TSTP Solution File: ALG139+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG139+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 : n023.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 16:37:05 EDT 2023
% Result : Unsatisfiable 10.60s 2.14s
% Output : Proof 66.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG139+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 06:21:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.64/0.61 ________ _____
% 0.64/0.61 ___ __ \_________(_)________________________________
% 0.64/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.64/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.64/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.64/0.61
% 0.64/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.64/0.61 (2023-06-19)
% 0.64/0.61
% 0.64/0.61 (c) Philipp Rümmer, 2009-2023
% 0.64/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.64/0.61 Amanda Stjerna.
% 0.64/0.61 Free software under BSD-3-Clause.
% 0.64/0.61
% 0.64/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.64/0.61
% 0.64/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.62 Running up to 7 provers in parallel.
% 0.64/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.64/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.64/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.64/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.64/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.64/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.64/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.09/1.29 Prover 4: Preprocessing ...
% 4.09/1.30 Prover 1: Preprocessing ...
% 4.59/1.33 Prover 2: Preprocessing ...
% 4.59/1.33 Prover 0: Preprocessing ...
% 4.59/1.33 Prover 6: Preprocessing ...
% 4.59/1.33 Prover 3: Preprocessing ...
% 4.59/1.33 Prover 5: Preprocessing ...
% 7.94/1.78 Prover 2: Constructing countermodel ...
% 7.94/1.78 Prover 3: Constructing countermodel ...
% 8.10/1.80 Prover 6: Constructing countermodel ...
% 8.10/1.81 Prover 0: Constructing countermodel ...
% 8.10/1.82 Prover 1: Constructing countermodel ...
% 8.36/1.84 Prover 4: Constructing countermodel ...
% 9.42/2.03 Prover 5: Constructing countermodel ...
% 10.60/2.14 Prover 0: proved (1514ms)
% 10.60/2.14
% 10.60/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.60/2.14
% 10.60/2.14 Prover 3: stopped
% 10.60/2.14 Prover 2: stopped
% 10.60/2.14 Prover 6: stopped
% 10.60/2.15 Prover 5: stopped
% 10.60/2.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.60/2.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.60/2.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.60/2.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.60/2.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.90/2.33 Prover 8: Preprocessing ...
% 11.90/2.34 Prover 11: Preprocessing ...
% 11.90/2.36 Prover 7: Preprocessing ...
% 11.90/2.37 Prover 10: Preprocessing ...
% 11.90/2.37 Prover 13: Preprocessing ...
% 12.63/2.43 Prover 8: Constructing countermodel ...
% 13.50/2.56 Prover 11: Constructing countermodel ...
% 13.50/2.56 Prover 7: Constructing countermodel ...
% 13.50/2.56 Prover 13: Constructing countermodel ...
% 13.50/2.57 Prover 10: Constructing countermodel ...
% 61.59/8.71 Prover 13: Found proof (size 22353)
% 61.59/8.71 Prover 13: proved (6558ms)
% 61.59/8.71 Prover 10: stopped
% 61.59/8.71 Prover 11: stopped
% 61.59/8.71 Prover 4: stopped
% 61.59/8.71 Prover 1: stopped
% 61.59/8.71 Prover 8: stopped
% 61.59/8.71 Prover 7: stopped
% 61.59/8.71
% 61.59/8.71 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.59/8.71
% 62.85/9.11 % SZS output start Proof for theBenchmark
% 62.85/9.13 Assumptions after simplification:
% 62.85/9.13 ---------------------------------
% 62.85/9.13
% 62.85/9.13 (ax1)
% 63.13/9.18 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.13/9.18 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 63.13/9.18 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 63.18/9.18 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 &
% 63.18/9.18 op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 &
% 63.18/9.18 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 &
% 63.18/9.18 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 &
% 63.18/9.18 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 63.18/9.18 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 63.18/9.18 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 63.18/9.18 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 63.18/9.18 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 63.18/9.18 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 63.18/9.18 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 63.18/9.18 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 63.18/9.18 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 63.18/9.18 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 63.18/9.18 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 63.18/9.18 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 63.18/9.18
% 63.18/9.18 (ax10)
% 63.18/9.19 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.19 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.18/9.19 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e2)))
% 63.18/9.19
% 63.18/9.19 (ax11)
% 63.18/9.19 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.19 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.18/9.19 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e0) | ~ (v0 = e1)))
% 63.18/9.19
% 63.18/9.19 (ax12)
% 63.18/9.19 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.19 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.18/9.19 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e3)))
% 63.18/9.19
% 63.18/9.19 (ax13)
% 63.18/9.19 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.19 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.18/9.20 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e1) | ~ (v0 = e2)))
% 63.18/9.20
% 63.18/9.20 (ax14)
% 63.18/9.20 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.20 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.18/9.20 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e3)))
% 63.18/9.20
% 63.18/9.20 (ax15)
% 63.18/9.20 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.20 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.18/9.20 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e1) | ~ (v0 = e0)))
% 63.18/9.20
% 63.18/9.20 (ax16)
% 63.18/9.20 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.20 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.18/9.20 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e2)))
% 63.18/9.20
% 63.18/9.20 (ax17)
% 63.18/9.20 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.18/9.20 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.18/9.20 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e1) | ~ (v0 = e0)))
% 63.18/9.20
% 63.18/9.20 (ax18)
% 63.30/9.21 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.30/9.21 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.30/9.21 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e3)))
% 63.30/9.21
% 63.30/9.21 (ax19)
% 63.30/9.21 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.30/9.21 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.30/9.21 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e2) | ~ (v0 = e1)))
% 63.30/9.21
% 63.30/9.21 (ax2)
% 63.38/9.23 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.23 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 63.38/9.23 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 63.38/9.23 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v3 & op(e3, e2) = v6 &
% 63.38/9.23 op(e3, e1) = v5 & op(e3, e0) = v4 & op(e2, e3) = v2 & op(e2, e2) = v9 &
% 63.38/9.23 op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, e3) = v1 & op(e1, e2) = v8 &
% 63.38/9.23 op(e1, e1) = v13 & op(e1, e0) = v14 & op(e0, e3) = v0 & op(e0, e2) = v7 &
% 63.38/9.23 op(e0, e1) = v12 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 63.38/9.23 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 63.38/9.23 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v10 = e3 | v4 =
% 63.38/9.23 e3) & (v15 = e3 | v12 = e3 | v7 = e3 | v0 = e3) & (v15 = e2 | v14 = e2 |
% 63.38/9.23 v10 = e2 | v4 = e2) & (v15 = e2 | v12 = e2 | v7 = e2 | v0 = e2) & (v15 =
% 63.38/9.23 e1 | v14 = e1 | v10 = e1 | v4 = e1) & (v15 = e1 | v12 = e1 | v7 = e1 | v0
% 63.38/9.23 = e1) & (v15 = e0 | v14 = e0 | v10 = e0 | v4 = e0) & (v15 = e0 | v12 = e0
% 63.38/9.23 | v7 = e0 | v0 = e0) & (v14 = e3 | v13 = e3 | v8 = e3 | v1 = e3) & (v14 =
% 63.38/9.23 e2 | v13 = e2 | v8 = e2 | v1 = e2) & (v14 = e1 | v13 = e1 | v8 = e1 | v1 =
% 63.38/9.23 e1) & (v14 = e0 | v13 = e0 | v8 = e0 | v1 = e0) & (v13 = e3 | v12 = e3 |
% 63.38/9.23 v11 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v11 = e2 | v5 = e2) & (v13 =
% 63.38/9.23 e1 | v12 = e1 | v11 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v11 = e0 | v5
% 63.38/9.23 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v2 = e3) & (v11 = e2 | v10 = e2 |
% 63.38/9.23 v9 = e2 | v2 = e2) & (v11 = e1 | v10 = e1 | v9 = e1 | v2 = e1) & (v11 = e0
% 63.38/9.23 | v10 = e0 | v9 = e0 | v2 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v6 = e3)
% 63.38/9.23 & (v9 = e2 | v8 = e2 | v7 = e2 | v6 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 63.38/9.23 v6 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v6 = e0) & (v6 = e3 | v5 = e3 |
% 63.38/9.23 v4 = e3 | v3 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v3 = e2) & (v6 = e1 |
% 63.38/9.23 v5 = e1 | v4 = e1 | v3 = e1) & (v6 = e0 | v5 = e0 | v4 = e0 | v3 = e0) &
% 63.38/9.23 (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0
% 63.38/9.23 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 = e0 | v1
% 63.38/9.23 = e0 | v0 = e0))
% 63.38/9.23
% 63.38/9.23 (ax20)
% 63.38/9.23 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.23 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.38/9.23 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e3)))
% 63.38/9.23
% 63.38/9.23 (ax21)
% 63.38/9.23 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.23 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.38/9.23 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e2) | ~ (v0 = e0)))
% 63.38/9.23
% 63.38/9.23 (ax22)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e1)))
% 63.38/9.24
% 63.38/9.24 (ax23)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e3) | ~ (v1 = e2) | ~ (v0 = e0)))
% 63.38/9.24
% 63.38/9.24 (ax24)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e2)))
% 63.38/9.24
% 63.38/9.24 (ax25)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e0) | ~ (v1 = e3) | ~ (v0 = e1)))
% 63.38/9.24
% 63.38/9.24 (ax26)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e2)))
% 63.38/9.24
% 63.38/9.24 (ax27)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e3) | ~ (v0 = e0)))
% 63.38/9.24
% 63.38/9.24 (ax28)
% 63.38/9.24 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.24 (op(v0, v0) = v2 & op(v0, e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 63.38/9.24 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e1)))
% 63.38/9.24
% 63.38/9.24 (ax29)
% 63.38/9.25 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.25 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.38/9.25 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e3) | ~ (v0 = e0)))
% 63.38/9.25
% 63.38/9.25 (ax3)
% 63.38/9.25 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.25 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 63.38/9.25 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 63.38/9.25 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 63.38/9.25 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 63.38/9.25 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 63.38/9.25 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 63.38/9.25 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 63.38/9.25 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 63.38/9.25 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 63.38/9.25 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 63.38/9.25 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 63.38/9.25 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 63.38/9.25 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0
% 63.38/9.25 & op(e3, e1) = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 &
% 63.38/9.25 op(e2, e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 63.38/9.25 op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) = v12 &
% 63.38/9.25 op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) & $i(v12)
% 63.38/9.25 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 63.38/9.25 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 63.38/9.25
% 63.38/9.25 (ax4)
% 63.38/9.25 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 63.38/9.25 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 63.38/9.25
% 63.38/9.25 (ax5)
% 63.38/9.26 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.26 ? [v3: $i] : (op(e3, e3) = v1 & op(e2, e2) = v3 & op(e1, e1) = v2 & op(e0, e0)
% 63.38/9.26 = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v3 = e3 & ~ (v1 = e2)) | (v2 =
% 63.38/9.26 e3 & ~ (v1 = e1)) | (v0 = e3 & ~ (v1 = e0))) & ((v3 = e1 & ~ (v2 =
