117.74/18.48 (28) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.48 (29) all_58_5 = all_52_9
% 117.74/18.48 (30) all_56_9 = all_52_3
% 117.74/18.48 (31) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.74/18.48 (32) all_58_15 = all_4_2
% 117.74/18.48 (33) all_58_2 = all_52_1
% 117.74/18.48 (34) ~ (all_10_2 = e3)
% 117.74/18.48 (35) all_58_13 = all_52_7
% 117.74/18.48 (36) ~ (all_52_1 = all_10_2)
% 117.74/18.48 (37) all_58_10 = all_52_13
% 117.74/18.48 (38) op(e3, all_10_2) = all_10_1
% 117.74/18.48 (39) ~ (all_10_1 = e2)
% 117.74/18.48 (40) all_58_1 = all_52_4
% 117.74/18.48 (41) all_58_14 = all_52_11
% 117.74/18.48 (42) all_54_1 = all_52_4
% 117.74/18.48 (43) all_56_13 = all_8_2
% 117.74/18.48 (44) ~ (all_8_2 = e2)
% 117.74/18.48 (45) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.48 (46) all_56_7 = all_52_6
% 117.74/18.48 (47) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.48 (48) ~ (all_10_0 = e1)
% 117.74/18.48 (49) all_56_4 = all_52_9
% 117.74/18.48 (50) all_56_5 = all_52_13
% 117.74/18.48 (51) ~ (all_52_6 = all_6_2)
% 117.74/18.48 (52) all_58_12 = all_52_3
% 117.74/18.48 (53) ~ (all_52_4 = all_10_2)
% 117.74/18.48 (54) ~ (all_10_1 = e1)
% 117.74/18.48 (55) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.48 (56) all_56_0 = all_52_4
% 117.74/18.48 (57) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.74/18.48 (58) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.48 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.48 (59) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.74/18.48 (60) ~ (all_6_2 = e1)
% 117.74/18.48
% 117.74/18.48 Begin of proof
% 117.74/18.48 |
% 117.74/18.48 | BETA: splitting (47) gives:
% 117.74/18.48 |
% 117.74/18.48 | Case 1:
% 117.74/18.48 | |
% 117.74/18.48 | | (61) all_54_0 = e3
% 117.74/18.48 | |
% 117.74/18.48 | | REF_CLOSE: (6), (34), (61) are inconsistent by sub-proof #451.
% 117.74/18.48 | |
% 117.74/18.48 | Case 2:
% 117.74/18.48 | |
% 117.74/18.48 | | (62) ~ (all_54_0 = e3)
% 117.74/18.48 | | (63) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.48 | |
% 117.74/18.48 | | BETA: splitting (63) gives:
% 117.74/18.48 | |
% 117.74/18.48 | | Case 1:
% 117.74/18.48 | | |
% 117.74/18.48 | | | (64) all_54_0 = e2
% 117.74/18.48 | | |
% 117.74/18.48 | | | REF_CLOSE: (6), (17), (64) are inconsistent by sub-proof #450.
% 117.74/18.48 | | |
% 117.74/18.48 | | Case 2:
% 117.74/18.48 | | |
% 117.74/18.48 | | | (65) all_54_0 = e1 | all_54_0 = e0
% 117.74/18.48 | | |
% 117.74/18.48 | | | BETA: splitting (65) gives:
% 117.74/18.48 | | |
% 117.74/18.48 | | | Case 1:
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | (66) all_54_0 = e1
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | REF_CLOSE: (6), (27), (66) are inconsistent by sub-proof #449.
% 117.74/18.48 | | | |
% 117.74/18.48 | | | Case 2:
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | (67) all_54_0 = e0
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | COMBINE_EQS: (6), (67) imply:
% 117.74/18.48 | | | | (68) all_10_2 = e0
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | SIMP: (68) implies:
% 117.74/18.48 | | | | (69) all_10_2 = e0
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | REDUCE: (11), (69) imply:
% 117.74/18.48 | | | | (70) ~ (all_52_12 = e0)
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | REDUCE: (38), (69) imply:
% 117.74/18.48 | | | | (71) op(e3, e0) = all_10_1
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | BETA: splitting (1) gives:
% 117.74/18.48 | | | |
% 117.74/18.48 | | | | Case 1:
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | | (72) ~ (all_56_2 = e3)
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | | REDUCE: (21), (72) imply:
% 117.74/18.48 | | | | | (73) ~ (all_52_12 = e3)
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | | REF_CLOSE: (7), (10), (16), (19), (39), (54), (70), (71), (73) are
% 117.74/18.48 | | | | | inconsistent by sub-proof #447.
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | Case 2:
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | | (74) all_56_2 = e3
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (13), (14),
% 117.74/18.48 | | | | | (15), (16), (18), (20), (22), (23), (24), (25), (26), (27),
% 117.74/18.48 | | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 117.74/18.48 | | | | | (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 117.74/18.48 | | | | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 117.74/18.48 | | | | | (59), (60), (74) are inconsistent by sub-proof #356.
% 117.74/18.48 | | | | |
% 117.74/18.48 | | | | End of split
% 117.74/18.48 | | | |
% 117.74/18.48 | | | End of split
% 117.74/18.48 | | |
% 117.74/18.48 | | End of split
% 117.74/18.48 | |
% 117.74/18.48 | End of split
% 117.74/18.48 |
% 117.74/18.48 End of proof
% 117.74/18.48
% 117.74/18.48 Sub-proof #356 shows that the following formulas are inconsistent:
% 117.74/18.48 ----------------------------------------------------------------
% 117.74/18.48 (1) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.74/18.48 (2) all_58_7 = all_52_6
% 117.74/18.48 (3) ~ (all_4_2 = e0)
% 117.74/18.48 (4) op(e3, e2) = all_52_4
% 117.74/18.48 (5) all_56_14 = all_6_2
% 117.74/18.48 (6) all_54_0 = all_10_2
% 117.74/18.48 (7) op(e0, e2) = all_52_7
% 117.74/18.48 (8) all_56_11 = all_52_11
% 117.74/18.48 (9) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.74/18.48 (10) all_56_12 = all_10_2
% 117.74/18.48 (11) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.74/18.48 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.74/18.48 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.74/18.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.74/18.48 (14) all_54_10 = all_6_2
% 117.74/18.48 (15) ~ (all_52_4 = all_52_7)
% 117.74/18.48 (16) all_58_3 = all_8_2
% 117.74/18.48 (17) ~ (all_10_0 = e2)
% 117.74/18.48 (18) op(all_10_1, all_10_2) = all_10_0
% 117.74/18.48 (19) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.48 (20) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.74/18.48 (21) ~ (all_10_2 = e1)
% 117.74/18.48 (22) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.74/18.48 (23) all_58_5 = all_52_9
% 117.74/18.48 (24) all_56_9 = all_52_3
% 117.74/18.48 (25) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.74/18.48 (26) all_58_15 = all_4_2
% 117.74/18.48 (27) all_58_2 = all_52_1
% 117.74/18.48 (28) ~ (all_10_2 = e3)
% 117.74/18.48 (29) all_58_13 = all_52_7
% 117.74/18.48 (30) ~ (all_52_1 = all_10_2)
% 117.74/18.48 (31) all_56_2 = e3
% 117.74/18.48 (32) all_58_10 = all_52_13
% 117.74/18.48 (33) op(e3, all_10_2) = all_10_1
% 117.74/18.48 (34) all_58_1 = all_52_4
% 117.74/18.48 (35) all_58_14 = all_52_11
% 117.74/18.48 (36) all_54_1 = all_52_4
% 117.74/18.48 (37) all_56_13 = all_8_2
% 117.74/18.48 (38) ~ (all_8_2 = e2)
% 117.74/18.48 (39) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.74/18.48 (40) all_56_7 = all_52_6
% 117.74/18.48 (41) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.48 (42) ~ (all_10_0 = e1)
% 117.74/18.48 (43) all_56_4 = all_52_9
% 117.74/18.48 (44) all_56_5 = all_52_13
% 117.74/18.48 (45) ~ (all_52_6 = all_6_2)
% 117.74/18.48 (46) all_58_12 = all_52_3
% 117.74/18.48 (47) ~ (all_52_4 = all_10_2)
% 117.74/18.48 (48) ~ (all_10_1 = e1)
% 117.74/18.48 (49) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.74/18.48 (50) all_56_0 = all_52_4
% 117.74/18.48 (51) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.74/18.48 (52) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.48 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.48 (53) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.74/18.48 (54) ~ (all_6_2 = e1)
% 117.74/18.48
% 117.74/18.48 Begin of proof
% 117.74/18.48 |
% 117.74/18.48 | BETA: splitting (1) gives:
% 117.74/18.48 |
% 117.74/18.48 | Case 1:
% 117.74/18.48 | |
% 117.74/18.48 | | (55) ~ (all_56_2 = e3)
% 117.74/18.48 | |
% 117.74/18.48 | | REDUCE: (31), (55) imply:
% 117.74/18.48 | | (56) $false
% 117.74/18.48 | |
% 117.74/18.48 | | CLOSE: (56) is inconsistent.
% 117.74/18.48 | |
% 117.74/18.48 | Case 2:
% 117.74/18.48 | |
% 117.74/18.48 | | (57) ~ (all_56_12 = e0)
% 117.74/18.48 | |
% 117.74/18.48 | | REDUCE: (10), (57) imply:
% 117.74/18.48 | | (58) ~ (all_10_2 = e0)
% 117.74/18.48 | |
% 117.74/18.48 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.74/18.48 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 117.74/18.48 | | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 117.74/18.48 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 117.74/18.48 | | (48), (49), (50), (51), (52), (53), (54), (58) are inconsistent
% 117.74/18.48 | | by sub-proof #422.
% 117.74/18.48 | |
% 117.74/18.48 | End of split
% 117.74/18.48 |
% 117.74/18.48 End of proof
% 117.74/18.48
% 117.74/18.48 Sub-proof #357 shows that the following formulas are inconsistent:
% 117.74/18.48 ----------------------------------------------------------------
% 117.74/18.48 (1) all_58_7 = all_52_6
% 117.74/18.48 (2) ~ (all_4_2 = e0)
% 117.74/18.48 (3) all_56_14 = all_6_2
% 117.74/18.48 (4) all_54_0 = all_10_2
% 117.74/18.48 (5) all_56_11 = all_52_11
% 117.74/18.48 (6) ~ (e3 = e1)
% 117.74/18.48 (7) all_56_12 = all_10_2
% 117.74/18.48 (8) all_56_10 = all_52_7
% 117.74/18.48 (9) ~ (all_10_2 = e2)
% 117.74/18.48 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.48 (11) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.48 (12) all_58_11 = all_52_14
% 117.74/18.48 (13) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.48 (14) ~ (all_4_2 = e3)
% 117.74/18.48 (15) all_56_9 = all_52_3
% 117.74/18.49 (16) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.49 (17) all_58_15 = all_4_2
% 117.74/18.49 (18) ~ (all_10_2 = e3)
% 117.74/18.49 (19) all_58_13 = all_52_7
% 117.74/18.49 (20) ~ (all_52_14 = all_4_2)
% 117.74/18.49 (21) all_58_6 = all_52_2
% 117.74/18.49 (22) all_56_15 = all_4_2
% 117.74/18.49 (23) all_58_14 = all_52_11
% 117.74/18.49 (24) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.49 (25) all_58_8 = all_6_2
% 117.74/18.49 (26) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 (27) all_56_6 = all_52_2
% 117.74/18.49 (28) all_58_12 = all_52_3
% 117.74/18.49 (29) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.74/18.49 (30) all_56_8 = all_52_14
% 117.74/18.49 (31) all_6_2 = e3
% 117.74/18.49 (32) ~ (all_52_6 = e1)
% 117.74/18.49 (33) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.74/18.49 (34) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.49 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.49 (35) all_54_15 = all_4_2
% 117.74/18.49
% 117.74/18.49 Begin of proof
% 117.74/18.49 |
% 117.74/18.49 | COMBINE_EQS: (3), (31) imply:
% 117.74/18.49 | (36) all_56_14 = e3
% 117.74/18.49 |
% 117.74/18.49 | COMBINE_EQS: (25), (31) imply:
% 117.74/18.49 | (37) all_58_8 = e3
% 117.74/18.49 |
% 117.74/18.49 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.74/18.49 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 117.74/18.49 | (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37)
% 117.74/18.49 | are inconsistent by sub-proof #358.
% 117.74/18.49 |
% 117.74/18.49 End of proof
% 117.74/18.49
% 117.74/18.49 Sub-proof #358 shows that the following formulas are inconsistent:
% 117.74/18.49 ----------------------------------------------------------------
% 117.74/18.49 (1) all_58_7 = all_52_6
% 117.74/18.49 (2) ~ (all_4_2 = e0)
% 117.74/18.49 (3) all_54_0 = all_10_2
% 117.74/18.49 (4) all_56_11 = all_52_11
% 117.74/18.49 (5) ~ (e3 = e1)
% 117.74/18.49 (6) all_56_12 = all_10_2
% 117.74/18.49 (7) all_56_10 = all_52_7
% 117.74/18.49 (8) ~ (all_10_2 = e2)
% 117.74/18.49 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.49 (10) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.49 (11) all_58_11 = all_52_14
% 117.74/18.49 (12) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.74/18.49 (13) ~ (all_4_2 = e3)
% 117.74/18.49 (14) all_56_9 = all_52_3
% 117.74/18.49 (15) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.49 (16) all_58_15 = all_4_2
% 117.74/18.49 (17) ~ (all_10_2 = e3)
% 117.74/18.49 (18) all_58_13 = all_52_7
% 117.74/18.49 (19) ~ (all_52_14 = all_4_2)
% 117.74/18.49 (20) all_58_6 = all_52_2
% 117.74/18.49 (21) all_58_8 = e3
% 117.74/18.49 (22) all_56_15 = all_4_2
% 117.74/18.49 (23) all_58_14 = all_52_11
% 117.74/18.49 (24) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.49 (25) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 (26) all_56_6 = all_52_2
% 117.74/18.49 (27) all_58_12 = all_52_3
% 117.74/18.49 (28) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.74/18.49 (29) all_56_14 = e3
% 117.74/18.49 (30) all_56_8 = all_52_14
% 117.74/18.49 (31) ~ (all_52_6 = e1)
% 117.74/18.49 (32) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.74/18.49 (33) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.49 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.49 (34) all_54_15 = all_4_2
% 117.74/18.49
% 117.74/18.49 Begin of proof
% 117.74/18.49 |
% 117.74/18.49 | BETA: splitting (12) gives:
% 117.74/18.49 |
% 117.74/18.49 | Case 1:
% 117.74/18.49 | |
% 117.74/18.49 | | (35) ~ (all_56_14 = e3)
% 117.74/18.49 | |
% 117.74/18.49 | | REDUCE: (29), (35) imply:
% 117.74/18.49 | | (36) $false
% 117.74/18.49 | |
% 117.74/18.49 | | CLOSE: (36) is inconsistent.
% 117.74/18.49 | |
% 117.74/18.49 | Case 2:
% 117.74/18.49 | |
% 117.74/18.49 | | (37) ~ (all_56_9 = e0)
% 117.74/18.49 | |
% 117.74/18.49 | | REDUCE: (14), (37) imply:
% 117.74/18.49 | | (38) ~ (all_52_3 = e0)
% 117.74/18.49 | |
% 117.74/18.49 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 117.74/18.49 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 117.74/18.49 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (38) are
% 117.74/18.49 | | inconsistent by sub-proof #359.
% 117.74/18.49 | |
% 117.74/18.49 | End of split
% 117.74/18.49 |
% 117.74/18.49 End of proof
% 117.74/18.49
% 117.74/18.49 Sub-proof #359 shows that the following formulas are inconsistent:
% 117.74/18.49 ----------------------------------------------------------------
% 117.74/18.49 (1) ~ (all_52_3 = e0)
% 117.74/18.49 (2) all_58_7 = all_52_6
% 117.74/18.49 (3) ~ (all_4_2 = e0)
% 117.74/18.49 (4) all_54_0 = all_10_2
% 117.74/18.49 (5) all_56_11 = all_52_11
% 117.74/18.49 (6) ~ (e3 = e1)
% 117.74/18.49 (7) all_56_12 = all_10_2
% 117.74/18.49 (8) all_56_10 = all_52_7
% 117.74/18.49 (9) ~ (all_10_2 = e2)
% 117.74/18.49 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.49 (11) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.74/18.49 (12) all_58_11 = all_52_14
% 117.74/18.49 (13) ~ (all_4_2 = e3)
% 117.74/18.49 (14) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.49 (15) all_58_15 = all_4_2
% 117.74/18.49 (16) ~ (all_10_2 = e3)
% 117.74/18.49 (17) all_58_13 = all_52_7
% 117.74/18.49 (18) ~ (all_52_14 = all_4_2)
% 117.74/18.49 (19) all_58_6 = all_52_2
% 117.74/18.49 (20) all_58_8 = e3
% 117.74/18.49 (21) all_56_15 = all_4_2
% 117.74/18.49 (22) all_58_14 = all_52_11
% 117.74/18.49 (23) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.49 (24) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 (25) all_56_6 = all_52_2
% 117.74/18.49 (26) all_58_12 = all_52_3
% 117.74/18.49 (27) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.74/18.49 (28) all_56_14 = e3
% 117.74/18.49 (29) all_56_8 = all_52_14
% 117.74/18.49 (30) ~ (all_52_6 = e1)
% 117.74/18.49 (31) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.74/18.49 (32) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.49 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.49 (33) all_54_15 = all_4_2
% 117.74/18.49
% 117.74/18.49 Begin of proof
% 117.74/18.49 |
% 117.74/18.49 | BETA: splitting (11) gives:
% 117.74/18.49 |
% 117.74/18.49 | Case 1:
% 117.74/18.49 | |
% 117.74/18.49 | | (34) ~ (all_56_6 = e1)
% 117.74/18.49 | |
% 117.74/18.49 | | REDUCE: (25), (34) imply:
% 117.74/18.49 | | (35) ~ (all_52_2 = e1)
% 117.74/18.49 | |
% 117.74/18.49 | | BETA: splitting (23) gives:
% 117.74/18.49 | |
% 117.74/18.49 | | Case 1:
% 117.74/18.49 | | |
% 117.74/18.49 | | | (36) all_58_6 = e1
% 117.74/18.49 | | |
% 117.74/18.49 | | | REF_CLOSE: (19), (35), (36) are inconsistent by sub-proof #452.
% 117.74/18.49 | | |
% 117.74/18.49 | | Case 2:
% 117.74/18.49 | | |
% 117.74/18.49 | | | (37) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.74/18.49 | | |
% 117.74/18.49 | | | BETA: splitting (37) gives:
% 117.74/18.49 | | |
% 117.74/18.49 | | | Case 1:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | (38) all_58_7 = e1
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | COMBINE_EQS: (2), (38) imply:
% 117.74/18.49 | | | | (39) all_52_6 = e1
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | REDUCE: (30), (39) imply:
% 117.74/18.49 | | | | (40) $false
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | CLOSE: (40) is inconsistent.
% 117.74/18.49 | | | |
% 117.74/18.49 | | | Case 2:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | (41) all_58_8 = e1 | all_58_11 = e1
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | BETA: splitting (41) gives:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | Case 1:
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | (42) all_58_8 = e1
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | COMBINE_EQS: (20), (42) imply:
% 117.74/18.49 | | | | | (43) e3 = e1
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | REDUCE: (6), (43) imply:
% 117.74/18.49 | | | | | (44) $false
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | CLOSE: (44) is inconsistent.
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | Case 2:
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | (45) all_58_11 = e1
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | COMBINE_EQS: (12), (45) imply:
% 117.74/18.49 | | | | | (46) all_52_14 = e1
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | COMBINE_EQS: (29), (46) imply:
% 117.74/18.49 | | | | | (47) all_56_8 = e1
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | REDUCE: (18), (46) imply:
% 117.74/18.49 | | | | | (48) ~ (all_4_2 = e1)
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | SIMP: (48) implies:
% 117.74/18.49 | | | | | (49) ~ (all_4_2 = e1)
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (13), (14), (15),
% 117.74/18.49 | | | | | (16), (17), (21), (22), (24), (26), (27), (31), (32), (33),
% 117.74/18.49 | | | | | (47), (49) are inconsistent by sub-proof #360.
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | End of split
% 117.74/18.49 | | | |
% 117.74/18.49 | | | End of split
% 117.74/18.49 | | |
% 117.74/18.49 | | End of split
% 117.74/18.49 | |
% 117.74/18.49 | Case 2:
% 117.74/18.49 | |
% 117.74/18.49 | | (50) ~ (all_56_14 = e3)
% 117.74/18.49 | |
% 117.74/18.49 | | REDUCE: (28), (50) imply:
% 117.74/18.49 | | (51) $false
% 117.74/18.49 | |
% 117.74/18.49 | | CLOSE: (51) is inconsistent.
% 117.74/18.49 | |
% 117.74/18.49 | End of split
% 117.74/18.49 |
% 117.74/18.49 End of proof
% 117.74/18.49
% 117.74/18.49 Sub-proof #360 shows that the following formulas are inconsistent:
% 117.74/18.49 ----------------------------------------------------------------
% 117.74/18.49 (1) ~ (all_52_3 = e0)
% 117.74/18.49 (2) ~ (all_4_2 = e0)
% 117.74/18.49 (3) all_54_0 = all_10_2
% 117.74/18.49 (4) ~ (all_4_2 = e1)
% 117.74/18.49 (5) all_56_11 = all_52_11
% 117.74/18.49 (6) all_56_12 = all_10_2
% 117.74/18.49 (7) all_56_10 = all_52_7
% 117.74/18.49 (8) all_56_8 = e1
% 117.74/18.49 (9) ~ (all_10_2 = e2)
% 117.74/18.49 (10) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.49 (11) ~ (all_4_2 = e3)
% 117.74/18.49 (12) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.74/18.49 (13) all_58_15 = all_4_2
% 117.74/18.49 (14) ~ (all_10_2 = e3)
% 117.74/18.49 (15) all_58_13 = all_52_7
% 117.74/18.49 (16) all_56_15 = all_4_2
% 117.74/18.49 (17) all_58_14 = all_52_11
% 117.74/18.49 (18) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 (19) all_58_12 = all_52_3
% 117.74/18.49 (20) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.74/18.49 (21) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.74/18.49 (22) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.49 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.74/18.49 (23) all_54_15 = all_4_2
% 117.74/18.49
% 117.74/18.49 Begin of proof
% 117.74/18.49 |
% 117.74/18.49 | BETA: splitting (10) gives:
% 117.74/18.49 |
% 117.74/18.49 | Case 1:
% 117.74/18.49 | |
% 117.74/18.49 | | (24) all_54_15 = e3
% 117.74/18.49 | |
% 117.74/18.49 | | COMBINE_EQS: (23), (24) imply:
% 117.74/18.49 | | (25) all_4_2 = e3
% 117.74/18.49 | |
% 117.74/18.49 | | REDUCE: (11), (25) imply:
% 117.74/18.49 | | (26) $false
% 117.74/18.49 | |
% 117.74/18.49 | | CLOSE: (26) is inconsistent.
% 117.74/18.49 | |
% 117.74/18.49 | Case 2:
% 117.74/18.49 | |
% 117.74/18.49 | | (27) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.74/18.49 | |
% 117.74/18.49 | | BETA: splitting (27) gives:
% 117.74/18.49 | |
% 117.74/18.49 | | Case 1:
% 117.74/18.49 | | |
% 117.74/18.49 | | | (28) all_54_15 = e2
% 117.74/18.49 | | |
% 117.74/18.49 | | | COMBINE_EQS: (23), (28) imply:
% 117.74/18.49 | | | (29) all_4_2 = e2
% 117.74/18.49 | | |
% 117.74/18.49 | | | COMBINE_EQS: (16), (29) imply:
% 117.74/18.49 | | | (30) all_56_15 = e2
% 117.74/18.49 | | |
% 117.74/18.49 | | | COMBINE_EQS: (13), (29) imply:
% 117.74/18.49 | | | (31) all_58_15 = e2
% 117.74/18.49 | | |
% 117.74/18.49 | | | REDUCE: (2), (29) imply:
% 117.74/18.49 | | | (32) ~ (e2 = e0)
% 117.74/18.49 | | |
% 117.74/18.49 | | | BETA: splitting (20) gives:
% 117.74/18.49 | | |
% 117.74/18.49 | | | Case 1:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | (33) ~ (all_56_15 = e2)
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | REDUCE: (30), (33) imply:
% 117.74/18.49 | | | | (34) $false
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | CLOSE: (34) is inconsistent.
% 117.74/18.49 | | | |
% 117.74/18.49 | | | Case 2:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | (35) ~ (all_56_10 = e0)
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | REDUCE: (7), (35) imply:
% 117.74/18.49 | | | | (36) ~ (all_52_7 = e0)
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | BETA: splitting (12) gives:
% 117.74/18.49 | | | |
% 117.74/18.49 | | | | Case 1:
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | (37) ~ (all_56_8 = e1)
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | REDUCE: (8), (37) imply:
% 117.74/18.49 | | | | | (38) $false
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | CLOSE: (38) is inconsistent.
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | Case 2:
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | (39) ~ (all_56_12 = e0)
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | REDUCE: (6), (39) imply:
% 117.74/18.49 | | | | | (40) ~ (all_10_2 = e0)
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | BETA: splitting (22) gives:
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | | Case 1:
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | (41) all_58_15 = e0
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | COMBINE_EQS: (31), (41) imply:
% 117.74/18.49 | | | | | | (42) e2 = e0
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | REDUCE: (32), (42) imply:
% 117.74/18.49 | | | | | | (43) $false
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | CLOSE: (43) is inconsistent.
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | Case 2:
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | (44) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.74/18.49 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | ALPHA: (44) implies:
% 117.74/18.49 | | | | | | (45) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | BETA: splitting (45) gives:
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | | Case 1:
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | | (46) all_58_12 = e0
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | | REF_CLOSE: (1), (19), (46) are inconsistent by sub-proof #362.
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | Case 2:
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | | (47) all_58_13 = e0 | all_58_14 = e0
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | | BETA: splitting (18) gives:
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | | Case 1:
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | | (48) all_54_0 = e3
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | | REF_CLOSE: (3), (14), (48) are inconsistent by sub-proof #451.
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | Case 2:
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | | (49) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | | BETA: splitting (49) gives:
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | | Case 1:
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | | (50) all_54_0 = e2
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | | REF_CLOSE: (3), (9), (50) are inconsistent by sub-proof #450.
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | Case 2:
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | | (51) all_54_0 = e1 | all_54_0 = e0
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | | BETA: splitting (51) gives:
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | | Case 1:
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | (52) all_54_0 = e1
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | COMBINE_EQS: (3), (52) imply:
% 117.74/18.49 | | | | | | | | | | (53) all_10_2 = e1
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | SIMP: (53) implies:
% 117.74/18.49 | | | | | | | | | | (54) all_10_2 = e1
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | COMBINE_EQS: (6), (54) imply:
% 117.74/18.49 | | | | | | | | | | (55) all_56_12 = e1
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | REF_CLOSE: (5), (15), (17), (21), (36), (47), (55) are
% 117.74/18.49 | | | | | | | | | | inconsistent by sub-proof #361.
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | Case 2:
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | (56) all_54_0 = e0
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | | REF_CLOSE: (3), (40), (56) are inconsistent by sub-proof
% 117.74/18.49 | | | | | | | | | | #424.
% 117.74/18.49 | | | | | | | | | |
% 117.74/18.49 | | | | | | | | | End of split
% 117.74/18.49 | | | | | | | | |
% 117.74/18.49 | | | | | | | | End of split
% 117.74/18.49 | | | | | | | |
% 117.74/18.49 | | | | | | | End of split
% 117.74/18.49 | | | | | | |
% 117.74/18.49 | | | | | | End of split
% 117.74/18.49 | | | | | |
% 117.74/18.49 | | | | | End of split
% 117.74/18.49 | | | | |
% 117.74/18.49 | | | | End of split
% 117.74/18.49 | | | |
% 117.74/18.49 | | | End of split
% 117.74/18.49 | | |
% 117.74/18.49 | | Case 2:
% 117.74/18.49 | | |
% 117.74/18.49 | | | (57) all_54_15 = e1 | all_54_15 = e0
% 117.74/18.49 | | |
% 117.96/18.49 | | | REF_CLOSE: (2), (4), (23), (57) are inconsistent by sub-proof #418.
% 117.96/18.49 | | |
% 117.96/18.49 | | End of split
% 117.96/18.49 | |
% 117.96/18.49 | End of split
% 117.96/18.49 |
% 117.96/18.49 End of proof
% 117.96/18.49
% 117.96/18.49 Sub-proof #361 shows that the following formulas are inconsistent:
% 117.96/18.49 ----------------------------------------------------------------
% 117.96/18.49 (1) all_56_11 = all_52_11
% 117.96/18.49 (2) all_58_13 = all_52_7
% 117.96/18.49 (3) ~ (all_52_7 = e0)
% 117.96/18.49 (4) all_56_12 = e1
% 117.96/18.49 (5) all_58_14 = all_52_11
% 117.96/18.49 (6) all_58_13 = e0 | all_58_14 = e0
% 117.96/18.49 (7) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.96/18.49
% 117.96/18.49 Begin of proof
% 117.96/18.49 |
% 117.96/18.49 | BETA: splitting (7) gives:
% 117.96/18.49 |
% 117.96/18.49 | Case 1:
% 117.96/18.49 | |
% 117.96/18.49 | | (8) ~ (all_56_12 = e1)
% 117.96/18.49 | |
% 117.96/18.49 | | REDUCE: (4), (8) imply:
% 117.96/18.49 | | (9) $false
% 117.96/18.49 | |
% 117.96/18.49 | | CLOSE: (9) is inconsistent.
% 117.96/18.49 | |
% 117.96/18.49 | Case 2:
% 117.96/18.49 | |
% 117.96/18.49 | | (10) ~ (all_56_11 = e0)
% 117.96/18.49 | |
% 117.96/18.49 | | REDUCE: (1), (10) imply:
% 117.96/18.49 | | (11) ~ (all_52_11 = e0)
% 117.96/18.49 | |
% 117.96/18.49 | | BETA: splitting (6) gives:
% 117.96/18.49 | |
% 117.96/18.49 | | Case 1:
% 117.96/18.49 | | |
% 117.96/18.49 | | | (12) all_58_13 = e0
% 117.96/18.49 | | |
% 117.96/18.49 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #430.
% 117.96/18.49 | | |
% 117.96/18.49 | | Case 2:
% 117.96/18.49 | | |
% 117.96/18.49 | | | (13) all_58_14 = e0
% 117.96/18.49 | | |
% 117.96/18.49 | | | REF_CLOSE: (5), (11), (13) are inconsistent by sub-proof #429.
% 117.96/18.49 | | |
% 117.96/18.49 | | End of split
% 117.96/18.49 | |
% 117.96/18.49 | End of split
% 117.96/18.49 |
% 117.96/18.49 End of proof
% 117.96/18.49
% 117.96/18.49 Sub-proof #362 shows that the following formulas are inconsistent:
% 117.96/18.49 ----------------------------------------------------------------
% 117.96/18.49 (1) all_58_12 = all_52_3
% 117.96/18.49 (2) all_58_12 = e0
% 117.96/18.49 (3) ~ (all_52_3 = e0)
% 117.96/18.49
% 117.96/18.49 Begin of proof
% 117.96/18.49 |
% 117.96/18.49 | COMBINE_EQS: (1), (2) imply:
% 117.96/18.49 | (4) all_52_3 = e0
% 117.96/18.49 |
% 117.96/18.49 | SIMP: (4) implies:
% 117.96/18.49 | (5) all_52_3 = e0
% 117.96/18.49 |
% 117.96/18.49 | REDUCE: (3), (5) imply:
% 117.96/18.49 | (6) $false
% 117.96/18.49 |
% 117.96/18.49 | CLOSE: (6) is inconsistent.