% 63.38/9.26 e2)) | (v1 = e1 & ~ (v2 = e3)) | (v0 = e1 & ~ (v2 = e0))) & ((v3 =
% 63.38/9.26 e0 & ~ (v0 = e2)) | (v2 = e0 & ~ (v0 = e1)) | (v1 = e0 & ~ (v0 =
% 63.38/9.26 e3))) & ((v2 = e2 & ~ (v3 = e1)) | (v1 = e2 & ~ (v3 = e3)) | (v0 =
% 63.38/9.26 e2 & ~ (v3 = e0))))
% 63.38/9.26
% 63.38/9.26 (ax6)
% 63.38/9.26 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.26 (op(v0, v0) = v2 & op(v0, e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 63.38/9.26 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e3)))
% 63.38/9.26
% 63.38/9.26 (ax7)
% 63.38/9.26 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.26 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.38/9.26 $i(v0) & ( ~ (v2 = e1) | ~ (v1 = e0) | ~ (v0 = e2)))
% 63.38/9.26
% 63.38/9.26 (ax8)
% 63.38/9.26 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.26 (op(v0, v0) = v2 & op(v0, e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 63.38/9.26 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e3)))
% 63.38/9.26
% 63.38/9.26 (ax9)
% 63.38/9.26 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 63.38/9.26 (op(v0, v0) = v2 & op(v0, e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 63.38/9.26 $i(v0) & ( ~ (v2 = e2) | ~ (v1 = e0) | ~ (v0 = e1)))
% 63.38/9.26
% 63.38/9.26 (function-axioms)
% 63.38/9.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 63.38/9.26 v2) = v1) | ~ (op(v3, v2) = v0))
% 63.38/9.26
% 63.38/9.26 Those formulas are unsatisfiable:
% 63.38/9.26 ---------------------------------
% 63.38/9.26
% 63.38/9.26 Begin of proof
% 63.38/9.26 |
% 63.38/9.27 | ALPHA: (ax1) implies:
% 63.38/9.27 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 63.38/9.27 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 63.38/9.27 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 63.38/9.27 | ? [v15: $i] : (op(e3, e3) = v0 & op(e3, e2) = v1 & op(e3, e1) = v2 &
% 63.38/9.27 | op(e3, e0) = v3 & op(e2, e3) = v4 & op(e2, e2) = v5 & op(e2, e1) = v6
% 63.38/9.27 | & op(e2, e0) = v7 & op(e1, e3) = v8 & op(e1, e2) = v9 & op(e1, e1) =
% 63.38/9.27 | v10 & op(e1, e0) = v11 & op(e0, e3) = v12 & op(e0, e2) = v13 & op(e0,
% 63.38/9.27 | e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) &
% 63.38/9.27 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 63.38/9.27 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 63.38/9.27 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 63.38/9.27 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 63.38/9.27 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 63.38/9.27 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 63.38/9.27 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 63.38/9.27 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 63.38/9.27 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 63.38/9.27 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 63.38/9.27 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 63.38/9.27 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 63.38/9.27 | = e0))
% 63.38/9.27 |
% 63.38/9.27 | ALPHA: (ax2) implies:
% 63.38/9.28 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 63.38/9.28 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 63.38/9.28 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 63.38/9.28 | ? [v15: $i] : (op(e3, e3) = v3 & op(e3, e2) = v6 & op(e3, e1) = v5 &
% 63.38/9.28 | op(e3, e0) = v4 & op(e2, e3) = v2 & op(e2, e2) = v9 & op(e2, e1) =
% 63.38/9.28 | v11 & op(e2, e0) = v10 & op(e1, e3) = v1 & op(e1, e2) = v8 & op(e1,
% 63.38/9.28 | e1) = v13 & op(e1, e0) = v14 & op(e0, e3) = v0 & op(e0, e2) = v7 &
% 63.38/9.28 | op(e0, e1) = v12 & op(e0, e0) = v15 & $i(v15) & $i(v14) & $i(v13) &
% 63.38/9.28 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 63.38/9.28 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 63.38/9.28 | = e3 | v10 = e3 | v4 = e3) & (v15 = e3 | v12 = e3 | v7 = e3 | v0 =
% 63.38/9.28 | e3) & (v15 = e2 | v14 = e2 | v10 = e2 | v4 = e2) & (v15 = e2 | v12
% 63.38/9.28 | = e2 | v7 = e2 | v0 = e2) & (v15 = e1 | v14 = e1 | v10 = e1 | v4 =
% 63.38/9.28 | e1) & (v15 = e1 | v12 = e1 | v7 = e1 | v0 = e1) & (v15 = e0 | v14 =
% 63.38/9.28 | e0 | v10 = e0 | v4 = e0) & (v15 = e0 | v12 = e0 | v7 = e0 | v0 =
% 63.38/9.28 | e0) & (v14 = e3 | v13 = e3 | v8 = e3 | v1 = e3) & (v14 = e2 | v13 =
% 63.38/9.28 | e2 | v8 = e2 | v1 = e2) & (v14 = e1 | v13 = e1 | v8 = e1 | v1 = e1)
% 63.38/9.28 | & (v14 = e0 | v13 = e0 | v8 = e0 | v1 = e0) & (v13 = e3 | v12 = e3 |
% 63.38/9.28 | v11 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v11 = e2 | v5 = e2) &
% 63.38/9.28 | (v13 = e1 | v12 = e1 | v11 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 63.38/9.28 | v11 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v9 = e3 | v2 = e3) &
% 63.38/9.28 | (v11 = e2 | v10 = e2 | v9 = e2 | v2 = e2) & (v11 = e1 | v10 = e1 | v9
% 63.38/9.28 | = e1 | v2 = e1) & (v11 = e0 | v10 = e0 | v9 = e0 | v2 = e0) & (v9 =
% 63.38/9.28 | e3 | v8 = e3 | v7 = e3 | v6 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 63.38/9.28 | v6 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v6 = e1) & (v9 = e0 | v8
% 63.38/9.28 | = e0 | v7 = e0 | v6 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v3 = e3)
% 63.38/9.28 | & (v6 = e2 | v5 = e2 | v4 = e2 | v3 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 63.38/9.28 | e1 | v3 = e1) & (v6 = e0 | v5 = e0 | v4 = e0 | v3 = e0) & (v3 = e3
% 63.38/9.28 | | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 | v2 = e2 | v1 = e2 | v0
% 63.38/9.28 | = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v3 = e0 | v2 =
% 63.38/9.28 | e0 | v1 = e0 | v0 = e0))
% 63.38/9.28 |
% 63.38/9.28 | ALPHA: (ax3) implies:
% 63.38/9.29 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 63.38/9.29 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 63.38/9.29 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 63.38/9.29 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 63.38/9.29 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 63.38/9.29 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 63.38/9.29 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 63.38/9.29 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 63.38/9.29 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 63.38/9.29 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 63.38/9.29 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 63.38/9.29 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 63.38/9.29 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 63.38/9.29 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 63.38/9.29 | v0) & ~ (v1 = v0) & op(e3, e3) = v1 & op(e3, e2) = v0 & op(e3, e1)
% 63.38/9.29 | = v2 & op(e3, e0) = v3 & op(e2, e3) = v5 & op(e2, e2) = v4 & op(e2,
% 63.38/9.29 | e1) = v6 & op(e2, e0) = v7 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 63.38/9.29 | op(e1, e1) = v10 & op(e1, e0) = v11 & op(e0, e3) = v13 & op(e0, e2) =
% 63.38/9.29 | v12 & op(e0, e1) = v14 & op(e0, e0) = v15 & $i(v15) & $i(v14) &
% 63.38/9.29 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 63.38/9.29 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 63.38/9.29 |
% 63.38/9.29 | ALPHA: (ax4) implies:
% 63.38/9.29 | (4) ~ (e1 = e0)
% 63.38/9.29 | (5) ~ (e2 = e0)
% 63.38/9.29 | (6) ~ (e2 = e1)
% 63.38/9.29 | (7) ~ (e3 = e0)
% 63.38/9.29 | (8) ~ (e3 = e1)
% 63.38/9.29 | (9) ~ (e3 = e2)
% 63.38/9.29 |
% 63.38/9.29 | ALPHA: (ax5) implies:
% 63.38/9.29 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (op(e3, e3) =
% 63.38/9.29 | v1 & op(e2, e2) = v3 & op(e1, e1) = v2 & op(e0, e0) = v0 & $i(v3) &
% 63.38/9.29 | $i(v2) & $i(v1) & $i(v0) & ((v3 = e3 & ~ (v1 = e2)) | (v2 = e3 & ~
% 63.38/9.29 | (v1 = e1)) | (v0 = e3 & ~ (v1 = e0))) & ((v3 = e1 & ~ (v2 =
% 63.38/9.29 | e2)) | (v1 = e1 & ~ (v2 = e3)) | (v0 = e1 & ~ (v2 = e0))) &
% 63.38/9.29 | ((v3 = e0 & ~ (v0 = e2)) | (v2 = e0 & ~ (v0 = e1)) | (v1 = e0 & ~
% 63.38/9.29 | (v0 = e3))) & ((v2 = e2 & ~ (v3 = e1)) | (v1 = e2 & ~ (v3 =
% 63.38/9.29 | e3)) | (v0 = e2 & ~ (v3 = e0))))
% 63.38/9.29 |
% 63.38/9.29 | ALPHA: (ax6) implies:
% 63.38/9.29 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.29 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.29 | e1) | ~ (v1 = e0) | ~ (v0 = e3)))
% 63.38/9.29 |
% 63.38/9.29 | ALPHA: (ax7) implies:
% 63.38/9.30 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e1) | ~ (v1 = e0) | ~ (v0 = e2)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax8) implies:
% 63.38/9.30 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e2) | ~ (v1 = e0) | ~ (v0 = e3)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax9) implies:
% 63.38/9.30 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e2) | ~ (v1 = e0) | ~ (v0 = e1)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax10) implies:
% 63.38/9.30 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e3) | ~ (v1 = e0) | ~ (v0 = e2)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax11) implies:
% 63.38/9.30 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e3) | ~ (v1 = e0) | ~ (v0 = e1)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax12) implies:
% 63.38/9.30 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e0) | ~ (v1 = e1) | ~ (v0 = e3)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax13) implies:
% 63.38/9.30 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e0) | ~ (v1 = e1) | ~ (v0 = e2)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax14) implies:
% 63.38/9.30 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e2) | ~ (v1 = e1) | ~ (v0 = e3)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax15) implies:
% 63.38/9.30 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e2) | ~ (v1 = e1) | ~ (v0 = e0)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax16) implies:
% 63.38/9.30 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e3) | ~ (v1 = e1) | ~ (v0 = e2)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax17) implies:
% 63.38/9.30 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e3) | ~ (v1 = e1) | ~ (v0 = e0)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax18) implies:
% 63.38/9.30 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e0) | ~ (v1 = e2) | ~ (v0 = e3)))
% 63.38/9.30 |
% 63.38/9.30 | ALPHA: (ax19) implies:
% 63.38/9.30 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.30 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.30 | e0) | ~ (v1 = e2) | ~ (v0 = e1)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax20) implies:
% 63.38/9.31 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e1) | ~ (v1 = e2) | ~ (v0 = e3)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax21) implies:
% 63.38/9.31 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e3) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e1) | ~ (v1 = e2) | ~ (v0 = e0)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax22) implies:
% 63.38/9.31 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e3) | ~ (v1 = e2) | ~ (v0 = e1)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax23) implies:
% 63.38/9.31 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e3) | ~ (v1 = e2) | ~ (v0 = e0)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax24) implies:
% 63.38/9.31 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e0) | ~ (v1 = e3) | ~ (v0 = e2)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax25) implies:
% 63.38/9.31 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e0) | ~ (v1 = e3) | ~ (v0 = e1)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax26) implies:
% 63.38/9.31 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e1) | ~ (v1 = e3) | ~ (v0 = e2)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax27) implies:
% 63.38/9.31 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e2) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e1) | ~ (v1 = e3) | ~ (v0 = e0)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax28) implies:
% 63.38/9.31 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.38/9.31 | e0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.38/9.31 | e2) | ~ (v1 = e3) | ~ (v0 = e1)))
% 63.38/9.31 |
% 63.38/9.31 | ALPHA: (ax29) implies:
% 63.82/9.31 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(v0, v0) = v2 & op(v0,
% 63.82/9.31 | e1) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 63.82/9.31 | e2) | ~ (v1 = e3) | ~ (v0 = e0)))
% 63.82/9.31 |
% 63.82/9.31 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 63.82/9.31 | (35) op(all_4_2, all_4_2) = all_4_0 & op(all_4_2, e3) = all_4_1 & op(e3,
% 63.82/9.31 | e3) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~
% 63.82/9.31 | (all_4_0 = e2) | ~ (all_4_1 = e1) | ~ (all_4_2 = e0))
% 63.82/9.31 |
% 63.82/9.31 | ALPHA: (35) implies:
% 63.82/9.31 | (36) op(e3, e3) = all_4_2
% 63.82/9.31 | (37) op(all_4_2, e3) = all_4_1
% 63.82/9.31 | (38) op(all_4_2, all_4_2) = all_4_0
% 63.82/9.31 | (39) ~ (all_4_0 = e2) | ~ (all_4_1 = e1) | ~ (all_4_2 = e0)
% 63.82/9.31 |
% 63.82/9.31 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 63.82/9.31 | (40) op(all_6_2, all_6_2) = all_6_0 & op(all_6_2, e0) = all_6_1 & op(e0,
% 63.82/9.31 | e0) = all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~
% 63.82/9.31 | (all_6_0 = e3) | ~ (all_6_1 = e2) | ~ (all_6_2 = e1))
% 63.82/9.31 |
% 63.82/9.32 | ALPHA: (40) implies:
% 63.82/9.32 | (41) op(e0, e0) = all_6_2
% 63.82/9.32 | (42) op(all_6_2, e0) = all_6_1