% 117.96/18.49 |
% 117.96/18.49 End of proof
% 117.96/18.49
% 117.96/18.49 Sub-proof #363 shows that the following formulas are inconsistent:
% 117.96/18.49 ----------------------------------------------------------------
% 117.96/18.49 (1) ~ (all_52_8 = all_10_2)
% 117.96/18.49 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.96/18.49 (3) ~ (all_52_2 = all_10_2)
% 117.96/18.49 (4) ~ (all_52_6 = all_52_14)
% 117.96/18.49 (5) all_58_7 = all_52_6
% 117.96/18.49 (6) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.96/18.49 (7) ~ (all_52_13 = all_52_14)
% 117.96/18.49 (8) ~ (all_4_2 = e0)
% 117.96/18.50 (9) op(e3, e2) = all_52_4
% 117.96/18.50 (10) all_56_14 = all_6_2
% 117.96/18.50 (11) all_56_3 = all_52_1
% 117.96/18.50 (12) all_38_1 = all_10_1
% 117.96/18.50 (13) all_54_0 = all_10_2
% 117.96/18.50 (14) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.96/18.50 (15) all_54_3 = all_52_12
% 117.96/18.50 (16) ~ (all_52_2 = all_52_6)
% 117.96/18.50 (17) op(e0, e2) = all_52_7
% 117.96/18.50 (18) all_56_11 = all_52_11
% 117.96/18.50 (19) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.96/18.50 (20) ~ (all_6_1 = e3)
% 117.96/18.50 (21) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.96/18.50 (22) ~ (all_52_12 = all_10_2)
% 117.96/18.50 (23) ~ (e3 = e1)
% 117.96/18.50 (24) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.96/18.50 (25) all_56_12 = all_10_2
% 117.96/18.50 (26) all_58_0 = all_10_2
% 117.96/18.50 (27) op(all_6_1, all_6_2) = all_6_0
% 117.96/18.50 (28) all_54_11 = all_52_14
% 117.96/18.50 (29) all_54_13 = all_52_7
% 117.96/18.50 (30) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.96/18.50 (31) ~ (all_52_14 = all_6_2)
% 117.96/18.50 (32) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.96/18.50 (33) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.96/18.50 (34) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.96/18.50 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.96/18.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.96/18.50 (36) all_54_8 = all_52_2
% 117.96/18.50 (37) ~ (all_52_2 = all_6_2)
% 117.96/18.50 (38) ~ (all_40_0 = e3) | ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.96/18.50 (39) ~ (all_38_0 = e0) | ~ (all_38_1 = e2) | ~ (all_38_2 = e1)
% 117.96/18.50 (40) all_54_10 = all_6_2
% 117.96/18.50 (41) op(e3, e0) = all_52_12
% 117.96/18.50 (42) all_38_0 = all_10_0
% 117.96/18.50 (43) ~ (all_52_8 = all_6_2)
% 117.96/18.50 (44) all_58_4 = all_52_8
% 117.96/18.50 (45) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.96/18.50 (46) ~ (all_52_4 = all_52_7)
% 117.96/18.50 (47) all_56_2 = all_52_12
% 117.96/18.50 (48) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.96/18.50 (49) all_58_3 = all_8_2
% 117.96/18.50 (50) all_54_6 = all_52_9
% 117.96/18.50 (51) ~ (all_10_0 = e2)
% 117.96/18.50 (52) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.96/18.50 (53) all_58_11 = all_52_14
% 117.96/18.50 (54) all_54_9 = all_52_6
% 117.96/18.50 (55) op(e3, e1) = all_52_8
% 117.96/18.50 (56) op(all_10_1, all_10_2) = all_10_0
% 117.96/18.50 (57) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.96/18.50 (58) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.96/18.50 (59) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.96/18.50 (60) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.96/18.50 (61) op(e1, e0) = all_52_14
% 117.96/18.50 (62) all_58_5 = all_52_9
% 117.96/18.50 (63) all_40_0 = all_6_0
% 117.96/18.50 (64) all_56_9 = all_52_3
% 117.96/18.50 (65) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 117.96/18.50 (66) op(e1, all_6_2) = all_6_1
% 117.96/18.50 (67) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.96/18.50 (68) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.96/18.50 (69) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.96/18.50 (70) all_58_15 = all_4_2
% 117.96/18.50 (71) all_58_2 = all_52_1
% 117.96/18.50 (72) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.96/18.50 (73) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.96/18.50 (74) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.96/18.50 (75) ~ (all_10_2 = e3)
% 117.96/18.50 (76) all_58_13 = all_52_7
% 117.96/18.50 (77) all_40_1 = all_6_1
% 117.96/18.50 (78) ~ (all_56_10 = e0) | ~ (all_56_14 = e2)
% 117.96/18.50 (79) ~ (all_52_14 = all_4_2)
% 117.96/18.50 (80) all_58_6 = all_52_2
% 117.96/18.50 (81) ~ (all_52_1 = all_10_2)
% 117.96/18.50 (82) all_56_15 = all_4_2
% 117.96/18.50 (83) all_58_10 = all_52_13
% 117.96/18.50 (84) ~ (all_52_11 = all_4_2)
% 117.96/18.50 (85) op(e3, all_10_2) = all_10_1
% 117.96/18.50 (86) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.96/18.50 (87) ~ (all_6_0 = e2)
% 117.96/18.50 (88) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.96/18.50 (89) all_38_2 = all_10_2
% 117.96/18.50 (90) all_58_1 = all_52_4
% 117.96/18.50 (91) all_58_14 = all_52_11
% 117.96/18.50 (92) all_54_1 = all_52_4
% 117.96/18.50 (93) all_56_13 = all_8_2
% 117.96/18.50 (94) ~ (all_8_2 = e2)
% 117.96/18.50 (95) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.96/18.50 (96) op(e1, e2) = all_52_6
% 117.96/18.50 (97) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.96/18.50 (98) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.96/18.50 (99) all_56_7 = all_52_6
% 117.96/18.50 (100) ~ (all_52_9 = all_6_2)
% 117.96/18.50 (101) all_58_8 = all_6_2
% 117.96/18.50 (102) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.96/18.50 (103) ~ (all_10_0 = e1)
% 117.97/18.50 (104) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 117.97/18.50 (105) all_40_2 = all_6_2
% 117.97/18.50 (106) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.50 (107) all_56_4 = all_52_9
% 117.97/18.50 (108) all_58_9 = all_52_12
% 117.97/18.50 (109) all_56_5 = all_52_13
% 117.97/18.50 (110) op(e2, e1) = all_52_9
% 117.97/18.50 (111) ~ (all_52_3 = all_4_2)
% 117.97/18.50 (112) ~ (all_52_6 = all_6_2)
% 117.97/18.50 (113) all_56_6 = all_52_2
% 117.97/18.50 (114) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.97/18.50 (115) all_58_12 = all_52_3
% 117.97/18.50 (116) ~ (all_52_2 = all_52_14)
% 117.97/18.50 (117) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.97/18.50 (118) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.50 (119) op(e2, e0) = all_52_13
% 117.97/18.50 (120) ~ (all_52_12 = all_4_2)
% 117.97/18.50 (121) ~ (all_52_3 = all_10_2)
% 117.97/18.50 (122) op(e1, e3) = all_52_2
% 117.97/18.50 (123) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.97/18.50 (124) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.50 (125) all_56_8 = all_52_14
% 117.97/18.50 (126) ~ (all_52_4 = all_10_2)
% 117.97/18.50 (127) ~ (all_10_1 = e1)
% 117.97/18.50 (128) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.97/18.50 (129) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.50 (130) all_56_0 = all_52_4
% 117.97/18.50 (131) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.50 (132) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.50 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.50 (133) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.97/18.50 (134) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.50 (135) all_54_15 = all_4_2
% 117.97/18.50 (136) ~ (all_6_2 = e1)
% 117.97/18.50 (137) ~ (all_6_1 = e2)
% 117.97/18.50 (138) ~ (all_52_6 = all_52_7)
% 117.97/18.50 (139) ~ (all_52_3 = all_52_11)
% 117.97/18.50 (140) all_54_12 = all_52_3
% 117.97/18.50
% 117.97/18.50 Begin of proof
% 117.97/18.50 |
% 117.97/18.50 | BETA: splitting (39) gives:
% 117.97/18.50 |
% 117.97/18.50 | Case 1:
% 117.97/18.50 | |
% 117.97/18.50 | | (141) ~ (all_38_1 = e2)
% 117.97/18.50 | |
% 117.97/18.50 | | REDUCE: (12), (141) imply:
% 117.97/18.50 | | (142) ~ (all_10_1 = e2)
% 117.97/18.50 | |
% 117.97/18.50 | | BETA: splitting (38) gives:
% 117.97/18.50 | |
% 117.97/18.50 | | Case 1:
% 117.97/18.50 | | |
% 117.97/18.50 | | | (143) ~ (all_40_0 = e3)
% 117.97/18.50 | | |
% 117.97/18.50 | | | REDUCE: (63), (143) imply:
% 117.97/18.50 | | | (144) ~ (all_6_0 = e3)
% 117.97/18.50 | | |
% 117.97/18.50 | | | BETA: splitting (78) gives:
% 117.97/18.50 | | |
% 117.97/18.50 | | | Case 1:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (145) ~ (all_56_14 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REDUCE: (10), (145) imply:
% 117.97/18.50 | | | | (146) ~ (all_6_2 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 117.97/18.50 | | | | (17), (18), (19), (20), (21), (22), (24), (25), (26), (28),
% 117.97/18.50 | | | | (30), (31), (33), (34), (35), (36), (37), (40), (41), (43),
% 117.97/18.50 | | | | (44), (45), (46), (47), (48), (49), (51), (53), (55), (56),
% 117.97/18.50 | | | | (57), (58), (59), (60), (61), (62), (64), (65), (66), (67),
% 117.97/18.50 | | | | (68), (70), (71), (72), (75), (76), (79), (80), (81), (82),
% 117.97/18.50 | | | | (83), (84), (85), (86), (88), (90), (91), (92), (93), (94),
% 117.97/18.50 | | | | (97), (98), (99), (101), (102), (103), (104), (106), (107),
% 117.97/18.50 | | | | (108), (109), (111), (112), (113), (115), (116), (117),
% 117.97/18.50 | | | | (118), (120), (121), (122), (123), (124), (125), (126),
% 117.97/18.50 | | | | (127), (128), (129), (130), (131), (132), (134), (135),
% 117.97/18.50 | | | | (136), (137), (139), (140), (142), (146) are inconsistent by
% 117.97/18.50 | | | | sub-proof #391.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | Case 2:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (147) all_56_14 = e2
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (3), (4), (5), (8), (10), (13), (14), (16), (17), (18), (20),
% 117.97/18.50 | | | | (23), (25), (27), (28), (29), (30), (31), (32), (35), (36),
% 117.97/18.50 | | | | (37), (46), (49), (52), (54), (60), (64), (66), (67), (69),
% 117.97/18.50 | | | | (70), (74), (76), (87), (90), (91), (93), (94), (95), (96),
% 117.97/18.50 | | | | (99), (102), (106), (112), (113), (115), (116), (125), (126),
% 117.97/18.50 | | | | (128), (130), (131), (132), (133), (136), (138), (144), (147)
% 117.97/18.50 | | | | are inconsistent by sub-proof #374.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | End of split
% 117.97/18.50 | | |
% 117.97/18.50 | | Case 2:
% 117.97/18.50 | | |
% 117.97/18.50 | | | (148) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.97/18.50 | | |
% 117.97/18.50 | | | BETA: splitting (78) gives:
% 117.97/18.50 | | |
% 117.97/18.50 | | | Case 1:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (149) ~ (all_56_14 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REDUCE: (10), (149) imply:
% 117.97/18.50 | | | | (150) ~ (all_6_2 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 117.97/18.50 | | | | (17), (18), (19), (20), (21), (22), (24), (25), (26), (28),
% 117.97/18.50 | | | | (30), (31), (33), (34), (35), (36), (37), (40), (41), (43),
% 117.97/18.50 | | | | (44), (45), (46), (47), (48), (49), (51), (53), (55), (56),
% 117.97/18.50 | | | | (57), (58), (59), (60), (61), (62), (64), (65), (66), (67),
% 117.97/18.50 | | | | (68), (70), (71), (72), (75), (76), (79), (80), (81), (82),
% 117.97/18.50 | | | | (83), (84), (85), (86), (88), (90), (91), (92), (93), (94),
% 117.97/18.50 | | | | (97), (98), (99), (101), (102), (103), (104), (106), (107),
% 117.97/18.50 | | | | (108), (109), (111), (112), (113), (115), (116), (117),
% 117.97/18.50 | | | | (118), (120), (121), (122), (123), (124), (125), (126),
% 117.97/18.50 | | | | (127), (128), (129), (130), (131), (132), (134), (135),
% 117.97/18.50 | | | | (136), (137), (139), (140), (142), (150) are inconsistent by
% 117.97/18.50 | | | | sub-proof #391.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | Case 2:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (151) all_56_14 = e2
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (10), (20), (32), (35), (52), (54), (66), (77), (96), (99),
% 117.97/18.50 | | | | (105), (112), (148), (151) are inconsistent by sub-proof
% 117.97/18.50 | | | | #372.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | End of split
% 117.97/18.50 | | |
% 117.97/18.50 | | End of split
% 117.97/18.50 | |
% 117.97/18.50 | Case 2:
% 117.97/18.50 | |
% 117.97/18.50 | | (152) all_38_1 = e2
% 117.97/18.50 | | (153) ~ (all_38_0 = e0) | ~ (all_38_2 = e1)
% 117.97/18.50 | |
% 117.97/18.50 | | COMBINE_EQS: (12), (152) imply:
% 117.97/18.50 | | (154) all_10_1 = e2
% 117.97/18.50 | |
% 117.97/18.50 | | REDUCE: (127), (154) imply:
% 117.97/18.50 | | (155) ~ (e2 = e1)
% 117.97/18.50 | |
% 117.97/18.50 | | REDUCE: (56), (154) imply:
% 117.97/18.50 | | (156) op(e2, all_10_2) = all_10_0
% 117.97/18.50 | |
% 117.97/18.50 | | REDUCE: (85), (154) imply:
% 117.97/18.50 | | (157) op(e3, all_10_2) = e2
% 117.97/18.50 | |
% 117.97/18.50 | | BETA: splitting (38) gives:
% 117.97/18.50 | |
% 117.97/18.50 | | Case 1:
% 117.97/18.50 | | |
% 117.97/18.50 | | | (158) ~ (all_40_0 = e3)
% 117.97/18.50 | | |
% 117.97/18.50 | | | REDUCE: (63), (158) imply:
% 117.97/18.50 | | | (159) ~ (all_6_0 = e3)
% 117.97/18.50 | | |
% 117.97/18.50 | | | BETA: splitting (78) gives:
% 117.97/18.50 | | |
% 117.97/18.50 | | | Case 1:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (160) ~ (all_56_14 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REDUCE: (10), (160) imply:
% 117.97/18.50 | | | | (161) ~ (all_6_2 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (13), (17), (18), (19),
% 117.97/18.50 | | | | (20), (24), (25), (26), (28), (30), (31), (34), (35), (36),
% 117.97/18.50 | | | | (37), (40), (41), (42), (43), (45), (46), (48), (49), (50),
% 117.97/18.50 | | | | (51), (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 117.97/18.50 | | | | (64), (65), (66), (67), (68), (70), (71), (72), (73), (75),
% 117.97/18.50 | | | | (76), (79), (80), (81), (82), (83), (85), (86), (89), (90),
% 117.97/18.50 | | | | (91), (92), (93), (94), (97), (98), (99), (100), (101),
% 117.97/18.50 | | | | (102), (103), (106), (107), (108), (109), (110), (112),
% 117.97/18.50 | | | | (113), (114), (115), (116), (117), (119), (120), (122),
% 117.97/18.50 | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 117.97/18.50 | | | | (132), (134), (135), (136), (137), (153), (155), (156),
% 117.97/18.50 | | | | (157), (161) are inconsistent by sub-proof #364.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | Case 2:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (162) all_56_14 = e2
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REF_CLOSE: (3), (4), (5), (8), (10), (13), (14), (16), (17), (18), (20),
% 117.97/18.50 | | | | (23), (25), (27), (28), (29), (30), (31), (32), (35), (36),
% 117.97/18.50 | | | | (37), (46), (49), (52), (54), (60), (64), (66), (67), (69),
% 117.97/18.50 | | | | (70), (74), (76), (87), (90), (91), (93), (94), (95), (96),
% 117.97/18.50 | | | | (99), (102), (106), (112), (113), (115), (116), (125), (126),
% 117.97/18.50 | | | | (128), (130), (131), (132), (133), (136), (138), (159), (162)
% 117.97/18.50 | | | | are inconsistent by sub-proof #374.
% 117.97/18.50 | | | |
% 117.97/18.50 | | | End of split
% 117.97/18.50 | | |
% 117.97/18.50 | | Case 2:
% 117.97/18.50 | | |
% 117.97/18.50 | | | (163) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.97/18.50 | | |
% 117.97/18.50 | | | BETA: splitting (78) gives:
% 117.97/18.50 | | |
% 117.97/18.50 | | | Case 1:
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | (164) ~ (all_56_14 = e2)
% 117.97/18.50 | | | |
% 117.97/18.50 | | | | REDUCE: (10), (164) imply:
% 117.97/18.50 | | | | (165) ~ (all_6_2 = e2)
% 117.97/18.50 | | | |
% 117.97/18.51 | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (13), (17), (18), (19),
% 117.97/18.51 | | | | (20), (24), (25), (26), (28), (30), (31), (34), (35), (36),
% 117.97/18.51 | | | | (37), (40), (41), (42), (43), (45), (46), (48), (49), (50),
% 117.97/18.51 | | | | (51), (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 117.97/18.51 | | | | (64), (65), (66), (67), (68), (70), (71), (72), (73), (75),
% 117.97/18.51 | | | | (76), (79), (80), (81), (82), (83), (85), (86), (89), (90),
% 117.97/18.51 | | | | (91), (92), (93), (94), (97), (98), (99), (100), (101),
% 117.97/18.51 | | | | (102), (103), (106), (107), (108), (109), (110), (112),
% 117.97/18.51 | | | | (113), (114), (115), (116), (117), (119), (120), (122),
% 117.97/18.51 | | | | (124), (125), (126), (127), (128), (129), (130), (131),
% 117.97/18.51 | | | | (132), (134), (135), (136), (137), (153), (155), (156),
% 117.97/18.51 | | | | (157), (165) are inconsistent by sub-proof #364.
% 117.97/18.51 | | | |
% 117.97/18.51 | | | Case 2:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | (166) all_56_14 = e2
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | REF_CLOSE: (10), (20), (32), (35), (52), (54), (66), (77), (96), (99),
% 117.97/18.51 | | | | (105), (112), (163), (166) are inconsistent by sub-proof
% 117.97/18.51 | | | | #372.
% 117.97/18.51 | | | |
% 117.97/18.51 | | | End of split
% 117.97/18.51 | | |
% 117.97/18.51 | | End of split
% 117.97/18.51 | |
% 117.97/18.51 | End of split
% 117.97/18.51 |
% 117.97/18.51 End of proof
% 117.97/18.51
% 117.97/18.51 Sub-proof #364 shows that the following formulas are inconsistent:
% 117.97/18.51 ----------------------------------------------------------------
% 117.97/18.51 (1) all_58_7 = all_52_6
% 117.97/18.51 (2) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.97/18.51 (3) ~ (all_52_13 = all_52_14)
% 117.97/18.51 (4) ~ (all_4_2 = e0)
% 117.97/18.51 (5) op(e3, e2) = all_52_4
% 117.97/18.51 (6) all_56_14 = all_6_2
% 117.97/18.51 (7) all_56_3 = all_52_1
% 117.97/18.51 (8) all_54_0 = all_10_2
% 117.97/18.51 (9) op(e0, e2) = all_52_7
% 117.97/18.51 (10) all_56_11 = all_52_11
% 117.97/18.51 (11) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.51 (12) ~ (all_6_1 = e3)
% 117.97/18.51 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.51 (14) all_56_12 = all_10_2
% 117.97/18.51 (15) all_58_0 = all_10_2
% 117.97/18.51 (16) all_54_11 = all_52_14
% 117.97/18.51 (17) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.51 (18) ~ (all_52_14 = all_6_2)
% 117.97/18.51 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.51 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.51 (21) all_54_8 = all_52_2
% 117.97/18.51 (22) ~ (all_52_2 = all_6_2)
% 117.97/18.51 (23) all_54_10 = all_6_2
% 117.97/18.51 (24) ~ (e2 = e1)
% 117.97/18.51 (25) op(e3, e0) = all_52_12
% 117.97/18.51 (26) all_38_0 = all_10_0
% 117.97/18.51 (27) ~ (all_52_8 = all_6_2)
% 117.97/18.51 (28) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.51 (29) ~ (all_52_4 = all_52_7)
% 117.97/18.51 (30) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.97/18.51 (31) all_58_3 = all_8_2
% 117.97/18.51 (32) all_54_6 = all_52_9
% 117.97/18.51 (33) ~ (all_10_0 = e2)
% 117.97/18.51 (34) all_58_11 = all_52_14
% 117.97/18.51 (35) op(e3, e1) = all_52_8
% 117.97/18.51 (36) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.51 (37) ~ (all_38_0 = e0) | ~ (all_38_2 = e1)
% 117.97/18.51 (38) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.51 (39) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.51 (40) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.51 (41) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.51 (42) op(e1, e0) = all_52_14
% 117.97/18.51 (43) all_58_5 = all_52_9
% 117.97/18.51 (44) all_56_9 = all_52_3
% 117.97/18.51 (45) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 117.97/18.51 (46) op(e1, all_6_2) = all_6_1
% 117.97/18.51 (47) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.51 (48) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.51 (49) all_58_15 = all_4_2
% 117.97/18.51 (50) all_58_2 = all_52_1
% 117.97/18.51 (51) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.97/18.51 (52) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.97/18.51 (53) ~ (all_10_2 = e3)
% 117.97/18.51 (54) all_58_13 = all_52_7
% 117.97/18.51 (55) op(e2, all_10_2) = all_10_0
% 117.97/18.51 (56) ~ (all_52_14 = all_4_2)
% 117.97/18.51 (57) all_58_6 = all_52_2
% 117.97/18.51 (58) ~ (all_52_1 = all_10_2)
% 117.97/18.51 (59) all_56_15 = all_4_2
% 117.97/18.51 (60) all_58_10 = all_52_13
% 117.97/18.51 (61) op(e3, all_10_2) = e2
% 117.97/18.51 (62) op(e3, all_10_2) = all_10_1
% 117.97/18.51 (63) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.97/18.51 (64) all_38_2 = all_10_2
% 117.97/18.51 (65) all_58_1 = all_52_4
% 117.97/18.51 (66) all_58_14 = all_52_11
% 117.97/18.51 (67) all_54_1 = all_52_4
% 117.97/18.51 (68) all_56_13 = all_8_2
% 117.97/18.51 (69) ~ (all_8_2 = e2)
% 117.97/18.51 (70) ~ (all_6_2 = e2)
% 117.97/18.51 (71) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.51 (72) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.51 (73) all_56_7 = all_52_6
% 117.97/18.51 (74) ~ (all_52_9 = all_6_2)
% 117.97/18.51 (75) all_58_8 = all_6_2
% 117.97/18.51 (76) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.51 (77) ~ (all_10_0 = e1)
% 117.97/18.51 (78) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.51 (79) all_56_4 = all_52_9
% 117.97/18.51 (80) all_58_9 = all_52_12
% 117.97/18.51 (81) all_56_5 = all_52_13
% 117.97/18.51 (82) op(e2, e1) = all_52_9
% 117.97/18.51 (83) ~ (all_52_6 = all_6_2)
% 117.97/18.51 (84) all_56_6 = all_52_2
% 117.97/18.51 (85) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.97/18.51 (86) all_58_12 = all_52_3
% 117.97/18.51 (87) ~ (all_52_2 = all_52_14)
% 117.97/18.51 (88) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.97/18.51 (89) op(e2, e0) = all_52_13
% 117.97/18.51 (90) ~ (all_52_12 = all_4_2)
% 117.97/18.51 (91) op(e1, e3) = all_52_2
% 117.97/18.51 (92) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.51 (93) all_56_8 = all_52_14
% 117.97/18.51 (94) ~ (all_52_4 = all_10_2)
% 117.97/18.51 (95) ~ (all_10_1 = e1)
% 117.97/18.51 (96) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.97/18.51 (97) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.51 (98) all_56_0 = all_52_4
% 117.97/18.51 (99) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.51 (100) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.51 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.51 (101) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.51 (102) all_54_15 = all_4_2
% 117.97/18.51 (103) ~ (all_6_2 = e1)
% 117.97/18.51 (104) ~ (all_6_1 = e2)
% 117.97/18.51
% 117.97/18.51 Begin of proof
% 117.97/18.51 |
% 117.97/18.51 | BETA: splitting (45) gives:
% 117.97/18.51 |
% 117.97/18.51 | Case 1:
% 117.97/18.51 | |
% 117.97/18.51 | | (105) ~ (all_56_15 = e1)
% 117.97/18.51 | |
% 117.97/18.51 | | REDUCE: (59), (105) imply:
% 117.97/18.51 | | (106) ~ (all_4_2 = e1)
% 117.97/18.51 | |
% 117.97/18.51 | | BETA: splitting (96) gives:
% 117.97/18.51 | |
% 117.97/18.51 | | Case 1:
% 117.97/18.51 | | |
% 117.97/18.51 | | | (107) ~ (all_56_12 = e1)
% 117.97/18.51 | | |
% 117.97/18.51 | | | REDUCE: (14), (107) imply:
% 117.97/18.51 | | | (108) ~ (all_10_2 = e1)
% 117.97/18.51 | | |
% 117.97/18.51 | | | BETA: splitting (2) gives:
% 117.97/18.51 | | |
% 117.97/18.51 | | | Case 1:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | (109) ~ (all_56_6 = e1)
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (13), (14), (17), (18),
% 117.97/18.51 | | | | (19), (20), (23), (24), (25), (28), (29), (31), (33), (34),
% 117.97/18.51 | | | | (36), (38), (39), (40), (43), (44), (47), (48), (49), (50),
% 117.97/18.51 | | | | (52), (53), (54), (55), (57), (58), (60), (61), (62), (65),
% 117.97/18.51 | | | | (66), (67), (68), (69), (71), (72), (73), (75), (76), (77),
% 117.97/18.51 | | | | (79), (80), (81), (83), (84), (86), (89), (90), (93), (94),
% 117.97/18.51 | | | | (95), (97), (98), (99), (100), (101), (102), (103), (106),
% 117.97/18.51 | | | | (108), (109) are inconsistent by sub-proof #366.
% 117.97/18.51 | | | |
% 117.97/18.51 | | | Case 2:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | (110) all_56_6 = e1
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | REF_CLOSE: (6), (11), (12), (15), (16), (18), (19), (20), (23), (30),
% 117.97/18.51 | | | | (42), (46), (53), (70), (78), (92), (93), (103), (104), (110)
% 117.97/18.51 | | | | are inconsistent by sub-proof #394.
% 117.97/18.51 | | | |
% 117.97/18.51 | | | End of split
% 117.97/18.51 | | |
% 117.97/18.51 | | Case 2:
% 117.97/18.51 | | |
% 117.97/18.51 | | | (111) all_56_12 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | COMBINE_EQS: (14), (111) imply:
% 117.97/18.51 | | | (112) all_10_2 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | SIMP: (112) implies:
% 117.97/18.51 | | | (113) all_10_2 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | COMBINE_EQS: (64), (113) imply:
% 117.97/18.51 | | | (114) all_38_2 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | REDUCE: (61), (113) imply:
% 117.97/18.51 | | | (115) op(e3, e1) = e2
% 117.97/18.51 | | |
% 117.97/18.51 | | | REDUCE: (55), (113) imply:
% 117.97/18.51 | | | (116) op(e2, e1) = all_10_0
% 117.97/18.51 | | |
% 117.97/18.51 | | | BETA: splitting (37) gives:
% 117.97/18.51 | | |
% 117.97/18.51 | | | Case 1:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | (117) ~ (all_38_2 = e1)
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | REDUCE: (114), (117) imply:
% 117.97/18.51 | | | | (118) $false
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | CLOSE: (118) is inconsistent.
% 117.97/18.51 | | | |
% 117.97/18.51 | | | Case 2:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | (119) ~ (all_38_0 = e0)
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | REDUCE: (26), (119) imply:
% 117.97/18.51 | | | | (120) ~ (all_10_0 = e0)
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | BETA: splitting (51) gives:
% 117.97/18.51 | | | |
% 117.97/18.51 | | | | Case 1:
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | (121) ~ (all_56_4 = e2)
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | REDUCE: (79), (121) imply:
% 117.97/18.51 | | | | | (122) ~ (all_52_9 = e2)
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | GROUND_INST: instantiating (20) with all_52_9, all_10_0, e1, e2,
% 117.97/18.51 | | | | | simplifying with (82), (116) gives:
% 117.97/18.51 | | | | | (123) all_52_9 = all_10_0
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | GROUND_INST: instantiating (20) with all_52_8, e2, e1, e3, simplifying
% 117.97/18.51 | | | | | with (35), (115) gives:
% 117.97/18.51 | | | | | (124) all_52_8 = e2
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | COMBINE_EQS: (32), (123) imply:
% 117.97/18.51 | | | | | (125) all_54_6 = all_10_0
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | REDUCE: (27), (124) imply:
% 117.97/18.51 | | | | | (126) ~ (all_6_2 = e2)
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | REDUCE: (74), (123) imply:
% 117.97/18.51 | | | | | (127) ~ (all_10_0 = all_6_2)
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | BETA: splitting (85) gives:
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | Case 1:
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | (128) all_54_6 = e3
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | COMBINE_EQS: (125), (128) imply:
% 117.97/18.51 | | | | | | (129) all_10_0 = e3
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | SIMP: (129) implies:
% 117.97/18.51 | | | | | | (130) all_10_0 = e3
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | REDUCE: (127), (130) imply:
% 117.97/18.51 | | | | | | (131) ~ (all_6_2 = e3)
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | SIMP: (131) implies:
% 117.97/18.51 | | | | | | (132) ~ (all_6_2 = e3)
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | REF_CLOSE: (6), (11), (12), (15), (16), (18), (19), (20), (23),
% 117.97/18.51 | | | | | | (42), (46), (53), (70), (78), (92), (93), (103), (104),
% 117.97/18.51 | | | | | | (132) are inconsistent by sub-proof #413.
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | Case 2:
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | (133) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | | REF_CLOSE: (33), (77), (120), (125), (133) are inconsistent by
% 117.97/18.51 | | | | | | sub-proof #365.
% 117.97/18.51 | | | | | |
% 117.97/18.51 | | | | | End of split
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | Case 2:
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | (134) ~ (all_56_12 = e1)
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | REDUCE: (111), (134) imply:
% 117.97/18.51 | | | | | (135) $false
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | | CLOSE: (135) is inconsistent.
% 117.97/18.51 | | | | |
% 117.97/18.51 | | | | End of split
% 117.97/18.51 | | | |
% 117.97/18.51 | | | End of split
% 117.97/18.51 | | |
% 117.97/18.51 | | End of split
% 117.97/18.51 | |
% 117.97/18.51 | Case 2:
% 117.97/18.51 | |
% 117.97/18.51 | | (136) all_56_15 = e1
% 117.97/18.51 | |
% 117.97/18.51 | | REF_CLOSE: (3), (6), (7), (11), (12), (15), (16), (18), (19), (20), (21),
% 117.97/18.51 | | (22), (23), (30), (31), (40), (41), (42), (43), (46), (50), (53),
% 117.97/18.51 | | (56), (59), (60), (63), (69), (70), (78), (79), (81), (84), (87),
% 117.97/18.51 | | (88), (91), (92), (93), (97), (103), (104), (136) are
% 117.97/18.51 | | inconsistent by sub-proof #392.
% 117.97/18.51 | |
% 117.97/18.51 | End of split
% 117.97/18.51 |
% 117.97/18.51 End of proof
% 117.97/18.51
% 117.97/18.51 Sub-proof #365 shows that the following formulas are inconsistent:
% 117.97/18.51 ----------------------------------------------------------------
% 117.97/18.51 (1) ~ (all_10_0 = e2)
% 117.97/18.51 (2) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 117.97/18.51 (3) ~ (all_10_0 = e1)
% 117.97/18.51 (4) all_54_6 = all_10_0
% 117.97/18.51 (5) ~ (all_10_0 = e0)
% 117.97/18.51
% 117.97/18.51 Begin of proof
% 117.97/18.51 |
% 117.97/18.51 | BETA: splitting (2) gives:
% 117.97/18.51 |
% 117.97/18.51 | Case 1:
% 117.97/18.51 | |
% 117.97/18.51 | | (6) all_54_6 = e2
% 117.97/18.51 | |
% 117.97/18.51 | | COMBINE_EQS: (4), (6) imply:
% 117.97/18.51 | | (7) all_10_0 = e2
% 117.97/18.51 | |
% 117.97/18.51 | | SIMP: (7) implies:
% 117.97/18.51 | | (8) all_10_0 = e2
% 117.97/18.51 | |
% 117.97/18.51 | | REDUCE: (1), (8) imply:
% 117.97/18.51 | | (9) $false
% 117.97/18.51 | |
% 117.97/18.51 | | CLOSE: (9) is inconsistent.
% 117.97/18.51 | |
% 117.97/18.51 | Case 2:
% 117.97/18.51 | |
% 117.97/18.51 | | (10) all_54_6 = e1 | all_54_6 = e0
% 117.97/18.51 | |
% 117.97/18.51 | | BETA: splitting (10) gives:
% 117.97/18.51 | |
% 117.97/18.51 | | Case 1:
% 117.97/18.51 | | |
% 117.97/18.51 | | | (11) all_54_6 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | COMBINE_EQS: (4), (11) imply:
% 117.97/18.51 | | | (12) all_10_0 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | SIMP: (12) implies:
% 117.97/18.51 | | | (13) all_10_0 = e1
% 117.97/18.51 | | |
% 117.97/18.51 | | | REDUCE: (3), (13) imply:
% 117.97/18.51 | | | (14) $false
% 117.97/18.51 | | |
% 117.97/18.51 | | | CLOSE: (14) is inconsistent.
% 117.97/18.51 | | |
% 117.97/18.51 | | Case 2:
% 117.97/18.51 | | |
% 117.97/18.51 | | | (15) all_54_6 = e0
% 117.97/18.51 | | |
% 117.97/18.51 | | | COMBINE_EQS: (4), (15) imply:
% 117.97/18.51 | | | (16) all_10_0 = e0
% 117.97/18.51 | | |
% 117.97/18.51 | | | SIMP: (16) implies:
% 117.97/18.51 | | | (17) all_10_0 = e0
% 117.97/18.51 | | |
% 117.97/18.51 | | | REDUCE: (5), (17) imply:
% 117.97/18.51 | | | (18) $false
% 117.97/18.51 | | |
% 117.97/18.51 | | | CLOSE: (18) is inconsistent.
% 117.97/18.51 | | |
% 117.97/18.51 | | End of split
% 117.97/18.51 | |
% 117.97/18.51 | End of split
% 117.97/18.51 |
% 117.97/18.51 End of proof
% 117.97/18.51
% 117.97/18.51 Sub-proof #366 shows that the following formulas are inconsistent:
% 117.97/18.51 ----------------------------------------------------------------
% 117.97/18.51 (1) all_58_7 = all_52_6
% 117.97/18.51 (2) ~ (all_4_2 = e0)
% 117.97/18.51 (3) op(e3, e2) = all_52_4
% 117.97/18.51 (4) all_56_14 = all_6_2
% 117.97/18.51 (5) all_54_0 = all_10_2
% 117.97/18.51 (6) ~ (all_4_2 = e1)
% 117.97/18.51 (7) op(e0, e2) = all_52_7
% 117.97/18.51 (8) all_56_11 = all_52_11
% 117.97/18.51 (9) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.51 (10) all_56_12 = all_10_2
% 117.97/18.51 (11) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.51 (12) ~ (all_52_14 = all_6_2)
% 117.97/18.51 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.51 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.51 (15) all_54_10 = all_6_2
% 117.97/18.51 (16) ~ (e2 = e1)
% 117.97/18.51 (17) op(e3, e0) = all_52_12
% 117.97/18.51 (18) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.51 (19) ~ (all_52_4 = all_52_7)
% 117.97/18.51 (20) all_58_3 = all_8_2
% 117.97/18.51 (21) ~ (all_10_0 = e2)
% 117.97/18.51 (22) all_58_11 = all_52_14
% 117.97/18.51 (23) ~ (all_56_6 = e1)
% 117.97/18.51 (24) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.52 (25) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.52 (26) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.52 (27) ~ (all_10_2 = e1)
% 117.97/18.52 (28) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.52 (29) all_58_5 = all_52_9
% 117.97/18.52 (30) all_56_9 = all_52_3
% 117.97/18.52 (31) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.52 (32) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.52 (33) all_58_15 = all_4_2
% 117.97/18.52 (34) all_58_2 = all_52_1
% 117.97/18.52 (35) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 (36) ~ (all_10_2 = e3)
% 117.97/18.52 (37) all_58_13 = all_52_7
% 117.97/18.52 (38) op(e2, all_10_2) = all_10_0
% 117.97/18.52 (39) all_58_6 = all_52_2
% 117.97/18.52 (40) ~ (all_52_1 = all_10_2)
% 117.97/18.52 (41) all_58_10 = all_52_13
% 117.97/18.52 (42) op(e3, all_10_2) = e2
% 117.97/18.52 (43) op(e3, all_10_2) = all_10_1
% 117.97/18.52 (44) all_58_1 = all_52_4
% 117.97/18.52 (45) all_58_14 = all_52_11
% 117.97/18.52 (46) all_54_1 = all_52_4
% 117.97/18.52 (47) all_56_13 = all_8_2
% 117.97/18.52 (48) ~ (all_8_2 = e2)
% 117.97/18.52 (49) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.52 (50) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.52 (51) all_56_7 = all_52_6
% 117.97/18.52 (52) all_58_8 = all_6_2
% 117.97/18.52 (53) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 (54) ~ (all_10_0 = e1)
% 117.97/18.52 (55) all_56_4 = all_52_9
% 117.97/18.52 (56) all_58_9 = all_52_12
% 117.97/18.52 (57) all_56_5 = all_52_13
% 117.97/18.52 (58) ~ (all_52_6 = all_6_2)
% 117.97/18.52 (59) all_56_6 = all_52_2
% 117.97/18.52 (60) all_58_12 = all_52_3
% 117.97/18.52 (61) op(e2, e0) = all_52_13
% 117.97/18.52 (62) ~ (all_52_12 = all_4_2)
% 117.97/18.52 (63) all_56_8 = all_52_14
% 117.97/18.52 (64) ~ (all_52_4 = all_10_2)
% 117.97/18.52 (65) ~ (all_10_1 = e1)
% 117.97/18.52 (66) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.52 (67) all_56_0 = all_52_4
% 117.97/18.52 (68) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.52 (69) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.52 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.52 (70) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.52 (71) all_54_15 = all_4_2
% 117.97/18.52 (72) ~ (all_6_2 = e1)
% 117.97/18.52
% 117.97/18.52 Begin of proof
% 117.97/18.52 |
% 117.97/18.52 | REDUCE: (23), (59) imply:
% 117.97/18.52 | (73) ~ (all_52_2 = e1)
% 117.97/18.52 |
% 117.97/18.52 | BETA: splitting (32) gives:
% 117.97/18.52 |
% 117.97/18.52 | Case 1:
% 117.97/18.52 | |
% 117.97/18.52 | | (74) ~ (all_56_7 = e1)
% 117.97/18.52 | |
% 117.97/18.52 | | REDUCE: (51), (74) imply:
% 117.97/18.52 | | (75) ~ (all_52_6 = e1)
% 117.97/18.52 | |
% 117.97/18.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 117.97/18.52 | | (14), (15), (19), (20), (21), (22), (24), (25), (26), (27), (28),
% 117.97/18.52 | | (29), (30), (31), (32), (33), (34), (36), (37), (39), (40), (41),
% 117.97/18.52 | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 117.97/18.52 | | (54), (55), (57), (58), (60), (63), (64), (65), (66), (67), (68),
% 117.97/18.52 | | (69), (70), (72), (73), (75) are inconsistent by sub-proof #371.
% 117.97/18.52 | |
% 117.97/18.52 | Case 2:
% 117.97/18.52 | |
% 117.97/18.52 | | (76) ~ (all_56_12 = e2)
% 117.97/18.52 | |
% 117.97/18.52 | | REDUCE: (10), (76) imply:
% 117.97/18.52 | | (77) ~ (all_10_2 = e2)
% 117.97/18.52 | |
% 117.97/18.52 | | REF_CLOSE: (2), (5), (6), (10), (14), (16), (17), (18), (22), (27), (31),
% 117.97/18.52 | | (33), (35), (36), (38), (41), (42), (53), (54), (56), (61), (62),
% 117.97/18.52 | | (63), (71), (77) are inconsistent by sub-proof #367.
% 117.97/18.52 | |
% 117.97/18.52 | End of split
% 117.97/18.52 |
% 117.97/18.52 End of proof
% 117.97/18.52
% 117.97/18.52 Sub-proof #367 shows that the following formulas are inconsistent:
% 117.97/18.52 ----------------------------------------------------------------
% 117.97/18.52 (1) ~ (all_4_2 = e0)
% 117.97/18.52 (2) all_54_0 = all_10_2
% 117.97/18.52 (3) ~ (all_4_2 = e1)
% 117.97/18.52 (4) all_56_12 = all_10_2
% 117.97/18.52 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.52 (6) ~ (all_10_2 = e2)
% 117.97/18.52 (7) ~ (e2 = e1)
% 117.97/18.52 (8) op(e3, e0) = all_52_12
% 117.97/18.52 (9) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.52 (10) all_58_11 = all_52_14
% 117.97/18.52 (11) ~ (all_10_2 = e1)
% 117.97/18.52 (12) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.52 (13) all_58_15 = all_4_2
% 117.97/18.52 (14) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 (15) ~ (all_10_2 = e3)
% 117.97/18.52 (16) op(e2, all_10_2) = all_10_0
% 117.97/18.52 (17) all_58_10 = all_52_13
% 117.97/18.52 (18) op(e3, all_10_2) = e2
% 117.97/18.52 (19) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 (20) ~ (all_10_0 = e1)
% 117.97/18.52 (21) all_58_9 = all_52_12
% 117.97/18.52 (22) op(e2, e0) = all_52_13
% 117.97/18.52 (23) ~ (all_52_12 = all_4_2)
% 117.97/18.52 (24) all_56_8 = all_52_14
% 117.97/18.52 (25) all_54_15 = all_4_2
% 117.97/18.52
% 117.97/18.52 Begin of proof
% 117.97/18.52 |
% 117.97/18.52 | BETA: splitting (19) gives:
% 117.97/18.52 |
% 117.97/18.52 | Case 1:
% 117.97/18.52 | |
% 117.97/18.52 | | (26) all_54_0 = e3
% 117.97/18.52 | |
% 117.97/18.52 | | REF_CLOSE: (2), (15), (26) are inconsistent by sub-proof #451.
% 117.97/18.52 | |
% 117.97/18.52 | Case 2:
% 117.97/18.52 | |
% 117.97/18.52 | | (27) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 | |
% 117.97/18.52 | | BETA: splitting (27) gives:
% 117.97/18.52 | |
% 117.97/18.52 | | Case 1:
% 117.97/18.52 | | |
% 117.97/18.52 | | | (28) all_54_0 = e2
% 117.97/18.52 | | |
% 117.97/18.52 | | | REF_CLOSE: (2), (6), (28) are inconsistent by sub-proof #450.
% 117.97/18.52 | | |
% 117.97/18.52 | | Case 2:
% 117.97/18.52 | | |
% 117.97/18.52 | | | (29) ~ (all_54_0 = e2)
% 117.97/18.52 | | | (30) all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 | | |
% 117.97/18.52 | | | BETA: splitting (30) gives:
% 117.97/18.52 | | |
% 117.97/18.52 | | | Case 1:
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | (31) all_54_0 = e1
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | REF_CLOSE: (2), (11), (31) are inconsistent by sub-proof #449.
% 117.97/18.52 | | | |
% 117.97/18.52 | | | Case 2:
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | (32) all_54_0 = e0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | COMBINE_EQS: (2), (32) imply:
% 117.97/18.52 | | | | (33) all_10_2 = e0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | SIMP: (33) implies:
% 117.97/18.52 | | | | (34) all_10_2 = e0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | REDUCE: (18), (34) imply:
% 117.97/18.52 | | | | (35) op(e3, e0) = e2
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | REDUCE: (16), (34) imply:
% 117.97/18.52 | | | | (36) op(e2, e0) = all_10_0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | GROUND_INST: instantiating (5) with all_52_13, all_10_0, e0, e2,
% 117.97/18.52 | | | | simplifying with (22), (36) gives:
% 117.97/18.52 | | | | (37) all_52_13 = all_10_0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | GROUND_INST: instantiating (5) with all_52_12, e2, e0, e3, simplifying
% 117.97/18.52 | | | | with (8), (35) gives:
% 117.97/18.52 | | | | (38) all_52_12 = e2
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | COMBINE_EQS: (17), (37) imply:
% 117.97/18.52 | | | | (39) all_58_10 = all_10_0
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | COMBINE_EQS: (21), (38) imply:
% 117.97/18.52 | | | | (40) all_58_9 = e2
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | REDUCE: (23), (38) imply:
% 117.97/18.52 | | | | (41) ~ (all_4_2 = e2)
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | SIMP: (41) implies:
% 117.97/18.52 | | | | (42) ~ (all_4_2 = e2)
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | BETA: splitting (9) gives:
% 117.97/18.52 | | | |
% 117.97/18.52 | | | | Case 1:
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | (43) all_54_15 = e3
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | COMBINE_EQS: (25), (43) imply:
% 117.97/18.52 | | | | | (44) all_4_2 = e3
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | SIMP: (44) implies:
% 117.97/18.52 | | | | | (45) all_4_2 = e3
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | COMBINE_EQS: (13), (45) imply:
% 117.97/18.52 | | | | | (46) all_58_15 = e3
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | REDUCE: (3), (45) imply:
% 117.97/18.52 | | | | | (47) ~ (e3 = e1)
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | REF_CLOSE: (2), (4), (6), (7), (10), (11), (12), (14), (20), (24),
% 117.97/18.52 | | | | | (27), (39), (40), (46), (47) are inconsistent by sub-proof
% 117.97/18.52 | | | | | #368.
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | Case 2:
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | (48) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | | REF_CLOSE: (1), (3), (25), (42), (48) are inconsistent by sub-proof
% 117.97/18.52 | | | | | #417.
% 117.97/18.52 | | | | |
% 117.97/18.52 | | | | End of split
% 117.97/18.52 | | | |
% 117.97/18.52 | | | End of split
% 117.97/18.52 | | |
% 117.97/18.52 | | End of split
% 117.97/18.52 | |
% 117.97/18.52 | End of split
% 117.97/18.52 |
% 117.97/18.52 End of proof
% 117.97/18.52
% 117.97/18.52 Sub-proof #368 shows that the following formulas are inconsistent:
% 117.97/18.52 ----------------------------------------------------------------
% 117.97/18.52 (1) all_54_0 = all_10_2
% 117.97/18.52 (2) all_58_15 = e3
% 117.97/18.52 (3) all_58_10 = all_10_0
% 117.97/18.52 (4) ~ (e3 = e1)
% 117.97/18.52 (5) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 (6) all_56_12 = all_10_2
% 117.97/18.52 (7) ~ (all_10_2 = e2)
% 117.97/18.52 (8) ~ (e2 = e1)
% 117.97/18.52 (9) all_58_11 = all_52_14
% 117.97/18.52 (10) ~ (all_10_2 = e1)
% 117.97/18.52 (11) all_58_9 = e2
% 117.97/18.52 (12) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.52 (13) all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 (14) ~ (all_10_0 = e1)
% 117.97/18.52 (15) all_56_8 = all_52_14
% 117.97/18.52
% 117.97/18.52 Begin of proof
% 117.97/18.52 |
% 117.97/18.52 | BETA: splitting (13) gives:
% 117.97/18.52 |
% 117.97/18.52 | Case 1:
% 117.97/18.52 | |
% 117.97/18.52 | | (16) all_58_9 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | REF_CLOSE: (8), (11), (16) are inconsistent by sub-proof #370.
% 117.97/18.52 | |
% 117.97/18.52 | Case 2:
% 117.97/18.52 | |
% 117.97/18.52 | | (17) all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | BETA: splitting (17) gives:
% 117.97/18.52 | |
% 117.97/18.52 | | Case 1:
% 117.97/18.52 | | |
% 117.97/18.52 | | | (18) all_58_10 = e1
% 117.97/18.52 | | |
% 117.97/18.52 | | | COMBINE_EQS: (3), (18) imply:
% 117.97/18.52 | | | (19) all_10_0 = e1
% 117.97/18.52 | | |
% 117.97/18.52 | | | SIMP: (19) implies:
% 117.97/18.52 | | | (20) all_10_0 = e1
% 117.97/18.52 | | |
% 117.97/18.52 | | | REDUCE: (14), (20) imply:
% 117.97/18.52 | | | (21) $false
% 117.97/18.52 | | |
% 117.97/18.52 | | | CLOSE: (21) is inconsistent.
% 117.97/18.52 | | |
% 117.97/18.52 | | Case 2:
% 117.97/18.52 | | |
% 117.97/18.52 | | | (22) all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 | | |
% 117.97/18.52 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (12), (15), (22) are
% 117.97/18.52 | | | inconsistent by sub-proof #369.
% 117.97/18.52 | | |
% 117.97/18.52 | | End of split
% 117.97/18.52 | |
% 117.97/18.52 | End of split
% 117.97/18.52 |
% 117.97/18.52 End of proof
% 117.97/18.52
% 117.97/18.52 Sub-proof #369 shows that the following formulas are inconsistent:
% 117.97/18.52 ----------------------------------------------------------------
% 117.97/18.52 (1) all_54_0 = all_10_2
% 117.97/18.52 (2) all_58_15 = e3
% 117.97/18.52 (3) ~ (e3 = e1)
% 117.97/18.52 (4) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 (5) all_56_12 = all_10_2
% 117.97/18.52 (6) ~ (all_10_2 = e2)
% 117.97/18.52 (7) all_58_11 = all_52_14
% 117.97/18.52 (8) ~ (all_10_2 = e1)
% 117.97/18.52 (9) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.52 (10) all_58_11 = e1 | all_58_15 = e1
% 117.97/18.52 (11) all_56_8 = all_52_14
% 117.97/18.52
% 117.97/18.52 Begin of proof
% 117.97/18.52 |
% 117.97/18.52 | BETA: splitting (10) gives:
% 117.97/18.52 |
% 117.97/18.52 | Case 1:
% 117.97/18.52 | |
% 117.97/18.52 | | (12) all_58_11 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | COMBINE_EQS: (7), (12) imply:
% 117.97/18.52 | | (13) all_52_14 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | SIMP: (13) implies:
% 117.97/18.52 | | (14) all_52_14 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | COMBINE_EQS: (11), (14) imply:
% 117.97/18.52 | | (15) all_56_8 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (15) are inconsistent by sub-proof
% 117.97/18.52 | | #385.
% 117.97/18.52 | |
% 117.97/18.52 | Case 2:
% 117.97/18.52 | |
% 117.97/18.52 | | (16) all_58_15 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | COMBINE_EQS: (2), (16) imply:
% 117.97/18.52 | | (17) e3 = e1
% 117.97/18.52 | |
% 117.97/18.52 | | REDUCE: (3), (17) imply:
% 117.97/18.52 | | (18) $false
% 117.97/18.52 | |
% 117.97/18.52 | | CLOSE: (18) is inconsistent.
% 117.97/18.52 | |
% 117.97/18.52 | End of split
% 117.97/18.52 |
% 117.97/18.52 End of proof
% 117.97/18.52
% 117.97/18.52 Sub-proof #370 shows that the following formulas are inconsistent:
% 117.97/18.52 ----------------------------------------------------------------
% 117.97/18.52 (1) all_58_9 = e2
% 117.97/18.52 (2) all_58_9 = e1
% 117.97/18.52 (3) ~ (e2 = e1)
% 117.97/18.52
% 117.97/18.52 Begin of proof
% 117.97/18.52 |
% 117.97/18.52 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.52 | (4) e2 = e1
% 117.97/18.52 |
% 117.97/18.52 | SIMP: (4) implies:
% 117.97/18.52 | (5) e2 = e1
% 117.97/18.52 |
% 117.97/18.52 | REDUCE: (3), (5) imply:
% 117.97/18.52 | (6) $false
% 117.97/18.52 |
% 117.97/18.52 | CLOSE: (6) is inconsistent.
% 117.97/18.52 |
% 117.97/18.52 End of proof
% 117.97/18.52
% 117.97/18.52 Sub-proof #371 shows that the following formulas are inconsistent:
% 117.97/18.52 ----------------------------------------------------------------
% 117.97/18.52 (1) all_58_7 = all_52_6
% 117.97/18.52 (2) ~ (all_4_2 = e0)
% 117.97/18.52 (3) op(e3, e2) = all_52_4
% 117.97/18.52 (4) all_56_14 = all_6_2
% 117.97/18.52 (5) all_54_0 = all_10_2
% 117.97/18.52 (6) op(e0, e2) = all_52_7
% 117.97/18.52 (7) all_56_11 = all_52_11
% 117.97/18.52 (8) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.52 (9) all_56_12 = all_10_2
% 117.97/18.52 (10) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.52 (11) ~ (all_52_14 = all_6_2)
% 117.97/18.52 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.52 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.52 (14) all_54_10 = all_6_2
% 117.97/18.52 (15) ~ (all_52_4 = all_52_7)
% 117.97/18.52 (16) all_58_3 = all_8_2
% 117.97/18.52 (17) ~ (all_10_0 = e2)
% 117.97/18.52 (18) all_58_11 = all_52_14
% 117.97/18.52 (19) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.52 (20) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.52 (21) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.52 (22) ~ (all_10_2 = e1)
% 117.97/18.52 (23) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.52 (24) all_58_5 = all_52_9
% 117.97/18.52 (25) all_56_9 = all_52_3
% 117.97/18.52 (26) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.52 (27) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.52 (28) all_58_15 = all_4_2
% 117.97/18.52 (29) all_58_2 = all_52_1
% 117.97/18.52 (30) ~ (all_10_2 = e3)
% 117.97/18.52 (31) all_58_13 = all_52_7
% 117.97/18.52 (32) all_58_6 = all_52_2
% 117.97/18.52 (33) ~ (all_52_2 = e1)
% 117.97/18.52 (34) ~ (all_52_1 = all_10_2)
% 117.97/18.52 (35) all_58_10 = all_52_13
% 117.97/18.52 (36) op(e3, all_10_2) = all_10_1
% 117.97/18.52 (37) all_58_1 = all_52_4
% 117.97/18.52 (38) all_58_14 = all_52_11
% 117.97/18.52 (39) all_54_1 = all_52_4
% 117.97/18.52 (40) all_56_13 = all_8_2
% 117.97/18.52 (41) ~ (all_8_2 = e2)
% 117.97/18.52 (42) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.52 (43) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.52 (44) all_56_7 = all_52_6
% 117.97/18.52 (45) all_58_8 = all_6_2
% 117.97/18.52 (46) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.52 (47) ~ (all_10_0 = e1)
% 117.97/18.52 (48) all_56_4 = all_52_9
% 117.97/18.52 (49) all_56_5 = all_52_13
% 117.97/18.52 (50) ~ (all_52_6 = all_6_2)
% 117.97/18.52 (51) all_58_12 = all_52_3
% 117.97/18.52 (52) all_56_8 = all_52_14
% 117.97/18.52 (53) ~ (all_52_4 = all_10_2)
% 117.97/18.52 (54) ~ (all_10_1 = e1)
% 117.97/18.52 (55) ~ (all_52_6 = e1)
% 117.97/18.52 (56) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.52 (57) all_56_0 = all_52_4
% 117.97/18.52 (58) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.52 (59) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.52 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.52 (60) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.53 (61) ~ (all_6_2 = e1)
% 117.97/18.53
% 117.97/18.53 Begin of proof
% 117.97/18.53 |
% 117.97/18.53 | BETA: splitting (42) gives:
% 117.97/18.53 |
% 117.97/18.53 | Case 1:
% 117.97/18.53 | |
% 117.97/18.53 | | (62) all_58_6 = e1
% 117.97/18.53 | |
% 117.97/18.53 | | REF_CLOSE: (32), (33), (62) are inconsistent by sub-proof #452.
% 117.97/18.53 | |
% 117.97/18.53 | Case 2:
% 117.97/18.53 | |
% 117.97/18.53 | | (63) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.53 | |
% 117.97/18.53 | | BETA: splitting (63) gives:
% 117.97/18.53 | |
% 117.97/18.53 | | Case 1:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (64) all_58_7 = e1
% 117.97/18.53 | | |
% 117.97/18.53 | | | COMBINE_EQS: (1), (64) imply:
% 117.97/18.53 | | | (65) all_52_6 = e1
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (55), (65) imply:
% 117.97/18.53 | | | (66) $false
% 117.97/18.53 | | |
% 117.97/18.53 | | | CLOSE: (66) is inconsistent.
% 117.97/18.53 | | |
% 117.97/18.53 | | Case 2:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (67) all_58_8 = e1 | all_58_11 = e1
% 117.97/18.53 | | |
% 117.97/18.53 | | | BETA: splitting (67) gives:
% 117.97/18.53 | | |
% 117.97/18.53 | | | Case 1:
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | (68) all_58_8 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | COMBINE_EQS: (45), (68) imply:
% 117.97/18.53 | | | | (69) all_6_2 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | REDUCE: (61), (69) imply:
% 117.97/18.53 | | | | (70) $false
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | CLOSE: (70) is inconsistent.
% 117.97/18.53 | | | |
% 117.97/18.53 | | | Case 2:
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | (71) all_58_11 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | COMBINE_EQS: (18), (71) imply:
% 117.97/18.53 | | | | (72) all_52_14 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | SIMP: (72) implies:
% 117.97/18.53 | | | | (73) all_52_14 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | COMBINE_EQS: (52), (73) imply:
% 117.97/18.53 | | | | (74) all_56_8 = e1
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | REDUCE: (11), (73) imply:
% 117.97/18.53 | | | | (75) ~ (all_6_2 = e1)
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | BETA: splitting (26) gives:
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | Case 1:
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | (76) ~ (all_56_8 = e1)
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | REDUCE: (74), (76) imply:
% 117.97/18.53 | | | | | (77) $false
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | CLOSE: (77) is inconsistent.
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | Case 2:
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | (78) ~ (all_56_12 = e0)
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | REDUCE: (9), (78) imply:
% 117.97/18.53 | | | | | (79) ~ (all_10_2 = e0)
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 117.97/18.53 | | | | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 117.97/18.53 | | | | | (24), (25), (27), (28), (29), (30), (31), (34), (35), (36),
% 117.97/18.53 | | | | | (37), (38), (39), (40), (41), (43), (44), (46), (47), (48),
% 117.97/18.53 | | | | | (49), (50), (51), (53), (54), (56), (57), (58), (59), (60),
% 117.97/18.53 | | | | | (61), (79) are inconsistent by sub-proof #422.
% 117.97/18.53 | | | | |
% 117.97/18.53 | | | | End of split
% 117.97/18.53 | | | |
% 117.97/18.53 | | | End of split
% 117.97/18.53 | | |
% 117.97/18.53 | | End of split
% 117.97/18.53 | |
% 117.97/18.53 | End of split
% 117.97/18.53 |
% 117.97/18.53 End of proof
% 117.97/18.53
% 117.97/18.53 Sub-proof #372 shows that the following formulas are inconsistent:
% 117.97/18.53 ----------------------------------------------------------------
% 117.97/18.53 (1) all_56_14 = all_6_2
% 117.97/18.53 (2) ~ (all_6_1 = e3)
% 117.97/18.53 (3) all_56_14 = e2
% 117.97/18.53 (4) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.97/18.53 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.53 (6) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 (7) all_54_9 = all_52_6
% 117.97/18.53 (8) ~ (all_40_1 = e0) | ~ (all_40_2 = e2)
% 117.97/18.53 (9) op(e1, all_6_2) = all_6_1
% 117.97/18.53 (10) all_40_1 = all_6_1
% 117.97/18.53 (11) op(e1, e2) = all_52_6
% 117.97/18.53 (12) all_56_7 = all_52_6
% 117.97/18.53 (13) all_40_2 = all_6_2
% 117.97/18.53 (14) ~ (all_52_6 = all_6_2)
% 117.97/18.53
% 117.97/18.53 Begin of proof
% 117.97/18.53 |
% 117.97/18.53 | COMBINE_EQS: (1), (3) imply:
% 117.97/18.53 | (15) all_6_2 = e2
% 117.97/18.53 |
% 117.97/18.53 | SIMP: (15) implies:
% 117.97/18.53 | (16) all_6_2 = e2
% 117.97/18.53 |
% 117.97/18.53 | COMBINE_EQS: (13), (16) imply:
% 117.97/18.53 | (17) all_40_2 = e2
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (14), (16) imply:
% 117.97/18.53 | (18) ~ (all_52_6 = e2)
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (9), (16) imply:
% 117.97/18.53 | (19) op(e1, e2) = all_6_1
% 117.97/18.53 |
% 117.97/18.53 | BETA: splitting (4) gives:
% 117.97/18.53 |
% 117.97/18.53 | Case 1:
% 117.97/18.53 | |
% 117.97/18.53 | | (20) ~ (all_56_7 = e1)
% 117.97/18.53 | |
% 117.97/18.53 | | REDUCE: (12), (20) imply:
% 117.97/18.53 | | (21) ~ (all_52_6 = e1)
% 117.97/18.53 | |
% 117.97/18.53 | | BETA: splitting (8) gives:
% 117.97/18.53 | |
% 117.97/18.53 | | Case 1:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (22) ~ (all_40_2 = e2)
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (17), (22) imply:
% 117.97/18.53 | | | (23) $false
% 117.97/18.53 | | |
% 117.97/18.53 | | | CLOSE: (23) is inconsistent.
% 117.97/18.53 | | |
% 117.97/18.53 | | Case 2:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (24) ~ (all_40_1 = e0)
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (10), (24) imply:
% 117.97/18.53 | | | (25) ~ (all_6_1 = e0)
% 117.97/18.53 | | |
% 117.97/18.53 | | | GROUND_INST: instantiating (5) with all_52_6, all_6_1, e2, e1, simplifying
% 117.97/18.53 | | | with (11), (19) gives:
% 117.97/18.53 | | | (26) all_52_6 = all_6_1
% 117.97/18.53 | | |
% 117.97/18.53 | | | COMBINE_EQS: (7), (26) imply:
% 117.97/18.53 | | | (27) all_54_9 = all_6_1
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (18), (26) imply:
% 117.97/18.53 | | | (28) ~ (all_6_1 = e2)
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (21), (26) imply:
% 117.97/18.53 | | | (29) ~ (all_6_1 = e1)
% 117.97/18.53 | | |
% 117.97/18.53 | | | BETA: splitting (6) gives:
% 117.97/18.53 | | |
% 117.97/18.53 | | | Case 1:
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | (30) all_54_9 = e3
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | COMBINE_EQS: (27), (30) imply:
% 117.97/18.53 | | | | (31) all_6_1 = e3
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | REDUCE: (2), (31) imply:
% 117.97/18.53 | | | | (32) $false
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | CLOSE: (32) is inconsistent.
% 117.97/18.53 | | | |
% 117.97/18.53 | | | Case 2:
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | (33) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 | | | |
% 117.97/18.53 | | | | REF_CLOSE: (25), (27), (28), (29), (33) are inconsistent by sub-proof
% 117.97/18.53 | | | | #373.
% 117.97/18.53 | | | |
% 117.97/18.53 | | | End of split
% 117.97/18.53 | | |
% 117.97/18.53 | | End of split
% 117.97/18.53 | |
% 117.97/18.53 | Case 2:
% 117.97/18.53 | |
% 117.97/18.53 | | (34) ~ (all_56_14 = e2)
% 117.97/18.53 | |
% 117.97/18.53 | | REDUCE: (3), (34) imply:
% 117.97/18.53 | | (35) $false
% 117.97/18.53 | |
% 117.97/18.53 | | CLOSE: (35) is inconsistent.
% 117.97/18.53 | |
% 117.97/18.53 | End of split
% 117.97/18.53 |
% 117.97/18.53 End of proof
% 117.97/18.53
% 117.97/18.53 Sub-proof #373 shows that the following formulas are inconsistent:
% 117.97/18.53 ----------------------------------------------------------------
% 117.97/18.53 (1) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 (2) ~ (all_6_1 = e1)
% 117.97/18.53 (3) ~ (all_6_1 = e0)
% 117.97/18.53 (4) all_54_9 = all_6_1
% 117.97/18.53 (5) ~ (all_6_1 = e2)
% 117.97/18.53
% 117.97/18.53 Begin of proof
% 117.97/18.53 |
% 117.97/18.53 | BETA: splitting (1) gives:
% 117.97/18.53 |
% 117.97/18.53 | Case 1:
% 117.97/18.53 | |
% 117.97/18.53 | | (6) all_54_9 = e2
% 117.97/18.53 | |
% 117.97/18.53 | | COMBINE_EQS: (4), (6) imply:
% 117.97/18.53 | | (7) all_6_1 = e2
% 117.97/18.53 | |
% 117.97/18.53 | | REDUCE: (5), (7) imply:
% 117.97/18.53 | | (8) $false
% 117.97/18.53 | |
% 117.97/18.53 | | CLOSE: (8) is inconsistent.
% 117.97/18.53 | |
% 117.97/18.53 | Case 2:
% 117.97/18.53 | |
% 117.97/18.53 | | (9) all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 | |
% 117.97/18.53 | | BETA: splitting (9) gives:
% 117.97/18.53 | |
% 117.97/18.53 | | Case 1:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (10) all_54_9 = e1
% 117.97/18.53 | | |
% 117.97/18.53 | | | COMBINE_EQS: (4), (10) imply:
% 117.97/18.53 | | | (11) all_6_1 = e1
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (2), (11) imply:
% 117.97/18.53 | | | (12) $false
% 117.97/18.53 | | |
% 117.97/18.53 | | | CLOSE: (12) is inconsistent.
% 117.97/18.53 | | |
% 117.97/18.53 | | Case 2:
% 117.97/18.53 | | |
% 117.97/18.53 | | | (13) all_54_9 = e0
% 117.97/18.53 | | |
% 117.97/18.53 | | | COMBINE_EQS: (4), (13) imply:
% 117.97/18.53 | | | (14) all_6_1 = e0
% 117.97/18.53 | | |
% 117.97/18.53 | | | REDUCE: (3), (14) imply:
% 117.97/18.53 | | | (15) $false
% 117.97/18.53 | | |
% 117.97/18.53 | | | CLOSE: (15) is inconsistent.
% 117.97/18.53 | | |
% 117.97/18.53 | | End of split
% 117.97/18.53 | |
% 117.97/18.53 | End of split
% 117.97/18.53 |
% 117.97/18.53 End of proof
% 117.97/18.53
% 117.97/18.53 Sub-proof #374 shows that the following formulas are inconsistent:
% 117.97/18.53 ----------------------------------------------------------------
% 117.97/18.53 (1) ~ (all_52_2 = all_10_2)
% 117.97/18.53 (2) ~ (all_52_6 = all_52_14)
% 117.97/18.53 (3) all_58_7 = all_52_6
% 117.97/18.53 (4) ~ (all_4_2 = e0)
% 117.97/18.53 (5) all_56_14 = all_6_2
% 117.97/18.53 (6) all_54_0 = all_10_2
% 117.97/18.53 (7) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.97/18.53 (8) ~ (all_52_2 = all_52_6)
% 117.97/18.53 (9) op(e0, e2) = all_52_7
% 117.97/18.53 (10) all_56_11 = all_52_11
% 117.97/18.53 (11) ~ (all_6_1 = e3)
% 117.97/18.53 (12) ~ (e3 = e1)
% 117.97/18.53 (13) all_56_12 = all_10_2
% 117.97/18.53 (14) all_56_14 = e2
% 117.97/18.53 (15) op(all_6_1, all_6_2) = all_6_0
% 117.97/18.53 (16) all_54_11 = all_52_14
% 117.97/18.53 (17) all_54_13 = all_52_7
% 117.97/18.53 (18) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.53 (19) ~ (all_52_14 = all_6_2)
% 117.97/18.53 (20) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.97/18.53 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.53 (22) all_54_8 = all_52_2
% 117.97/18.53 (23) ~ (all_52_2 = all_6_2)
% 117.97/18.53 (24) ~ (all_52_4 = all_52_7)
% 117.97/18.53 (25) all_58_3 = all_8_2
% 117.97/18.53 (26) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 (27) all_54_9 = all_52_6
% 117.97/18.53 (28) ~ (all_6_0 = e3)
% 117.97/18.53 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.53 (30) all_56_9 = all_52_3
% 117.97/18.53 (31) op(e1, all_6_2) = all_6_1
% 117.97/18.53 (32) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.53 (33) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.97/18.53 (34) all_58_15 = all_4_2
% 117.97/18.53 (35) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.97/18.53 (36) all_58_13 = all_52_7
% 117.97/18.53 (37) ~ (all_6_0 = e2)
% 117.97/18.53 (38) all_58_1 = all_52_4
% 117.97/18.53 (39) all_58_14 = all_52_11
% 117.97/18.53 (40) all_56_13 = all_8_2
% 117.97/18.53 (41) ~ (all_8_2 = e2)
% 117.97/18.53 (42) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.97/18.53 (43) op(e1, e2) = all_52_6
% 117.97/18.53 (44) all_56_7 = all_52_6
% 117.97/18.53 (45) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.53 (46) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.53 (47) ~ (all_52_6 = all_6_2)
% 117.97/18.53 (48) all_56_6 = all_52_2
% 117.97/18.53 (49) all_58_12 = all_52_3
% 117.97/18.53 (50) ~ (all_52_2 = all_52_14)
% 117.97/18.53 (51) all_56_8 = all_52_14
% 117.97/18.53 (52) ~ (all_52_4 = all_10_2)
% 117.97/18.53 (53) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.97/18.53 (54) all_56_0 = all_52_4
% 117.97/18.53 (55) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.53 (56) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.53 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.53 (57) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.97/18.53 (58) ~ (all_6_2 = e1)
% 117.97/18.53 (59) ~ (all_52_6 = all_52_7)
% 117.97/18.53
% 117.97/18.53 Begin of proof
% 117.97/18.53 |
% 117.97/18.53 | COMBINE_EQS: (5), (14) imply:
% 117.97/18.53 | (60) all_6_2 = e2
% 117.97/18.53 |
% 117.97/18.53 | SIMP: (60) implies:
% 117.97/18.53 | (61) all_6_2 = e2
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (23), (61) imply:
% 117.97/18.53 | (62) ~ (all_52_2 = e2)
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (47), (61) imply:
% 117.97/18.53 | (63) ~ (all_52_6 = e2)
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (19), (61) imply:
% 117.97/18.53 | (64) ~ (all_52_14 = e2)
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (58), (61) imply:
% 117.97/18.53 | (65) ~ (e2 = e1)
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (15), (61) imply:
% 117.97/18.53 | (66) op(all_6_1, e2) = all_6_0
% 117.97/18.53 |
% 117.97/18.53 | REDUCE: (31), (61) imply:
% 117.97/18.53 | (67) op(e1, e2) = all_6_1
% 117.97/18.53 |
% 117.97/18.53 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.97/18.53 | (14), (16), (17), (18), (20), (21), (22), (24), (25), (26), (27),
% 117.97/18.53 | (28), (29), (30), (32), (33), (34), (35), (36), (37), (38), (39),
% 117.97/18.53 | (40), (41), (42), (43), (44), (45), (46), (48), (49), (50), (51),
% 117.97/18.53 | (52), (53), (54), (55), (56), (57), (59), (62), (63), (64), (65),
% 117.97/18.53 | (66), (67) are inconsistent by sub-proof #375.