% 63.82/9.32 | (43) op(all_6_2, all_6_2) = all_6_0
% 63.82/9.32 | (44) ~ (all_6_0 = e3) | ~ (all_6_1 = e2) | ~ (all_6_2 = e1)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 63.82/9.32 | (45) op(all_8_2, all_8_2) = all_8_0 & op(all_8_2, e0) = all_8_1 & op(e0,
% 63.82/9.32 | e0) = all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~
% 63.82/9.32 | (all_8_0 = e3) | ~ (all_8_1 = e1) | ~ (all_8_2 = e2))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (45) implies:
% 63.82/9.32 | (46) op(e0, e0) = all_8_2
% 63.82/9.32 | (47) op(all_8_2, e0) = all_8_1
% 63.82/9.32 | (48) op(all_8_2, all_8_2) = all_8_0
% 63.82/9.32 | (49) ~ (all_8_0 = e3) | ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (50) op(all_10_2, all_10_2) = all_10_0 & op(all_10_2, e2) = all_10_1 &
% 63.82/9.32 | op(e2, e2) = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & (
% 63.82/9.32 | ~ (all_10_0 = e1) | ~ (all_10_1 = e0) | ~ (all_10_2 = e3))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (50) implies:
% 63.82/9.32 | (51) op(e2, e2) = all_10_2
% 63.82/9.32 | (52) op(all_10_2, e2) = all_10_1
% 63.82/9.32 | (53) op(all_10_2, all_10_2) = all_10_0
% 63.82/9.32 | (54) ~ (all_10_0 = e1) | ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (55) op(all_12_2, all_12_2) = all_12_0 & op(all_12_2, e2) = all_12_1 &
% 63.82/9.32 | op(e2, e2) = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & (
% 63.82/9.32 | ~ (all_12_0 = e3) | ~ (all_12_1 = e1) | ~ (all_12_2 = e0))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (55) implies:
% 63.82/9.32 | (56) op(e2, e2) = all_12_2
% 63.82/9.32 | (57) op(all_12_2, e2) = all_12_1
% 63.82/9.32 | (58) op(all_12_2, all_12_2) = all_12_0
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (59) op(all_14_2, all_14_2) = all_14_0 & op(all_14_2, e1) = all_14_1 &
% 63.82/9.32 | op(e1, e1) = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & (
% 63.82/9.32 | ~ (all_14_0 = e0) | ~ (all_14_1 = e3) | ~ (all_14_2 = e2))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (59) implies:
% 63.82/9.32 | (60) op(e1, e1) = all_14_2
% 63.82/9.32 | (61) op(all_14_2, e1) = all_14_1
% 63.82/9.32 | (62) op(all_14_2, all_14_2) = all_14_0
% 63.82/9.32 | (63) ~ (all_14_0 = e0) | ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1, all_16_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (64) op(all_16_2, all_16_2) = all_16_0 & op(all_16_2, e0) = all_16_1 &
% 63.82/9.32 | op(e0, e0) = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & (
% 63.82/9.32 | ~ (all_16_0 = e1) | ~ (all_16_1 = e3) | ~ (all_16_2 = e2))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (64) implies:
% 63.82/9.32 | (65) op(e0, e0) = all_16_2
% 63.82/9.32 | (66) op(all_16_2, e0) = all_16_1
% 63.82/9.32 | (67) op(all_16_2, all_16_2) = all_16_0
% 63.82/9.32 | (68) ~ (all_16_0 = e1) | ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1, all_18_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (69) op(all_18_2, all_18_2) = all_18_0 & op(all_18_2, e1) = all_18_1 &
% 63.82/9.32 | op(e1, e1) = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & (
% 63.82/9.32 | ~ (all_18_0 = e0) | ~ (all_18_1 = e2) | ~ (all_18_2 = e3))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (69) implies:
% 63.82/9.32 | (70) op(e1, e1) = all_18_2
% 63.82/9.32 | (71) op(all_18_2, e1) = all_18_1
% 63.82/9.32 | (72) op(all_18_2, all_18_2) = all_18_0
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (73) op(all_20_2, all_20_2) = all_20_0 & op(all_20_2, e1) = all_20_1 &
% 63.82/9.32 | op(e1, e1) = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & (
% 63.82/9.32 | ~ (all_20_0 = e2) | ~ (all_20_1 = e0) | ~ (all_20_2 = e3))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (73) implies:
% 63.82/9.32 | (74) op(e1, e1) = all_20_2
% 63.82/9.32 | (75) op(all_20_2, e1) = all_20_1
% 63.82/9.32 | (76) op(all_20_2, all_20_2) = all_20_0
% 63.82/9.32 | (77) ~ (all_20_0 = e2) | ~ (all_20_1 = e0) | ~ (all_20_2 = e3)
% 63.82/9.32 |
% 63.82/9.32 | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2
% 63.82/9.32 | gives:
% 63.82/9.32 | (78) op(all_22_2, all_22_2) = all_22_0 & op(all_22_2, e1) = all_22_1 &
% 63.82/9.32 | op(e1, e1) = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & (
% 63.82/9.32 | ~ (all_22_0 = e3) | ~ (all_22_1 = e2) | ~ (all_22_2 = e0))
% 63.82/9.32 |
% 63.82/9.32 | ALPHA: (78) implies:
% 63.82/9.33 | (79) op(e1, e1) = all_22_2
% 63.82/9.33 | (80) op(all_22_2, e1) = all_22_1
% 63.82/9.33 | (81) op(all_22_2, all_22_2) = all_22_0
% 63.82/9.33 | (82) ~ (all_22_0 = e3) | ~ (all_22_1 = e2) | ~ (all_22_2 = e0)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (83) op(all_24_2, all_24_2) = all_24_0 & op(all_24_2, e2) = all_24_1 &
% 63.82/9.33 | op(e2, e2) = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & (
% 63.82/9.33 | ~ (all_24_0 = e0) | ~ (all_24_1 = e3) | ~ (all_24_2 = e1))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (83) implies:
% 63.82/9.33 | (84) op(e2, e2) = all_24_2
% 63.82/9.33 | (85) op(all_24_2, e2) = all_24_1
% 63.82/9.33 | (86) op(all_24_2, all_24_2) = all_24_0
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (87) op(all_26_2, all_26_2) = all_26_0 & op(all_26_2, e3) = all_26_1 &
% 63.82/9.33 | op(e3, e3) = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & (
% 63.82/9.33 | ~ (all_26_0 = e1) | ~ (all_26_1 = e0) | ~ (all_26_2 = e2))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (87) implies:
% 63.82/9.33 | (88) op(e3, e3) = all_26_2
% 63.82/9.33 | (89) op(all_26_2, e3) = all_26_1
% 63.82/9.33 | (90) op(all_26_2, all_26_2) = all_26_0
% 63.82/9.33 | (91) ~ (all_26_0 = e1) | ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (92) op(all_28_2, all_28_2) = all_28_0 & op(all_28_2, e0) = all_28_1 &
% 63.82/9.33 | op(e0, e0) = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & (
% 63.82/9.33 | ~ (all_28_0 = e2) | ~ (all_28_1 = e1) | ~ (all_28_2 = e3))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (92) implies:
% 63.82/9.33 | (93) op(e0, e0) = all_28_2
% 63.82/9.33 | (94) op(all_28_2, e0) = all_28_1
% 63.82/9.33 | (95) op(all_28_2, all_28_2) = all_28_0
% 63.82/9.33 | (96) ~ (all_28_0 = e2) | ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (97) op(all_30_2, all_30_2) = all_30_0 & op(all_30_2, e2) = all_30_1 &
% 63.82/9.33 | op(e2, e2) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & (
% 63.82/9.33 | ~ (all_30_0 = e1) | ~ (all_30_1 = e3) | ~ (all_30_2 = e0))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (97) implies:
% 63.82/9.33 | (98) op(e2, e2) = all_30_2
% 63.82/9.33 | (99) op(all_30_2, e2) = all_30_1
% 63.82/9.33 | (100) op(all_30_2, all_30_2) = all_30_0
% 63.82/9.33 | (101) ~ (all_30_0 = e1) | ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1, all_32_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (102) op(all_32_2, all_32_2) = all_32_0 & op(all_32_2, e1) = all_32_1 &
% 63.82/9.33 | op(e1, e1) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) &
% 63.82/9.33 | ( ~ (all_32_0 = e2) | ~ (all_32_1 = e3) | ~ (all_32_2 = e0))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (102) implies:
% 63.82/9.33 | (103) op(e1, e1) = all_32_2
% 63.82/9.33 | (104) op(all_32_2, e1) = all_32_1
% 63.82/9.33 | (105) op(all_32_2, all_32_2) = all_32_0
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1, all_34_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (106) op(all_34_2, all_34_2) = all_34_0 & op(all_34_2, e3) = all_34_1 &
% 63.82/9.33 | op(e3, e3) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) &
% 63.82/9.33 | ( ~ (all_34_0 = e0) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (106) implies:
% 63.82/9.33 | (107) op(e3, e3) = all_34_2
% 63.82/9.33 | (108) op(all_34_2, e3) = all_34_1
% 63.82/9.33 | (109) op(all_34_2, all_34_2) = all_34_0
% 63.82/9.33 | (110) ~ (all_34_0 = e0) | ~ (all_34_1 = e2) | ~ (all_34_2 = e1)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (111) op(all_36_2, all_36_2) = all_36_0 & op(all_36_2, e0) = all_36_1 &
% 63.82/9.33 | op(e0, e0) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) &
% 63.82/9.33 | ( ~ (all_36_0 = e1) | ~ (all_36_1 = e2) | ~ (all_36_2 = e3))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (111) implies:
% 63.82/9.33 | (112) op(e0, e0) = all_36_2
% 63.82/9.33 | (113) op(all_36_2, e0) = all_36_1
% 63.82/9.33 | (114) op(all_36_2, all_36_2) = all_36_0
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (115) op(all_38_2, all_38_2) = all_38_0 & op(all_38_2, e0) = all_38_1 &
% 63.82/9.33 | op(e0, e0) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) &
% 63.82/9.33 | ( ~ (all_38_0 = e2) | ~ (all_38_1 = e3) | ~ (all_38_2 = e1))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (115) implies:
% 63.82/9.33 | (116) op(e0, e0) = all_38_2
% 63.82/9.33 | (117) op(all_38_2, e0) = all_38_1
% 63.82/9.33 | (118) op(all_38_2, all_38_2) = all_38_0
% 63.82/9.33 | (119) ~ (all_38_0 = e2) | ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 63.82/9.33 | gives:
% 63.82/9.33 | (120) op(all_40_2, all_40_2) = all_40_0 & op(all_40_2, e3) = all_40_1 &
% 63.82/9.33 | op(e3, e3) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) &
% 63.82/9.33 | ( ~ (all_40_0 = e1) | ~ (all_40_1 = e2) | ~ (all_40_2 = e0))
% 63.82/9.33 |
% 63.82/9.33 | ALPHA: (120) implies:
% 63.82/9.33 | (121) op(e3, e3) = all_40_2
% 63.82/9.33 | (122) op(all_40_2, e3) = all_40_1
% 63.82/9.33 | (123) op(all_40_2, all_40_2) = all_40_0
% 63.82/9.33 |
% 63.82/9.33 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2
% 63.82/9.33 | gives:
% 63.82/9.34 | (124) op(all_42_2, all_42_2) = all_42_0 & op(all_42_2, e3) = all_42_1 &
% 63.82/9.34 | op(e3, e3) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) &
% 63.82/9.34 | ( ~ (all_42_0 = e2) | ~ (all_42_1 = e0) | ~ (all_42_2 = e1))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (124) implies:
% 63.82/9.34 | (125) op(e3, e3) = all_42_2
% 63.82/9.34 | (126) op(all_42_2, e3) = all_42_1
% 63.82/9.34 | (127) op(all_42_2, all_42_2) = all_42_0
% 63.82/9.34 | (128) ~ (all_42_0 = e2) | ~ (all_42_1 = e0) | ~ (all_42_2 = e1)
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1, all_44_2
% 63.82/9.34 | gives:
% 63.82/9.34 | (129) op(all_44_2, all_44_2) = all_44_0 & op(all_44_2, e1) = all_44_1 &
% 63.82/9.34 | op(e1, e1) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) &
% 63.82/9.34 | ( ~ (all_44_0 = e3) | ~ (all_44_1 = e0) | ~ (all_44_2 = e2))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (129) implies:
% 63.82/9.34 | (130) op(e1, e1) = all_44_2
% 63.82/9.34 | (131) op(all_44_2, e1) = all_44_1
% 63.82/9.34 | (132) op(all_44_2, all_44_2) = all_44_0
% 63.82/9.34 | (133) ~ (all_44_0 = e3) | ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 63.82/9.34 | gives:
% 63.82/9.34 | (134) op(all_46_2, all_46_2) = all_46_0 & op(all_46_2, e2) = all_46_1 &
% 63.82/9.34 | op(e2, e2) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) &
% 63.82/9.34 | ( ~ (all_46_0 = e3) | ~ (all_46_1 = e0) | ~ (all_46_2 = e1))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (134) implies:
% 63.82/9.34 | (135) op(e2, e2) = all_46_2
% 63.82/9.34 | (136) op(all_46_2, e2) = all_46_1
% 63.82/9.34 | (137) op(all_46_2, all_46_2) = all_46_0
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1, all_48_2
% 63.82/9.34 | gives:
% 63.82/9.34 | (138) op(all_48_2, all_48_2) = all_48_0 & op(all_48_2, e2) = all_48_1 &
% 63.82/9.34 | op(e2, e2) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 63.82/9.34 | ( ~ (all_48_0 = e0) | ~ (all_48_1 = e1) | ~ (all_48_2 = e3))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (138) implies:
% 63.82/9.34 | (139) op(e2, e2) = all_48_2
% 63.82/9.34 | (140) op(all_48_2, e2) = all_48_1
% 63.82/9.34 | (141) op(all_48_2, all_48_2) = all_48_0
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2
% 63.82/9.34 | gives:
% 63.82/9.34 | (142) op(all_50_2, all_50_2) = all_50_0 & op(all_50_2, e3) = all_50_1 &
% 63.82/9.34 | op(e3, e3) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) &
% 63.82/9.34 | ( ~ (all_50_0 = e0) | ~ (all_50_1 = e1) | ~ (all_50_2 = e2))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (142) implies:
% 63.82/9.34 | (143) op(e3, e3) = all_50_2
% 63.82/9.34 | (144) op(all_50_2, e3) = all_50_1
% 63.82/9.34 | (145) op(all_50_2, all_50_2) = all_50_0
% 63.82/9.34 | (146) ~ (all_50_0 = e0) | ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2,
% 63.82/9.34 | all_52_3 gives:
% 63.82/9.34 | (147) op(e3, e3) = all_52_2 & op(e2, e2) = all_52_0 & op(e1, e1) = all_52_1
% 63.82/9.34 | & op(e0, e0) = all_52_3 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2)
% 63.82/9.34 | & $i(all_52_3) & ((all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 =
% 63.82/9.34 | e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0)))
% 63.82/9.34 | & ((all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~
% 63.82/9.34 | (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))) &
% 63.82/9.34 | ((all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3
% 63.82/9.34 | = e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))) & ((all_52_1 =
% 63.82/9.34 | e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 = e3)) |
% 63.82/9.34 | (all_52_3 = e2 & ~ (all_52_0 = e0)))
% 63.82/9.34 |
% 63.82/9.34 | ALPHA: (147) implies:
% 63.82/9.34 | (148) op(e0, e0) = all_52_3
% 63.82/9.34 | (149) op(e1, e1) = all_52_1
% 63.82/9.34 | (150) op(e2, e2) = all_52_0