% 117.97/18.53 |
% 117.97/18.53 End of proof
% 117.97/18.53
% 117.97/18.53 Sub-proof #375 shows that the following formulas are inconsistent:
% 117.97/18.53 ----------------------------------------------------------------
% 117.97/18.53 (1) ~ (all_52_2 = all_10_2)
% 117.97/18.53 (2) ~ (all_52_6 = all_52_14)
% 117.97/18.53 (3) all_58_7 = all_52_6
% 117.97/18.53 (4) ~ (all_4_2 = e0)
% 117.97/18.53 (5) all_54_0 = all_10_2
% 117.97/18.53 (6) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.97/18.53 (7) op(all_6_1, e2) = all_6_0
% 117.97/18.53 (8) ~ (all_52_2 = all_52_6)
% 117.97/18.53 (9) op(e0, e2) = all_52_7
% 117.97/18.53 (10) all_56_11 = all_52_11
% 117.97/18.53 (11) ~ (all_6_1 = e3)
% 117.97/18.53 (12) ~ (e3 = e1)
% 117.97/18.53 (13) all_56_12 = all_10_2
% 117.97/18.53 (14) all_56_14 = e2
% 117.97/18.53 (15) all_54_11 = all_52_14
% 117.97/18.53 (16) all_54_13 = all_52_7
% 117.97/18.53 (17) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.53 (18) ~ (all_56_7 = e1) | ~ (all_56_14 = e2)
% 117.97/18.53 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.53 (20) all_54_8 = all_52_2
% 117.97/18.53 (21) ~ (e2 = e1)
% 117.97/18.53 (22) ~ (all_52_4 = all_52_7)
% 117.97/18.53 (23) ~ (all_52_6 = e2)
% 117.97/18.53 (24) all_58_3 = all_8_2
% 117.97/18.53 (25) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.53 (26) all_54_9 = all_52_6
% 117.97/18.53 (27) ~ (all_6_0 = e3)
% 117.97/18.53 (28) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.53 (29) all_56_9 = all_52_3
% 117.97/18.53 (30) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.53 (31) ~ (all_56_6 = e1) | ~ (all_56_13 = e3)
% 117.97/18.53 (32) all_58_15 = all_4_2
% 117.97/18.53 (33) ~ (all_56_9 = e0) | ~ (all_56_13 = e3)
% 117.97/18.53 (34) op(e1, e2) = all_6_1
% 117.97/18.53 (35) all_58_13 = all_52_7
% 117.97/18.53 (36) ~ (all_6_0 = e2)
% 117.97/18.53 (37) all_58_1 = all_52_4
% 117.97/18.53 (38) all_58_14 = all_52_11
% 117.97/18.53 (39) all_56_13 = all_8_2
% 117.97/18.53 (40) ~ (all_8_2 = e2)
% 117.97/18.53 (41) all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.97/18.53 (42) ~ (all_52_14 = e2)
% 117.97/18.53 (43) op(e1, e2) = all_52_6
% 117.97/18.53 (44) all_56_7 = all_52_6
% 117.97/18.53 (45) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.53 (46) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.53 (47) all_56_6 = all_52_2
% 117.97/18.53 (48) all_58_12 = all_52_3
% 117.97/18.53 (49) ~ (all_52_2 = all_52_14)
% 117.97/18.53 (50) all_56_8 = all_52_14
% 117.97/18.53 (51) ~ (all_52_4 = all_10_2)
% 117.97/18.53 (52) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.97/18.53 (53) all_56_0 = all_52_4
% 117.97/18.53 (54) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.53 (55) ~ (all_52_2 = e2)
% 117.97/18.53 (56) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.53 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.54 (57) ~ (all_56_0 = e3) | ~ (all_56_14 = e2)
% 117.97/18.54 (58) ~ (all_52_6 = all_52_7)
% 117.97/18.54
% 117.97/18.54 Begin of proof
% 117.97/18.54 |
% 117.97/18.54 | BETA: splitting (57) gives:
% 117.97/18.54 |
% 117.97/18.54 | Case 1:
% 117.97/18.54 | |
% 117.97/18.54 | | (59) ~ (all_56_0 = e3)
% 117.97/18.54 | |
% 117.97/18.54 | | REDUCE: (53), (59) imply:
% 117.97/18.54 | | (60) ~ (all_52_4 = e3)
% 117.97/18.54 | |
% 117.97/18.54 | | BETA: splitting (18) gives:
% 117.97/18.54 | |
% 117.97/18.54 | | Case 1:
% 117.97/18.54 | | |
% 117.97/18.54 | | | (61) ~ (all_56_7 = e1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (44), (61) imply:
% 117.97/18.54 | | | (62) ~ (all_52_6 = e1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | GROUND_INST: instantiating (19) with all_52_6, all_6_1, e2, e1,
% 117.97/18.54 | | | simplifying with (34), (43) gives:
% 117.97/18.54 | | | (63) all_52_6 = all_6_1
% 117.97/18.54 | | |
% 117.97/18.54 | | | COMBINE_EQS: (26), (63) imply:
% 117.97/18.54 | | | (64) all_54_9 = all_6_1
% 117.97/18.54 | | |
% 117.97/18.54 | | | COMBINE_EQS: (3), (63) imply:
% 117.97/18.54 | | | (65) all_58_7 = all_6_1
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (8), (63) imply:
% 117.97/18.54 | | | (66) ~ (all_52_2 = all_6_1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (58), (63) imply:
% 117.97/18.54 | | | (67) ~ (all_52_7 = all_6_1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | SIMP: (67) implies:
% 117.97/18.54 | | | (68) ~ (all_52_7 = all_6_1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (2), (63) imply:
% 117.97/18.54 | | | (69) ~ (all_52_14 = all_6_1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | SIMP: (69) implies:
% 117.97/18.54 | | | (70) ~ (all_52_14 = all_6_1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (23), (63) imply:
% 117.97/18.54 | | | (71) ~ (all_6_1 = e2)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (62), (63) imply:
% 117.97/18.54 | | | (72) ~ (all_6_1 = e1)
% 117.97/18.54 | | |
% 117.97/18.54 | | | BETA: splitting (25) gives:
% 117.97/18.54 | | |
% 117.97/18.54 | | | Case 1:
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | (73) all_54_9 = e3
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | COMBINE_EQS: (64), (73) imply:
% 117.97/18.54 | | | | (74) all_6_1 = e3
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | REDUCE: (11), (74) imply:
% 117.97/18.54 | | | | (75) $false
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | CLOSE: (75) is inconsistent.
% 117.97/18.54 | | | |
% 117.97/18.54 | | | Case 2:
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | (76) ~ (all_54_9 = e3)
% 117.97/18.54 | | | | (77) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | BETA: splitting (77) gives:
% 117.97/18.54 | | | |
% 117.97/18.54 | | | | Case 1:
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | (78) all_54_9 = e2
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | COMBINE_EQS: (64), (78) imply:
% 117.97/18.54 | | | | | (79) all_6_1 = e2
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | REDUCE: (71), (79) imply:
% 117.97/18.54 | | | | | (80) $false
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | CLOSE: (80) is inconsistent.
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | Case 2:
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | (81) ~ (all_54_9 = e2)
% 117.97/18.54 | | | | | (82) all_54_9 = e1 | all_54_9 = e0
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | BETA: splitting (82) gives:
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | | Case 1:
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | (83) all_54_9 = e1
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | COMBINE_EQS: (64), (83) imply:
% 117.97/18.54 | | | | | | (84) all_6_1 = e1
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (72), (84) imply:
% 117.97/18.54 | | | | | | (85) $false
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | CLOSE: (85) is inconsistent.
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | Case 2:
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | (86) all_54_9 = e0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | COMBINE_EQS: (64), (86) imply:
% 117.97/18.54 | | | | | | (87) all_6_1 = e0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | COMBINE_EQS: (65), (87) imply:
% 117.97/18.54 | | | | | | (88) all_58_7 = e0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (66), (87) imply:
% 117.97/18.54 | | | | | | (89) ~ (all_52_2 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (68), (87) imply:
% 117.97/18.54 | | | | | | (90) ~ (all_52_7 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (70), (87) imply:
% 117.97/18.54 | | | | | | (91) ~ (all_52_14 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (11), (87) imply:
% 117.97/18.54 | | | | | | (92) ~ (e3 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | SIMP: (92) implies:
% 117.97/18.54 | | | | | | (93) ~ (e3 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (71), (87) imply:
% 117.97/18.54 | | | | | | (94) ~ (e2 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | SIMP: (94) implies:
% 117.97/18.54 | | | | | | (95) ~ (e2 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (72), (87) imply:
% 117.97/18.54 | | | | | | (96) ~ (e1 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | SIMP: (96) implies:
% 117.97/18.54 | | | | | | (97) ~ (e1 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (7), (87) imply:
% 117.97/18.54 | | | | | | (98) op(e0, e2) = all_6_0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | GROUND_INST: instantiating (19) with all_52_7, all_6_0, e2, e0,
% 117.97/18.54 | | | | | | simplifying with (9), (98) gives:
% 117.97/18.54 | | | | | | (99) all_52_7 = all_6_0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | COMBINE_EQS: (16), (99) imply:
% 117.97/18.54 | | | | | | (100) all_54_13 = all_6_0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | COMBINE_EQS: (35), (99) imply:
% 117.97/18.54 | | | | | | (101) all_58_13 = all_6_0
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (22), (99) imply:
% 117.97/18.54 | | | | | | (102) ~ (all_52_4 = all_6_0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | REDUCE: (90), (99) imply:
% 117.97/18.54 | | | | | | (103) ~ (all_6_0 = e0)
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | BETA: splitting (17) gives:
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | | Case 1:
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | (104) all_58_1 = e2
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | COMBINE_EQS: (37), (104) imply:
% 117.97/18.54 | | | | | | | (105) all_52_4 = e2
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | REDUCE: (51), (105) imply:
% 117.97/18.54 | | | | | | | (106) ~ (all_10_2 = e2)
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | SIMP: (106) implies:
% 117.97/18.54 | | | | | | | (107) ~ (all_10_2 = e2)
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | REDUCE: (102), (105) imply:
% 117.97/18.54 | | | | | | | (108) ~ (all_6_0 = e2)
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | REDUCE: (60), (105) imply:
% 117.97/18.54 | | | | | | | (109) ~ (e3 = e2)
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | SIMP: (109) implies:
% 117.97/18.54 | | | | | | | (110) ~ (e3 = e2)
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | BETA: splitting (41) gives:
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | (111) all_58_1 = e3
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | REF_CLOSE: (104), (110), (111) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | #390.
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | (112) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | BETA: splitting (112) gives:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | (113) all_58_3 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | COMBINE_EQS: (24), (113) imply:
% 117.97/18.54 | | | | | | | | | (114) all_8_2 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | COMBINE_EQS: (39), (114) imply:
% 117.97/18.54 | | | | | | | | | (115) all_56_13 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | BETA: splitting (31) gives:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | (116) ~ (all_56_6 = e1)
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | REDUCE: (47), (116) imply:
% 117.97/18.54 | | | | | | | | | | (117) ~ (all_52_2 = e1)
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | BETA: splitting (28) gives:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | (118) all_54_8 = e3
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | COMBINE_EQS: (20), (118) imply:
% 117.97/18.54 | | | | | | | | | | | (119) all_52_2 = e3
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | SIMP: (119) implies:
% 117.97/18.54 | | | | | | | | | | | (120) all_52_2 = e3
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | REDUCE: (49), (120) imply:
% 117.97/18.54 | | | | | | | | | | | (121) ~ (all_52_14 = e3)
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | SIMP: (121) implies:
% 117.97/18.54 | | | | | | | | | | | (122) ~ (all_52_14 = e3)
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | REDUCE: (1), (120) imply:
% 117.97/18.54 | | | | | | | | | | | (123) ~ (all_10_2 = e3)
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | SIMP: (123) implies:
% 117.97/18.54 | | | | | | | | | | | (124) ~ (all_10_2 = e3)
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | BETA: splitting (54) gives:
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | (125) all_58_1 = e1
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | COMBINE_EQS: (104), (125) imply:
% 117.97/18.54 | | | | | | | | | | | | (126) e2 = e1
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | REDUCE: (21), (126) imply:
% 117.97/18.54 | | | | | | | | | | | | (127) $false
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | (128) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | BETA: splitting (33) gives:
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | (129) ~ (all_56_13 = e3)
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | REDUCE: (115), (129) imply:
% 117.97/18.54 | | | | | | | | | | | | | (130) $false
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | CLOSE: (130) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | (131) ~ (all_56_9 = e0)
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | REDUCE: (29), (131) imply:
% 117.97/18.54 | | | | | | | | | | | | | (132) ~ (all_52_3 = e0)
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | BETA: splitting (128) gives:
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | (133) all_58_3 = e1
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | COMBINE_EQS: (113), (133) imply:
% 117.97/18.54 | | | | | | | | | | | | | | (134) e3 = e1
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | REDUCE: (12), (134) imply:
% 117.97/18.54 | | | | | | | | | | | | | | (135) $false
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | (136) all_58_7 = e1 | all_58_13 = e1
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | (137) all_58_7 = e1
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | REF_CLOSE: (88), (97), (137) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | | | | | | | | #389.
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | (138) all_58_13 = e1
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | COMBINE_EQS: (101), (138) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | (139) all_6_0 = e1
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | (140) all_58_15 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (140) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | (141) all_4_2 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | REDUCE: (4), (141) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | (142) $false
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | (143) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 117.97/18.54 | | | | | | | | | | | | | | | | & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 117.97/18.54 | | | | | | | | | | | | | | | | e0)
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 117.97/18.54 | | | | | | | | | | | | | | | | (144) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | (145) all_58_12 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (145) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | (146) all_52_3 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | REDUCE: (132), (146) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | (147) $false
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | (148) all_58_13 = e0 | all_58_14 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | (149) all_54_11 = e3
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (122), (149) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | | | | | | | | | | | #388.
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | (150) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | (151) all_54_11 = e2
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (42), (151) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | #387.
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | (152) all_54_11 = e1 | all_54_11 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (153) all_58_13 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (153) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (154) e1 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (154) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (155) $false
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (156) all_58_14 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (156) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (157) all_52_11 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (157) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | (158) all_56_11 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | (159) ~ (all_56_12 = e1)
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (159) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | (160) ~ (all_10_2 = e1)
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | (161) all_54_0 = e3
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (124), (161) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | #451.
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | (162) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (15), (30), (50), (91), (107), (152),
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | | (160), (162) are inconsistent by sub-proof #383.
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | (163) ~ (all_56_11 = e0)
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (163) imply:
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | (164) $false
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | (165) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | REF_CLOSE: (20), (55), (89), (117), (165) are inconsistent by
% 117.97/18.54 | | | | | | | | | | | sub-proof #381.
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | (166) ~ (all_56_13 = e3)
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | REDUCE: (115), (166) imply:
% 117.97/18.54 | | | | | | | | | | (167) $false
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | CLOSE: (167) is inconsistent.
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | (168) all_58_7 = e3 | all_58_13 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | REF_CLOSE: (6), (12), (27), (36), (88), (93), (100), (101),
% 117.97/18.54 | | | | | | | | | (103), (168) are inconsistent by sub-proof #377.
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | End of split
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | End of split
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | Case 2:
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | (169) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | BETA: splitting (41) gives:
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | (170) all_58_1 = e3
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | COMBINE_EQS: (37), (170) imply:
% 117.97/18.54 | | | | | | | | (171) all_52_4 = e3
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | REDUCE: (60), (171) imply:
% 117.97/18.54 | | | | | | | | (172) $false
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | CLOSE: (172) is inconsistent.
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | (173) all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | BETA: splitting (173) gives:
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | (174) all_58_3 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | COMBINE_EQS: (24), (174) imply:
% 117.97/18.54 | | | | | | | | | (175) all_8_2 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | REDUCE: (40), (175) imply:
% 117.97/18.54 | | | | | | | | | (176) ~ (e3 = e2)
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | BETA: splitting (169) gives:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | (177) all_58_3 = e2
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | COMBINE_EQS: (174), (177) imply:
% 117.97/18.54 | | | | | | | | | | (178) e3 = e2
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | REDUCE: (176), (178) imply:
% 117.97/18.54 | | | | | | | | | | (179) $false
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | CLOSE: (179) is inconsistent.
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | (180) all_58_7 = e2 | all_58_13 = e2
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | BETA: splitting (180) gives:
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | Case 1:
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | (181) all_58_7 = e2
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | REF_CLOSE: (88), (95), (181) are inconsistent by sub-proof
% 117.97/18.54 | | | | | | | | | | | #376.
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | (182) all_58_13 = e2
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | COMBINE_EQS: (101), (182) imply:
% 117.97/18.54 | | | | | | | | | | | (183) all_6_0 = e2
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | REDUCE: (36), (183) imply:
% 117.97/18.54 | | | | | | | | | | | (184) $false
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 117.97/18.54 | | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | | |
% 117.97/18.54 | | | | | | | | | End of split
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | Case 2:
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | (185) all_58_7 = e3 | all_58_13 = e3
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | | REF_CLOSE: (6), (12), (27), (36), (88), (93), (100), (101),
% 117.97/18.54 | | | | | | | | | (103), (185) are inconsistent by sub-proof #377.
% 117.97/18.54 | | | | | | | | |
% 117.97/18.54 | | | | | | | | End of split
% 117.97/18.54 | | | | | | | |
% 117.97/18.54 | | | | | | | End of split
% 117.97/18.54 | | | | | | |
% 117.97/18.54 | | | | | | End of split
% 117.97/18.54 | | | | | |
% 117.97/18.54 | | | | | End of split
% 117.97/18.54 | | | | |
% 117.97/18.54 | | | | End of split
% 117.97/18.54 | | | |
% 117.97/18.54 | | | End of split
% 117.97/18.54 | | |
% 117.97/18.54 | | Case 2:
% 117.97/18.54 | | |
% 117.97/18.54 | | | (186) ~ (all_56_14 = e2)
% 117.97/18.54 | | |
% 117.97/18.54 | | | REDUCE: (14), (186) imply:
% 117.97/18.54 | | | (187) $false
% 117.97/18.54 | | |
% 117.97/18.54 | | | CLOSE: (187) is inconsistent.
% 117.97/18.54 | | |
% 117.97/18.54 | | End of split
% 117.97/18.54 | |
% 117.97/18.54 | Case 2:
% 117.97/18.54 | |
% 117.97/18.54 | | (188) ~ (all_56_14 = e2)
% 117.97/18.54 | |
% 117.97/18.54 | | REDUCE: (14), (188) imply:
% 117.97/18.54 | | (189) $false
% 117.97/18.54 | |
% 117.97/18.54 | | CLOSE: (189) is inconsistent.
% 117.97/18.54 | |
% 117.97/18.54 | End of split
% 117.97/18.54 |
% 117.97/18.54 End of proof
% 117.97/18.54
% 117.97/18.54 Sub-proof #376 shows that the following formulas are inconsistent:
% 117.97/18.54 ----------------------------------------------------------------
% 117.97/18.54 (1) all_58_7 = e2
% 117.97/18.54 (2) all_58_7 = e0
% 117.97/18.54 (3) ~ (e2 = e0)
% 117.97/18.54
% 117.97/18.54 Begin of proof
% 117.97/18.54 |
% 117.97/18.54 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.54 | (4) e2 = e0
% 117.97/18.54 |
% 117.97/18.54 | SIMP: (4) implies:
% 117.97/18.54 | (5) e2 = e0
% 117.97/18.54 |
% 117.97/18.54 | REDUCE: (3), (5) imply:
% 117.97/18.54 | (6) $false
% 117.97/18.54 |
% 117.97/18.54 | CLOSE: (6) is inconsistent.
% 117.97/18.54 |
% 117.97/18.54 End of proof
% 117.97/18.54
% 117.97/18.54 Sub-proof #377 shows that the following formulas are inconsistent:
% 117.97/18.54 ----------------------------------------------------------------
% 117.97/18.54 (1) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.97/18.54 (2) ~ (e3 = e1)
% 117.97/18.54 (3) all_54_13 = all_6_0
% 117.97/18.54 (4) ~ (e3 = e0)
% 117.97/18.54 (5) ~ (all_6_0 = e3)
% 117.97/18.54 (6) ~ (all_6_0 = e0)
% 117.97/18.54 (7) ~ (all_6_0 = e2)
% 117.97/18.54 (8) all_58_7 = e0
% 117.97/18.54 (9) all_58_13 = all_6_0
% 117.97/18.54 (10) all_58_7 = e3 | all_58_13 = e3
% 117.97/18.54
% 117.97/18.54 Begin of proof
% 117.97/18.54 |
% 117.97/18.54 | BETA: splitting (1) gives:
% 117.97/18.54 |
% 117.97/18.54 | Case 1:
% 117.97/18.54 | |
% 117.97/18.54 | | (11) all_54_13 = e3
% 117.97/18.54 | |
% 117.97/18.54 | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #380.
% 117.97/18.54 | |
% 117.97/18.54 | Case 2:
% 117.97/18.54 | |
% 117.97/18.55 | | (12) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 117.97/18.55 | |
% 117.97/18.55 | | BETA: splitting (12) gives:
% 117.97/18.55 | |
% 117.97/18.55 | | Case 1:
% 117.97/18.55 | | |
% 117.97/18.55 | | | (13) all_54_13 = e2
% 117.97/18.55 | | |
% 117.97/18.55 | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #379.
% 117.97/18.55 | | |
% 117.97/18.55 | | Case 2:
% 117.97/18.55 | | |
% 117.97/18.55 | | | (14) all_54_13 = e1 | all_54_13 = e0
% 117.97/18.55 | | |
% 117.97/18.55 | | | BETA: splitting (14) gives:
% 117.97/18.55 | | |
% 117.97/18.55 | | | Case 1:
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | (15) all_54_13 = e1
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | COMBINE_EQS: (3), (15) imply:
% 117.97/18.55 | | | | (16) all_6_0 = e1
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | SIMP: (16) implies:
% 117.97/18.55 | | | | (17) all_6_0 = e1
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | COMBINE_EQS: (9), (17) imply:
% 117.97/18.55 | | | | (18) all_58_13 = e1
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | BETA: splitting (10) gives:
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | Case 1:
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | (19) all_58_7 = e3
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | COMBINE_EQS: (8), (19) imply:
% 117.97/18.55 | | | | | (20) e3 = e0
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | SIMP: (20) implies:
% 117.97/18.55 | | | | | (21) e3 = e0
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | REDUCE: (4), (21) imply:
% 117.97/18.55 | | | | | (22) $false
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | CLOSE: (22) is inconsistent.
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | Case 2:
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | (23) all_58_13 = e3
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | COMBINE_EQS: (18), (23) imply:
% 117.97/18.55 | | | | | (24) e3 = e1
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | SIMP: (24) implies:
% 117.97/18.55 | | | | | (25) e3 = e1
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | REDUCE: (2), (25) imply:
% 117.97/18.55 | | | | | (26) $false
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | | CLOSE: (26) is inconsistent.
% 117.97/18.55 | | | | |
% 117.97/18.55 | | | | End of split
% 117.97/18.55 | | | |
% 117.97/18.55 | | | Case 2:
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | (27) all_54_13 = e0
% 117.97/18.55 | | | |
% 117.97/18.55 | | | | REF_CLOSE: (3), (6), (27) are inconsistent by sub-proof #378.
% 117.97/18.55 | | | |
% 117.97/18.55 | | | End of split
% 117.97/18.55 | | |
% 117.97/18.55 | | End of split
% 117.97/18.55 | |
% 117.97/18.55 | End of split
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #378 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_13 = all_6_0
% 117.97/18.55 (2) all_54_13 = e0
% 117.97/18.55 (3) ~ (all_6_0 = e0)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_6_0 = e0
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_6_0 = e0
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #379 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_13 = all_6_0
% 117.97/18.55 (2) all_54_13 = e2
% 117.97/18.55 (3) ~ (all_6_0 = e2)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_6_0 = e2
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_6_0 = e2
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #380 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_13 = all_6_0
% 117.97/18.55 (2) all_54_13 = e3
% 117.97/18.55 (3) ~ (all_6_0 = e3)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_6_0 = e3
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_6_0 = e3
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #381 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) ~ (all_52_2 = e0)
% 117.97/18.55 (2) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.55 (3) all_54_8 = all_52_2
% 117.97/18.55 (4) ~ (all_52_2 = e1)
% 117.97/18.55 (5) ~ (all_52_2 = e2)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | BETA: splitting (2) gives:
% 117.97/18.55 |
% 117.97/18.55 | Case 1:
% 117.97/18.55 | |
% 117.97/18.55 | | (6) all_54_8 = e2
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #382.
% 117.97/18.55 | |
% 117.97/18.55 | Case 2:
% 117.97/18.55 | |
% 117.97/18.55 | | (7) all_54_8 = e1 | all_54_8 = e0
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #396.
% 117.97/18.55 | |
% 117.97/18.55 | End of split
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #382 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_8 = all_52_2
% 117.97/18.55 (2) all_54_8 = e2
% 117.97/18.55 (3) ~ (all_52_2 = e2)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_52_2 = e2
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_52_2 = e2
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #383 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_0 = all_10_2
% 117.97/18.55 (2) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.55 (3) ~ (all_52_14 = e0)
% 117.97/18.55 (4) all_56_12 = all_10_2
% 117.97/18.55 (5) all_54_11 = all_52_14
% 117.97/18.55 (6) ~ (all_10_2 = e2)
% 117.97/18.55 (7) all_54_11 = e1 | all_54_11 = e0
% 117.97/18.55 (8) ~ (all_10_2 = e1)
% 117.97/18.55 (9) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.55 (10) all_56_8 = all_52_14
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | BETA: splitting (7) gives:
% 117.97/18.55 |
% 117.97/18.55 | Case 1:
% 117.97/18.55 | |
% 117.97/18.55 | | (11) all_54_11 = e1
% 117.97/18.55 | |
% 117.97/18.55 | | COMBINE_EQS: (5), (11) imply:
% 117.97/18.55 | | (12) all_52_14 = e1
% 117.97/18.55 | |
% 117.97/18.55 | | SIMP: (12) implies:
% 117.97/18.55 | | (13) all_52_14 = e1
% 117.97/18.55 | |
% 117.97/18.55 | | COMBINE_EQS: (10), (13) imply:
% 117.97/18.55 | | (14) all_56_8 = e1
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (14) are inconsistent by sub-proof
% 117.97/18.55 | | #385.
% 117.97/18.55 | |
% 117.97/18.55 | Case 2:
% 117.97/18.55 | |
% 117.97/18.55 | | (15) all_54_11 = e0
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #384.
% 117.97/18.55 | |
% 117.97/18.55 | End of split
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #384 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_11 = all_52_14
% 117.97/18.55 (2) all_54_11 = e0
% 117.97/18.55 (3) ~ (all_52_14 = e0)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_52_14 = e0
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_52_14 = e0
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #385 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_0 = all_10_2
% 117.97/18.55 (2) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.55 (3) all_56_12 = all_10_2
% 117.97/18.55 (4) all_56_8 = e1
% 117.97/18.55 (5) ~ (all_10_2 = e2)
% 117.97/18.55 (6) ~ (all_10_2 = e1)
% 117.97/18.55 (7) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | BETA: splitting (7) gives:
% 117.97/18.55 |
% 117.97/18.55 | Case 1:
% 117.97/18.55 | |
% 117.97/18.55 | | (8) ~ (all_56_8 = e1)
% 117.97/18.55 | |
% 117.97/18.55 | | REDUCE: (4), (8) imply:
% 117.97/18.55 | | (9) $false
% 117.97/18.55 | |
% 117.97/18.55 | | CLOSE: (9) is inconsistent.
% 117.97/18.55 | |
% 117.97/18.55 | Case 2:
% 117.97/18.55 | |
% 117.97/18.55 | | (10) ~ (all_56_12 = e0)
% 117.97/18.55 | |
% 117.97/18.55 | | REDUCE: (3), (10) imply:
% 117.97/18.55 | | (11) ~ (all_10_2 = e0)
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #386.
% 117.97/18.55 | |
% 117.97/18.55 | End of split
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #386 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_0 = all_10_2
% 117.97/18.55 (2) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.55 (3) ~ (all_10_2 = e2)
% 117.97/18.55 (4) ~ (all_10_2 = e1)
% 117.97/18.55 (5) ~ (all_10_2 = e0)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | BETA: splitting (2) gives:
% 117.97/18.55 |
% 117.97/18.55 | Case 1:
% 117.97/18.55 | |
% 117.97/18.55 | | (6) all_54_0 = e2
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #450.
% 117.97/18.55 | |
% 117.97/18.55 | Case 2:
% 117.97/18.55 | |
% 117.97/18.55 | | (7) all_54_0 = e1 | all_54_0 = e0
% 117.97/18.55 | |
% 117.97/18.55 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #423.
% 117.97/18.55 | |
% 117.97/18.55 | End of split
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #387 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_11 = all_52_14
% 117.97/18.55 (2) all_54_11 = e2
% 117.97/18.55 (3) ~ (all_52_14 = e2)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_52_14 = e2
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_52_14 = e2
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #388 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_54_11 = all_52_14
% 117.97/18.55 (2) all_54_11 = e3
% 117.97/18.55 (3) ~ (all_52_14 = e3)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) all_52_14 = e3
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) all_52_14 = e3
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #389 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_58_7 = e1
% 117.97/18.55 (2) all_58_7 = e0
% 117.97/18.55 (3) ~ (e1 = e0)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) e1 = e0
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) e1 = e0
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #390 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) all_58_1 = e3
% 117.97/18.55 (2) all_58_1 = e2
% 117.97/18.55 (3) ~ (e3 = e2)
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.55 | (4) e3 = e2
% 117.97/18.55 |
% 117.97/18.55 | SIMP: (4) implies:
% 117.97/18.55 | (5) e3 = e2
% 117.97/18.55 |
% 117.97/18.55 | REDUCE: (3), (5) imply:
% 117.97/18.55 | (6) $false
% 117.97/18.55 |
% 117.97/18.55 | CLOSE: (6) is inconsistent.
% 117.97/18.55 |
% 117.97/18.55 End of proof
% 117.97/18.55
% 117.97/18.55 Sub-proof #391 shows that the following formulas are inconsistent:
% 117.97/18.55 ----------------------------------------------------------------
% 117.97/18.55 (1) ~ (all_52_8 = all_10_2)
% 117.97/18.55 (2) ~ (all_56_2 = e3) | ~ (all_56_12 = e0)
% 117.97/18.55 (3) all_58_7 = all_52_6
% 117.97/18.55 (4) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.97/18.55 (5) ~ (all_52_13 = all_52_14)
% 117.97/18.55 (6) ~ (all_4_2 = e0)
% 117.97/18.55 (7) op(e3, e2) = all_52_4
% 117.97/18.55 (8) all_56_14 = all_6_2
% 117.97/18.55 (9) all_56_3 = all_52_1
% 117.97/18.55 (10) all_54_0 = all_10_2
% 117.97/18.55 (11) all_54_3 = all_52_12
% 117.97/18.55 (12) op(e0, e2) = all_52_7
% 117.97/18.55 (13) all_56_11 = all_52_11
% 117.97/18.55 (14) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.55 (15) ~ (all_6_1 = e3)
% 117.97/18.55 (16) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.97/18.55 (17) ~ (all_52_12 = all_10_2)
% 117.97/18.55 (18) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.55 (19) all_56_12 = all_10_2
% 117.97/18.55 (20) all_58_0 = all_10_2
% 117.97/18.55 (21) all_54_11 = all_52_14
% 117.97/18.55 (22) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.55 (23) ~ (all_52_14 = all_6_2)
% 117.97/18.55 (24) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.97/18.55 (25) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.55 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.55 (27) all_54_8 = all_52_2
% 117.97/18.55 (28) ~ (all_52_2 = all_6_2)
% 117.97/18.55 (29) all_54_10 = all_6_2
% 117.97/18.55 (30) op(e3, e0) = all_52_12
% 117.97/18.55 (31) ~ (all_52_8 = all_6_2)
% 117.97/18.55 (32) all_58_4 = all_52_8
% 117.97/18.55 (33) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.55 (34) ~ (all_52_4 = all_52_7)
% 117.97/18.55 (35) all_56_2 = all_52_12
% 117.97/18.55 (36) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.97/18.55 (37) all_58_3 = all_8_2
% 117.97/18.55 (38) ~ (all_10_0 = e2)
% 117.97/18.55 (39) all_58_11 = all_52_14
% 117.97/18.55 (40) op(e3, e1) = all_52_8
% 117.97/18.55 (41) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.55 (42) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.55 (43) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.55 (44) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.55 (45) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.55 (46) op(e1, e0) = all_52_14
% 117.97/18.55 (47) all_58_5 = all_52_9
% 117.97/18.55 (48) all_56_9 = all_52_3
% 117.97/18.55 (49) ~ (all_56_11 = e0) | ~ (all_56_15 = e1)
% 117.97/18.55 (50) op(e1, all_6_2) = all_6_1
% 117.97/18.55 (51) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.55 (52) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.55 (53) all_58_15 = all_4_2
% 117.97/18.55 (54) all_58_2 = all_52_1
% 117.97/18.55 (55) ~ (all_56_4 = e2) | ~ (all_56_12 = e1)
% 117.97/18.55 (56) ~ (all_10_2 = e3)
% 117.97/18.55 (57) all_58_13 = all_52_7
% 117.97/18.55 (58) ~ (all_52_14 = all_4_2)
% 117.97/18.55 (59) all_58_6 = all_52_2
% 117.97/18.55 (60) ~ (all_52_1 = all_10_2)
% 117.97/18.55 (61) all_56_15 = all_4_2
% 117.97/18.55 (62) all_58_10 = all_52_13
% 117.97/18.55 (63) ~ (all_52_11 = all_4_2)
% 117.97/18.55 (64) op(e3, all_10_2) = all_10_1
% 117.97/18.55 (65) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.97/18.55 (66) ~ (all_56_0 = e3) | ~ (all_56_15 = e2)
% 117.97/18.55 (67) ~ (all_10_1 = e2)
% 117.97/18.55 (68) all_58_1 = all_52_4
% 117.97/18.55 (69) all_58_14 = all_52_11
% 117.97/18.55 (70) all_54_1 = all_52_4
% 117.97/18.55 (71) all_56_13 = all_8_2
% 117.97/18.55 (72) ~ (all_8_2 = e2)
% 117.97/18.55 (73) ~ (all_6_2 = e2)
% 117.97/18.55 (74) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.55 (75) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.55 (76) all_56_7 = all_52_6
% 117.97/18.55 (77) all_58_8 = all_6_2
% 117.97/18.55 (78) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.55 (79) ~ (all_10_0 = e1)
% 117.97/18.55 (80) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 117.97/18.55 (81) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.55 (82) all_56_4 = all_52_9
% 117.97/18.55 (83) all_58_9 = all_52_12
% 117.97/18.55 (84) all_56_5 = all_52_13
% 117.97/18.55 (85) ~ (all_52_3 = all_4_2)
% 117.97/18.55 (86) ~ (all_52_6 = all_6_2)
% 117.97/18.55 (87) all_56_6 = all_52_2
% 117.97/18.55 (88) all_58_12 = all_52_3
% 117.97/18.55 (89) ~ (all_52_2 = all_52_14)
% 117.97/18.55 (90) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.97/18.55 (91) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.55 (92) ~ (all_52_12 = all_4_2)
% 117.97/18.55 (93) ~ (all_52_3 = all_10_2)
% 117.97/18.55 (94) op(e1, e3) = all_52_2
% 117.97/18.55 (95) ~ (all_56_10 = e0) | ~ (all_56_15 = e2)
% 117.97/18.55 (96) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.55 (97) all_56_8 = all_52_14
% 117.97/18.55 (98) ~ (all_52_4 = all_10_2)
% 117.97/18.55 (99) ~ (all_10_1 = e1)
% 117.97/18.55 (100) ~ (all_56_11 = e0) | ~ (all_56_12 = e1)
% 117.97/18.55 (101) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.55 (102) all_56_0 = all_52_4
% 117.97/18.55 (103) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.55 (104) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.55 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.55 (105) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.55 (106) all_54_15 = all_4_2
% 117.97/18.55 (107) ~ (all_6_2 = e1)
% 117.97/18.55 (108) ~ (all_6_1 = e2)
% 117.97/18.55 (109) ~ (all_52_3 = all_52_11)
% 117.97/18.55 (110) all_54_12 = all_52_3
% 117.97/18.55
% 117.97/18.55 Begin of proof
% 117.97/18.55 |
% 117.97/18.55 | BETA: splitting (49) gives:
% 117.97/18.55 |
% 117.97/18.55 | Case 1:
% 117.97/18.55 | |
% 117.97/18.55 | | (111) ~ (all_56_15 = e1)
% 117.97/18.55 | |
% 117.97/18.55 | | REDUCE: (61), (111) imply:
% 117.97/18.55 | | (112) ~ (all_4_2 = e1)
% 117.97/18.55 | |
% 117.97/18.55 | | BETA: splitting (100) gives:
% 117.97/18.55 | |
% 117.97/18.55 | | Case 1:
% 117.97/18.55 | | |
% 117.97/18.55 | | | (113) ~ (all_56_12 = e1)
% 117.97/18.55 | | |
% 117.97/18.55 | | | REDUCE: (19), (113) imply:
% 117.97/18.56 | | | (114) ~ (all_10_2 = e1)
% 117.97/18.56 | | |
% 117.97/18.56 | | | BETA: splitting (95) gives:
% 117.97/18.56 | | |
% 117.97/18.56 | | | Case 1:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (115) ~ (all_56_15 = e2)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (61), (115) imply:
% 117.97/18.56 | | | | (116) ~ (all_4_2 = e2)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (13), (16), (17),
% 117.97/18.56 | | | | (18), (19), (22), (23), (25), (26), (29), (30), (33), (34),
% 117.97/18.56 | | | | (37), (38), (39), (41), (42), (43), (44), (47), (48), (51),
% 117.97/18.56 | | | | (52), (53), (54), (56), (57), (59), (60), (61), (62), (64),
% 117.97/18.56 | | | | (67), (68), (69), (70), (71), (72), (74), (75), (76), (77),
% 117.97/18.56 | | | | (78), (79), (82), (84), (86), (87), (88), (92), (97), (98),
% 117.97/18.56 | | | | (99), (101), (102), (103), (104), (105), (106), (107), (112),
% 117.97/18.56 | | | | (114), (116) are inconsistent by sub-proof #416.
% 117.97/18.56 | | | |
% 117.97/18.56 | | | Case 2:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (117) all_56_15 = e2
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | BETA: splitting (66) gives:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | Case 1:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | (118) ~ (all_56_0 = e3)
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | REDUCE: (102), (118) imply:
% 117.97/18.56 | | | | | (119) ~ (all_52_4 = e3)
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | BETA: splitting (2) gives:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | Case 1:
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | (120) ~ (all_56_2 = e3)
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REDUCE: (35), (120) imply:
% 117.97/18.56 | | | | | | (121) ~ (all_52_12 = e3)
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REF_CLOSE: (1), (8), (14), (15), (20), (21), (23), (25), (26), (29),
% 117.97/18.56 | | | | | | (31), (32), (46), (50), (56), (68), (73), (81), (83),
% 117.97/18.56 | | | | | | (96), (97), (107), (108), (119), (121) are inconsistent
% 117.97/18.56 | | | | | | by sub-proof #411.
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | Case 2:
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | (122) all_56_2 = e3
% 117.97/18.56 | | | | | | (123) ~ (all_56_12 = e0)
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | COMBINE_EQS: (35), (122) imply:
% 117.97/18.56 | | | | | | (124) all_52_12 = e3
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REDUCE: (19), (123) imply:
% 117.97/18.56 | | | | | | (125) ~ (all_10_2 = e0)
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REDUCE: (17), (124) imply:
% 117.97/18.56 | | | | | | (126) ~ (all_10_2 = e3)
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (12), (13), (18), (19), (22),
% 117.97/18.56 | | | | | | (25), (26), (29), (34), (37), (38), (41), (42), (43),
% 117.97/18.56 | | | | | | (44), (47), (48), (52), (53), (54), (56), (57), (60),
% 117.97/18.56 | | | | | | (62), (64), (68), (69), (70), (71), (72), (75), (76),
% 117.97/18.56 | | | | | | (78), (79), (82), (84), (86), (88), (98), (99), (101),
% 117.97/18.56 | | | | | | (102), (103), (104), (105), (107), (114), (125) are
% 117.97/18.56 | | | | | | inconsistent by sub-proof #422.
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | End of split
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | Case 2:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | (127) ~ (all_56_15 = e2)
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | REDUCE: (117), (127) imply:
% 117.97/18.56 | | | | | (128) $false
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | CLOSE: (128) is inconsistent.
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | End of split
% 117.97/18.56 | | | |
% 117.97/18.56 | | | End of split
% 117.97/18.56 | | |
% 117.97/18.56 | | Case 2:
% 117.97/18.56 | | |
% 117.97/18.56 | | | (129) all_56_12 = e1
% 117.97/18.56 | | |
% 117.97/18.56 | | | COMBINE_EQS: (19), (129) imply:
% 117.97/18.56 | | | (130) all_10_2 = e1
% 117.97/18.56 | | |
% 117.97/18.56 | | | SIMP: (130) implies:
% 117.97/18.56 | | | (131) all_10_2 = e1
% 117.97/18.56 | | |
% 117.97/18.56 | | | REDUCE: (93), (131) imply:
% 117.97/18.56 | | | (132) ~ (all_52_3 = e1)
% 117.97/18.56 | | |
% 117.97/18.56 | | | REDUCE: (64), (131) imply:
% 117.97/18.56 | | | (133) op(e3, e1) = all_10_1
% 117.97/18.56 | | |
% 117.97/18.56 | | | BETA: splitting (55) gives:
% 117.97/18.56 | | |
% 117.97/18.56 | | | Case 1:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (134) ~ (all_56_4 = e2)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (82), (134) imply:
% 117.97/18.56 | | | | (135) ~ (all_52_9 = e2)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REF_CLOSE: (6), (24), (26), (32), (33), (40), (47), (48), (61), (63),
% 117.97/18.56 | | | | (67), (69), (73), (77), (80), (85), (91), (106), (109),
% 117.97/18.56 | | | | (110), (112), (132), (133), (135) are inconsistent by
% 117.97/18.56 | | | | sub-proof #403.
% 117.97/18.56 | | | |
% 117.97/18.56 | | | Case 2:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (136) ~ (all_56_12 = e1)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (129), (136) imply:
% 117.97/18.56 | | | | (137) $false
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | CLOSE: (137) is inconsistent.
% 117.97/18.56 | | | |
% 117.97/18.56 | | | End of split
% 117.97/18.56 | | |
% 117.97/18.56 | | End of split
% 117.97/18.56 | |
% 117.97/18.56 | Case 2:
% 117.97/18.56 | |
% 117.97/18.56 | | (138) all_56_15 = e1
% 117.97/18.56 | |
% 117.97/18.56 | | REF_CLOSE: (5), (8), (9), (14), (15), (20), (21), (23), (25), (26), (27),
% 117.97/18.56 | | (28), (29), (36), (37), (44), (45), (46), (47), (50), (54), (56),
% 117.97/18.56 | | (58), (61), (62), (65), (72), (73), (81), (82), (84), (87), (89),
% 117.97/18.56 | | (90), (94), (96), (97), (101), (107), (108), (138) are
% 117.97/18.56 | | inconsistent by sub-proof #392.
% 117.97/18.56 | |
% 117.97/18.56 | End of split
% 117.97/18.56 |
% 117.97/18.56 End of proof
% 117.97/18.56
% 117.97/18.56 Sub-proof #392 shows that the following formulas are inconsistent:
% 117.97/18.56 ----------------------------------------------------------------
% 117.97/18.56 (1) ~ (all_52_13 = all_52_14)
% 117.97/18.56 (2) all_56_14 = all_6_2
% 117.97/18.56 (3) all_56_3 = all_52_1
% 117.97/18.56 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.56 (5) ~ (all_6_1 = e3)
% 117.97/18.56 (6) all_58_0 = all_10_2
% 117.97/18.56 (7) all_54_11 = all_52_14
% 117.97/18.56 (8) ~ (all_52_14 = all_6_2)
% 117.97/18.56 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.56 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.56 (11) all_54_8 = all_52_2
% 117.97/18.56 (12) ~ (all_52_2 = all_6_2)
% 117.97/18.56 (13) all_54_10 = all_6_2
% 117.97/18.56 (14) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.97/18.56 (15) all_58_3 = all_8_2
% 117.97/18.56 (16) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.56 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.56 (18) all_56_15 = e1
% 117.97/18.56 (19) op(e1, e0) = all_52_14
% 117.97/18.56 (20) all_58_5 = all_52_9
% 117.97/18.56 (21) op(e1, all_6_2) = all_6_1
% 117.97/18.56 (22) all_58_2 = all_52_1
% 117.97/18.56 (23) ~ (all_10_2 = e3)
% 117.97/18.56 (24) ~ (all_52_14 = all_4_2)
% 117.97/18.56 (25) all_56_15 = all_4_2
% 117.97/18.56 (26) all_58_10 = all_52_13
% 117.97/18.56 (27) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.97/18.56 (28) ~ (all_8_2 = e2)
% 117.97/18.56 (29) ~ (all_6_2 = e2)
% 117.97/18.56 (30) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.56 (31) all_56_4 = all_52_9
% 117.97/18.56 (32) all_56_5 = all_52_13
% 117.97/18.56 (33) all_56_6 = all_52_2
% 117.97/18.56 (34) ~ (all_52_2 = all_52_14)
% 117.97/18.56 (35) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.97/18.56 (36) op(e1, e3) = all_52_2
% 117.97/18.56 (37) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.56 (38) all_56_8 = all_52_14
% 117.97/18.56 (39) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.56 (40) ~ (all_6_2 = e1)
% 117.97/18.56 (41) ~ (all_6_1 = e2)
% 117.97/18.56
% 117.97/18.56 Begin of proof
% 117.97/18.56 |
% 117.97/18.56 | COMBINE_EQS: (18), (25) imply:
% 117.97/18.56 | (42) all_4_2 = e1
% 117.97/18.56 |
% 117.97/18.56 | SIMP: (42) implies:
% 117.97/18.56 | (43) all_4_2 = e1
% 117.97/18.56 |
% 117.97/18.56 | REDUCE: (24), (43) imply:
% 117.97/18.56 | (44) ~ (all_52_14 = e1)
% 117.97/18.56 |
% 117.97/18.56 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 117.97/18.56 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 117.97/18.56 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 117.97/18.56 | (37), (38), (39), (40), (41), (44) are inconsistent by sub-proof
% 117.97/18.56 | #393.
% 117.97/18.56 |
% 117.97/18.56 End of proof
% 117.97/18.56
% 117.97/18.56 Sub-proof #393 shows that the following formulas are inconsistent:
% 117.97/18.56 ----------------------------------------------------------------
% 117.97/18.56 (1) ~ (all_52_13 = all_52_14)
% 117.97/18.56 (2) all_56_14 = all_6_2
% 117.97/18.56 (3) all_56_3 = all_52_1
% 117.97/18.56 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.56 (5) ~ (all_6_1 = e3)
% 117.97/18.56 (6) all_58_0 = all_10_2
% 117.97/18.56 (7) all_54_11 = all_52_14
% 117.97/18.56 (8) ~ (all_52_14 = all_6_2)
% 117.97/18.56 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.56 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.56 (11) all_54_8 = all_52_2
% 117.97/18.56 (12) ~ (all_52_2 = all_6_2)
% 117.97/18.56 (13) all_54_10 = all_6_2
% 117.97/18.56 (14) ~ (all_52_14 = e1)
% 117.97/18.56 (15) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.97/18.56 (16) all_58_3 = all_8_2
% 117.97/18.56 (17) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.56 (18) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.56 (19) all_56_15 = e1
% 117.97/18.56 (20) op(e1, e0) = all_52_14
% 117.97/18.56 (21) all_58_5 = all_52_9
% 117.97/18.56 (22) op(e1, all_6_2) = all_6_1
% 117.97/18.56 (23) all_58_2 = all_52_1
% 117.97/18.56 (24) ~ (all_10_2 = e3)
% 117.97/18.56 (25) all_58_10 = all_52_13
% 117.97/18.56 (26) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.97/18.56 (27) ~ (all_8_2 = e2)
% 117.97/18.56 (28) ~ (all_6_2 = e2)
% 117.97/18.56 (29) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.56 (30) all_56_4 = all_52_9
% 117.97/18.56 (31) all_56_5 = all_52_13
% 117.97/18.56 (32) all_56_6 = all_52_2
% 117.97/18.56 (33) ~ (all_52_2 = all_52_14)
% 117.97/18.56 (34) ~ (all_56_4 = e2) | ~ (all_56_15 = e1)
% 117.97/18.56 (35) op(e1, e3) = all_52_2
% 117.97/18.56 (36) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.56 (37) all_56_8 = all_52_14
% 117.97/18.56 (38) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.56 (39) ~ (all_6_2 = e1)
% 117.97/18.56 (40) ~ (all_6_1 = e2)
% 117.97/18.56
% 117.97/18.56 Begin of proof
% 117.97/18.56 |
% 117.97/18.56 | BETA: splitting (34) gives:
% 117.97/18.56 |
% 117.97/18.56 | Case 1:
% 117.97/18.56 | |
% 117.97/18.56 | | (41) ~ (all_56_4 = e2)
% 117.97/18.56 | |
% 117.97/18.56 | | REDUCE: (30), (41) imply:
% 117.97/18.56 | | (42) ~ (all_52_9 = e2)
% 117.97/18.56 | |
% 117.97/18.56 | | BETA: splitting (17) gives:
% 117.97/18.56 | |
% 117.97/18.56 | | Case 1:
% 117.97/18.56 | | |
% 117.97/18.56 | | | (43) ~ (all_56_5 = e2)
% 117.97/18.56 | | |
% 117.97/18.56 | | | REDUCE: (31), (43) imply:
% 117.97/18.56 | | | (44) ~ (all_52_13 = e2)
% 117.97/18.56 | | |
% 117.97/18.56 | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (13), (14), (16),
% 117.97/18.56 | | | (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 117.97/18.56 | | | (36), (38), (39), (40), (42), (44) are inconsistent by
% 117.97/18.56 | | | sub-proof #400.
% 117.97/18.56 | | |
% 117.97/18.56 | | Case 2:
% 117.97/18.56 | | |
% 117.97/18.56 | | | (45) all_56_5 = e2
% 117.97/18.56 | | |
% 117.97/18.56 | | | COMBINE_EQS: (31), (45) imply:
% 117.97/18.56 | | | (46) all_52_13 = e2
% 117.97/18.56 | | |
% 117.97/18.56 | | | REDUCE: (1), (46) imply:
% 117.97/18.56 | | | (47) ~ (all_52_14 = e2)
% 117.97/18.56 | | |
% 117.97/18.56 | | | SIMP: (47) implies:
% 117.97/18.56 | | | (48) ~ (all_52_14 = e2)
% 117.97/18.56 | | |
% 117.97/18.56 | | | BETA: splitting (9) gives:
% 117.97/18.56 | | |
% 117.97/18.56 | | | Case 1:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (49) all_54_10 = e3
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | COMBINE_EQS: (13), (49) imply:
% 117.97/18.56 | | | | (50) all_6_2 = e3
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | SIMP: (50) implies:
% 117.97/18.56 | | | | (51) all_6_2 = e3
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (12), (51) imply:
% 117.97/18.56 | | | | (52) ~ (all_52_2 = e3)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (8), (51) imply:
% 117.97/18.56 | | | | (53) ~ (all_52_14 = e3)
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REDUCE: (22), (51) imply:
% 117.97/18.56 | | | | (54) op(e1, e3) = all_6_1
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | BETA: splitting (15) gives:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | Case 1:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | (55) ~ (all_56_6 = e1)
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | REDUCE: (32), (55) imply:
% 117.97/18.56 | | | | | (56) ~ (all_52_2 = e1)
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | BETA: splitting (29) gives:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | Case 1:
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | (57) all_54_11 = e3
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | COMBINE_EQS: (7), (57) imply:
% 117.97/18.56 | | | | | | (58) all_52_14 = e3
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | REDUCE: (53), (58) imply:
% 117.97/18.56 | | | | | | (59) $false
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | CLOSE: (59) is inconsistent.
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | Case 2:
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | (60) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | BETA: splitting (60) gives:
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | | Case 1:
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | (61) all_54_11 = e2
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | COMBINE_EQS: (7), (61) imply:
% 117.97/18.56 | | | | | | | (62) all_52_14 = e2
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | REDUCE: (48), (62) imply:
% 117.97/18.56 | | | | | | | (63) $false
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | CLOSE: (63) is inconsistent.
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | Case 2:
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | (64) all_54_11 = e1 | all_54_11 = e0
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | BETA: splitting (64) gives:
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | | Case 1:
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | (65) all_54_11 = e1
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | COMBINE_EQS: (7), (65) imply:
% 117.97/18.56 | | | | | | | | (66) all_52_14 = e1
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | REDUCE: (14), (66) imply:
% 117.97/18.56 | | | | | | | | (67) $false
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | CLOSE: (67) is inconsistent.
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | Case 2:
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | (68) all_54_11 = e0
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | COMBINE_EQS: (7), (68) imply:
% 117.97/18.56 | | | | | | | | (69) all_52_14 = e0
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | REDUCE: (33), (69) imply:
% 117.97/18.56 | | | | | | | | (70) ~ (all_52_2 = e0)
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | | REF_CLOSE: (10), (11), (18), (35), (40), (52), (54), (56), (70)
% 117.97/18.56 | | | | | | | | are inconsistent by sub-proof #395.
% 117.97/18.56 | | | | | | | |
% 117.97/18.56 | | | | | | | End of split
% 117.97/18.56 | | | | | | |
% 117.97/18.56 | | | | | | End of split
% 117.97/18.56 | | | | | |
% 117.97/18.56 | | | | | End of split
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | Case 2:
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | (71) all_56_6 = e1
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (13), (15), (20),
% 117.97/18.56 | | | | | (22), (24), (28), (29), (36), (37), (39), (40), (71) are
% 117.97/18.56 | | | | | inconsistent by sub-proof #394.
% 117.97/18.56 | | | | |
% 117.97/18.56 | | | | End of split
% 117.97/18.56 | | | |
% 117.97/18.56 | | | Case 2:
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | (72) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.56 | | | |
% 117.97/18.56 | | | | REF_CLOSE: (2), (13), (17), (28), (39), (45), (72) are inconsistent by
% 117.97/18.56 | | | | sub-proof #434.
% 117.97/18.56 | | | |
% 117.97/18.56 | | | End of split
% 117.97/18.56 | | |
% 117.97/18.56 | | End of split
% 117.97/18.56 | |
% 117.97/18.56 | Case 2:
% 117.97/18.56 | |
% 117.97/18.56 | | (73) ~ (all_56_15 = e1)
% 117.97/18.56 | |
% 117.97/18.56 | | REDUCE: (19), (73) imply:
% 117.97/18.56 | | (74) $false
% 117.97/18.56 | |
% 117.97/18.56 | | CLOSE: (74) is inconsistent.
% 117.97/18.56 | |
% 117.97/18.56 | End of split
% 117.97/18.56 |
% 117.97/18.56 End of proof
% 117.97/18.56
% 117.97/18.56 Sub-proof #394 shows that the following formulas are inconsistent:
% 117.97/18.56 ----------------------------------------------------------------
% 117.97/18.56 (1) all_56_14 = all_6_2
% 117.97/18.56 (2) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.56 (3) ~ (all_6_1 = e3)
% 117.97/18.56 (4) all_58_0 = all_10_2
% 117.97/18.56 (5) all_54_11 = all_52_14
% 117.97/18.56 (6) ~ (all_52_14 = all_6_2)
% 117.97/18.56 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.57 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.57 (9) all_54_10 = all_6_2
% 117.97/18.57 (10) ~ (all_56_6 = e1) | ~ (all_56_14 = e3)
% 117.97/18.57 (11) all_56_6 = e1
% 117.97/18.57 (12) op(e1, e0) = all_52_14
% 117.97/18.57 (13) op(e1, all_6_2) = all_6_1
% 117.97/18.57 (14) ~ (all_10_2 = e3)
% 117.97/18.57 (15) ~ (all_6_2 = e2)
% 117.97/18.57 (16) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.57 (17) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.57 (18) all_56_8 = all_52_14
% 117.97/18.57 (19) ~ (all_6_2 = e1)
% 117.97/18.57 (20) ~ (all_6_1 = e2)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (10) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (21) ~ (all_56_6 = e1)
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (11), (21) imply:
% 117.97/18.57 | | (22) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (22) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (23) ~ (all_56_14 = e3)
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (1), (23) imply:
% 117.97/18.57 | | (24) ~ (all_6_2 = e3)
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 117.97/18.57 | | (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 117.97/18.57 | | sub-proof #413.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #395 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ~ (all_52_2 = e0)
% 117.97/18.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.57 (3) all_54_8 = all_52_2
% 117.97/18.57 (4) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.57 (5) ~ (all_52_2 = e3)
% 117.97/18.57 (6) ~ (all_52_2 = e1)
% 117.97/18.57 (7) op(e1, e3) = all_6_1
% 117.97/18.57 (8) op(e1, e3) = all_52_2
% 117.97/18.57 (9) ~ (all_6_1 = e2)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (4) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (10) all_54_8 = e3
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #399.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (11) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 117.97/18.57 | |
% 117.97/18.57 | | BETA: splitting (11) gives:
% 117.97/18.57 | |
% 117.97/18.57 | | Case 1:
% 117.97/18.57 | | |
% 117.97/18.57 | | | (12) all_54_8 = e2
% 117.97/18.57 | | |
% 117.97/18.57 | | | COMBINE_EQS: (3), (12) imply:
% 117.97/18.57 | | | (13) all_52_2 = e2
% 117.97/18.57 | | |
% 117.97/18.57 | | | SIMP: (13) implies:
% 117.97/18.57 | | | (14) all_52_2 = e2
% 117.97/18.57 | | |
% 117.97/18.57 | | | REDUCE: (8), (14) imply:
% 117.97/18.57 | | | (15) op(e1, e3) = e2
% 117.97/18.57 | | |
% 117.97/18.57 | | | REF_CLOSE: (2), (7), (9), (15) are inconsistent by sub-proof #398.
% 117.97/18.57 | | |
% 117.97/18.57 | | Case 2:
% 117.97/18.57 | | |
% 117.97/18.57 | | | (16) all_54_8 = e1 | all_54_8 = e0
% 117.97/18.57 | | |
% 117.97/18.57 | | | REF_CLOSE: (1), (3), (6), (16) are inconsistent by sub-proof #396.
% 117.97/18.57 | | |
% 117.97/18.57 | | End of split
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #396 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) all_54_8 = e1 | all_54_8 = e0
% 117.97/18.57 (2) all_54_8 = all_52_2
% 117.97/18.57 (3) ~ (all_52_2 = e1)
% 117.97/18.57 (4) ~ (all_52_2 = e0)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (1) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (5) all_54_8 = e1
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #397.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (6) all_54_8 = e0
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (2), (6) imply:
% 117.97/18.57 | | (7) all_52_2 = e0
% 117.97/18.57 | |
% 117.97/18.57 | | SIMP: (7) implies:
% 117.97/18.57 | | (8) all_52_2 = e0
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (4), (8) imply:
% 117.97/18.57 | | (9) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (9) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #397 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) all_54_8 = all_52_2
% 117.97/18.57 (2) all_54_8 = e1
% 117.97/18.57 (3) ~ (all_52_2 = e1)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.57 | (4) all_52_2 = e1
% 117.97/18.57 |
% 117.97/18.57 | SIMP: (4) implies:
% 117.97/18.57 | (5) all_52_2 = e1
% 117.97/18.57 |
% 117.97/18.57 | REDUCE: (3), (5) imply:
% 117.97/18.57 | (6) $false
% 117.97/18.57 |
% 117.97/18.57 | CLOSE: (6) is inconsistent.
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #398 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.57 (2) op(e1, e3) = all_6_1
% 117.97/18.57 (3) op(e1, e3) = e2
% 117.97/18.57 (4) ~ (all_6_1 = e2)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | GROUND_INST: instantiating (1) with e2, all_6_1, e3, e1, simplifying with (2),
% 117.97/18.57 | (3) gives:
% 117.97/18.57 | (5) all_6_1 = e2
% 117.97/18.57 |
% 117.97/18.57 | REDUCE: (4), (5) imply:
% 117.97/18.57 | (6) $false
% 117.97/18.57 |
% 117.97/18.57 | CLOSE: (6) is inconsistent.
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #399 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) all_54_8 = all_52_2
% 117.97/18.57 (2) all_54_8 = e3
% 117.97/18.57 (3) ~ (all_52_2 = e3)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.57 | (4) all_52_2 = e3
% 117.97/18.57 |
% 117.97/18.57 | SIMP: (4) implies:
% 117.97/18.57 | (5) all_52_2 = e3
% 117.97/18.57 |
% 117.97/18.57 | REDUCE: (3), (5) imply:
% 117.97/18.57 | (6) $false
% 117.97/18.57 |
% 117.97/18.57 | CLOSE: (6) is inconsistent.
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #400 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ~ (all_52_9 = e2)
% 117.97/18.57 (2) all_56_14 = all_6_2
% 117.97/18.57 (3) all_56_3 = all_52_1
% 117.97/18.57 (4) ~ (all_6_1 = e3)
% 117.97/18.57 (5) all_58_0 = all_10_2
% 117.97/18.57 (6) all_54_11 = all_52_14
% 117.97/18.57 (7) ~ (all_52_14 = all_6_2)
% 117.97/18.57 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.57 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.57 (10) all_54_10 = all_6_2
% 117.97/18.57 (11) ~ (all_52_14 = e1)
% 117.97/18.57 (12) all_58_3 = all_8_2
% 117.97/18.57 (13) op(e1, e0) = all_52_14
% 117.97/18.57 (14) all_58_5 = all_52_9
% 117.97/18.57 (15) op(e1, all_6_2) = all_6_1
% 117.97/18.57 (16) all_58_2 = all_52_1
% 117.97/18.57 (17) ~ (all_10_2 = e3)
% 117.97/18.57 (18) ~ (all_52_13 = e2)
% 117.97/18.57 (19) all_58_10 = all_52_13
% 117.97/18.57 (20) ~ (all_56_3 = e2) | ~ (all_56_14 = e3)
% 117.97/18.57 (21) ~ (all_8_2 = e2)
% 117.97/18.57 (22) ~ (all_6_2 = e2)
% 117.97/18.57 (23) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.57 (24) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.57 (25) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.57 (26) ~ (all_6_2 = e1)
% 117.97/18.57 (27) ~ (all_6_1 = e2)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (25) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (28) all_58_2 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (16), (28) imply:
% 117.97/18.57 | | (29) all_52_1 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | SIMP: (29) implies:
% 117.97/18.57 | | (30) all_52_1 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (3), (30) imply:
% 117.97/18.57 | | (31) all_56_3 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | BETA: splitting (20) gives:
% 117.97/18.57 | |
% 117.97/18.57 | | Case 1:
% 117.97/18.57 | | |
% 117.97/18.57 | | | (32) ~ (all_56_3 = e2)
% 117.97/18.57 | | |
% 117.97/18.57 | | | REDUCE: (31), (32) imply:
% 117.97/18.57 | | | (33) $false
% 117.97/18.57 | | |
% 117.97/18.57 | | | CLOSE: (33) is inconsistent.
% 117.97/18.57 | | |
% 117.97/18.57 | | Case 2:
% 117.97/18.57 | | |
% 117.97/18.57 | | | (34) ~ (all_56_14 = e3)
% 117.97/18.57 | | |
% 117.97/18.57 | | | REDUCE: (2), (34) imply:
% 117.97/18.57 | | | (35) ~ (all_6_2 = e3)
% 117.97/18.57 | | |
% 117.97/18.57 | | | BETA: splitting (8) gives:
% 117.97/18.57 | | |
% 117.97/18.57 | | | Case 1:
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | (36) all_54_10 = e3
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | COMBINE_EQS: (10), (36) imply:
% 117.97/18.57 | | | | (37) all_6_2 = e3
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | REDUCE: (35), (37) imply:
% 117.97/18.57 | | | | (38) $false
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | CLOSE: (38) is inconsistent.
% 117.97/18.57 | | | |
% 117.97/18.57 | | | Case 2:
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | (39) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | BETA: splitting (39) gives:
% 117.97/18.57 | | | |
% 117.97/18.57 | | | | Case 1:
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | (40) all_54_10 = e2
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | COMBINE_EQS: (10), (40) imply:
% 117.97/18.57 | | | | | (41) all_6_2 = e2
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | REDUCE: (22), (41) imply:
% 117.97/18.57 | | | | | (42) $false
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | CLOSE: (42) is inconsistent.
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | Case 2:
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | (43) all_54_10 = e1 | all_54_10 = e0
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | BETA: splitting (43) gives:
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | | Case 1:
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | (44) all_54_10 = e1
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | COMBINE_EQS: (10), (44) imply:
% 117.97/18.57 | | | | | | (45) all_6_2 = e1
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | REDUCE: (26), (45) imply:
% 117.97/18.57 | | | | | | (46) $false
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | CLOSE: (46) is inconsistent.
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | Case 2:
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | (47) all_54_10 = e0
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | COMBINE_EQS: (10), (47) imply:
% 117.97/18.57 | | | | | | (48) all_6_2 = e0
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | REDUCE: (7), (48) imply:
% 117.97/18.57 | | | | | | (49) ~ (all_52_14 = e0)
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | REDUCE: (15), (48) imply:
% 117.97/18.57 | | | | | | (50) op(e1, e0) = all_6_1
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | | REF_CLOSE: (4), (5), (6), (9), (11), (13), (17), (23), (24), (27),
% 117.97/18.57 | | | | | | (49), (50) are inconsistent by sub-proof #415.