% 63.82/9.34 | (151) op(e3, e3) = all_52_2
% 63.82/9.34 | (152) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0
% 63.82/9.34 | = e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 63.82/9.34 | (153) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3
% 63.82/9.34 | = e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 63.82/9.34 | (154) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1
% 63.82/9.34 | = e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 63.82/9.34 | (155) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2
% 63.82/9.34 | = e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 63.82/9.34 |
% 63.82/9.34 | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2,
% 63.82/9.34 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 63.82/9.34 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 63.82/9.34 | (156) ~ (all_54_0 = all_54_1) & ~ (all_54_0 = all_54_2) & ~ (all_54_0 =
% 63.82/9.34 | all_54_3) & ~ (all_54_0 = all_54_4) & ~ (all_54_0 = all_54_8) &
% 63.82/9.35 | ~ (all_54_0 = all_54_12) & ~ (all_54_1 = all_54_2) & ~ (all_54_1 =
% 63.82/9.35 | all_54_3) & ~ (all_54_1 = all_54_5) & ~ (all_54_1 = all_54_9) &
% 63.82/9.35 | ~ (all_54_1 = all_54_13) & ~ (all_54_2 = all_54_3) & ~ (all_54_2 =
% 63.82/9.35 | all_54_6) & ~ (all_54_2 = all_54_10) & ~ (all_54_2 = all_54_14) &
% 63.82/9.35 | ~ (all_54_3 = all_54_7) & ~ (all_54_3 = all_54_11) & ~ (all_54_3 =
% 63.82/9.35 | all_54_15) & ~ (all_54_4 = all_54_5) & ~ (all_54_4 = all_54_6) &
% 63.82/9.35 | ~ (all_54_4 = all_54_7) & ~ (all_54_4 = all_54_8) & ~ (all_54_4 =
% 63.82/9.35 | all_54_12) & ~ (all_54_5 = all_54_6) & ~ (all_54_5 = all_54_7) &
% 63.82/9.35 | ~ (all_54_5 = all_54_9) & ~ (all_54_5 = all_54_13) & ~ (all_54_6 =
% 63.82/9.35 | all_54_7) & ~ (all_54_6 = all_54_10) & ~ (all_54_6 = all_54_14) &
% 63.82/9.35 | ~ (all_54_7 = all_54_11) & ~ (all_54_7 = all_54_15) & ~ (all_54_8
% 63.82/9.35 | = all_54_9) & ~ (all_54_8 = all_54_10) & ~ (all_54_8 = all_54_11)
% 63.82/9.35 | & ~ (all_54_8 = all_54_12) & ~ (all_54_9 = all_54_10) & ~
% 63.82/9.35 | (all_54_9 = all_54_11) & ~ (all_54_9 = all_54_13) & ~ (all_54_10 =
% 63.82/9.35 | all_54_11) & ~ (all_54_10 = all_54_14) & ~ (all_54_11 =
% 63.82/9.35 | all_54_15) & ~ (all_54_12 = all_54_13) & ~ (all_54_12 =
% 63.82/9.35 | all_54_14) & ~ (all_54_12 = all_54_15) & ~ (all_54_13 =
% 63.82/9.35 | all_54_14) & ~ (all_54_13 = all_54_15) & ~ (all_54_14 =
% 63.82/9.35 | all_54_15) & op(e3, e3) = all_54_14 & op(e3, e2) = all_54_15 &
% 63.82/9.35 | op(e3, e1) = all_54_13 & op(e3, e0) = all_54_12 & op(e2, e3) =
% 63.82/9.35 | all_54_10 & op(e2, e2) = all_54_11 & op(e2, e1) = all_54_9 & op(e2,
% 63.82/9.35 | e0) = all_54_8 & op(e1, e3) = all_54_6 & op(e1, e2) = all_54_7 &
% 63.82/9.35 | op(e1, e1) = all_54_5 & op(e1, e0) = all_54_4 & op(e0, e3) = all_54_2
% 63.82/9.35 | & op(e0, e2) = all_54_3 & op(e0, e1) = all_54_1 & op(e0, e0) =
% 63.82/9.35 | all_54_0 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3)
% 63.82/9.35 | & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) & $i(all_54_7) &
% 63.82/9.35 | $i(all_54_8) & $i(all_54_9) & $i(all_54_10) & $i(all_54_11) &
% 63.82/9.35 | $i(all_54_12) & $i(all_54_13) & $i(all_54_14) & $i(all_54_15)
% 63.82/9.35 |
% 63.82/9.35 | ALPHA: (156) implies:
% 63.82/9.35 | (157) ~ (all_54_14 = all_54_15)
% 63.82/9.35 | (158) ~ (all_54_13 = all_54_15)
% 63.82/9.35 | (159) ~ (all_54_13 = all_54_14)
% 63.82/9.35 | (160) ~ (all_54_12 = all_54_15)
% 63.82/9.35 | (161) ~ (all_54_12 = all_54_14)
% 63.82/9.35 | (162) ~ (all_54_11 = all_54_15)
% 63.82/9.35 | (163) ~ (all_54_10 = all_54_14)
% 63.82/9.35 | (164) ~ (all_54_10 = all_54_11)
% 63.82/9.35 | (165) ~ (all_54_9 = all_54_13)
% 63.82/9.35 | (166) ~ (all_54_9 = all_54_11)
% 63.82/9.35 | (167) ~ (all_54_9 = all_54_10)
% 63.82/9.35 | (168) ~ (all_54_8 = all_54_12)
% 63.82/9.35 | (169) ~ (all_54_8 = all_54_11)
% 63.82/9.35 | (170) ~ (all_54_8 = all_54_10)
% 63.82/9.35 | (171) ~ (all_54_7 = all_54_15)
% 63.82/9.35 | (172) ~ (all_54_7 = all_54_11)
% 63.82/9.35 | (173) ~ (all_54_6 = all_54_14)
% 63.82/9.35 | (174) ~ (all_54_6 = all_54_10)
% 63.82/9.35 | (175) ~ (all_54_6 = all_54_7)
% 63.82/9.35 | (176) ~ (all_54_5 = all_54_13)
% 63.82/9.35 | (177) ~ (all_54_5 = all_54_9)
% 63.82/9.35 | (178) ~ (all_54_5 = all_54_7)
% 63.82/9.35 | (179) ~ (all_54_5 = all_54_6)
% 63.82/9.35 | (180) ~ (all_54_4 = all_54_12)
% 63.82/9.35 | (181) ~ (all_54_4 = all_54_8)
% 63.82/9.35 | (182) ~ (all_54_4 = all_54_7)
% 63.82/9.35 | (183) ~ (all_54_4 = all_54_6)
% 63.82/9.35 | (184) ~ (all_54_4 = all_54_5)
% 63.82/9.35 | (185) ~ (all_54_3 = all_54_15)
% 63.82/9.35 | (186) ~ (all_54_3 = all_54_7)
% 63.82/9.35 | (187) ~ (all_54_2 = all_54_14)
% 63.82/9.35 | (188) ~ (all_54_2 = all_54_10)
% 63.82/9.35 | (189) ~ (all_54_2 = all_54_6)
% 63.82/9.35 | (190) ~ (all_54_2 = all_54_3)
% 63.82/9.35 | (191) ~ (all_54_1 = all_54_13)
% 63.82/9.35 | (192) ~ (all_54_1 = all_54_9)
% 63.82/9.35 | (193) ~ (all_54_1 = all_54_5)
% 63.82/9.35 | (194) ~ (all_54_1 = all_54_3)
% 63.82/9.35 | (195) ~ (all_54_1 = all_54_2)
% 63.82/9.35 | (196) ~ (all_54_0 = all_54_12)
% 63.82/9.35 | (197) ~ (all_54_0 = all_54_8)
% 63.82/9.35 | (198) ~ (all_54_0 = all_54_4)
% 63.82/9.35 | (199) ~ (all_54_0 = all_54_3)
% 63.82/9.35 | (200) ~ (all_54_0 = all_54_2)
% 63.82/9.35 | (201) ~ (all_54_0 = all_54_1)
% 63.82/9.35 | (202) op(e0, e0) = all_54_0
% 63.82/9.35 | (203) op(e0, e1) = all_54_1
% 63.82/9.35 | (204) op(e0, e2) = all_54_3
% 63.82/9.35 | (205) op(e0, e3) = all_54_2
% 63.82/9.35 | (206) op(e1, e0) = all_54_4
% 63.82/9.35 | (207) op(e1, e1) = all_54_5
% 63.82/9.35 | (208) op(e1, e2) = all_54_7
% 63.82/9.35 | (209) op(e1, e3) = all_54_6
% 63.82/9.35 | (210) op(e2, e0) = all_54_8
% 63.82/9.35 | (211) op(e2, e1) = all_54_9
% 63.82/9.35 | (212) op(e2, e2) = all_54_11
% 63.82/9.35 | (213) op(e2, e3) = all_54_10
% 63.82/9.35 | (214) op(e3, e0) = all_54_12
% 63.82/9.35 | (215) op(e3, e1) = all_54_13
% 63.82/9.35 | (216) op(e3, e2) = all_54_15
% 63.82/9.35 | (217) op(e3, e3) = all_54_14
% 63.82/9.35 |
% 63.82/9.35 | DELTA: instantiating (1) with fresh symbols all_56_0, all_56_1, all_56_2,
% 63.82/9.35 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 63.82/9.35 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 63.82/9.35 | (218) op(e3, e3) = all_56_15 & op(e3, e2) = all_56_14 & op(e3, e1) =
% 63.82/9.35 | all_56_13 & op(e3, e0) = all_56_12 & op(e2, e3) = all_56_11 & op(e2,
% 63.82/9.35 | e2) = all_56_10 & op(e2, e1) = all_56_9 & op(e2, e0) = all_56_8 &
% 63.82/9.35 | op(e1, e3) = all_56_7 & op(e1, e2) = all_56_6 & op(e1, e1) = all_56_5
% 63.82/9.35 | & op(e1, e0) = all_56_4 & op(e0, e3) = all_56_3 & op(e0, e2) =
% 63.82/9.35 | all_56_2 & op(e0, e1) = all_56_1 & op(e0, e0) = all_56_0 &
% 63.82/9.35 | $i(all_56_0) & $i(all_56_1) & $i(all_56_2) & $i(all_56_3) &
% 63.82/9.35 | $i(all_56_4) & $i(all_56_5) & $i(all_56_6) & $i(all_56_7) &
% 63.82/9.35 | $i(all_56_8) & $i(all_56_9) & $i(all_56_10) & $i(all_56_11) &
% 63.82/9.35 | $i(all_56_12) & $i(all_56_13) & $i(all_56_14) & $i(all_56_15) &
% 63.82/9.35 | (all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0) &
% 63.82/9.35 | (all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0) &
% 63.82/9.35 | (all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0) &
% 63.82/9.35 | (all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0) &
% 63.82/9.35 | (all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0) &
% 63.82/9.35 | (all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0) &
% 63.82/9.35 | (all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0) &
% 63.82/9.35 | (all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0) &
% 63.82/9.35 | (all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0) &
% 63.82/9.35 | (all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0) &
% 63.82/9.35 | (all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0) &
% 63.82/9.35 | (all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0) &
% 63.82/9.35 | (all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0) &
% 63.82/9.35 | (all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0) &
% 63.82/9.35 | (all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0) &
% 63.82/9.35 | (all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0)
% 63.82/9.35 |
% 63.82/9.35 | ALPHA: (218) implies:
% 63.82/9.35 | (219) op(e0, e0) = all_56_0
% 63.82/9.35 | (220) op(e0, e1) = all_56_1
% 63.82/9.35 | (221) op(e0, e2) = all_56_2
% 63.82/9.36 | (222) op(e0, e3) = all_56_3
% 63.82/9.36 | (223) op(e1, e0) = all_56_4
% 63.82/9.36 | (224) op(e1, e1) = all_56_5
% 63.82/9.36 | (225) op(e1, e2) = all_56_6
% 63.82/9.36 | (226) op(e1, e3) = all_56_7
% 63.82/9.36 | (227) op(e2, e0) = all_56_8
% 63.82/9.36 | (228) op(e2, e1) = all_56_9
% 63.82/9.36 | (229) op(e2, e2) = all_56_10
% 63.82/9.36 | (230) op(e2, e3) = all_56_11
% 63.82/9.36 | (231) op(e3, e0) = all_56_12
% 63.82/9.36 | (232) op(e3, e1) = all_56_13
% 63.82/9.36 | (233) op(e3, e2) = all_56_14
% 63.82/9.36 | (234) op(e3, e3) = all_56_15
% 63.82/9.36 | (235) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 63.82/9.36 | (236) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 63.82/9.36 | (237) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 63.82/9.36 | (238) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 63.82/9.36 | (239) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 63.82/9.36 | (240) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 63.82/9.36 | (241) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 63.82/9.36 | (242) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 63.82/9.36 | (243) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 63.82/9.36 | (244) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 63.82/9.36 | (245) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 63.82/9.36 | (246) all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 63.82/9.36 | (247) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 63.82/9.36 |
% 63.82/9.36 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 63.82/9.36 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 63.82/9.36 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 63.82/9.36 | (248) op(e3, e3) = all_58_12 & op(e3, e2) = all_58_9 & op(e3, e1) =
% 63.82/9.36 | all_58_10 & op(e3, e0) = all_58_11 & op(e2, e3) = all_58_13 & op(e2,
% 63.82/9.36 | e2) = all_58_6 & op(e2, e1) = all_58_4 & op(e2, e0) = all_58_5 &
% 63.82/9.36 | op(e1, e3) = all_58_14 & op(e1, e2) = all_58_7 & op(e1, e1) =
% 63.82/9.36 | all_58_2 & op(e1, e0) = all_58_1 & op(e0, e3) = all_58_15 & op(e0,
% 63.82/9.36 | e2) = all_58_8 & op(e0, e1) = all_58_3 & op(e0, e0) = all_58_0 &
% 63.82/9.36 | $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) &
% 63.82/9.36 | $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) &
% 63.82/9.36 | $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) &
% 63.82/9.36 | $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) &
% 63.82/9.36 | (all_58_0 = e3 | all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3) &
% 63.82/9.36 | (all_58_0 = e3 | all_58_3 = e3 | all_58_8 = e3 | all_58_15 = e3) &
% 63.82/9.36 | (all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2) &
% 63.82/9.36 | (all_58_0 = e2 | all_58_3 = e2 | all_58_8 = e2 | all_58_15 = e2) &
% 63.82/9.36 | (all_58_0 = e1 | all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1) &
% 63.82/9.36 | (all_58_0 = e1 | all_58_3 = e1 | all_58_8 = e1 | all_58_15 = e1) &
% 63.82/9.36 | (all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0) &
% 63.82/9.36 | (all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0) &
% 63.82/9.36 | (all_58_1 = e3 | all_58_2 = e3 | all_58_7 = e3 | all_58_14 = e3) &
% 63.82/9.36 | (all_58_1 = e2 | all_58_2 = e2 | all_58_7 = e2 | all_58_14 = e2) &
% 63.82/9.36 | (all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1) &
% 63.82/9.36 | (all_58_1 = e0 | all_58_2 = e0 | all_58_7 = e0 | all_58_14 = e0) &
% 63.82/9.36 | (all_58_2 = e3 | all_58_3 = e3 | all_58_4 = e3 | all_58_10 = e3) &
% 63.82/9.36 | (all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2) &
% 63.82/9.36 | (all_58_2 = e1 | all_58_3 = e1 | all_58_4 = e1 | all_58_10 = e1) &
% 63.82/9.36 | (all_58_2 = e0 | all_58_3 = e0 | all_58_4 = e0 | all_58_10 = e0) &
% 63.82/9.36 | (all_58_4 = e3 | all_58_5 = e3 | all_58_6 = e3 | all_58_13 = e3) &
% 63.82/9.36 | (all_58_4 = e2 | all_58_5 = e2 | all_58_6 = e2 | all_58_13 = e2) &
% 63.82/9.36 | (all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1) &
% 63.82/9.36 | (all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0) &
% 63.82/9.36 | (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3) &
% 63.82/9.36 | (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2) &
% 63.82/9.36 | (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_9 = e1) &
% 63.82/9.36 | (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0) &
% 63.82/9.36 | (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_12 = e3) &
% 63.82/9.36 | (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_12 = e2) &
% 63.82/9.36 | (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_12 = e1) &
% 63.82/9.36 | (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0) &
% 63.82/9.36 | (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) &
% 63.82/9.36 | (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) &