% 117.97/18.57 | | | | | |
% 117.97/18.57 | | | | | End of split
% 117.97/18.57 | | | | |
% 117.97/18.57 | | | | End of split
% 117.97/18.57 | | | |
% 117.97/18.57 | | | End of split
% 117.97/18.57 | | |
% 117.97/18.57 | | End of split
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (51) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (1), (12), (14), (18), (19), (21), (51) are inconsistent by
% 117.97/18.57 | | sub-proof #401.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #401 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.57 (2) ~ (all_52_9 = e2)
% 117.97/18.57 (3) all_58_3 = all_8_2
% 117.97/18.57 (4) all_58_5 = all_52_9
% 117.97/18.57 (5) ~ (all_52_13 = e2)
% 117.97/18.57 (6) all_58_10 = all_52_13
% 117.97/18.57 (7) ~ (all_8_2 = e2)
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (1) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (8) all_58_3 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (3), (8) imply:
% 117.97/18.57 | | (9) all_8_2 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (7), (9) imply:
% 117.97/18.57 | | (10) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (10) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (11) all_58_5 = e2 | all_58_10 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (2), (4), (5), (6), (11) are inconsistent by sub-proof #402.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #402 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ~ (all_52_9 = e2)
% 117.97/18.57 (2) all_58_5 = e2 | all_58_10 = e2
% 117.97/18.57 (3) all_58_5 = all_52_9
% 117.97/18.57 (4) ~ (all_52_13 = e2)
% 117.97/18.57 (5) all_58_10 = all_52_13
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (2) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (6) all_58_5 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (3), (6) imply:
% 117.97/18.57 | | (7) all_52_9 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (1), (7) imply:
% 117.97/18.57 | | (8) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (8) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (9) all_58_10 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (5), (9) imply:
% 117.97/18.57 | | (10) all_52_13 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (4), (10) imply:
% 117.97/18.57 | | (11) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (11) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #403 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ~ (all_52_9 = e2)
% 117.97/18.57 (2) ~ (all_4_2 = e0)
% 117.97/18.57 (3) ~ (all_4_2 = e1)
% 117.97/18.57 (4) all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.97/18.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.57 (6) all_58_4 = all_52_8
% 117.97/18.57 (7) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.57 (8) op(e3, e1) = all_52_8
% 117.97/18.57 (9) all_58_5 = all_52_9
% 117.97/18.57 (10) all_56_9 = all_52_3
% 117.97/18.57 (11) all_56_15 = all_4_2
% 117.97/18.57 (12) ~ (all_52_11 = all_4_2)
% 117.97/18.57 (13) ~ (all_10_1 = e2)
% 117.97/18.57 (14) all_58_14 = all_52_11
% 117.97/18.57 (15) ~ (all_6_2 = e2)
% 117.97/18.57 (16) all_58_8 = all_6_2
% 117.97/18.57 (17) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 117.97/18.57 (18) ~ (all_52_3 = all_4_2)
% 117.97/18.57 (19) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.57 (20) ~ (all_52_3 = e1)
% 117.97/18.57 (21) op(e3, e1) = all_10_1
% 117.97/18.57 (22) all_54_15 = all_4_2
% 117.97/18.57 (23) ~ (all_52_3 = all_52_11)
% 117.97/18.57 (24) all_54_12 = all_52_3
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | GROUND_INST: instantiating (5) with all_52_8, all_10_1, e1, e3, simplifying
% 117.97/18.57 | with (8), (21) gives:
% 117.97/18.57 | (25) all_52_8 = all_10_1
% 117.97/18.57 |
% 117.97/18.57 | COMBINE_EQS: (6), (25) imply:
% 117.97/18.57 | (26) all_58_4 = all_10_1
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (4) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (27) all_58_4 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (26), (27) imply:
% 117.97/18.57 | | (28) all_10_1 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REDUCE: (13), (28) imply:
% 117.97/18.57 | | (29) $false
% 117.97/18.57 | |
% 117.97/18.57 | | CLOSE: (29) is inconsistent.
% 117.97/18.57 | |
% 117.97/18.57 | Case 2:
% 117.97/18.57 | |
% 117.97/18.57 | | (30) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (11), (12), (14), (15), (16),
% 117.97/18.57 | | (17), (18), (19), (20), (22), (23), (24), (30) are inconsistent
% 117.97/18.57 | | by sub-proof #404.
% 117.97/18.57 | |
% 117.97/18.57 | End of split
% 117.97/18.57 |
% 117.97/18.57 End of proof
% 117.97/18.57
% 117.97/18.57 Sub-proof #404 shows that the following formulas are inconsistent:
% 117.97/18.57 ----------------------------------------------------------------
% 117.97/18.57 (1) ~ (all_52_9 = e2)
% 117.97/18.57 (2) ~ (all_4_2 = e0)
% 117.97/18.57 (3) ~ (all_4_2 = e1)
% 117.97/18.57 (4) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.57 (5) all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 117.97/18.57 (6) all_58_5 = all_52_9
% 117.97/18.57 (7) all_56_9 = all_52_3
% 117.97/18.57 (8) all_56_15 = all_4_2
% 117.97/18.57 (9) ~ (all_52_11 = all_4_2)
% 117.97/18.57 (10) all_58_14 = all_52_11
% 117.97/18.57 (11) ~ (all_6_2 = e2)
% 117.97/18.57 (12) all_58_8 = all_6_2
% 117.97/18.57 (13) ~ (all_56_9 = e0) | ~ (all_56_15 = e3)
% 117.97/18.57 (14) ~ (all_52_3 = all_4_2)
% 117.97/18.57 (15) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.57 (16) ~ (all_52_3 = e1)
% 117.97/18.57 (17) all_54_15 = all_4_2
% 117.97/18.57 (18) ~ (all_52_3 = all_52_11)
% 117.97/18.57 (19) all_54_12 = all_52_3
% 117.97/18.57
% 117.97/18.57 Begin of proof
% 117.97/18.57 |
% 117.97/18.57 | BETA: splitting (5) gives:
% 117.97/18.57 |
% 117.97/18.57 | Case 1:
% 117.97/18.57 | |
% 117.97/18.57 | | (20) all_58_5 = e2
% 117.97/18.57 | |
% 117.97/18.57 | | COMBINE_EQS: (6), (20) imply:
% 117.97/18.58 | | (21) all_52_9 = e2
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (1), (21) imply:
% 117.97/18.58 | | (22) $false
% 117.97/18.58 | |
% 117.97/18.58 | | CLOSE: (22) is inconsistent.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (23) all_58_8 = e2 | all_58_14 = e2
% 117.97/18.58 | |
% 117.97/18.58 | | BETA: splitting (23) gives:
% 117.97/18.58 | |
% 117.97/18.58 | | Case 1:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (24) all_58_8 = e2
% 117.97/18.58 | | |
% 117.97/18.58 | | | COMBINE_EQS: (12), (24) imply:
% 117.97/18.58 | | | (25) all_6_2 = e2
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (11), (25) imply:
% 117.97/18.58 | | | (26) $false
% 117.97/18.58 | | |
% 117.97/18.58 | | | CLOSE: (26) is inconsistent.
% 117.97/18.58 | | |
% 117.97/18.58 | | Case 2:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (27) all_58_14 = e2
% 117.97/18.58 | | |
% 117.97/18.58 | | | COMBINE_EQS: (10), (27) imply:
% 117.97/18.58 | | | (28) all_52_11 = e2
% 117.97/18.58 | | |
% 117.97/18.58 | | | SIMP: (28) implies:
% 117.97/18.58 | | | (29) all_52_11 = e2
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (18), (29) imply:
% 117.97/18.58 | | | (30) ~ (all_52_3 = e2)
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (9), (29) imply:
% 117.97/18.58 | | | (31) ~ (all_4_2 = e2)
% 117.97/18.58 | | |
% 117.97/18.58 | | | SIMP: (31) implies:
% 117.97/18.58 | | | (32) ~ (all_4_2 = e2)
% 117.97/18.58 | | |
% 117.97/18.58 | | | BETA: splitting (4) gives:
% 117.97/18.58 | | |
% 117.97/18.58 | | | Case 1:
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | (33) all_54_15 = e3
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | COMBINE_EQS: (17), (33) imply:
% 117.97/18.58 | | | | (34) all_4_2 = e3
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | SIMP: (34) implies:
% 117.97/18.58 | | | | (35) all_4_2 = e3
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | COMBINE_EQS: (8), (35) imply:
% 117.97/18.58 | | | | (36) all_56_15 = e3
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | REDUCE: (14), (35) imply:
% 117.97/18.58 | | | | (37) ~ (all_52_3 = e3)
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | BETA: splitting (13) gives:
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | Case 1:
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | (38) ~ (all_56_15 = e3)
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | REDUCE: (36), (38) imply:
% 117.97/18.58 | | | | | (39) $false
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | CLOSE: (39) is inconsistent.
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | Case 2:
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | (40) ~ (all_56_9 = e0)
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | REDUCE: (7), (40) imply:
% 117.97/18.58 | | | | | (41) ~ (all_52_3 = e0)
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | | REF_CLOSE: (15), (16), (19), (30), (37), (41) are inconsistent by
% 117.97/18.58 | | | | | sub-proof #405.
% 117.97/18.58 | | | | |
% 117.97/18.58 | | | | End of split
% 117.97/18.58 | | | |
% 117.97/18.58 | | | Case 2:
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | (42) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | REF_CLOSE: (2), (3), (17), (32), (42) are inconsistent by sub-proof
% 117.97/18.58 | | | | #417.
% 117.97/18.58 | | | |
% 117.97/18.58 | | | End of split
% 117.97/18.58 | | |
% 117.97/18.58 | | End of split
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #405 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) ~ (all_52_3 = e0)
% 117.97/18.58 (2) ~ (all_52_3 = e3)
% 117.97/18.58 (3) ~ (all_52_3 = e2)
% 117.97/18.58 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.58 (5) ~ (all_52_3 = e1)
% 117.97/18.58 (6) all_54_12 = all_52_3
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (4) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (7) all_54_12 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #410.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (8) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.58 | |
% 117.97/18.58 | | REF_CLOSE: (1), (3), (5), (6), (8) are inconsistent by sub-proof #406.
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #406 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) ~ (all_52_3 = e0)
% 117.97/18.58 (2) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 117.97/18.58 (3) ~ (all_52_3 = e2)
% 117.97/18.58 (4) ~ (all_52_3 = e1)
% 117.97/18.58 (5) all_54_12 = all_52_3
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (2) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (6) all_54_12 = e2
% 117.97/18.58 | |
% 117.97/18.58 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #409.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (7) all_54_12 = e1 | all_54_12 = e0
% 117.97/18.58 | |
% 117.97/18.58 | | BETA: splitting (7) gives:
% 117.97/18.58 | |
% 117.97/18.58 | | Case 1:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (8) all_54_12 = e1
% 117.97/18.58 | | |
% 117.97/18.58 | | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #408.
% 117.97/18.58 | | |
% 117.97/18.58 | | Case 2:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (9) all_54_12 = e0
% 117.97/18.58 | | |
% 117.97/18.58 | | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #407.
% 117.97/18.58 | | |
% 117.97/18.58 | | End of split
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #407 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_54_12 = all_52_3
% 117.97/18.58 (2) all_54_12 = e0
% 117.97/18.58 (3) ~ (all_52_3 = e0)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.58 | (4) all_52_3 = e0
% 117.97/18.58 |
% 117.97/18.58 | SIMP: (4) implies:
% 117.97/18.58 | (5) all_52_3 = e0
% 117.97/18.58 |
% 117.97/18.58 | REDUCE: (3), (5) imply:
% 117.97/18.58 | (6) $false
% 117.97/18.58 |
% 117.97/18.58 | CLOSE: (6) is inconsistent.
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #408 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_54_12 = all_52_3
% 117.97/18.58 (2) all_54_12 = e1
% 117.97/18.58 (3) ~ (all_52_3 = e1)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.58 | (4) all_52_3 = e1
% 117.97/18.58 |
% 117.97/18.58 | SIMP: (4) implies:
% 117.97/18.58 | (5) all_52_3 = e1
% 117.97/18.58 |
% 117.97/18.58 | REDUCE: (3), (5) imply:
% 117.97/18.58 | (6) $false
% 117.97/18.58 |
% 117.97/18.58 | CLOSE: (6) is inconsistent.
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #409 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_54_12 = all_52_3
% 117.97/18.58 (2) all_54_12 = e2
% 117.97/18.58 (3) ~ (all_52_3 = e2)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.58 | (4) all_52_3 = e2
% 117.97/18.58 |
% 117.97/18.58 | SIMP: (4) implies:
% 117.97/18.58 | (5) all_52_3 = e2
% 117.97/18.58 |
% 117.97/18.58 | REDUCE: (3), (5) imply:
% 117.97/18.58 | (6) $false
% 117.97/18.58 |
% 117.97/18.58 | CLOSE: (6) is inconsistent.
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #410 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_54_12 = all_52_3
% 117.97/18.58 (2) all_54_12 = e3
% 117.97/18.58 (3) ~ (all_52_3 = e3)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.58 | (4) all_52_3 = e3
% 117.97/18.58 |
% 117.97/18.58 | SIMP: (4) implies:
% 117.97/18.58 | (5) all_52_3 = e3
% 117.97/18.58 |
% 117.97/18.58 | REDUCE: (3), (5) imply:
% 117.97/18.58 | (6) $false
% 117.97/18.58 |
% 117.97/18.58 | CLOSE: (6) is inconsistent.
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #411 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) ~ (all_52_8 = all_10_2)
% 117.97/18.58 (2) all_56_14 = all_6_2
% 117.97/18.58 (3) ~ (all_52_4 = e3)
% 117.97/18.58 (4) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.58 (5) ~ (all_6_1 = e3)
% 117.97/18.58 (6) all_58_0 = all_10_2
% 117.97/18.58 (7) all_54_11 = all_52_14
% 117.97/18.58 (8) ~ (all_52_14 = all_6_2)
% 117.97/18.58 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.58 (11) all_54_10 = all_6_2
% 117.97/18.58 (12) ~ (all_52_8 = all_6_2)
% 117.97/18.58 (13) all_58_4 = all_52_8
% 117.97/18.58 (14) op(e1, e0) = all_52_14
% 117.97/18.58 (15) op(e1, all_6_2) = all_6_1
% 117.97/18.58 (16) ~ (all_10_2 = e3)
% 117.97/18.58 (17) ~ (all_52_12 = e3)
% 117.97/18.58 (18) all_58_1 = all_52_4
% 117.97/18.58 (19) ~ (all_6_2 = e2)
% 117.97/18.58 (20) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.58 (21) all_58_9 = all_52_12
% 117.97/18.58 (22) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 (23) all_56_8 = all_52_14
% 117.97/18.58 (24) ~ (all_6_2 = e1)
% 117.97/18.58 (25) ~ (all_6_1 = e2)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (22) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (26) all_58_0 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | COMBINE_EQS: (6), (26) imply:
% 117.97/18.58 | | (27) all_10_2 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (16), (27) imply:
% 117.97/18.58 | | (28) $false
% 117.97/18.58 | |
% 117.97/18.58 | | CLOSE: (28) is inconsistent.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (29) all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | BETA: splitting (29) gives:
% 117.97/18.58 | |
% 117.97/18.58 | | Case 1:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (30) all_58_1 = e3
% 117.97/18.58 | | |
% 117.97/18.58 | | | COMBINE_EQS: (18), (30) imply:
% 117.97/18.58 | | | (31) all_52_4 = e3
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (3), (31) imply:
% 117.97/18.58 | | | (32) $false
% 117.97/18.58 | | |
% 117.97/18.58 | | | CLOSE: (32) is inconsistent.
% 117.97/18.58 | | |
% 117.97/18.58 | | Case 2:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (33) all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 | | |
% 117.97/18.58 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 117.97/18.58 | | | (14), (15), (17), (19), (20), (21), (22), (23), (24), (25),
% 117.97/18.58 | | | (33) are inconsistent by sub-proof #412.
% 117.97/18.58 | | |
% 117.97/18.58 | | End of split
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #412 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) ~ (all_52_8 = all_10_2)
% 117.97/18.58 (2) all_56_14 = all_6_2
% 117.97/18.58 (3) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.58 (4) ~ (all_6_1 = e3)
% 117.97/18.58 (5) all_58_0 = all_10_2
% 117.97/18.58 (6) all_54_11 = all_52_14
% 117.97/18.58 (7) ~ (all_52_14 = all_6_2)
% 117.97/18.58 (8) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.58 (10) all_54_10 = all_6_2
% 117.97/18.58 (11) ~ (all_52_8 = all_6_2)
% 117.97/18.58 (12) all_58_4 = all_52_8
% 117.97/18.58 (13) op(e1, e0) = all_52_14
% 117.97/18.58 (14) op(e1, all_6_2) = all_6_1
% 117.97/18.58 (15) ~ (all_52_12 = e3)
% 117.97/18.58 (16) all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 (17) ~ (all_6_2 = e2)
% 117.97/18.58 (18) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.58 (19) all_58_9 = all_52_12
% 117.97/18.58 (20) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 (21) all_56_8 = all_52_14
% 117.97/18.58 (22) ~ (all_6_2 = e1)
% 117.97/18.58 (23) ~ (all_6_1 = e2)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (16) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (24) all_58_4 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | COMBINE_EQS: (12), (24) imply:
% 117.97/18.58 | | (25) all_52_8 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (1), (25) imply:
% 117.97/18.58 | | (26) ~ (all_10_2 = e3)
% 117.97/18.58 | |
% 117.97/18.58 | | SIMP: (26) implies:
% 117.97/18.58 | | (27) ~ (all_10_2 = e3)
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (11), (25) imply:
% 117.97/18.58 | | (28) ~ (all_6_2 = e3)
% 117.97/18.58 | |
% 117.97/18.58 | | SIMP: (28) implies:
% 117.97/18.58 | | (29) ~ (all_6_2 = e3)
% 117.97/18.58 | |
% 117.97/18.58 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (17),
% 117.97/18.58 | | (18), (20), (21), (22), (23), (27), (29) are inconsistent by
% 117.97/18.58 | | sub-proof #413.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (30) all_58_9 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | COMBINE_EQS: (19), (30) imply:
% 117.97/18.58 | | (31) all_52_12 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (15), (31) imply:
% 117.97/18.58 | | (32) $false
% 117.97/18.58 | |
% 117.97/18.58 | | CLOSE: (32) is inconsistent.
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #413 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_56_14 = all_6_2
% 117.97/18.58 (2) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.58 (3) ~ (all_6_1 = e3)
% 117.97/18.58 (4) all_58_0 = all_10_2
% 117.97/18.58 (5) all_54_11 = all_52_14
% 117.97/18.58 (6) ~ (all_52_14 = all_6_2)
% 117.97/18.58 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.58 (9) all_54_10 = all_6_2
% 117.97/18.58 (10) op(e1, e0) = all_52_14
% 117.97/18.58 (11) op(e1, all_6_2) = all_6_1
% 117.97/18.58 (12) ~ (all_10_2 = e3)
% 117.97/18.58 (13) ~ (all_6_2 = e2)
% 117.97/18.58 (14) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.58 (15) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 (16) all_56_8 = all_52_14
% 117.97/18.58 (17) ~ (all_6_2 = e3)
% 117.97/18.58 (18) ~ (all_6_2 = e1)
% 117.97/18.58 (19) ~ (all_6_1 = e2)
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (7) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (20) all_54_10 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | COMBINE_EQS: (9), (20) imply:
% 117.97/18.58 | | (21) all_6_2 = e3
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (17), (21) imply:
% 117.97/18.58 | | (22) $false
% 117.97/18.58 | |
% 117.97/18.58 | | CLOSE: (22) is inconsistent.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58 | |
% 117.97/18.58 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 117.97/18.58 | | (14), (15), (16), (18), (19), (23) are inconsistent by sub-proof
% 117.97/18.58 | | #414.
% 117.97/18.58 | |
% 117.97/18.58 | End of split
% 117.97/18.58 |
% 117.97/18.58 End of proof
% 117.97/18.58
% 117.97/18.58 Sub-proof #414 shows that the following formulas are inconsistent:
% 117.97/18.58 ----------------------------------------------------------------
% 117.97/18.58 (1) all_56_14 = all_6_2
% 117.97/18.58 (2) ~ (all_56_8 = e1) | ~ (all_56_14 = e0)
% 117.97/18.58 (3) ~ (all_6_1 = e3)
% 117.97/18.58 (4) all_58_0 = all_10_2
% 117.97/18.58 (5) all_54_11 = all_52_14
% 117.97/18.58 (6) ~ (all_52_14 = all_6_2)
% 117.97/18.58 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.58 (8) all_54_10 = all_6_2
% 117.97/18.58 (9) op(e1, e0) = all_52_14
% 117.97/18.58 (10) op(e1, all_6_2) = all_6_1
% 117.97/18.58 (11) ~ (all_10_2 = e3)
% 117.97/18.58 (12) ~ (all_6_2 = e2)
% 117.97/18.58 (13) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.58 (14) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.58 (15) all_56_8 = all_52_14
% 117.97/18.58 (16) ~ (all_6_2 = e1)
% 117.97/18.58 (17) ~ (all_6_1 = e2)
% 117.97/18.58 (18) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58
% 117.97/18.58 Begin of proof
% 117.97/18.58 |
% 117.97/18.58 | BETA: splitting (18) gives:
% 117.97/18.58 |
% 117.97/18.58 | Case 1:
% 117.97/18.58 | |
% 117.97/18.58 | | (19) all_54_10 = e2
% 117.97/18.58 | |
% 117.97/18.58 | | COMBINE_EQS: (8), (19) imply:
% 117.97/18.58 | | (20) all_6_2 = e2
% 117.97/18.58 | |
% 117.97/18.58 | | REDUCE: (12), (20) imply:
% 117.97/18.58 | | (21) $false
% 117.97/18.58 | |
% 117.97/18.58 | | CLOSE: (21) is inconsistent.
% 117.97/18.58 | |
% 117.97/18.58 | Case 2:
% 117.97/18.58 | |
% 117.97/18.58 | | (22) all_54_10 = e1 | all_54_10 = e0
% 117.97/18.58 | |
% 117.97/18.58 | | BETA: splitting (22) gives:
% 117.97/18.58 | |
% 117.97/18.58 | | Case 1:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (23) all_54_10 = e1
% 117.97/18.58 | | |
% 117.97/18.58 | | | REF_CLOSE: (8), (16), (23) are inconsistent by sub-proof #437.
% 117.97/18.58 | | |
% 117.97/18.58 | | Case 2:
% 117.97/18.58 | | |
% 117.97/18.58 | | | (24) all_54_10 = e0
% 117.97/18.58 | | |
% 117.97/18.58 | | | COMBINE_EQS: (8), (24) imply:
% 117.97/18.58 | | | (25) all_6_2 = e0
% 117.97/18.58 | | |
% 117.97/18.58 | | | SIMP: (25) implies:
% 117.97/18.58 | | | (26) all_6_2 = e0
% 117.97/18.58 | | |
% 117.97/18.58 | | | COMBINE_EQS: (1), (26) imply:
% 117.97/18.58 | | | (27) all_56_14 = e0
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (6), (26) imply:
% 117.97/18.58 | | | (28) ~ (all_52_14 = e0)
% 117.97/18.58 | | |
% 117.97/18.58 | | | REDUCE: (10), (26) imply:
% 117.97/18.58 | | | (29) op(e1, e0) = all_6_1
% 117.97/18.58 | | |
% 117.97/18.58 | | | BETA: splitting (2) gives:
% 117.97/18.58 | | |
% 117.97/18.58 | | | Case 1:
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | (30) ~ (all_56_8 = e1)
% 117.97/18.58 | | | |
% 117.97/18.58 | | | | REDUCE: (15), (30) imply:
% 117.97/18.58 | | | | (31) ~ (all_52_14 = e1)
% 117.97/18.58 | | | |
% 117.97/18.59 | | | | REF_CLOSE: (3), (4), (5), (7), (9), (11), (13), (14), (17), (28), (29),
% 117.97/18.59 | | | | (31) are inconsistent by sub-proof #415.
% 117.97/18.59 | | | |
% 117.97/18.59 | | | Case 2:
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | (32) ~ (all_56_14 = e0)
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | REDUCE: (27), (32) imply:
% 117.97/18.59 | | | | (33) $false
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | CLOSE: (33) is inconsistent.
% 117.97/18.59 | | | |
% 117.97/18.59 | | | End of split
% 117.97/18.59 | | |
% 117.97/18.59 | | End of split
% 117.97/18.59 | |
% 117.97/18.59 | End of split
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #415 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) ~ (all_6_1 = e3)
% 117.97/18.59 (2) ~ (all_52_14 = e0)
% 117.97/18.59 (3) all_58_0 = all_10_2
% 117.97/18.59 (4) all_54_11 = all_52_14
% 117.97/18.59 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.59 (6) op(e1, e0) = all_6_1
% 117.97/18.59 (7) ~ (all_52_14 = e1)
% 117.97/18.59 (8) op(e1, e0) = all_52_14
% 117.97/18.59 (9) ~ (all_10_2 = e3)
% 117.97/18.59 (10) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.59 (11) all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 117.97/18.59 (12) ~ (all_6_1 = e2)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | BETA: splitting (11) gives:
% 117.97/18.59 |
% 117.97/18.59 | Case 1:
% 117.97/18.59 | |
% 117.97/18.59 | | (13) all_58_0 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | COMBINE_EQS: (3), (13) imply:
% 117.97/18.59 | | (14) all_10_2 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | REDUCE: (9), (14) imply:
% 117.97/18.59 | | (15) $false
% 117.97/18.59 | |
% 117.97/18.59 | | CLOSE: (15) is inconsistent.
% 117.97/18.59 | |
% 117.97/18.59 | Case 2:
% 117.97/18.59 | |
% 117.97/18.59 | |
% 117.97/18.59 | | GROUND_INST: instantiating (5) with all_52_14, all_6_1, e0, e1, simplifying
% 117.97/18.59 | | with (6), (8) gives:
% 117.97/18.59 | | (16) all_52_14 = all_6_1
% 117.97/18.59 | |
% 117.97/18.59 | | COMBINE_EQS: (4), (16) imply:
% 117.97/18.59 | | (17) all_54_11 = all_6_1
% 117.97/18.59 | |
% 117.97/18.59 | | REDUCE: (7), (16) imply:
% 117.97/18.59 | | (18) ~ (all_6_1 = e1)
% 117.97/18.59 | |
% 117.97/18.59 | | REDUCE: (2), (16) imply:
% 117.97/18.59 | | (19) ~ (all_6_1 = e0)
% 117.97/18.59 | |
% 117.97/18.59 | | BETA: splitting (10) gives:
% 117.97/18.59 | |
% 117.97/18.59 | | Case 1:
% 117.97/18.59 | | |
% 117.97/18.59 | | | (20) all_54_11 = e3
% 117.97/18.59 | | |
% 117.97/18.59 | | | COMBINE_EQS: (17), (20) imply:
% 117.97/18.59 | | | (21) all_6_1 = e3
% 117.97/18.59 | | |
% 117.97/18.59 | | | SIMP: (21) implies:
% 117.97/18.59 | | | (22) all_6_1 = e3
% 117.97/18.59 | | |
% 117.97/18.59 | | | REDUCE: (1), (22) imply:
% 117.97/18.59 | | | (23) $false
% 117.97/18.59 | | |
% 117.97/18.59 | | | CLOSE: (23) is inconsistent.
% 117.97/18.59 | | |
% 117.97/18.59 | | Case 2:
% 117.97/18.59 | | |
% 117.97/18.59 | | | (24) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 117.97/18.59 | | |
% 117.97/18.59 | | | BETA: splitting (24) gives:
% 117.97/18.59 | | |
% 117.97/18.59 | | | Case 1:
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | (25) all_54_11 = e2
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | COMBINE_EQS: (17), (25) imply:
% 117.97/18.59 | | | | (26) all_6_1 = e2
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | SIMP: (26) implies:
% 117.97/18.59 | | | | (27) all_6_1 = e2
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | REDUCE: (12), (27) imply:
% 117.97/18.59 | | | | (28) $false
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | CLOSE: (28) is inconsistent.
% 117.97/18.59 | | | |
% 117.97/18.59 | | | Case 2:
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | (29) all_54_11 = e1 | all_54_11 = e0
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | BETA: splitting (29) gives:
% 117.97/18.59 | | | |
% 117.97/18.59 | | | | Case 1:
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | (30) all_54_11 = e1
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | COMBINE_EQS: (17), (30) imply:
% 117.97/18.59 | | | | | (31) all_6_1 = e1
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | SIMP: (31) implies:
% 117.97/18.59 | | | | | (32) all_6_1 = e1
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | REDUCE: (18), (32) imply:
% 117.97/18.59 | | | | | (33) $false
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | CLOSE: (33) is inconsistent.
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | Case 2:
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | (34) all_54_11 = e0
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | COMBINE_EQS: (17), (34) imply:
% 117.97/18.59 | | | | | (35) all_6_1 = e0
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | SIMP: (35) implies:
% 117.97/18.59 | | | | | (36) all_6_1 = e0
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | REDUCE: (19), (36) imply:
% 117.97/18.59 | | | | | (37) $false
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | | CLOSE: (37) is inconsistent.
% 117.97/18.59 | | | | |
% 117.97/18.59 | | | | End of split
% 117.97/18.59 | | | |
% 117.97/18.59 | | | End of split
% 117.97/18.59 | | |
% 117.97/18.59 | | End of split
% 117.97/18.59 | |
% 117.97/18.59 | End of split
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #416 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) all_58_7 = all_52_6
% 117.97/18.59 (2) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.97/18.59 (3) ~ (all_4_2 = e0)
% 117.97/18.59 (4) op(e3, e2) = all_52_4
% 117.97/18.59 (5) all_56_14 = all_6_2
% 117.97/18.59 (6) all_54_0 = all_10_2
% 117.97/18.59 (7) all_54_3 = all_52_12
% 117.97/18.59 (8) ~ (all_4_2 = e1)
% 117.97/18.59 (9) op(e0, e2) = all_52_7
% 117.97/18.59 (10) all_56_11 = all_52_11
% 117.97/18.59 (11) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.97/18.59 (12) ~ (all_52_12 = all_10_2)
% 117.97/18.59 (13) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.59 (14) all_56_12 = all_10_2
% 117.97/18.59 (15) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.59 (16) ~ (all_52_14 = all_6_2)
% 117.97/18.59 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.59 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.59 (19) all_54_10 = all_6_2
% 117.97/18.59 (20) op(e3, e0) = all_52_12
% 117.97/18.59 (21) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.59 (22) ~ (all_52_4 = all_52_7)
% 117.97/18.59 (23) all_58_3 = all_8_2
% 117.97/18.59 (24) ~ (all_10_0 = e2)
% 117.97/18.59 (25) all_58_11 = all_52_14
% 117.97/18.59 (26) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.59 (27) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.59 (28) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.59 (29) ~ (all_10_2 = e1)
% 117.97/18.59 (30) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.59 (31) all_58_5 = all_52_9
% 117.97/18.59 (32) all_56_9 = all_52_3
% 117.97/18.59 (33) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.59 (34) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.59 (35) all_58_15 = all_4_2
% 117.97/18.59 (36) all_58_2 = all_52_1
% 117.97/18.59 (37) ~ (all_10_2 = e3)
% 117.97/18.59 (38) all_58_13 = all_52_7
% 117.97/18.59 (39) all_58_6 = all_52_2
% 117.97/18.59 (40) ~ (all_52_1 = all_10_2)
% 117.97/18.59 (41) all_56_15 = all_4_2
% 117.97/18.59 (42) all_58_10 = all_52_13
% 117.97/18.59 (43) op(e3, all_10_2) = all_10_1
% 117.97/18.59 (44) ~ (all_10_1 = e2)
% 117.97/18.59 (45) all_58_1 = all_52_4
% 117.97/18.59 (46) all_58_14 = all_52_11
% 117.97/18.59 (47) all_54_1 = all_52_4
% 117.97/18.59 (48) all_56_13 = all_8_2
% 117.97/18.59 (49) ~ (all_8_2 = e2)
% 117.97/18.59 (50) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.59 (51) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.59 (52) all_56_7 = all_52_6
% 117.97/18.59 (53) all_58_8 = all_6_2
% 117.97/18.59 (54) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.59 (55) ~ (all_10_0 = e1)
% 117.97/18.59 (56) all_56_4 = all_52_9
% 117.97/18.59 (57) all_56_5 = all_52_13
% 117.97/18.59 (58) ~ (all_52_6 = all_6_2)
% 117.97/18.59 (59) all_56_6 = all_52_2
% 117.97/18.59 (60) all_58_12 = all_52_3
% 117.97/18.59 (61) ~ (all_52_12 = all_4_2)
% 117.97/18.59 (62) ~ (all_4_2 = e2)
% 117.97/18.59 (63) all_56_8 = all_52_14
% 117.97/18.59 (64) ~ (all_52_4 = all_10_2)
% 117.97/18.59 (65) ~ (all_10_1 = e1)
% 117.97/18.59 (66) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.59 (67) all_56_0 = all_52_4
% 117.97/18.59 (68) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.59 (69) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.59 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.59 (70) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.59 (71) all_54_15 = all_4_2
% 117.97/18.59 (72) ~ (all_6_2 = e1)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | BETA: splitting (21) gives:
% 117.97/18.59 |
% 117.97/18.59 | Case 1:
% 117.97/18.59 | |
% 117.97/18.59 | | (73) all_54_15 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | COMBINE_EQS: (71), (73) imply:
% 117.97/18.59 | | (74) all_4_2 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | SIMP: (74) implies:
% 117.97/18.59 | | (75) all_4_2 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | COMBINE_EQS: (41), (75) imply:
% 117.97/18.59 | | (76) all_56_15 = e3
% 117.97/18.59 | |
% 117.97/18.59 | | REDUCE: (61), (75) imply:
% 117.97/18.59 | | (77) ~ (all_52_12 = e3)
% 117.97/18.59 | |
% 117.97/18.59 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 117.97/18.59 | | (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 117.97/18.59 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 117.97/18.59 | | (37), (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 117.97/18.59 | | (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 117.97/18.59 | | (60), (63), (64), (65), (66), (67), (68), (69), (70), (72), (76),
% 117.97/18.59 | | (77) are inconsistent by sub-proof #421.
% 117.97/18.59 | |
% 117.97/18.59 | Case 2:
% 117.97/18.59 | |
% 117.97/18.59 | | (78) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.59 | |
% 117.97/18.59 | | REF_CLOSE: (3), (8), (62), (71), (78) are inconsistent by sub-proof #417.
% 117.97/18.59 | |
% 117.97/18.59 | End of split
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #417 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) ~ (all_4_2 = e0)
% 117.97/18.59 (2) ~ (all_4_2 = e1)
% 117.97/18.59 (3) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 117.97/18.59 (4) ~ (all_4_2 = e2)
% 117.97/18.59 (5) all_54_15 = all_4_2
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | BETA: splitting (3) gives:
% 117.97/18.59 |
% 117.97/18.59 | Case 1:
% 117.97/18.59 | |
% 117.97/18.59 | | (6) all_54_15 = e2
% 117.97/18.59 | |
% 117.97/18.59 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #420.
% 117.97/18.59 | |
% 117.97/18.59 | Case 2:
% 117.97/18.59 | |
% 117.97/18.59 | | (7) all_54_15 = e1 | all_54_15 = e0
% 117.97/18.59 | |
% 117.97/18.59 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #418.
% 117.97/18.59 | |
% 117.97/18.59 | End of split
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #418 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) all_54_15 = e1 | all_54_15 = e0
% 117.97/18.59 (2) all_54_15 = all_4_2
% 117.97/18.59 (3) ~ (all_4_2 = e1)
% 117.97/18.59 (4) ~ (all_4_2 = e0)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | BETA: splitting (1) gives:
% 117.97/18.59 |
% 117.97/18.59 | Case 1:
% 117.97/18.59 | |
% 117.97/18.59 | | (5) all_54_15 = e1
% 117.97/18.59 | |
% 117.97/18.59 | | COMBINE_EQS: (2), (5) imply:
% 117.97/18.59 | | (6) all_4_2 = e1
% 117.97/18.59 | |
% 117.97/18.59 | | SIMP: (6) implies:
% 117.97/18.59 | | (7) all_4_2 = e1
% 117.97/18.59 | |
% 117.97/18.59 | | REDUCE: (3), (7) imply:
% 117.97/18.59 | | (8) $false
% 117.97/18.59 | |
% 117.97/18.59 | | CLOSE: (8) is inconsistent.
% 117.97/18.59 | |
% 117.97/18.59 | Case 2:
% 117.97/18.59 | |
% 117.97/18.59 | | (9) all_54_15 = e0
% 117.97/18.59 | |
% 117.97/18.59 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #419.
% 117.97/18.59 | |
% 117.97/18.59 | End of split
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #419 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) all_54_15 = all_4_2
% 117.97/18.59 (2) all_54_15 = e0
% 117.97/18.59 (3) ~ (all_4_2 = e0)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.59 | (4) all_4_2 = e0
% 117.97/18.59 |
% 117.97/18.59 | SIMP: (4) implies:
% 117.97/18.59 | (5) all_4_2 = e0
% 117.97/18.59 |
% 117.97/18.59 | REDUCE: (3), (5) imply:
% 117.97/18.59 | (6) $false
% 117.97/18.59 |
% 117.97/18.59 | CLOSE: (6) is inconsistent.
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #420 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) all_54_15 = all_4_2
% 117.97/18.59 (2) all_54_15 = e2
% 117.97/18.59 (3) ~ (all_4_2 = e2)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.59 |
% 117.97/18.59 | COMBINE_EQS: (1), (2) imply:
% 117.97/18.59 | (4) all_4_2 = e2
% 117.97/18.59 |
% 117.97/18.59 | SIMP: (4) implies:
% 117.97/18.59 | (5) all_4_2 = e2
% 117.97/18.59 |
% 117.97/18.59 | REDUCE: (3), (5) imply:
% 117.97/18.59 | (6) $false
% 117.97/18.59 |
% 117.97/18.59 | CLOSE: (6) is inconsistent.
% 117.97/18.59 |
% 117.97/18.59 End of proof
% 117.97/18.59
% 117.97/18.59 Sub-proof #421 shows that the following formulas are inconsistent:
% 117.97/18.59 ----------------------------------------------------------------
% 117.97/18.59 (1) all_58_7 = all_52_6
% 117.97/18.59 (2) ~ (all_56_6 = e1) | ~ (all_56_15 = e3)
% 117.97/18.59 (3) ~ (all_4_2 = e0)
% 117.97/18.59 (4) op(e3, e2) = all_52_4
% 117.97/18.59 (5) all_56_14 = all_6_2
% 117.97/18.59 (6) all_54_0 = all_10_2
% 117.97/18.59 (7) all_54_3 = all_52_12
% 117.97/18.59 (8) op(e0, e2) = all_52_7
% 117.97/18.59 (9) all_56_11 = all_52_11
% 117.97/18.59 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 117.97/18.59 (11) ~ (all_52_12 = all_10_2)
% 117.97/18.59 (12) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.59 (13) all_56_12 = all_10_2
% 117.97/18.59 (14) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.59 (15) ~ (all_52_14 = all_6_2)
% 117.97/18.59 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.59 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.59 (18) all_54_10 = all_6_2
% 117.97/18.59 (19) op(e3, e0) = all_52_12
% 117.97/18.59 (20) ~ (all_52_4 = all_52_7)
% 117.97/18.59 (21) all_58_3 = all_8_2
% 117.97/18.59 (22) ~ (all_10_0 = e2)
% 117.97/18.59 (23) all_58_11 = all_52_14
% 117.97/18.59 (24) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.59 (25) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.59 (26) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.59 (27) ~ (all_10_2 = e1)
% 117.97/18.59 (28) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.59 (29) all_58_5 = all_52_9
% 117.97/18.59 (30) all_56_9 = all_52_3
% 117.97/18.59 (31) ~ (all_56_8 = e1) | ~ (all_56_12 = e0)
% 117.97/18.59 (32) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.59 (33) all_58_15 = all_4_2
% 117.97/18.59 (34) all_58_2 = all_52_1
% 117.97/18.59 (35) ~ (all_10_2 = e3)
% 117.97/18.59 (36) all_58_13 = all_52_7
% 117.97/18.59 (37) all_58_6 = all_52_2
% 117.97/18.59 (38) ~ (all_52_1 = all_10_2)
% 117.97/18.59 (39) ~ (all_52_12 = e3)
% 117.97/18.59 (40) all_58_10 = all_52_13
% 117.97/18.59 (41) op(e3, all_10_2) = all_10_1
% 117.97/18.59 (42) ~ (all_10_1 = e2)
% 117.97/18.59 (43) all_58_1 = all_52_4
% 117.97/18.59 (44) all_58_14 = all_52_11
% 117.97/18.59 (45) all_54_1 = all_52_4
% 117.97/18.59 (46) all_56_13 = all_8_2
% 117.97/18.59 (47) ~ (all_8_2 = e2)
% 117.97/18.59 (48) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 117.97/18.59 (49) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 117.97/18.59 (50) all_56_7 = all_52_6
% 117.97/18.59 (51) all_58_8 = all_6_2
% 117.97/18.59 (52) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 117.97/18.59 (53) ~ (all_10_0 = e1)
% 117.97/18.59 (54) all_56_4 = all_52_9
% 117.97/18.59 (55) all_56_5 = all_52_13
% 117.97/18.59 (56) ~ (all_52_6 = all_6_2)
% 117.97/18.59 (57) all_56_6 = all_52_2
% 117.97/18.59 (58) all_58_12 = all_52_3
% 117.97/18.59 (59) all_56_15 = e3
% 117.97/18.59 (60) all_56_8 = all_52_14
% 117.97/18.59 (61) ~ (all_52_4 = all_10_2)
% 117.97/18.59 (62) ~ (all_10_1 = e1)
% 117.97/18.59 (63) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 117.97/18.59 (64) all_56_0 = all_52_4
% 117.97/18.59 (65) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 117.97/18.59 (66) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 117.97/18.59 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 117.97/18.59 (67) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 117.97/18.59 (68) ~ (all_6_2 = e1)
% 117.97/18.59
% 117.97/18.59 Begin of proof
% 117.97/18.60 |
% 117.97/18.60 | BETA: splitting (2) gives:
% 117.97/18.60 |
% 117.97/18.60 | Case 1:
% 117.97/18.60 | |
% 117.97/18.60 | | (69) ~ (all_56_6 = e1)
% 117.97/18.60 | |
% 117.97/18.60 | | REDUCE: (57), (69) imply:
% 117.97/18.60 | | (70) ~ (all_52_2 = e1)
% 117.97/18.60 | |
% 117.97/18.60 | | BETA: splitting (31) gives:
% 117.97/18.60 | |
% 117.97/18.60 | | Case 1:
% 117.97/18.60 | | |
% 117.97/18.60 | | | (71) ~ (all_56_8 = e1)
% 117.97/18.60 | | |
% 117.97/18.60 | | | REDUCE: (60), (71) imply:
% 117.97/18.60 | | | (72) ~ (all_52_14 = e1)
% 117.97/18.60 | | |
% 117.97/18.60 | | | REF_CLOSE: (1), (6), (7), (10), (11), (13), (17), (19), (23), (27), (32),
% 117.97/18.60 | | | (35), (37), (39), (41), (42), (48), (50), (51), (52), (62),
% 117.97/18.60 | | | (68), (70), (72) are inconsistent by sub-proof #444.
% 117.97/18.60 | | |
% 117.97/18.60 | | Case 2:
% 117.97/18.60 | | |
% 117.97/18.60 | | | (73) all_56_8 = e1
% 117.97/18.60 | | | (74) ~ (all_56_12 = e0)
% 117.97/18.60 | | |
% 117.97/18.60 | | | COMBINE_EQS: (60), (73) imply:
% 117.97/18.60 | | | (75) all_52_14 = e1
% 117.97/18.60 | | |
% 117.97/18.60 | | | SIMP: (75) implies:
% 117.97/18.60 | | | (76) all_52_14 = e1
% 117.97/18.60 | | |
% 117.97/18.60 | | | REDUCE: (13), (74) imply:
% 117.97/18.60 | | | (77) ~ (all_10_2 = e0)
% 117.97/18.60 | | |
% 117.97/18.60 | | | REDUCE: (15), (76) imply:
% 117.97/18.60 | | | (78) ~ (all_6_2 = e1)
% 117.97/18.60 | | |
% 117.97/18.60 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (12), (13), (14), (16),
% 117.97/18.60 | | | (17), (18), (20), (21), (22), (24), (25), (26), (27), (28),
% 117.97/18.60 | | | (29), (30), (32), (33), (34), (35), (36), (38), (40), (41),
% 117.97/18.60 | | | (43), (44), (45), (46), (47), (49), (50), (52), (53), (54),
% 117.97/18.60 | | | (55), (56), (58), (61), (62), (63), (64), (65), (66), (67),
% 117.97/18.60 | | | (68), (77) are inconsistent by sub-proof #422.
% 117.97/18.60 | | |
% 117.97/18.60 | | End of split
% 117.97/18.60 | |
% 117.97/18.60 | Case 2:
% 117.97/18.60 | |
% 117.97/18.60 | | (79) ~ (all_56_15 = e3)
% 117.97/18.60 | |
% 117.97/18.60 | | REDUCE: (59), (79) imply:
% 117.97/18.60 | | (80) $false
% 117.97/18.60 | |
% 117.97/18.60 | | CLOSE: (80) is inconsistent.
% 117.97/18.60 | |
% 117.97/18.60 | End of split
% 117.97/18.60 |
% 117.97/18.60 End of proof
% 117.97/18.60
% 117.97/18.60 Sub-proof #422 shows that the following formulas are inconsistent:
% 117.97/18.60 ----------------------------------------------------------------
% 117.97/18.60 (1) all_58_7 = all_52_6
% 117.97/18.60 (2) ~ (all_4_2 = e0)
% 117.97/18.60 (3) op(e3, e2) = all_52_4
% 117.97/18.60 (4) all_56_14 = all_6_2
% 117.97/18.60 (5) all_54_0 = all_10_2
% 117.97/18.60 (6) op(e0, e2) = all_52_7
% 117.97/18.60 (7) all_56_11 = all_52_11
% 117.97/18.60 (8) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 117.97/18.60 (9) all_56_12 = all_10_2
% 117.97/18.60 (10) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 117.97/18.60 (11) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 117.97/18.60 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.97/18.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 117.97/18.60 (13) all_54_10 = all_6_2
% 117.97/18.60 (14) ~ (all_52_4 = all_52_7)
% 117.97/18.60 (15) all_58_3 = all_8_2
% 117.97/18.60 (16) ~ (all_10_0 = e2)
% 117.97/18.60 (17) op(all_10_1, all_10_2) = all_10_0
% 117.97/18.60 (18) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 117.97/18.60 (19) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 117.97/18.60 (20) ~ (all_10_2 = e1)
% 117.97/18.60 (21) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 117.97/18.60 (22) all_58_5 = all_52_9
% 117.97/18.60 (23) all_56_9 = all_52_3
% 117.97/18.60 (24) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 117.97/18.60 (25) all_58_15 = all_4_2
% 117.97/18.60 (26) all_58_2 = all_52_1
% 117.97/18.60 (27) ~ (all_10_2 = e3)
% 117.97/18.60 (28) all_58_13 = all_52_7
% 117.97/18.60 (29) ~ (all_52_1 = all_10_2)
% 118.22/18.60 (30) all_58_10 = all_52_13
% 118.22/18.60 (31) op(e3, all_10_2) = all_10_1
% 118.22/18.60 (32) all_58_1 = all_52_4
% 118.22/18.60 (33) all_58_14 = all_52_11
% 118.22/18.60 (34) all_54_1 = all_52_4
% 118.22/18.60 (35) all_56_13 = all_8_2
% 118.22/18.60 (36) ~ (all_8_2 = e2)
% 118.22/18.60 (37) ~ (all_10_2 = e0)
% 118.22/18.60 (38) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 118.22/18.60 (39) all_56_7 = all_52_6
% 118.22/18.60 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 118.22/18.60 (41) ~ (all_10_0 = e1)
% 118.22/18.60 (42) all_56_4 = all_52_9
% 118.22/18.60 (43) all_56_5 = all_52_13
% 118.22/18.60 (44) ~ (all_52_6 = all_6_2)
% 118.22/18.60 (45) all_58_12 = all_52_3
% 118.22/18.60 (46) ~ (all_52_4 = all_10_2)
% 118.22/18.60 (47) ~ (all_10_1 = e1)
% 118.22/18.60 (48) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 118.22/18.60 (49) all_56_0 = all_52_4
% 118.22/18.60 (50) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 118.22/18.60 (51) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 118.22/18.60 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 118.22/18.60 (52) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 118.22/18.60 (53) ~ (all_6_2 = e1)
% 118.22/18.60
% 118.22/18.60 Begin of proof
% 118.22/18.60 |
% 118.22/18.60 | BETA: splitting (40) gives:
% 118.22/18.60 |
% 118.22/18.60 | Case 1:
% 118.22/18.60 | |
% 118.22/18.60 | | (54) all_54_0 = e3
% 118.22/18.60 | |
% 118.22/18.60 | | REF_CLOSE: (5), (27), (54) are inconsistent by sub-proof #451.
% 118.22/18.60 | |
% 118.22/18.60 | Case 2:
% 118.22/18.60 | |
% 118.22/18.60 | | (55) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 118.22/18.60 | |
% 118.22/18.60 | | BETA: splitting (55) gives:
% 118.22/18.60 | |
% 118.22/18.60 | | Case 1:
% 118.22/18.60 | | |
% 118.22/18.60 | | | (56) all_54_0 = e2
% 118.22/18.60 | | |
% 118.22/18.60 | | | COMBINE_EQS: (5), (56) imply:
% 118.22/18.60 | | | (57) all_10_2 = e2
% 118.22/18.60 | | |
% 118.22/18.60 | | | SIMP: (57) implies:
% 118.22/18.60 | | | (58) all_10_2 = e2
% 118.22/18.60 | | |
% 118.22/18.60 | | | COMBINE_EQS: (9), (58) imply:
% 118.22/18.60 | | | (59) all_56_12 = e2
% 118.22/18.60 | | |
% 118.22/18.60 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13),
% 118.22/18.60 | | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 118.22/18.60 | | | (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 118.22/18.60 | | | (36), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 118.22/18.60 | | | (48), (49), (50), (51), (52), (53), (58), (59) are inconsistent
% 118.22/18.60 | | | by sub-proof #425.
% 118.22/18.60 | | |
% 118.22/18.60 | | Case 2:
% 118.22/18.60 | | |
% 118.22/18.60 | | | (60) all_54_0 = e1 | all_54_0 = e0
% 118.22/18.60 | | |
% 118.22/18.60 | | | REF_CLOSE: (5), (20), (37), (60) are inconsistent by sub-proof #423.
% 118.22/18.60 | | |
% 118.22/18.60 | | End of split
% 118.22/18.60 | |
% 118.22/18.60 | End of split
% 118.22/18.60 |
% 118.22/18.60 End of proof
% 118.22/18.60
% 118.22/18.60 Sub-proof #423 shows that the following formulas are inconsistent:
% 118.22/18.60 ----------------------------------------------------------------
% 118.22/18.60 (1) all_54_0 = e1 | all_54_0 = e0
% 118.22/18.60 (2) all_54_0 = all_10_2
% 118.22/18.60 (3) ~ (all_10_2 = e1)
% 118.22/18.60 (4) ~ (all_10_2 = e0)
% 118.22/18.60
% 118.22/18.60 Begin of proof
% 118.22/18.60 |
% 118.22/18.60 | BETA: splitting (1) gives:
% 118.22/18.60 |
% 118.22/18.60 | Case 1:
% 118.22/18.60 | |
% 118.22/18.60 | | (5) all_54_0 = e1
% 118.22/18.60 | |
% 118.22/18.60 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #449.
% 118.22/18.60 | |
% 118.22/18.60 | Case 2:
% 118.22/18.60 | |
% 118.22/18.60 | | (6) all_54_0 = e0
% 118.22/18.60 | |
% 118.22/18.60 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #424.
% 118.22/18.60 | |
% 118.22/18.60 | End of split
% 118.22/18.60 |
% 118.22/18.60 End of proof
% 118.22/18.60
% 118.22/18.60 Sub-proof #424 shows that the following formulas are inconsistent:
% 118.22/18.60 ----------------------------------------------------------------
% 118.22/18.60 (1) all_54_0 = all_10_2
% 118.22/18.60 (2) all_54_0 = e0
% 118.22/18.60 (3) ~ (all_10_2 = e0)
% 118.22/18.60
% 118.22/18.60 Begin of proof
% 118.22/18.60 |
% 118.22/18.60 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.60 | (4) all_10_2 = e0
% 118.22/18.60 |
% 118.22/18.60 | SIMP: (4) implies:
% 118.22/18.60 | (5) all_10_2 = e0
% 118.22/18.60 |
% 118.22/18.60 | REDUCE: (3), (5) imply:
% 118.22/18.60 | (6) $false
% 118.22/18.60 |
% 118.22/18.60 | CLOSE: (6) is inconsistent.
% 118.22/18.60 |
% 118.22/18.60 End of proof
% 118.22/18.60
% 118.22/18.60 Sub-proof #425 shows that the following formulas are inconsistent:
% 118.22/18.60 ----------------------------------------------------------------
% 118.22/18.60 (1) all_58_7 = all_52_6
% 118.22/18.60 (2) ~ (all_4_2 = e0)
% 118.22/18.60 (3) op(e3, e2) = all_52_4
% 118.22/18.60 (4) all_56_14 = all_6_2
% 118.22/18.60 (5) op(e0, e2) = all_52_7
% 118.22/18.60 (6) all_56_11 = all_52_11
% 118.22/18.60 (7) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 118.22/18.60 (8) all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 118.22/18.60 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.60 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.22/18.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 118.22/18.60 (11) all_10_2 = e2
% 118.22/18.60 (12) all_54_10 = all_6_2
% 118.22/18.60 (13) ~ (all_52_4 = all_52_7)
% 118.22/18.60 (14) all_56_12 = e2
% 118.22/18.60 (15) all_58_3 = all_8_2
% 118.22/18.60 (16) ~ (all_10_0 = e2)
% 118.22/18.60 (17) op(all_10_1, all_10_2) = all_10_0
% 118.22/18.60 (18) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 118.22/18.60 (19) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 118.22/18.60 (20) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.60 (21) all_58_5 = all_52_9
% 118.22/18.60 (22) all_56_9 = all_52_3
% 118.22/18.60 (23) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 118.22/18.60 (24) all_58_15 = all_4_2
% 118.22/18.60 (25) all_58_2 = all_52_1
% 118.22/18.60 (26) all_58_13 = all_52_7
% 118.22/18.60 (27) ~ (all_52_1 = all_10_2)
% 118.22/18.60 (28) all_58_10 = all_52_13
% 118.22/18.60 (29) op(e3, all_10_2) = all_10_1
% 118.22/18.60 (30) all_58_1 = all_52_4
% 118.22/18.60 (31) all_58_14 = all_52_11
% 118.22/18.60 (32) all_54_1 = all_52_4
% 118.22/18.60 (33) all_56_13 = all_8_2
% 118.22/18.60 (34) ~ (all_8_2 = e2)
% 118.22/18.60 (35) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 118.22/18.60 (36) all_56_7 = all_52_6
% 118.22/18.60 (37) ~ (all_10_0 = e1)
% 118.22/18.60 (38) all_56_4 = all_52_9
% 118.22/18.60 (39) all_56_5 = all_52_13
% 118.22/18.60 (40) ~ (all_52_6 = all_6_2)
% 118.22/18.60 (41) all_58_12 = all_52_3
% 118.22/18.60 (42) ~ (all_52_4 = all_10_2)
% 118.22/18.60 (43) ~ (all_10_1 = e1)
% 118.22/18.60 (44) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 118.22/18.60 (45) all_56_0 = all_52_4
% 118.22/18.60 (46) all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 118.22/18.60 (47) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 118.22/18.60 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 118.22/18.60 (48) ~ (all_56_0 = e3) | ~ (all_56_12 = e2)
% 118.22/18.60 (49) ~ (all_6_2 = e1)
% 118.22/18.60
% 118.22/18.60 Begin of proof
% 118.22/18.60 |
% 118.22/18.60 | REDUCE: (11), (27) imply:
% 118.22/18.60 | (50) ~ (all_52_1 = e2)
% 118.22/18.60 |
% 118.22/18.60 | REDUCE: (11), (42) imply:
% 118.22/18.60 | (51) ~ (all_52_4 = e2)
% 118.22/18.60 |
% 118.22/18.60 | REDUCE: (11), (17) imply:
% 118.22/18.60 | (52) op(all_10_1, e2) = all_10_0
% 118.22/18.60 |
% 118.22/18.60 | REDUCE: (11), (29) imply:
% 118.22/18.60 | (53) op(e3, e2) = all_10_1
% 118.22/18.60 |
% 118.22/18.60 | BETA: splitting (23) gives:
% 118.22/18.60 |
% 118.22/18.60 | Case 1:
% 118.22/18.60 | |
% 118.22/18.60 | | (54) ~ (all_56_7 = e1)
% 118.22/18.60 | |
% 118.22/18.60 | | REDUCE: (36), (54) imply:
% 118.22/18.60 | | (55) ~ (all_52_6 = e1)
% 118.22/18.60 | |
% 118.22/18.60 | | BETA: splitting (48) gives:
% 118.22/18.60 | |
% 118.22/18.60 | | Case 1:
% 118.22/18.60 | | |
% 118.22/18.60 | | | (56) ~ (all_56_0 = e3)
% 118.22/18.60 | | |
% 118.22/18.60 | | | REDUCE: (45), (56) imply:
% 118.22/18.60 | | | (57) ~ (all_52_4 = e3)
% 118.22/18.60 | | |
% 118.22/18.60 | | | GROUND_INST: instantiating (10) with all_52_4, all_10_1, e2, e3,
% 118.22/18.60 | | | simplifying with (3), (53) gives:
% 118.22/18.60 | | | (58) all_52_4 = all_10_1
% 118.22/18.60 | | |
% 118.22/18.60 | | | COMBINE_EQS: (32), (58) imply:
% 118.22/18.60 | | | (59) all_54_1 = all_10_1
% 118.22/18.60 | | |
% 118.22/18.60 | | | COMBINE_EQS: (30), (58) imply:
% 118.22/18.60 | | | (60) all_58_1 = all_10_1
% 118.22/18.60 | | |
% 118.22/18.60 | | | REDUCE: (13), (58) imply:
% 118.22/18.60 | | | (61) ~ (all_52_7 = all_10_1)
% 118.22/18.60 | | |
% 118.22/18.60 | | | SIMP: (61) implies:
% 118.22/18.60 | | | (62) ~ (all_52_7 = all_10_1)
% 118.22/18.60 | | |
% 118.22/18.60 | | | REDUCE: (57), (58) imply:
% 118.22/18.60 | | | (63) ~ (all_10_1 = e3)
% 118.22/18.60 | | |
% 118.22/18.60 | | | REDUCE: (51), (58) imply:
% 118.22/18.60 | | | (64) ~ (all_10_1 = e2)
% 118.22/18.60 | | |
% 118.22/18.60 | | | BETA: splitting (35) gives:
% 118.22/18.60 | | |
% 118.22/18.60 | | | Case 1:
% 118.22/18.60 | | | |
% 118.22/18.60 | | | | (65) all_54_1 = e3
% 118.22/18.60 | | | |
% 118.22/18.60 | | | | REF_CLOSE: (59), (63), (65) are inconsistent by sub-proof #443.
% 118.22/18.60 | | | |
% 118.22/18.60 | | | Case 2:
% 118.22/18.60 | | | |
% 118.22/18.60 | | | | (66) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 118.22/18.60 | | | |
% 118.22/18.60 | | | | BETA: splitting (66) gives:
% 118.22/18.60 | | | |
% 118.22/18.60 | | | | Case 1:
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | | (67) all_54_1 = e2
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | | REF_CLOSE: (59), (64), (67) are inconsistent by sub-proof #442.
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | Case 2:
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | | (68) ~ (all_54_1 = e2)
% 118.22/18.60 | | | | | (69) all_54_1 = e1 | all_54_1 = e0
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | | BETA: splitting (69) gives:
% 118.22/18.60 | | | | |
% 118.22/18.60 | | | | | Case 1:
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | (70) all_54_1 = e1
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | COMBINE_EQS: (59), (70) imply:
% 118.22/18.60 | | | | | | (71) all_10_1 = e1
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | SIMP: (71) implies:
% 118.22/18.60 | | | | | | (72) all_10_1 = e1
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | REDUCE: (43), (72) imply:
% 118.22/18.60 | | | | | | (73) $false
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | CLOSE: (73) is inconsistent.
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | Case 2:
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | (74) all_54_1 = e0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | COMBINE_EQS: (59), (74) imply:
% 118.22/18.60 | | | | | | (75) all_10_1 = e0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | SIMP: (75) implies:
% 118.22/18.60 | | | | | | (76) all_10_1 = e0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | COMBINE_EQS: (60), (76) imply:
% 118.22/18.60 | | | | | | (77) all_58_1 = e0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | REDUCE: (62), (76) imply:
% 118.22/18.60 | | | | | | (78) ~ (all_52_7 = e0)
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | REDUCE: (64), (76) imply:
% 118.22/18.60 | | | | | | (79) ~ (e2 = e0)
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | SIMP: (79) implies:
% 118.22/18.60 | | | | | | (80) ~ (e2 = e0)
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | REDUCE: (43), (76) imply:
% 118.22/18.60 | | | | | | (81) ~ (e1 = e0)
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | SIMP: (81) implies:
% 118.22/18.60 | | | | | | (82) ~ (e1 = e0)
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | REDUCE: (52), (76) imply:
% 118.22/18.60 | | | | | | (83) op(e0, e2) = all_10_0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | GROUND_INST: instantiating (10) with all_52_7, all_10_0, e2, e0,
% 118.22/18.60 | | | | | | simplifying with (5), (83) gives:
% 118.22/18.60 | | | | | | (84) all_52_7 = all_10_0
% 118.22/18.60 | | | | | |
% 118.22/18.60 | | | | | | COMBINE_EQS: (26), (84) imply:
% 118.22/18.61 | | | | | | (85) all_58_13 = all_10_0
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | BETA: splitting (8) gives:
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | Case 1:
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | (86) all_58_1 = e2
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | REF_CLOSE: (77), (80), (86) are inconsistent by sub-proof #441.
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | Case 2:
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | (87) all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | BETA: splitting (87) gives:
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | Case 1:
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | (88) all_58_3 = e2
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | COMBINE_EQS: (15), (88) imply:
% 118.22/18.61 | | | | | | | | (89) all_8_2 = e2
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | REDUCE: (34), (89) imply:
% 118.22/18.61 | | | | | | | | (90) $false
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | CLOSE: (90) is inconsistent.
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | Case 2:
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | (91) all_58_7 = e2 | all_58_13 = e2
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | BETA: splitting (91) gives:
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | | Case 1:
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | (92) all_58_7 = e2
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | COMBINE_EQS: (1), (92) imply:
% 118.22/18.61 | | | | | | | | | (93) all_52_6 = e2
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | REDUCE: (40), (93) imply:
% 118.22/18.61 | | | | | | | | | (94) ~ (all_6_2 = e2)
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | SIMP: (94) implies:
% 118.22/18.61 | | | | | | | | | (95) ~ (all_6_2 = e2)
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | REDUCE: (55), (93) imply:
% 118.22/18.61 | | | | | | | | | (96) ~ (e2 = e1)
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | BETA: splitting (46) gives:
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | Case 1:
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | (97) all_58_1 = e1
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | REF_CLOSE: (77), (82), (97) are inconsistent by sub-proof
% 118.22/18.61 | | | | | | | | | | #440.
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | Case 2:
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | (98) all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | BETA: splitting (98) gives:
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | Case 1:
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | (99) all_58_3 = e1
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | COMBINE_EQS: (15), (99) imply:
% 118.22/18.61 | | | | | | | | | | | (100) all_8_2 = e1
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (12), (15), (18), (19),
% 118.22/18.61 | | | | | | | | | | | (20), (21), (22), (24), (25), (26), (28), (31),
% 118.22/18.61 | | | | | | | | | | | (33), (38), (39), (41), (44), (47), (49), (50),
% 118.22/18.61 | | | | | | | | | | | (78), (95), (96), (100) are inconsistent by
% 118.22/18.61 | | | | | | | | | | | sub-proof #426.
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | Case 2:
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | (101) all_58_7 = e1 | all_58_13 = e1
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | BETA: splitting (101) gives:
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | Case 1:
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | (102) all_58_7 = e1
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | COMBINE_EQS: (92), (102) imply:
% 118.22/18.61 | | | | | | | | | | | | (103) e2 = e1
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | REDUCE: (96), (103) imply:
% 118.22/18.61 | | | | | | | | | | | | (104) $false
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | CLOSE: (104) is inconsistent.
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | Case 2:
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | (105) all_58_13 = e1
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | COMBINE_EQS: (85), (105) imply:
% 118.22/18.61 | | | | | | | | | | | | (106) all_10_0 = e1
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | REDUCE: (37), (106) imply:
% 118.22/18.61 | | | | | | | | | | | | (107) $false
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 118.22/18.61 | | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | | End of split
% 118.22/18.61 | | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | | End of split
% 118.22/18.61 | | | | | | | | | |
% 118.22/18.61 | | | | | | | | | End of split
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | Case 2:
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | (108) all_58_13 = e2
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | COMBINE_EQS: (85), (108) imply:
% 118.22/18.61 | | | | | | | | | (109) all_10_0 = e2
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | SIMP: (109) implies:
% 118.22/18.61 | | | | | | | | | (110) all_10_0 = e2
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | REDUCE: (16), (110) imply:
% 118.22/18.61 | | | | | | | | | (111) $false
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | | CLOSE: (111) is inconsistent.
% 118.22/18.61 | | | | | | | | |
% 118.22/18.61 | | | | | | | | End of split
% 118.22/18.61 | | | | | | | |
% 118.22/18.61 | | | | | | | End of split
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | End of split
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | End of split
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | End of split
% 118.22/18.61 | | | |
% 118.22/18.61 | | | End of split
% 118.22/18.61 | | |
% 118.22/18.61 | | Case 2:
% 118.22/18.61 | | |
% 118.22/18.61 | | | (112) ~ (all_56_12 = e2)
% 118.22/18.61 | | |
% 118.22/18.61 | | | REDUCE: (14), (112) imply:
% 118.22/18.61 | | | (113) $false
% 118.22/18.61 | | |
% 118.22/18.61 | | | CLOSE: (113) is inconsistent.
% 118.22/18.61 | | |
% 118.22/18.61 | | End of split
% 118.22/18.61 | |
% 118.22/18.61 | Case 2:
% 118.22/18.61 | |
% 118.22/18.61 | | (114) ~ (all_56_12 = e2)
% 118.22/18.61 | |
% 118.22/18.61 | | REDUCE: (14), (114) imply:
% 118.22/18.61 | | (115) $false
% 118.22/18.61 | |
% 118.22/18.61 | | CLOSE: (115) is inconsistent.
% 118.22/18.61 | |
% 118.22/18.61 | End of split
% 118.22/18.61 |
% 118.22/18.61 End of proof
% 118.22/18.61
% 118.22/18.61 Sub-proof #426 shows that the following formulas are inconsistent:
% 118.22/18.61 ----------------------------------------------------------------
% 118.22/18.61 (1) ~ (all_52_1 = e2)
% 118.22/18.61 (2) ~ (all_4_2 = e0)
% 118.22/18.61 (3) all_56_14 = all_6_2
% 118.22/18.61 (4) all_56_11 = all_52_11
% 118.22/18.61 (5) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 118.22/18.61 (6) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.61 (7) all_54_10 = all_6_2
% 118.22/18.61 (8) ~ (e2 = e1)
% 118.22/18.61 (9) all_58_3 = all_8_2
% 118.22/18.61 (10) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 118.22/18.61 (11) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 118.22/18.61 (12) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.61 (13) all_58_5 = all_52_9
% 118.22/18.61 (14) all_56_9 = all_52_3
% 118.22/18.61 (15) all_58_15 = all_4_2
% 118.22/18.61 (16) all_58_2 = all_52_1
% 118.22/18.61 (17) all_58_13 = all_52_7
% 118.22/18.61 (18) ~ (all_52_7 = e0)
% 118.22/18.61 (19) all_58_10 = all_52_13
% 118.22/18.61 (20) all_8_2 = e1
% 118.22/18.61 (21) all_58_14 = all_52_11
% 118.22/18.61 (22) all_56_13 = all_8_2
% 118.22/18.61 (23) ~ (all_6_2 = e2)
% 118.22/18.61 (24) all_56_4 = all_52_9
% 118.22/18.61 (25) all_56_5 = all_52_13
% 118.22/18.61 (26) all_58_12 = all_52_3
% 118.22/18.61 (27) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 118.22/18.61 (28) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 118.22/18.61 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 118.22/18.61 (29) ~ (all_6_2 = e1)
% 118.22/18.61
% 118.22/18.61 Begin of proof
% 118.22/18.61 |
% 118.22/18.61 | COMBINE_EQS: (20), (22) imply:
% 118.22/18.61 | (30) all_56_13 = e1
% 118.22/18.61 |
% 118.22/18.61 | COMBINE_EQS: (9), (20) imply:
% 118.22/18.61 | (31) all_58_3 = e1
% 118.22/18.61 |
% 118.22/18.61 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 118.22/18.61 | (14), (15), (16), (17), (18), (19), (21), (23), (24), (25), (26),
% 118.22/18.61 | (27), (28), (29), (30), (31) are inconsistent by sub-proof #427.
% 118.22/18.61 |
% 118.22/18.61 End of proof
% 118.22/18.61
% 118.22/18.61 Sub-proof #427 shows that the following formulas are inconsistent:
% 118.22/18.61 ----------------------------------------------------------------
% 118.22/18.61 (1) ~ (all_52_1 = e2)
% 118.22/18.61 (2) all_58_3 = e1
% 118.22/18.61 (3) ~ (all_4_2 = e0)
% 118.22/18.61 (4) all_56_14 = all_6_2
% 118.22/18.61 (5) all_56_11 = all_52_11
% 118.22/18.61 (6) ~ (all_56_4 = e2) | ~ (all_56_13 = e1)
% 118.22/18.61 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.61 (8) all_54_10 = all_6_2
% 118.22/18.61 (9) ~ (e2 = e1)
% 118.22/18.61 (10) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 118.22/18.61 (11) ~ (all_56_11 = e0) | ~ (all_56_13 = e1)
% 118.22/18.61 (12) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.61 (13) all_58_5 = all_52_9
% 118.22/18.61 (14) all_56_9 = all_52_3
% 118.22/18.61 (15) all_58_15 = all_4_2
% 118.22/18.61 (16) all_58_2 = all_52_1
% 118.22/18.61 (17) all_58_13 = all_52_7
% 118.22/18.61 (18) ~ (all_52_7 = e0)
% 118.22/18.61 (19) all_58_10 = all_52_13
% 118.22/18.61 (20) all_58_14 = all_52_11
% 118.22/18.61 (21) ~ (all_6_2 = e2)
% 118.22/18.61 (22) all_56_13 = e1
% 118.22/18.61 (23) all_56_4 = all_52_9
% 118.22/18.61 (24) all_56_5 = all_52_13
% 118.22/18.61 (25) all_58_12 = all_52_3
% 118.22/18.61 (26) all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 118.22/18.61 (27) all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 118.22/18.61 (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 118.22/18.61 (28) ~ (all_6_2 = e1)
% 118.22/18.61
% 118.22/18.61 Begin of proof
% 118.22/18.61 |
% 118.22/18.61 | BETA: splitting (6) gives:
% 118.22/18.61 |
% 118.22/18.61 | Case 1:
% 118.22/18.61 | |
% 118.22/18.61 | | (29) ~ (all_56_4 = e2)
% 118.22/18.61 | |
% 118.22/18.61 | | REDUCE: (23), (29) imply:
% 118.22/18.61 | | (30) ~ (all_52_9 = e2)
% 118.22/18.61 | |
% 118.22/18.61 | | BETA: splitting (11) gives:
% 118.22/18.61 | |
% 118.22/18.61 | | Case 1:
% 118.22/18.61 | | |
% 118.22/18.61 | | | (31) ~ (all_56_13 = e1)
% 118.22/18.61 | | |
% 118.22/18.61 | | | REDUCE: (22), (31) imply:
% 118.22/18.61 | | | (32) $false
% 118.22/18.61 | | |
% 118.22/18.61 | | | CLOSE: (32) is inconsistent.
% 118.22/18.61 | | |
% 118.22/18.61 | | Case 2:
% 118.22/18.61 | | |
% 118.22/18.61 | | | (33) ~ (all_56_11 = e0)
% 118.22/18.61 | | |
% 118.22/18.61 | | | REDUCE: (5), (33) imply:
% 118.22/18.61 | | | (34) ~ (all_52_11 = e0)
% 118.22/18.61 | | |
% 118.22/18.61 | | | BETA: splitting (26) gives:
% 118.22/18.61 | | |
% 118.22/18.61 | | | Case 1:
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | (35) all_58_2 = e2
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | COMBINE_EQS: (16), (35) imply:
% 118.22/18.61 | | | | (36) all_52_1 = e2
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | REDUCE: (1), (36) imply:
% 118.22/18.61 | | | | (37) $false
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | CLOSE: (37) is inconsistent.
% 118.22/18.61 | | | |
% 118.22/18.61 | | | Case 2:
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | (38) all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | BETA: splitting (38) gives:
% 118.22/18.61 | | | |
% 118.22/18.61 | | | | Case 1:
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | | (39) all_58_3 = e2
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | | REF_CLOSE: (2), (9), (39) are inconsistent by sub-proof #439.
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | Case 2:
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | | (40) all_58_5 = e2 | all_58_10 = e2
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | | BETA: splitting (27) gives:
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | | Case 1:
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | (41) all_58_15 = e0
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | COMBINE_EQS: (15), (41) imply:
% 118.22/18.61 | | | | | | (42) all_4_2 = e0
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | REDUCE: (3), (42) imply:
% 118.22/18.61 | | | | | | (43) $false
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | CLOSE: (43) is inconsistent.
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | Case 2:
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | (44) (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 118.22/18.61 | | | | | | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | ALPHA: (44) implies:
% 118.22/18.61 | | | | | | (45) all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | BETA: splitting (45) gives:
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | | Case 1:
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | (46) all_58_12 = e0
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | COMBINE_EQS: (25), (46) imply:
% 118.22/18.61 | | | | | | | (47) all_52_3 = e0
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | COMBINE_EQS: (14), (47) imply:
% 118.22/18.61 | | | | | | | (48) all_56_9 = e0
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | REF_CLOSE: (4), (7), (8), (10), (12), (13), (19), (21), (24),
% 118.22/18.61 | | | | | | | (28), (30), (40), (48) are inconsistent by sub-proof
% 118.22/18.61 | | | | | | | #431.
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | Case 2:
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | (49) all_58_13 = e0 | all_58_14 = e0
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | | REF_CLOSE: (17), (18), (20), (34), (49) are inconsistent by
% 118.22/18.61 | | | | | | | sub-proof #428.
% 118.22/18.61 | | | | | | |
% 118.22/18.61 | | | | | | End of split
% 118.22/18.61 | | | | | |
% 118.22/18.61 | | | | | End of split
% 118.22/18.61 | | | | |
% 118.22/18.61 | | | | End of split
% 118.22/18.61 | | | |
% 118.22/18.61 | | | End of split
% 118.22/18.61 | | |
% 118.22/18.61 | | End of split
% 118.22/18.61 | |
% 118.22/18.61 | Case 2:
% 118.22/18.61 | |
% 118.22/18.61 | | (50) ~ (all_56_13 = e1)
% 118.22/18.61 | |
% 118.22/18.61 | | REDUCE: (22), (50) imply:
% 118.22/18.61 | | (51) $false
% 118.22/18.61 | |
% 118.22/18.61 | | CLOSE: (51) is inconsistent.
% 118.22/18.61 | |
% 118.22/18.61 | End of split
% 118.22/18.61 |
% 118.22/18.61 End of proof
% 118.22/18.61
% 118.22/18.61 Sub-proof #428 shows that the following formulas are inconsistent:
% 118.22/18.61 ----------------------------------------------------------------
% 118.22/18.61 (1) all_58_13 = all_52_7
% 118.22/18.61 (2) ~ (all_52_7 = e0)
% 118.22/18.61 (3) all_58_14 = all_52_11
% 118.22/18.61 (4) all_58_13 = e0 | all_58_14 = e0
% 118.22/18.61 (5) ~ (all_52_11 = e0)
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | BETA: splitting (4) gives:
% 118.22/18.62 |
% 118.22/18.62 | Case 1:
% 118.22/18.62 | |
% 118.22/18.62 | | (6) all_58_13 = e0
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #430.
% 118.22/18.62 | |
% 118.22/18.62 | Case 2:
% 118.22/18.62 | |
% 118.22/18.62 | | (7) all_58_14 = e0
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #429.
% 118.22/18.62 | |
% 118.22/18.62 | End of split
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #429 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) all_58_14 = all_52_11
% 118.22/18.62 (2) all_58_14 = e0
% 118.22/18.62 (3) ~ (all_52_11 = e0)
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.62 | (4) all_52_11 = e0
% 118.22/18.62 |
% 118.22/18.62 | SIMP: (4) implies:
% 118.22/18.62 | (5) all_52_11 = e0
% 118.22/18.62 |
% 118.22/18.62 | REDUCE: (3), (5) imply:
% 118.22/18.62 | (6) $false
% 118.22/18.62 |
% 118.22/18.62 | CLOSE: (6) is inconsistent.
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #430 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) all_58_13 = all_52_7
% 118.22/18.62 (2) all_58_13 = e0
% 118.22/18.62 (3) ~ (all_52_7 = e0)
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.62 | (4) all_52_7 = e0
% 118.22/18.62 |
% 118.22/18.62 | SIMP: (4) implies:
% 118.22/18.62 | (5) all_52_7 = e0
% 118.22/18.62 |
% 118.22/18.62 | REDUCE: (3), (5) imply:
% 118.22/18.62 | (6) $false
% 118.22/18.62 |
% 118.22/18.62 | CLOSE: (6) is inconsistent.
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #431 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) ~ (all_52_9 = e2)
% 118.22/18.62 (2) all_56_14 = all_6_2
% 118.22/18.62 (3) all_58_5 = e2 | all_58_10 = e2
% 118.22/18.62 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.62 (5) all_54_10 = all_6_2
% 118.22/18.62 (6) ~ (all_56_9 = e0) | ~ (all_56_14 = e3)
% 118.22/18.62 (7) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.62 (8) all_58_5 = all_52_9
% 118.22/18.62 (9) all_58_10 = all_52_13
% 118.22/18.62 (10) ~ (all_6_2 = e2)
% 118.22/18.62 (11) all_56_9 = e0
% 118.22/18.62 (12) all_56_5 = all_52_13
% 118.22/18.62 (13) ~ (all_6_2 = e1)
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | BETA: splitting (6) gives:
% 118.22/18.62 |
% 118.22/18.62 | Case 1:
% 118.22/18.62 | |
% 118.22/18.62 | | (14) ~ (all_56_14 = e3)
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (2), (14) imply:
% 118.22/18.62 | | (15) ~ (all_6_2 = e3)
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (15)
% 118.22/18.62 | | are inconsistent by sub-proof #432.
% 118.22/18.62 | |
% 118.22/18.62 | Case 2:
% 118.22/18.62 | |
% 118.22/18.62 | | (16) ~ (all_56_9 = e0)
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (11), (16) imply:
% 118.22/18.62 | | (17) $false
% 118.22/18.62 | |
% 118.22/18.62 | | CLOSE: (17) is inconsistent.
% 118.22/18.62 | |
% 118.22/18.62 | End of split
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #432 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) ~ (all_52_9 = e2)
% 118.22/18.62 (2) all_56_14 = all_6_2
% 118.22/18.62 (3) all_58_5 = e2 | all_58_10 = e2
% 118.22/18.62 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.62 (5) all_54_10 = all_6_2
% 118.22/18.62 (6) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.62 (7) all_58_5 = all_52_9
% 118.22/18.62 (8) all_58_10 = all_52_13
% 118.22/18.62 (9) ~ (all_6_2 = e2)
% 118.22/18.62 (10) all_56_5 = all_52_13
% 118.22/18.62 (11) ~ (all_6_2 = e3)
% 118.22/18.62 (12) ~ (all_6_2 = e1)
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | BETA: splitting (4) gives:
% 118.22/18.62 |
% 118.22/18.62 | Case 1:
% 118.22/18.62 | |
% 118.22/18.62 | | (13) all_54_10 = e3
% 118.22/18.62 | |
% 118.22/18.62 | | COMBINE_EQS: (5), (13) imply:
% 118.22/18.62 | | (14) all_6_2 = e3
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (11), (14) imply:
% 118.22/18.62 | | (15) $false
% 118.22/18.62 | |
% 118.22/18.62 | | CLOSE: (15) is inconsistent.
% 118.22/18.62 | |
% 118.22/18.62 | Case 2:
% 118.22/18.62 | |
% 118.22/18.62 | | (16) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (16) are
% 118.22/18.62 | | inconsistent by sub-proof #433.
% 118.22/18.62 | |
% 118.22/18.62 | End of split
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #433 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) ~ (all_52_9 = e2)
% 118.22/18.62 (2) all_56_14 = all_6_2
% 118.22/18.62 (3) all_58_5 = e2 | all_58_10 = e2
% 118.22/18.62 (4) all_54_10 = all_6_2
% 118.22/18.62 (5) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.62 (6) all_58_5 = all_52_9
% 118.22/18.62 (7) all_58_10 = all_52_13
% 118.22/18.62 (8) ~ (all_6_2 = e2)
% 118.22/18.62 (9) all_56_5 = all_52_13
% 118.22/18.62 (10) ~ (all_6_2 = e1)
% 118.22/18.62 (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | BETA: splitting (3) gives:
% 118.22/18.62 |
% 118.22/18.62 | Case 1:
% 118.22/18.62 | |
% 118.22/18.62 | | (12) all_58_5 = e2
% 118.22/18.62 | |
% 118.22/18.62 | | COMBINE_EQS: (6), (12) imply:
% 118.22/18.62 | | (13) all_52_9 = e2
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (1), (13) imply:
% 118.22/18.62 | | (14) $false
% 118.22/18.62 | |
% 118.22/18.62 | | CLOSE: (14) is inconsistent.
% 118.22/18.62 | |
% 118.22/18.62 | Case 2:
% 118.22/18.62 | |
% 118.22/18.62 | | (15) all_58_10 = e2
% 118.22/18.62 | |
% 118.22/18.62 | | COMBINE_EQS: (7), (15) imply:
% 118.22/18.62 | | (16) all_52_13 = e2
% 118.22/18.62 | |
% 118.22/18.62 | | COMBINE_EQS: (9), (16) imply:
% 118.22/18.62 | | (17) all_56_5 = e2
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (17) are inconsistent by
% 118.22/18.62 | | sub-proof #434.
% 118.22/18.62 | |
% 118.22/18.62 | End of split
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #434 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) all_56_14 = all_6_2
% 118.22/18.62 (2) all_54_10 = all_6_2
% 118.22/18.62 (3) ~ (all_56_5 = e2) | ~ (all_56_14 = e0)
% 118.22/18.62 (4) all_56_5 = e2
% 118.22/18.62 (5) ~ (all_6_2 = e2)
% 118.22/18.62 (6) ~ (all_6_2 = e1)
% 118.22/18.62 (7) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.62
% 118.22/18.62 Begin of proof
% 118.22/18.62 |
% 118.22/18.62 | BETA: splitting (3) gives:
% 118.22/18.62 |
% 118.22/18.62 | Case 1:
% 118.22/18.62 | |
% 118.22/18.62 | | (8) ~ (all_56_5 = e2)
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (4), (8) imply:
% 118.22/18.62 | | (9) $false
% 118.22/18.62 | |
% 118.22/18.62 | | CLOSE: (9) is inconsistent.
% 118.22/18.62 | |
% 118.22/18.62 | Case 2:
% 118.22/18.62 | |
% 118.22/18.62 | | (10) ~ (all_56_14 = e0)
% 118.22/18.62 | |
% 118.22/18.62 | | REDUCE: (1), (10) imply:
% 118.22/18.62 | | (11) ~ (all_6_2 = e0)
% 118.22/18.62 | |
% 118.22/18.62 | | REF_CLOSE: (2), (5), (6), (7), (11) are inconsistent by sub-proof #435.
% 118.22/18.62 | |
% 118.22/18.62 | End of split
% 118.22/18.62 |
% 118.22/18.62 End of proof
% 118.22/18.62
% 118.22/18.62 Sub-proof #435 shows that the following formulas are inconsistent:
% 118.22/18.62 ----------------------------------------------------------------
% 118.22/18.62 (1) all_54_10 = all_6_2
% 118.22/18.62 (2) ~ (all_6_2 = e2)
% 118.22/18.62 (3) ~ (all_6_2 = e0)
% 118.22/18.62 (4) ~ (all_6_2 = e1)
% 118.22/18.63 (5) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | BETA: splitting (5) gives:
% 118.22/18.63 |
% 118.22/18.63 | Case 1:
% 118.22/18.63 | |
% 118.22/18.63 | | (6) all_54_10 = e2
% 118.22/18.63 | |
% 118.22/18.63 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #438.
% 118.22/18.63 | |
% 118.22/18.63 | Case 2:
% 118.22/18.63 | |
% 118.22/18.63 | | (7) all_54_10 = e1 | all_54_10 = e0
% 118.22/18.63 | |
% 118.22/18.63 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #436.
% 118.22/18.63 | |
% 118.22/18.63 | End of split
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #436 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_54_10 = e1 | all_54_10 = e0
% 118.22/18.63 (2) all_54_10 = all_6_2
% 118.22/18.63 (3) ~ (all_6_2 = e1)
% 118.22/18.63 (4) ~ (all_6_2 = e0)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | BETA: splitting (1) gives:
% 118.22/18.63 |
% 118.22/18.63 | Case 1:
% 118.22/18.63 | |
% 118.22/18.63 | | (5) all_54_10 = e1
% 118.22/18.63 | |
% 118.22/18.63 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #437.
% 118.22/18.63 | |
% 118.22/18.63 | Case 2:
% 118.22/18.63 | |
% 118.22/18.63 | | (6) all_54_10 = e0
% 118.22/18.63 | |
% 118.22/18.63 | | COMBINE_EQS: (2), (6) imply:
% 118.22/18.63 | | (7) all_6_2 = e0
% 118.22/18.63 | |
% 118.22/18.63 | | SIMP: (7) implies:
% 118.22/18.63 | | (8) all_6_2 = e0
% 118.22/18.63 | |
% 118.22/18.63 | | REDUCE: (4), (8) imply:
% 118.22/18.63 | | (9) $false
% 118.22/18.63 | |
% 118.22/18.63 | | CLOSE: (9) is inconsistent.
% 118.22/18.63 | |
% 118.22/18.63 | End of split
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #437 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_54_10 = all_6_2
% 118.22/18.63 (2) all_54_10 = e1
% 118.22/18.63 (3) ~ (all_6_2 = e1)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) all_6_2 = e1
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) all_6_2 = e1
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #438 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_54_10 = all_6_2
% 118.22/18.63 (2) all_54_10 = e2
% 118.22/18.63 (3) ~ (all_6_2 = e2)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) all_6_2 = e2
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) all_6_2 = e2
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #439 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_58_3 = e2
% 118.22/18.63 (2) all_58_3 = e1
% 118.22/18.63 (3) ~ (e2 = e1)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) e2 = e1
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) e2 = e1
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #440 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_58_1 = e1
% 118.22/18.63 (2) all_58_1 = e0
% 118.22/18.63 (3) ~ (e1 = e0)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) e1 = e0
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) e1 = e0
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #441 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_58_1 = e2
% 118.22/18.63 (2) all_58_1 = e0
% 118.22/18.63 (3) ~ (e2 = e0)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) e2 = e0
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) e2 = e0
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #442 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_54_1 = all_10_1
% 118.22/18.63 (2) all_54_1 = e2
% 118.22/18.63 (3) ~ (all_10_1 = e2)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) all_10_1 = e2
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) all_10_1 = e2
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #443 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_54_1 = all_10_1
% 118.22/18.63 (2) all_54_1 = e3
% 118.22/18.63 (3) ~ (all_10_1 = e3)
% 118.22/18.63
% 118.22/18.63 Begin of proof
% 118.22/18.63 |
% 118.22/18.63 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.63 | (4) all_10_1 = e3
% 118.22/18.63 |
% 118.22/18.63 | SIMP: (4) implies:
% 118.22/18.63 | (5) all_10_1 = e3
% 118.22/18.63 |
% 118.22/18.63 | REDUCE: (3), (5) imply:
% 118.22/18.63 | (6) $false
% 118.22/18.63 |
% 118.22/18.63 | CLOSE: (6) is inconsistent.
% 118.22/18.63 |
% 118.22/18.63 End of proof
% 118.22/18.63
% 118.22/18.63 Sub-proof #444 shows that the following formulas are inconsistent:
% 118.22/18.63 ----------------------------------------------------------------
% 118.22/18.63 (1) all_58_7 = all_52_6
% 118.22/18.63 (2) all_54_0 = all_10_2
% 118.22/18.63 (3) all_54_3 = all_52_12
% 118.22/18.63 (4) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 118.22/18.63 (5) ~ (all_52_12 = all_10_2)
% 118.22/18.63 (6) all_56_12 = all_10_2
% 118.22/18.63 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.22/18.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 118.22/18.63 (8) ~ (all_52_14 = e1)
% 118.22/18.63 (9) op(e3, e0) = all_52_12
% 118.22/18.63 (10) all_58_11 = all_52_14
% 118.22/18.63 (11) ~ (all_10_2 = e1)
% 118.22/18.63 (12) ~ (all_56_7 = e1) | ~ (all_56_12 = e2)
% 118.22/18.63 (13) ~ (all_10_2 = e3)
% 118.22/18.63 (14) all_58_6 = all_52_2
% 118.22/18.63 (15) ~ (all_52_2 = e1)
% 118.22/18.63 (16) ~ (all_52_12 = e3)
% 118.22/18.63 (17) op(e3, all_10_2) = all_10_1
% 118.22/18.63 (18) ~ (all_10_1 = e2)
% 118.22/18.64 (19) all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 118.22/18.64 (20) all_56_7 = all_52_6
% 118.22/18.64 (21) all_58_8 = all_6_2
% 118.22/18.64 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 118.22/18.64 (23) ~ (all_10_1 = e1)
% 118.22/18.64 (24) ~ (all_6_2 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | BETA: splitting (19) gives:
% 118.22/18.64 |
% 118.22/18.64 | Case 1:
% 118.22/18.64 | |
% 118.22/18.64 | | (25) all_58_6 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | REF_CLOSE: (14), (15), (25) are inconsistent by sub-proof #452.
% 118.22/18.64 | |
% 118.22/18.64 | Case 2:
% 118.22/18.64 | |
% 118.22/18.64 | | (26) all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | BETA: splitting (26) gives:
% 118.22/18.64 | |
% 118.22/18.64 | | Case 1:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (27) all_58_7 = e1
% 118.22/18.64 | | |
% 118.22/18.64 | | | COMBINE_EQS: (1), (27) imply:
% 118.22/18.64 | | | (28) all_52_6 = e1
% 118.22/18.64 | | |
% 118.22/18.64 | | | COMBINE_EQS: (20), (28) imply:
% 118.22/18.64 | | | (29) all_56_7 = e1
% 118.22/18.64 | | |
% 118.22/18.64 | | | BETA: splitting (12) gives:
% 118.22/18.64 | | |
% 118.22/18.64 | | | Case 1:
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | (30) ~ (all_56_7 = e1)
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REDUCE: (29), (30) imply:
% 118.22/18.64 | | | | (31) $false
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | CLOSE: (31) is inconsistent.
% 118.22/18.64 | | | |
% 118.22/18.64 | | | Case 2:
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | (32) ~ (all_56_12 = e2)
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REDUCE: (6), (32) imply:
% 118.22/18.64 | | | | (33) ~ (all_10_2 = e2)
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (11), (13), (16), (17), (18),
% 118.22/18.64 | | | | (22), (23), (33) are inconsistent by sub-proof #446.
% 118.22/18.64 | | | |
% 118.22/18.64 | | | End of split
% 118.22/18.64 | | |
% 118.22/18.64 | | Case 2:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (34) all_58_8 = e1 | all_58_11 = e1
% 118.22/18.64 | | |
% 118.22/18.64 | | | REF_CLOSE: (8), (10), (21), (24), (34) are inconsistent by sub-proof #445.
% 118.22/18.64 | | |
% 118.22/18.64 | | End of split
% 118.22/18.64 | |
% 118.22/18.64 | End of split
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #445 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) ~ (all_52_14 = e1)
% 118.22/18.64 (2) all_58_11 = all_52_14
% 118.22/18.64 (3) all_58_8 = all_6_2
% 118.22/18.64 (4) all_58_8 = e1 | all_58_11 = e1
% 118.22/18.64 (5) ~ (all_6_2 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | BETA: splitting (4) gives:
% 118.22/18.64 |
% 118.22/18.64 | Case 1:
% 118.22/18.64 | |
% 118.22/18.64 | | (6) all_58_8 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | COMBINE_EQS: (3), (6) imply:
% 118.22/18.64 | | (7) all_6_2 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | REDUCE: (5), (7) imply:
% 118.22/18.64 | | (8) $false
% 118.22/18.64 | |
% 118.22/18.64 | | CLOSE: (8) is inconsistent.
% 118.22/18.64 | |
% 118.22/18.64 | Case 2:
% 118.22/18.64 | |
% 118.22/18.64 | | (9) all_58_11 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | COMBINE_EQS: (2), (9) imply:
% 118.22/18.64 | | (10) all_52_14 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | SIMP: (10) implies:
% 118.22/18.64 | | (11) all_52_14 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | REDUCE: (1), (11) imply:
% 118.22/18.64 | | (12) $false
% 118.22/18.64 | |
% 118.22/18.64 | | CLOSE: (12) is inconsistent.
% 118.22/18.64 | |
% 118.22/18.64 | End of split
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #446 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_0 = all_10_2
% 118.22/18.64 (2) all_54_3 = all_52_12
% 118.22/18.64 (3) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 118.22/18.64 (4) ~ (all_52_12 = all_10_2)
% 118.22/18.64 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.22/18.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 118.22/18.64 (6) ~ (all_10_2 = e2)
% 118.22/18.64 (7) op(e3, e0) = all_52_12
% 118.22/18.64 (8) ~ (all_10_2 = e1)
% 118.22/18.64 (9) ~ (all_10_2 = e3)
% 118.22/18.64 (10) ~ (all_52_12 = e3)
% 118.22/18.64 (11) op(e3, all_10_2) = all_10_1
% 118.22/18.64 (12) ~ (all_10_1 = e2)
% 118.22/18.64 (13) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 118.22/18.64 (14) ~ (all_10_1 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | BETA: splitting (13) gives:
% 118.22/18.64 |
% 118.22/18.64 | Case 1:
% 118.22/18.64 | |
% 118.22/18.64 | | (15) all_54_0 = e3
% 118.22/18.64 | |
% 118.22/18.64 | | REF_CLOSE: (1), (9), (15) are inconsistent by sub-proof #451.
% 118.22/18.64 | |
% 118.22/18.64 | Case 2:
% 118.22/18.64 | |
% 118.22/18.64 | | (16) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 118.22/18.64 | |
% 118.22/18.64 | | BETA: splitting (16) gives:
% 118.22/18.64 | |
% 118.22/18.64 | | Case 1:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (17) all_54_0 = e2
% 118.22/18.64 | | |
% 118.22/18.64 | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #450.
% 118.22/18.64 | | |
% 118.22/18.64 | | Case 2:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (18) all_54_0 = e1 | all_54_0 = e0
% 118.22/18.64 | | |
% 118.22/18.64 | | | BETA: splitting (18) gives:
% 118.22/18.64 | | |
% 118.22/18.64 | | | Case 1:
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | (19) all_54_0 = e1
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REF_CLOSE: (1), (8), (19) are inconsistent by sub-proof #449.
% 118.22/18.64 | | | |
% 118.22/18.64 | | | Case 2:
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | (20) all_54_0 = e0
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | COMBINE_EQS: (1), (20) imply:
% 118.22/18.64 | | | | (21) all_10_2 = e0
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | SIMP: (21) implies:
% 118.22/18.64 | | | | (22) all_10_2 = e0
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REDUCE: (4), (22) imply:
% 118.22/18.64 | | | | (23) ~ (all_52_12 = e0)
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REDUCE: (11), (22) imply:
% 118.22/18.64 | | | | (24) op(e3, e0) = all_10_1
% 118.22/18.64 | | | |
% 118.22/18.64 | | | | REF_CLOSE: (2), (3), (5), (7), (10), (12), (14), (23), (24) are
% 118.22/18.64 | | | | inconsistent by sub-proof #447.
% 118.22/18.64 | | | |
% 118.22/18.64 | | | End of split
% 118.22/18.64 | | |
% 118.22/18.64 | | End of split
% 118.22/18.64 | |
% 118.22/18.64 | End of split
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #447 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_3 = all_52_12
% 118.22/18.64 (2) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 118.22/18.64 (3) op(e3, e0) = all_10_1
% 118.22/18.64 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 118.22/18.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 118.22/18.64 (5) op(e3, e0) = all_52_12
% 118.22/18.64 (6) ~ (all_52_12 = e0)
% 118.22/18.64 (7) ~ (all_52_12 = e3)
% 118.22/18.64 (8) ~ (all_10_1 = e2)
% 118.22/18.64 (9) ~ (all_10_1 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | GROUND_INST: instantiating (4) with all_52_12, all_10_1, e0, e3, simplifying
% 118.22/18.64 | with (3), (5) gives:
% 118.22/18.64 | (10) all_52_12 = all_10_1
% 118.22/18.64 |
% 118.22/18.64 | COMBINE_EQS: (1), (10) imply:
% 118.22/18.64 | (11) all_54_3 = all_10_1
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (7), (10) imply:
% 118.22/18.64 | (12) ~ (all_10_1 = e3)
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (6), (10) imply:
% 118.22/18.64 | (13) ~ (all_10_1 = e0)
% 118.22/18.64 |
% 118.22/18.64 | BETA: splitting (2) gives:
% 118.22/18.64 |
% 118.22/18.64 | Case 1:
% 118.22/18.64 | |
% 118.22/18.64 | | (14) all_54_3 = e3
% 118.22/18.64 | |
% 118.22/18.64 | | COMBINE_EQS: (11), (14) imply:
% 118.22/18.64 | | (15) all_10_1 = e3
% 118.22/18.64 | |
% 118.22/18.64 | | REDUCE: (12), (15) imply:
% 118.22/18.64 | | (16) $false
% 118.22/18.64 | |
% 118.22/18.64 | | CLOSE: (16) is inconsistent.
% 118.22/18.64 | |
% 118.22/18.64 | Case 2:
% 118.22/18.64 | |
% 118.22/18.64 | | (17) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 118.22/18.64 | |
% 118.22/18.64 | | BETA: splitting (17) gives:
% 118.22/18.64 | |
% 118.22/18.64 | | Case 1:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (18) all_54_3 = e2
% 118.22/18.64 | | |
% 118.22/18.64 | | | COMBINE_EQS: (11), (18) imply:
% 118.22/18.64 | | | (19) all_10_1 = e2
% 118.22/18.64 | | |
% 118.22/18.64 | | | REDUCE: (8), (19) imply:
% 118.22/18.64 | | | (20) $false
% 118.22/18.64 | | |
% 118.22/18.64 | | | CLOSE: (20) is inconsistent.
% 118.22/18.64 | | |
% 118.22/18.64 | | Case 2:
% 118.22/18.64 | | |
% 118.22/18.64 | | | (21) all_54_3 = e1 | all_54_3 = e0
% 118.22/18.64 | | |
% 118.22/18.64 | | | REF_CLOSE: (9), (11), (13), (21) are inconsistent by sub-proof #448.
% 118.22/18.64 | | |
% 118.22/18.64 | | End of split
% 118.22/18.64 | |
% 118.22/18.64 | End of split
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #448 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_3 = e1 | all_54_3 = e0
% 118.22/18.64 (2) all_54_3 = all_10_1
% 118.22/18.64 (3) ~ (all_10_1 = e1)
% 118.22/18.64 (4) ~ (all_10_1 = e0)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | BETA: splitting (1) gives:
% 118.22/18.64 |
% 118.22/18.64 | Case 1:
% 118.22/18.64 | |
% 118.22/18.64 | | (5) all_54_3 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | COMBINE_EQS: (2), (5) imply:
% 118.22/18.64 | | (6) all_10_1 = e1
% 118.22/18.64 | |
% 118.22/18.64 | | REDUCE: (3), (6) imply:
% 118.22/18.64 | | (7) $false
% 118.22/18.64 | |
% 118.22/18.64 | | CLOSE: (7) is inconsistent.
% 118.22/18.64 | |
% 118.22/18.64 | Case 2:
% 118.22/18.64 | |
% 118.22/18.64 | | (8) all_54_3 = e0
% 118.22/18.64 | |
% 118.22/18.64 | | COMBINE_EQS: (2), (8) imply:
% 118.22/18.64 | | (9) all_10_1 = e0
% 118.22/18.64 | |
% 118.22/18.64 | | REDUCE: (4), (9) imply:
% 118.22/18.64 | | (10) $false
% 118.22/18.64 | |
% 118.22/18.64 | | CLOSE: (10) is inconsistent.
% 118.22/18.64 | |
% 118.22/18.64 | End of split
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #449 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_0 = all_10_2
% 118.22/18.64 (2) all_54_0 = e1
% 118.22/18.64 (3) ~ (all_10_2 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.64 | (4) all_10_2 = e1
% 118.22/18.64 |
% 118.22/18.64 | SIMP: (4) implies:
% 118.22/18.64 | (5) all_10_2 = e1
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (3), (5) imply:
% 118.22/18.64 | (6) $false
% 118.22/18.64 |
% 118.22/18.64 | CLOSE: (6) is inconsistent.
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #450 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_0 = all_10_2
% 118.22/18.64 (2) all_54_0 = e2
% 118.22/18.64 (3) ~ (all_10_2 = e2)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.64 | (4) all_10_2 = e2
% 118.22/18.64 |
% 118.22/18.64 | SIMP: (4) implies:
% 118.22/18.64 | (5) all_10_2 = e2
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (3), (5) imply:
% 118.22/18.64 | (6) $false
% 118.22/18.64 |
% 118.22/18.64 | CLOSE: (6) is inconsistent.
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #451 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_54_0 = all_10_2
% 118.22/18.64 (2) all_54_0 = e3
% 118.22/18.64 (3) ~ (all_10_2 = e3)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.64 | (4) all_10_2 = e3
% 118.22/18.64 |
% 118.22/18.64 | SIMP: (4) implies:
% 118.22/18.64 | (5) all_10_2 = e3
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (3), (5) imply:
% 118.22/18.64 | (6) $false
% 118.22/18.64 |
% 118.22/18.64 | CLOSE: (6) is inconsistent.
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64
% 118.22/18.64 Sub-proof #452 shows that the following formulas are inconsistent:
% 118.22/18.64 ----------------------------------------------------------------
% 118.22/18.64 (1) all_58_6 = all_52_2
% 118.22/18.64 (2) all_58_6 = e1
% 118.22/18.64 (3) ~ (all_52_2 = e1)
% 118.22/18.64
% 118.22/18.64 Begin of proof
% 118.22/18.64 |
% 118.22/18.64 | COMBINE_EQS: (1), (2) imply:
% 118.22/18.64 | (4) all_52_2 = e1
% 118.22/18.64 |
% 118.22/18.64 | SIMP: (4) implies:
% 118.22/18.64 | (5) all_52_2 = e1
% 118.22/18.64 |
% 118.22/18.64 | REDUCE: (3), (5) imply:
% 118.22/18.64 | (6) $false
% 118.22/18.64 |
% 118.22/18.64 | CLOSE: (6) is inconsistent.
% 118.22/18.64 |
% 118.22/18.64 End of proof
% 118.22/18.64 % SZS output end Proof for theBenchmark
% 118.22/18.64
% 118.22/18.64 18040ms
%------------------------------------------------------------------------------