% 63.82/9.36 | (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) &
% 63.82/9.36 | (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0 | all_58_15 = e0)
% 63.82/9.36 |
% 63.82/9.36 | ALPHA: (248) implies:
% 63.82/9.36 | (249) op(e0, e0) = all_58_0
% 63.82/9.36 | (250) op(e0, e1) = all_58_3
% 63.82/9.36 | (251) op(e0, e2) = all_58_8
% 63.82/9.36 | (252) op(e0, e3) = all_58_15
% 63.82/9.36 | (253) op(e1, e0) = all_58_1
% 63.82/9.36 | (254) op(e1, e1) = all_58_2
% 63.82/9.36 | (255) op(e1, e2) = all_58_7
% 63.82/9.36 | (256) op(e1, e3) = all_58_14
% 63.82/9.36 | (257) op(e2, e0) = all_58_5
% 63.82/9.36 | (258) op(e2, e1) = all_58_4
% 63.82/9.36 | (259) op(e2, e2) = all_58_6
% 63.82/9.36 | (260) op(e2, e3) = all_58_13
% 63.82/9.36 | (261) op(e3, e0) = all_58_11
% 63.82/9.36 | (262) op(e3, e1) = all_58_10
% 63.82/9.36 | (263) op(e3, e2) = all_58_9
% 63.82/9.36 | (264) op(e3, e3) = all_58_12
% 63.82/9.37 | (265) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 63.82/9.37 | (266) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 63.82/9.37 | (267) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0
% 63.82/9.37 | (268) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_12 = e2
% 63.82/9.37 | (269) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 63.82/9.37 | (270) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2
% 63.82/9.37 | (271) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 63.82/9.37 | (272) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 63.82/9.37 | (273) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 63.82/9.37 | (274) all_58_4 = e3 | all_58_5 = e3 | all_58_6 = e3 | all_58_13 = e3
% 63.82/9.37 | (275) all_58_2 = e0 | all_58_3 = e0 | all_58_4 = e0 | all_58_10 = e0
% 63.82/9.37 | (276) all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 63.82/9.37 | (277) all_58_2 = e3 | all_58_3 = e3 | all_58_4 = e3 | all_58_10 = e3
% 63.82/9.37 | (278) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1
% 63.82/9.37 | (279) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0
% 63.82/9.37 | (280) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0
% 63.82/9.37 | (281) all_58_0 = e1 | all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1
% 63.82/9.37 | (282) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 63.82/9.37 | (283) all_58_0 = e3 | all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_38_2, e0, e0,
% 63.82/9.37 | simplifying with (93), (116) gives:
% 63.82/9.37 | (284) all_38_2 = all_28_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_38_2, e0, e0,
% 63.82/9.37 | simplifying with (65), (116) gives:
% 63.82/9.37 | (285) all_38_2 = all_16_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_38_2, e0, e0,
% 63.82/9.37 | simplifying with (46), (116) gives:
% 63.82/9.37 | (286) all_38_2 = all_8_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_3, e0, e0,
% 63.82/9.37 | simplifying with (65), (148) gives:
% 63.82/9.37 | (287) all_52_3 = all_16_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_0, e0, e0,
% 63.82/9.37 | simplifying with (148), (202) gives:
% 63.82/9.37 | (288) all_54_0 = all_52_3
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_56_0, e0, e0,
% 63.82/9.37 | simplifying with (116), (219) gives:
% 63.82/9.37 | (289) all_56_0 = all_38_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_56_0, e0, e0,
% 63.82/9.37 | simplifying with (112), (219) gives:
% 63.82/9.37 | (290) all_56_0 = all_36_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_58_0, e0, e0,
% 63.82/9.37 | simplifying with (202), (249) gives:
% 63.82/9.37 | (291) all_58_0 = all_54_0
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_58_0, e0, e0,
% 63.82/9.37 | simplifying with (41), (249) gives:
% 63.82/9.37 | (292) all_58_0 = all_6_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_3, e1, e0,
% 63.82/9.37 | simplifying with (220), (250) gives:
% 63.82/9.37 | (293) all_58_3 = all_56_1
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_54_1, all_58_3, e1, e0,
% 63.82/9.37 | simplifying with (203), (250) gives:
% 63.82/9.37 | (294) all_58_3 = all_54_1
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_8, e2, e0,
% 63.82/9.37 | simplifying with (221), (251) gives:
% 63.82/9.37 | (295) all_58_8 = all_56_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_54_3, all_58_8, e2, e0,
% 63.82/9.37 | simplifying with (204), (251) gives:
% 63.82/9.37 | (296) all_58_8 = all_54_3
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_15, e3, e0,
% 63.82/9.37 | simplifying with (222), (252) gives:
% 63.82/9.37 | (297) all_58_15 = all_56_3
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_58_15, e3, e0,
% 63.82/9.37 | simplifying with (205), (252) gives:
% 63.82/9.37 | (298) all_58_15 = all_54_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_1, e0, e1,
% 63.82/9.37 | simplifying with (223), (253) gives:
% 63.82/9.37 | (299) all_58_1 = all_56_4
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_54_4, all_58_1, e0, e1,
% 63.82/9.37 | simplifying with (206), (253) gives:
% 63.82/9.37 | (300) all_58_1 = all_54_4
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_22_2, e1, e1,
% 63.82/9.37 | simplifying with (60), (79) gives:
% 63.82/9.37 | (301) all_22_2 = all_14_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_44_2, e1, e1,
% 63.82/9.37 | simplifying with (79), (130) gives:
% 63.82/9.37 | (302) all_44_2 = all_22_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_44_2, e1, e1,
% 63.82/9.37 | simplifying with (74), (130) gives:
% 63.82/9.37 | (303) all_44_2 = all_20_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_54_5, e1, e1,
% 63.82/9.37 | simplifying with (79), (207) gives:
% 63.82/9.37 | (304) all_54_5 = all_22_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_5, e1, e1,
% 63.82/9.37 | simplifying with (70), (207) gives:
% 63.82/9.37 | (305) all_54_5 = all_18_2
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_56_5, all_58_2, e1, e1,
% 63.82/9.37 | simplifying with (224), (254) gives:
% 63.82/9.37 | (306) all_58_2 = all_56_5
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_2, e1, e1,
% 63.82/9.37 | simplifying with (149), (254) gives:
% 63.82/9.37 | (307) all_58_2 = all_52_1
% 63.82/9.37 |
% 63.82/9.37 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_58_2, e1, e1,
% 63.82/9.37 | simplifying with (130), (254) gives:
% 63.82/9.37 | (308) all_58_2 = all_44_2
% 63.82/9.37 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_58_2, e1, e1,
% 63.82/9.38 | simplifying with (103), (254) gives:
% 63.82/9.38 | (309) all_58_2 = all_32_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_7, e2, e1,
% 63.82/9.38 | simplifying with (225), (255) gives:
% 63.82/9.38 | (310) all_58_7 = all_56_6
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_7, all_58_7, e2, e1,
% 63.82/9.38 | simplifying with (208), (255) gives:
% 63.82/9.38 | (311) all_58_7 = all_54_7
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_14, e3, e1,
% 63.82/9.38 | simplifying with (226), (256) gives:
% 63.82/9.38 | (312) all_58_14 = all_56_7
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_6, all_58_14, e3, e1,
% 63.82/9.38 | simplifying with (209), (256) gives:
% 63.82/9.38 | (313) all_58_14 = all_54_6
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_5, e0, e2,
% 63.82/9.38 | simplifying with (227), (257) gives:
% 63.82/9.38 | (314) all_58_5 = all_56_8
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_8, all_58_5, e0, e2,
% 63.82/9.38 | simplifying with (210), (257) gives:
% 63.82/9.38 | (315) all_58_5 = all_54_8
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_4, e1, e2,
% 63.82/9.38 | simplifying with (228), (258) gives:
% 63.82/9.38 | (316) all_58_4 = all_56_9
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_9, all_58_4, e1, e2,
% 63.82/9.38 | simplifying with (211), (258) gives:
% 63.82/9.38 | (317) all_58_4 = all_54_9
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_48_2, e2, e2,
% 63.82/9.38 | simplifying with (135), (139) gives:
% 63.82/9.38 | (318) all_48_2 = all_46_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_48_2, e2, e2,
% 63.82/9.38 | simplifying with (51), (139) gives:
% 63.82/9.38 | (319) all_48_2 = all_10_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_52_0, e2, e2,
% 63.82/9.38 | simplifying with (56), (150) gives:
% 63.82/9.38 | (320) all_52_0 = all_12_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_54_11, e2, e2,
% 63.82/9.38 | simplifying with (150), (212) gives:
% 63.82/9.38 | (321) all_54_11 = all_52_0
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_52_0, all_56_10, e2, e2,
% 63.82/9.38 | simplifying with (150), (229) gives:
% 63.82/9.38 | (322) all_56_10 = all_52_0
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_56_10, e2, e2,
% 63.82/9.38 | simplifying with (139), (229) gives:
% 63.82/9.38 | (323) all_56_10 = all_48_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_56_10, e2, e2,
% 63.82/9.38 | simplifying with (84), (229) gives:
% 63.82/9.38 | (324) all_56_10 = all_24_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_11, all_58_6, e2, e2,
% 63.82/9.38 | simplifying with (212), (259) gives:
% 63.82/9.38 | (325) all_58_6 = all_54_11
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_58_6, e2, e2,
% 63.82/9.38 | simplifying with (98), (259) gives:
% 63.82/9.38 | (326) all_58_6 = all_30_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_13, e3,
% 63.82/9.38 | e2, simplifying with (230), (260) gives:
% 63.82/9.38 | (327) all_58_13 = all_56_11
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_58_13, e3,
% 63.82/9.38 | e2, simplifying with (213), (260) gives:
% 63.82/9.38 | (328) all_58_13 = all_54_10
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_11, e0,
% 63.82/9.38 | e3, simplifying with (231), (261) gives:
% 63.82/9.38 | (329) all_58_11 = all_56_12
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_12, all_58_11, e0,
% 63.82/9.38 | e3, simplifying with (214), (261) gives:
% 63.82/9.38 | (330) all_58_11 = all_54_12
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_10, e1,
% 63.82/9.38 | e3, simplifying with (232), (262) gives:
% 63.82/9.38 | (331) all_58_10 = all_56_13
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_13, all_58_10, e1,
% 63.82/9.38 | e3, simplifying with (215), (262) gives:
% 63.82/9.38 | (332) all_58_10 = all_54_13
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_14, all_58_9, e2, e3,
% 63.82/9.38 | simplifying with (233), (263) gives:
% 63.82/9.38 | (333) all_58_9 = all_56_14
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_58_9, e2, e3,
% 63.82/9.38 | simplifying with (216), (263) gives:
% 63.82/9.38 | (334) all_58_9 = all_54_15
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_50_2, e3, e3,
% 63.82/9.38 | simplifying with (121), (143) gives:
% 63.82/9.38 | (335) all_50_2 = all_40_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_50_2, e3, e3,
% 63.82/9.38 | simplifying with (36), (143) gives:
% 63.82/9.38 | (336) all_50_2 = all_4_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_2, e3, e3,
% 63.82/9.38 | simplifying with (143), (151) gives:
% 63.82/9.38 | (337) all_52_2 = all_50_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_2, e3, e3,
% 63.82/9.38 | simplifying with (107), (151) gives:
% 63.82/9.38 | (338) all_52_2 = all_34_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_52_2, e3, e3,
% 63.82/9.38 | simplifying with (88), (151) gives:
% 63.82/9.38 | (339) all_52_2 = all_26_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_14, e3, e3,
% 63.82/9.38 | simplifying with (143), (217) gives:
% 63.82/9.38 | (340) all_54_14 = all_50_2
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_54_14, all_56_15, e3,
% 63.82/9.38 | e3, simplifying with (217), (234) gives:
% 63.82/9.38 | (341) all_56_15 = all_54_14
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_56_15, all_58_12, e3,
% 63.82/9.38 | e3, simplifying with (234), (264) gives:
% 63.82/9.38 | (342) all_58_12 = all_56_15
% 63.82/9.38 |
% 63.82/9.38 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_58_12, e3, e3,
% 63.82/9.38 | simplifying with (125), (264) gives:
% 63.82/9.38 | (343) all_58_12 = all_42_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (291), (292) imply:
% 63.82/9.38 | (344) all_54_0 = all_6_2
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (344) implies:
% 63.82/9.38 | (345) all_54_0 = all_6_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (299), (300) imply:
% 63.82/9.38 | (346) all_56_4 = all_54_4
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (306), (309) imply:
% 63.82/9.38 | (347) all_56_5 = all_32_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (306), (308) imply:
% 63.82/9.38 | (348) all_56_5 = all_44_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (306), (307) imply:
% 63.82/9.38 | (349) all_56_5 = all_52_1
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (293), (294) imply:
% 63.82/9.38 | (350) all_56_1 = all_54_1
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (350) implies:
% 63.82/9.38 | (351) all_56_1 = all_54_1
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (316), (317) imply:
% 63.82/9.38 | (352) all_56_9 = all_54_9
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (352) implies:
% 63.82/9.38 | (353) all_56_9 = all_54_9
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (314), (315) imply:
% 63.82/9.38 | (354) all_56_8 = all_54_8
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (354) implies:
% 63.82/9.38 | (355) all_56_8 = all_54_8
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (325), (326) imply:
% 63.82/9.38 | (356) all_54_11 = all_30_2
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (356) implies:
% 63.82/9.38 | (357) all_54_11 = all_30_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (310), (311) imply:
% 63.82/9.38 | (358) all_56_6 = all_54_7
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (358) implies:
% 63.82/9.38 | (359) all_56_6 = all_54_7
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (295), (296) imply:
% 63.82/9.38 | (360) all_56_2 = all_54_3
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (333), (334) imply:
% 63.82/9.38 | (361) all_56_14 = all_54_15
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (331), (332) imply:
% 63.82/9.38 | (362) all_56_13 = all_54_13
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (329), (330) imply:
% 63.82/9.38 | (363) all_56_12 = all_54_12
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (342), (343) imply:
% 63.82/9.38 | (364) all_56_15 = all_42_2
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (364) implies:
% 63.82/9.38 | (365) all_56_15 = all_42_2
% 63.82/9.38 |
% 63.82/9.38 | COMBINE_EQS: (327), (328) imply:
% 63.82/9.38 | (366) all_56_11 = all_54_10
% 63.82/9.38 |
% 63.82/9.38 | SIMP: (366) implies:
% 63.82/9.38 | (367) all_56_11 = all_54_10
% 63.82/9.38 |
% 63.82/9.39 | COMBINE_EQS: (312), (313) imply:
% 63.82/9.39 | (368) all_56_7 = all_54_6
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (368) implies:
% 63.82/9.39 | (369) all_56_7 = all_54_6
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (297), (298) imply:
% 63.82/9.39 | (370) all_56_3 = all_54_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (370) implies:
% 63.82/9.39 | (371) all_56_3 = all_54_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (289), (290) imply:
% 63.82/9.39 | (372) all_38_2 = all_36_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (372) implies:
% 63.82/9.39 | (373) all_38_2 = all_36_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (347), (349) imply:
% 63.82/9.39 | (374) all_52_1 = all_32_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (348), (349) imply:
% 63.82/9.39 | (375) all_52_1 = all_44_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (323), (324) imply:
% 63.82/9.39 | (376) all_48_2 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (376) implies:
% 63.82/9.39 | (377) all_48_2 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (322), (324) imply:
% 63.82/9.39 | (378) all_52_0 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (378) implies:
% 63.82/9.39 | (379) all_52_0 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (341), (365) imply:
% 63.82/9.39 | (380) all_54_14 = all_42_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (380) implies:
% 63.82/9.39 | (381) all_54_14 = all_42_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (288), (345) imply:
% 63.82/9.39 | (382) all_52_3 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (382) implies:
% 63.82/9.39 | (383) all_52_3 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (304), (305) imply:
% 63.82/9.39 | (384) all_22_2 = all_18_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (384) implies:
% 63.82/9.39 | (385) all_22_2 = all_18_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (321), (357) imply:
% 63.82/9.39 | (386) all_52_0 = all_30_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (386) implies:
% 63.82/9.39 | (387) all_52_0 = all_30_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (340), (381) imply:
% 63.82/9.39 | (388) all_50_2 = all_42_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (388) implies:
% 63.82/9.39 | (389) all_50_2 = all_42_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (320), (387) imply:
% 63.82/9.39 | (390) all_30_2 = all_12_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (379), (387) imply:
% 63.82/9.39 | (391) all_30_2 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (374), (375) imply:
% 63.82/9.39 | (392) all_44_2 = all_32_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (392) implies:
% 63.82/9.39 | (393) all_44_2 = all_32_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (337), (338) imply:
% 63.82/9.39 | (394) all_50_2 = all_34_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (394) implies:
% 63.82/9.39 | (395) all_50_2 = all_34_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (338), (339) imply:
% 63.82/9.39 | (396) all_34_2 = all_26_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (287), (383) imply:
% 63.82/9.39 | (397) all_16_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (397) implies:
% 63.82/9.39 | (398) all_16_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (336), (389) imply:
% 63.82/9.39 | (399) all_42_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (335), (389) imply:
% 63.82/9.39 | (400) all_42_2 = all_40_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (389), (395) imply:
% 63.82/9.39 | (401) all_42_2 = all_34_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (318), (319) imply:
% 63.82/9.39 | (402) all_46_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (318), (377) imply:
% 63.82/9.39 | (403) all_46_2 = all_24_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (402), (403) imply:
% 63.82/9.39 | (404) all_24_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (404) implies:
% 63.82/9.39 | (405) all_24_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (302), (393) imply:
% 63.82/9.39 | (406) all_32_2 = all_22_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (303), (393) imply:
% 63.82/9.39 | (407) all_32_2 = all_20_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (400), (401) imply:
% 63.82/9.39 | (408) all_40_2 = all_34_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (399), (400) imply:
% 63.82/9.39 | (409) all_40_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (408), (409) imply:
% 63.82/9.39 | (410) all_34_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (410) implies:
% 63.82/9.39 | (411) all_34_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (284), (373) imply:
% 63.82/9.39 | (412) all_36_2 = all_28_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (286), (373) imply:
% 63.82/9.39 | (413) all_36_2 = all_8_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (285), (373) imply:
% 63.82/9.39 | (414) all_36_2 = all_16_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (412), (414) imply:
% 63.82/9.39 | (415) all_28_2 = all_16_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (412), (413) imply:
% 63.82/9.39 | (416) all_28_2 = all_8_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (396), (411) imply:
% 63.82/9.39 | (417) all_26_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (417) implies:
% 63.82/9.39 | (418) all_26_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (406), (407) imply:
% 63.82/9.39 | (419) all_22_2 = all_20_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (419) implies:
% 63.82/9.39 | (420) all_22_2 = all_20_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (390), (391) imply:
% 63.82/9.39 | (421) all_24_2 = all_12_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (421) implies:
% 63.82/9.39 | (422) all_24_2 = all_12_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (415), (416) imply:
% 63.82/9.39 | (423) all_16_2 = all_8_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (423) implies:
% 63.82/9.39 | (424) all_16_2 = all_8_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (405), (422) imply:
% 63.82/9.39 | (425) all_12_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (425) implies:
% 63.82/9.39 | (426) all_12_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (301), (420) imply:
% 63.82/9.39 | (427) all_20_2 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (385), (420) imply:
% 63.82/9.39 | (428) all_20_2 = all_18_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (427), (428) imply:
% 63.82/9.39 | (429) all_18_2 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (398), (424) imply:
% 63.82/9.39 | (430) all_8_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (430) implies:
% 63.82/9.39 | (431) all_8_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (416), (431) imply:
% 63.82/9.39 | (432) all_28_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (390), (426) imply:
% 63.82/9.39 | (433) all_30_2 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (407), (427) imply:
% 63.82/9.39 | (434) all_32_2 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (412), (432) imply:
% 63.82/9.39 | (435) all_36_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (373), (435) imply:
% 63.82/9.39 | (436) all_38_2 = all_6_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (393), (434) imply:
% 63.82/9.39 | (437) all_44_2 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (338), (411) imply:
% 63.82/9.39 | (438) all_52_2 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (374), (434) imply:
% 63.82/9.39 | (439) all_52_1 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (387), (433) imply:
% 63.82/9.39 | (440) all_52_0 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (381), (399) imply:
% 63.82/9.39 | (441) all_54_14 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (357), (433) imply:
% 63.82/9.39 | (442) all_54_11 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (305), (429) imply:
% 63.82/9.39 | (443) all_54_5 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (324), (405) imply:
% 63.82/9.39 | (444) all_56_10 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (349), (439) imply:
% 63.82/9.39 | (445) all_56_5 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (343), (399) imply:
% 63.82/9.39 | (446) all_58_12 = all_4_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (326), (433) imply:
% 63.82/9.39 | (447) all_58_6 = all_10_2
% 63.82/9.39 |
% 63.82/9.39 | COMBINE_EQS: (306), (445) imply:
% 63.82/9.39 | (448) all_58_2 = all_14_2
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (201), (345) imply:
% 63.82/9.39 | (449) ~ (all_54_1 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (449) implies:
% 63.82/9.39 | (450) ~ (all_54_1 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (200), (345) imply:
% 63.82/9.39 | (451) ~ (all_54_2 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (451) implies:
% 63.82/9.39 | (452) ~ (all_54_2 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (199), (345) imply:
% 63.82/9.39 | (453) ~ (all_54_3 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (453) implies:
% 63.82/9.39 | (454) ~ (all_54_3 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (198), (345) imply:
% 63.82/9.39 | (455) ~ (all_54_4 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (455) implies:
% 63.82/9.39 | (456) ~ (all_54_4 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (197), (345) imply:
% 63.82/9.39 | (457) ~ (all_54_8 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (457) implies:
% 63.82/9.39 | (458) ~ (all_54_8 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (196), (345) imply:
% 63.82/9.39 | (459) ~ (all_54_12 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (459) implies:
% 63.82/9.39 | (460) ~ (all_54_12 = all_6_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (193), (443) imply:
% 63.82/9.39 | (461) ~ (all_54_1 = all_14_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (187), (441) imply:
% 63.82/9.39 | (462) ~ (all_54_2 = all_4_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (184), (443) imply:
% 63.82/9.39 | (463) ~ (all_54_4 = all_14_2)
% 63.82/9.39 |
% 63.82/9.39 | REDUCE: (179), (443) imply:
% 63.82/9.39 | (464) ~ (all_54_6 = all_14_2)
% 63.82/9.39 |
% 63.82/9.39 | SIMP: (464) implies:
% 63.82/9.39 | (465) ~ (all_54_6 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (178), (443) imply:
% 63.82/9.40 | (466) ~ (all_54_7 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | SIMP: (466) implies:
% 63.82/9.40 | (467) ~ (all_54_7 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (177), (443) imply:
% 63.82/9.40 | (468) ~ (all_54_9 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | SIMP: (468) implies:
% 63.82/9.40 | (469) ~ (all_54_9 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (176), (443) imply:
% 63.82/9.40 | (470) ~ (all_54_13 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | SIMP: (470) implies:
% 63.82/9.40 | (471) ~ (all_54_13 = all_14_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (173), (441) imply:
% 63.82/9.40 | (472) ~ (all_54_6 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (172), (442) imply:
% 63.82/9.40 | (473) ~ (all_54_7 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (169), (442) imply:
% 63.82/9.40 | (474) ~ (all_54_8 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (166), (442) imply:
% 63.82/9.40 | (475) ~ (all_54_9 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (164), (442) imply:
% 63.82/9.40 | (476) ~ (all_54_10 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (163), (441) imply:
% 63.82/9.40 | (477) ~ (all_54_10 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (162), (442) imply:
% 63.82/9.40 | (478) ~ (all_54_15 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | SIMP: (478) implies:
% 63.82/9.40 | (479) ~ (all_54_15 = all_10_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (161), (441) imply:
% 63.82/9.40 | (480) ~ (all_54_12 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (159), (441) imply:
% 63.82/9.40 | (481) ~ (all_54_13 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (157), (441) imply:
% 63.82/9.40 | (482) ~ (all_54_15 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | SIMP: (482) implies:
% 63.82/9.40 | (483) ~ (all_54_15 = all_4_2)
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (145), (336) imply:
% 63.82/9.40 | (484) op(all_4_2, all_4_2) = all_50_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (144), (336) imply:
% 63.82/9.40 | (485) op(all_4_2, e3) = all_50_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (141), (319) imply:
% 63.82/9.40 | (486) op(all_10_2, all_10_2) = all_48_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (140), (319) imply:
% 63.82/9.40 | (487) op(all_10_2, e2) = all_48_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (137), (402) imply:
% 63.82/9.40 | (488) op(all_10_2, all_10_2) = all_46_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (136), (402) imply:
% 63.82/9.40 | (489) op(all_10_2, e2) = all_46_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (132), (437) imply:
% 63.82/9.40 | (490) op(all_14_2, all_14_2) = all_44_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (131), (437) imply:
% 63.82/9.40 | (491) op(all_14_2, e1) = all_44_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (127), (399) imply:
% 63.82/9.40 | (492) op(all_4_2, all_4_2) = all_42_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (126), (399) imply:
% 63.82/9.40 | (493) op(all_4_2, e3) = all_42_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (123), (409) imply:
% 63.82/9.40 | (494) op(all_4_2, all_4_2) = all_40_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (122), (409) imply:
% 63.82/9.40 | (495) op(all_4_2, e3) = all_40_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (118), (436) imply:
% 63.82/9.40 | (496) op(all_6_2, all_6_2) = all_38_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (117), (436) imply:
% 63.82/9.40 | (497) op(all_6_2, e0) = all_38_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (114), (435) imply:
% 63.82/9.40 | (498) op(all_6_2, all_6_2) = all_36_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (113), (435) imply:
% 63.82/9.40 | (499) op(all_6_2, e0) = all_36_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (109), (411) imply:
% 63.82/9.40 | (500) op(all_4_2, all_4_2) = all_34_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (108), (411) imply:
% 63.82/9.40 | (501) op(all_4_2, e3) = all_34_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (105), (434) imply:
% 63.82/9.40 | (502) op(all_14_2, all_14_2) = all_32_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (104), (434) imply:
% 63.82/9.40 | (503) op(all_14_2, e1) = all_32_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (100), (433) imply:
% 63.82/9.40 | (504) op(all_10_2, all_10_2) = all_30_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (99), (433) imply:
% 63.82/9.40 | (505) op(all_10_2, e2) = all_30_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (95), (432) imply:
% 63.82/9.40 | (506) op(all_6_2, all_6_2) = all_28_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (94), (432) imply:
% 63.82/9.40 | (507) op(all_6_2, e0) = all_28_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (90), (418) imply:
% 63.82/9.40 | (508) op(all_4_2, all_4_2) = all_26_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (89), (418) imply:
% 63.82/9.40 | (509) op(all_4_2, e3) = all_26_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (86), (405) imply:
% 63.82/9.40 | (510) op(all_10_2, all_10_2) = all_24_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (85), (405) imply:
% 63.82/9.40 | (511) op(all_10_2, e2) = all_24_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (81), (301) imply:
% 63.82/9.40 | (512) op(all_14_2, all_14_2) = all_22_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (80), (301) imply:
% 63.82/9.40 | (513) op(all_14_2, e1) = all_22_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (76), (427) imply:
% 63.82/9.40 | (514) op(all_14_2, all_14_2) = all_20_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (75), (427) imply:
% 63.82/9.40 | (515) op(all_14_2, e1) = all_20_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (72), (429) imply:
% 63.82/9.40 | (516) op(all_14_2, all_14_2) = all_18_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (71), (429) imply:
% 63.82/9.40 | (517) op(all_14_2, e1) = all_18_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (67), (398) imply:
% 63.82/9.40 | (518) op(all_6_2, all_6_2) = all_16_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (66), (398) imply:
% 63.82/9.40 | (519) op(all_6_2, e0) = all_16_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (58), (426) imply:
% 63.82/9.40 | (520) op(all_10_2, all_10_2) = all_12_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (57), (426) imply:
% 63.82/9.40 | (521) op(all_10_2, e2) = all_12_1
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (48), (431) imply:
% 63.82/9.40 | (522) op(all_6_2, all_6_2) = all_8_0
% 63.82/9.40 |
% 63.82/9.40 | REDUCE: (47), (431) imply:
% 63.82/9.40 | (523) op(all_6_2, e0) = all_8_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_26_1, all_34_1, e3,
% 63.82/9.40 | all_4_2, simplifying with (501), (509) gives:
% 63.82/9.40 | (524) all_34_1 = all_26_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_34_1, all_40_1, e3,
% 63.82/9.40 | all_4_2, simplifying with (495), (501) gives:
% 63.82/9.40 | (525) all_40_1 = all_34_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_40_1, all_42_1, e3,
% 63.82/9.40 | all_4_2, simplifying with (493), (495) gives:
% 63.82/9.40 | (526) all_42_1 = all_40_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_4_1, all_50_1, e3,
% 63.82/9.40 | all_4_2, simplifying with (37), (485) gives:
% 63.82/9.40 | (527) all_50_1 = all_4_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_42_1, all_50_1, e3,
% 63.82/9.40 | all_4_2, simplifying with (485), (493) gives:
% 63.82/9.40 | (528) all_50_1 = all_42_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_26_0, all_34_0, all_4_2,
% 63.82/9.40 | all_4_2, simplifying with (500), (508) gives:
% 63.82/9.40 | (529) all_34_0 = all_26_0
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_4_0, all_42_0, all_4_2,
% 63.82/9.40 | all_4_2, simplifying with (38), (492) gives:
% 63.82/9.40 | (530) all_42_0 = all_4_0
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_34_0, all_42_0, all_4_2,
% 63.82/9.40 | all_4_2, simplifying with (492), (500) gives:
% 63.82/9.40 | (531) all_42_0 = all_34_0
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_42_0, all_50_0, all_4_2,
% 63.82/9.40 | all_4_2, simplifying with (484), (492) gives:
% 63.82/9.40 | (532) all_50_0 = all_42_0
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_40_0, all_50_0, all_4_2,
% 63.82/9.40 | all_4_2, simplifying with (484), (494) gives:
% 63.82/9.40 | (533) all_50_0 = all_40_0
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_6_1, all_36_1, e0,
% 63.82/9.40 | all_6_2, simplifying with (42), (499) gives:
% 63.82/9.40 | (534) all_36_1 = all_6_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_36_1, e0,
% 63.82/9.40 | all_6_2, simplifying with (499), (507) gives:
% 63.82/9.40 | (535) all_36_1 = all_28_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_16_1, all_36_1, e0,
% 63.82/9.40 | all_6_2, simplifying with (499), (519) gives:
% 63.82/9.40 | (536) all_36_1 = all_16_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_28_1, all_38_1, e0,
% 63.82/9.40 | all_6_2, simplifying with (497), (507) gives:
% 63.82/9.40 | (537) all_38_1 = all_28_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_8_1, all_38_1, e0,
% 63.82/9.40 | all_6_2, simplifying with (497), (523) gives:
% 63.82/9.40 | (538) all_38_1 = all_8_1
% 63.82/9.40 |
% 63.82/9.40 | GROUND_INST: instantiating (function-axioms) with all_6_0, all_16_0, all_6_2,
% 63.82/9.40 | all_6_2, simplifying with (43), (518) gives:
% 63.82/9.41 | (539) all_16_0 = all_6_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_16_0, all_28_0, all_6_2,
% 63.82/9.41 | all_6_2, simplifying with (506), (518) gives:
% 63.82/9.41 | (540) all_28_0 = all_16_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_28_0, all_36_0, all_6_2,
% 63.82/9.41 | all_6_2, simplifying with (498), (506) gives:
% 63.82/9.41 | (541) all_36_0 = all_28_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_36_0, all_38_0, all_6_2,
% 63.82/9.41 | all_6_2, simplifying with (496), (498) gives:
% 63.82/9.41 | (542) all_38_0 = all_36_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_8_0, all_38_0, all_6_2,
% 63.82/9.41 | all_6_2, simplifying with (496), (522) gives:
% 63.82/9.41 | (543) all_38_0 = all_8_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_10_1, all_24_1, e2,
% 63.82/9.41 | all_10_2, simplifying with (52), (511) gives:
% 63.82/9.41 | (544) all_24_1 = all_10_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_24_1, all_30_1, e2,
% 63.82/9.41 | all_10_2, simplifying with (505), (511) gives:
% 63.82/9.41 | (545) all_30_1 = all_24_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_30_1, all_46_1, e2,
% 63.82/9.41 | all_10_2, simplifying with (489), (505) gives:
% 63.82/9.41 | (546) all_46_1 = all_30_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_46_1, all_48_1, e2,
% 63.82/9.41 | all_10_2, simplifying with (487), (489) gives:
% 63.82/9.41 | (547) all_48_1 = all_46_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_12_1, all_48_1, e2,
% 63.82/9.41 | all_10_2, simplifying with (487), (521) gives:
% 63.82/9.41 | (548) all_48_1 = all_12_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_30_0, all_46_0,
% 63.82/9.41 | all_10_2, all_10_2, simplifying with (488), (504) gives:
% 63.82/9.41 | (549) all_46_0 = all_30_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_46_0,
% 63.82/9.41 | all_10_2, all_10_2, simplifying with (488), (510) gives:
% 63.82/9.41 | (550) all_46_0 = all_24_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_12_0, all_46_0,
% 63.82/9.41 | all_10_2, all_10_2, simplifying with (488), (520) gives:
% 63.82/9.41 | (551) all_46_0 = all_12_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_10_0, all_48_0,
% 63.82/9.41 | all_10_2, all_10_2, simplifying with (53), (486) gives:
% 63.82/9.41 | (552) all_48_0 = all_10_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_24_0, all_48_0,
% 63.82/9.41 | all_10_2, all_10_2, simplifying with (486), (510) gives:
% 63.82/9.41 | (553) all_48_0 = all_24_0
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_14_1, all_22_1, e1,
% 63.82/9.41 | all_14_2, simplifying with (61), (513) gives:
% 63.82/9.41 | (554) all_22_1 = all_14_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_18_1, all_22_1, e1,
% 63.82/9.41 | all_14_2, simplifying with (513), (517) gives:
% 63.82/9.41 | (555) all_22_1 = all_18_1
% 63.82/9.41 |
% 63.82/9.41 | GROUND_INST: instantiating (function-axioms) with all_22_1, all_32_1, e1,
% 63.82/9.41 | all_14_2, simplifying with (503), (513) gives:
% 64.25/9.41 | (556) all_32_1 = all_22_1
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_32_1, all_44_1, e1,
% 64.25/9.41 | all_14_2, simplifying with (491), (503) gives:
% 64.25/9.41 | (557) all_44_1 = all_32_1
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_20_1, all_44_1, e1,
% 64.25/9.41 | all_14_2, simplifying with (491), (515) gives:
% 64.25/9.41 | (558) all_44_1 = all_20_1
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_14_0, all_22_0,
% 64.25/9.41 | all_14_2, all_14_2, simplifying with (62), (512) gives:
% 64.25/9.41 | (559) all_22_0 = all_14_0
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_32_0,
% 64.25/9.41 | all_14_2, all_14_2, simplifying with (502), (512) gives:
% 64.25/9.41 | (560) all_32_0 = all_22_0
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_18_0, all_32_0,
% 64.25/9.41 | all_14_2, all_14_2, simplifying with (502), (516) gives:
% 64.25/9.41 | (561) all_32_0 = all_18_0
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_22_0, all_44_0,
% 64.25/9.41 | all_14_2, all_14_2, simplifying with (490), (512) gives:
% 64.25/9.41 | (562) all_44_0 = all_22_0
% 64.25/9.41 |
% 64.25/9.41 | GROUND_INST: instantiating (function-axioms) with all_20_0, all_44_0,
% 64.25/9.41 | all_14_2, all_14_2, simplifying with (490), (514) gives:
% 64.25/9.41 | (563) all_44_0 = all_20_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (532), (533) imply:
% 64.25/9.41 | (564) all_42_0 = all_40_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (564) implies:
% 64.25/9.41 | (565) all_42_0 = all_40_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (527), (528) imply:
% 64.25/9.41 | (566) all_42_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (566) implies:
% 64.25/9.41 | (567) all_42_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (552), (553) imply:
% 64.25/9.41 | (568) all_24_0 = all_10_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (568) implies:
% 64.25/9.41 | (569) all_24_0 = all_10_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (547), (548) imply:
% 64.25/9.41 | (570) all_46_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (570) implies:
% 64.25/9.41 | (571) all_46_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (549), (551) imply:
% 64.25/9.41 | (572) all_30_0 = all_12_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (549), (550) imply:
% 64.25/9.41 | (573) all_30_0 = all_24_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (546), (571) imply:
% 64.25/9.41 | (574) all_30_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (574) implies:
% 64.25/9.41 | (575) all_30_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (562), (563) imply:
% 64.25/9.41 | (576) all_22_0 = all_20_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (576) implies:
% 64.25/9.41 | (577) all_22_0 = all_20_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (557), (558) imply:
% 64.25/9.41 | (578) all_32_1 = all_20_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (578) implies:
% 64.25/9.41 | (579) all_32_1 = all_20_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (531), (565) imply:
% 64.25/9.41 | (580) all_40_0 = all_34_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (530), (565) imply:
% 64.25/9.41 | (581) all_40_0 = all_4_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (526), (567) imply:
% 64.25/9.41 | (582) all_40_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (582) implies:
% 64.25/9.41 | (583) all_40_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (580), (581) imply:
% 64.25/9.41 | (584) all_34_0 = all_4_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (584) implies:
% 64.25/9.41 | (585) all_34_0 = all_4_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (525), (583) imply:
% 64.25/9.41 | (586) all_34_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (586) implies:
% 64.25/9.41 | (587) all_34_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (542), (543) imply:
% 64.25/9.41 | (588) all_36_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (588) implies:
% 64.25/9.41 | (589) all_36_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (537), (538) imply:
% 64.25/9.41 | (590) all_28_1 = all_8_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (590) implies:
% 64.25/9.41 | (591) all_28_1 = all_8_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (541), (589) imply:
% 64.25/9.41 | (592) all_28_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (592) implies:
% 64.25/9.41 | (593) all_28_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (535), (536) imply:
% 64.25/9.41 | (594) all_28_1 = all_16_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (594) implies:
% 64.25/9.41 | (595) all_28_1 = all_16_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (534), (536) imply:
% 64.25/9.41 | (596) all_16_1 = all_6_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (529), (585) imply:
% 64.25/9.41 | (597) all_26_0 = all_4_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (524), (587) imply:
% 64.25/9.41 | (598) all_26_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (598) implies:
% 64.25/9.41 | (599) all_26_1 = all_4_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (560), (561) imply:
% 64.25/9.41 | (600) all_22_0 = all_18_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (600) implies:
% 64.25/9.41 | (601) all_22_0 = all_18_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (556), (579) imply:
% 64.25/9.41 | (602) all_22_1 = all_20_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (602) implies:
% 64.25/9.41 | (603) all_22_1 = all_20_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (572), (573) imply:
% 64.25/9.41 | (604) all_24_0 = all_12_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (604) implies:
% 64.25/9.41 | (605) all_24_0 = all_12_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (545), (575) imply:
% 64.25/9.41 | (606) all_24_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (606) implies:
% 64.25/9.41 | (607) all_24_1 = all_12_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (540), (593) imply:
% 64.25/9.41 | (608) all_16_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (608) implies:
% 64.25/9.41 | (609) all_16_0 = all_8_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (591), (595) imply:
% 64.25/9.41 | (610) all_16_1 = all_8_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (610) implies:
% 64.25/9.41 | (611) all_16_1 = all_8_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (569), (605) imply:
% 64.25/9.41 | (612) all_12_0 = all_10_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (544), (607) imply:
% 64.25/9.41 | (613) all_12_1 = all_10_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (613) implies:
% 64.25/9.41 | (614) all_12_1 = all_10_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (559), (577) imply:
% 64.25/9.41 | (615) all_20_0 = all_14_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (577), (601) imply:
% 64.25/9.41 | (616) all_20_0 = all_18_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (555), (603) imply:
% 64.25/9.41 | (617) all_20_1 = all_18_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (554), (603) imply:
% 64.25/9.41 | (618) all_20_1 = all_14_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (615), (616) imply:
% 64.25/9.41 | (619) all_18_0 = all_14_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (617), (618) imply:
% 64.25/9.41 | (620) all_18_1 = all_14_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (620) implies:
% 64.25/9.41 | (621) all_18_1 = all_14_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (539), (609) imply:
% 64.25/9.41 | (622) all_8_0 = all_6_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (596), (611) imply:
% 64.25/9.41 | (623) all_8_1 = all_6_1
% 64.25/9.41 |
% 64.25/9.41 | SIMP: (623) implies:
% 64.25/9.41 | (624) all_8_1 = all_6_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (591), (624) imply:
% 64.25/9.41 | (625) all_28_1 = all_6_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (593), (622) imply:
% 64.25/9.41 | (626) all_28_0 = all_6_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (575), (614) imply:
% 64.25/9.41 | (627) all_30_1 = all_10_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (572), (612) imply:
% 64.25/9.41 | (628) all_30_0 = all_10_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (538), (624) imply:
% 64.25/9.41 | (629) all_38_1 = all_6_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (543), (622) imply:
% 64.25/9.41 | (630) all_38_0 = all_6_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (558), (618) imply:
% 64.25/9.41 | (631) all_44_1 = all_14_1
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (563), (615) imply:
% 64.25/9.41 | (632) all_44_0 = all_14_0
% 64.25/9.41 |
% 64.25/9.41 | COMBINE_EQS: (533), (581) imply:
% 64.25/9.41 | (633) all_50_0 = all_4_0
% 64.25/9.41 |
% 64.25/9.41 | BETA: splitting (39) gives:
% 64.25/9.41 |
% 64.25/9.41 | Case 1:
% 64.25/9.41 | |
% 64.25/9.41 | | (634) ~ (all_4_0 = e2)
% 64.25/9.41 | |
% 64.25/9.41 | | BETA: splitting (44) gives:
% 64.25/9.41 | |
% 64.25/9.41 | | Case 1:
% 64.25/9.41 | | |
% 64.25/9.42 | | | (635) ~ (all_6_0 = e3)
% 64.25/9.42 | | |
% 64.25/9.42 | | | BETA: splitting (54) gives:
% 64.25/9.42 | | |
% 64.25/9.42 | | | Case 1:
% 64.25/9.42 | | | |
% 64.25/9.42 | | | | (636) ~ (all_10_0 = e1)
% 64.25/9.42 | | | |
% 64.25/9.42 | | | | BETA: splitting (63) gives:
% 64.25/9.42 | | | |
% 64.25/9.42 | | | | Case 1:
% 64.25/9.42 | | | | |
% 64.25/9.42 | | | | | (637) ~ (all_14_0 = e0)
% 64.25/9.42 | | | | |
% 64.25/9.42 | | | | | BETA: splitting (68) gives:
% 64.25/9.42 | | | | |
% 64.25/9.42 | | | | | Case 1:
% 64.25/9.42 | | | | | |
% 64.25/9.42 | | | | | | (638) ~ (all_16_0 = e1)
% 64.25/9.42 | | | | | |
% 64.25/9.42 | | | | | | REDUCE: (539), (638) imply:
% 64.25/9.42 | | | | | | (639) ~ (all_6_0 = e1)
% 64.25/9.42 | | | | | |
% 64.25/9.42 | | | | | | BETA: splitting (77) gives:
% 64.25/9.42 | | | | | |
% 64.25/9.42 | | | | | | Case 1:
% 64.25/9.42 | | | | | | |
% 64.25/9.42 | | | | | | | (640) ~ (all_20_0 = e2)
% 64.25/9.42 | | | | | | |
% 64.25/9.42 | | | | | | | REDUCE: (615), (640) imply:
% 64.25/9.42 | | | | | | | (641) ~ (all_14_0 = e2)
% 64.25/9.42 | | | | | | |
% 64.25/9.42 | | | | | | | BETA: splitting (82) gives:
% 64.25/9.42 | | | | | | |
% 64.25/9.42 | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | |
% 64.25/9.42 | | | | | | | | (642) ~ (all_22_0 = e3)
% 64.25/9.42 | | | | | | | |
% 64.25/9.42 | | | | | | | | REDUCE: (559), (642) imply:
% 64.25/9.42 | | | | | | | | (643) ~ (all_14_0 = e3)
% 64.25/9.42 | | | | | | | |
% 64.25/9.42 | | | | | | | | BETA: splitting (91) gives:
% 64.25/9.42 | | | | | | | |
% 64.25/9.42 | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | |
% 64.25/9.42 | | | | | | | | | (644) ~ (all_26_0 = e1)
% 64.25/9.42 | | | | | | | | |
% 64.25/9.42 | | | | | | | | | REDUCE: (597), (644) imply:
% 64.25/9.42 | | | | | | | | | (645) ~ (all_4_0 = e1)
% 64.25/9.42 | | | | | | | | |
% 64.25/9.42 | | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.42 | | | | | | | | |
% 64.25/9.42 | | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | (646) ~ (all_28_0 = e2)
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | REDUCE: (626), (646) imply:
% 64.25/9.42 | | | | | | | | | | (647) ~ (all_6_0 = e2)
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | (648) ~ (all_34_0 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (585), (648) imply:
% 64.25/9.42 | | | | | | | | | | | (649) ~ (all_4_0 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (38), (43), (51), (60),
% 64.25/9.42 | | | | | | | | | | | (62), (152), (153), (154), (155), (383), (438),
% 64.25/9.42 | | | | | | | | | | | (439), (440), (637), (639), (643), (645), (649),
% 64.25/9.42 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.42 | | | | | | | | | | | #167.
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | Case 2:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | (650) all_34_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | COMBINE_EQS: (585), (650) imply:
% 64.25/9.42 | | | | | | | | | | | (651) all_4_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | SIMP: (651) implies:
% 64.25/9.42 | | | | | | | | | | | (652) all_4_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (634), (652) imply:
% 64.25/9.42 | | | | | | | | | | | (653) ~ (e2 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (645), (652) imply:
% 64.25/9.42 | | | | | | | | | | | (654) ~ (e1 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (38), (652) imply:
% 64.25/9.42 | | | | | | | | | | | (655) op(all_4_2, all_4_2) = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | | (656) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.25/9.42 | | | | | | | | | | | | (438), (439), (440), (637), (643), (656),
% 64.25/9.42 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.42 | | | | | | | | | | | | #165.
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | Case 2:
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | | (657) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.42 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (43), (51), (53), (154), (239),
% 64.25/9.42 | | | | | | | | | | | | (383), (438), (440), (444), (635), (636), (639),
% 64.25/9.42 | | | | | | | | | | | | (647), (655), (657), (function-axioms) are
% 64.25/9.42 | | | | | | | | | | | | inconsistent by sub-proof #160.
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | End of split
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | End of split
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | Case 2:
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | (658) all_28_0 = e2
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | COMBINE_EQS: (626), (658) imply:
% 64.25/9.42 | | | | | | | | | | (659) all_6_0 = e2
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | SIMP: (659) implies:
% 64.25/9.42 | | | | | | | | | | (660) all_6_0 = e2
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | REDUCE: (635), (660) imply:
% 64.25/9.42 | | | | | | | | | | (661) ~ (e3 = e2)
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | REDUCE: (43), (660) imply:
% 64.25/9.42 | | | | | | | | | | (662) op(all_6_2, all_6_2) = e2
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.42 | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | (663) ~ (all_34_0 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (585), (663) imply:
% 64.25/9.42 | | | | | | | | | | | (664) ~ (all_4_0 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (38), (43), (51), (60),
% 64.25/9.42 | | | | | | | | | | | (62), (152), (153), (154), (155), (383), (438),
% 64.25/9.42 | | | | | | | | | | | (439), (440), (637), (639), (643), (645), (664),
% 64.25/9.42 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.42 | | | | | | | | | | | #167.
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | Case 2:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | (665) all_34_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | COMBINE_EQS: (585), (665) imply:
% 64.25/9.42 | | | | | | | | | | | (666) all_4_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | SIMP: (666) implies:
% 64.25/9.42 | | | | | | | | | | | (667) all_4_0 = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (634), (667) imply:
% 64.25/9.42 | | | | | | | | | | | (668) ~ (e2 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (645), (667) imply:
% 64.25/9.42 | | | | | | | | | | | (669) ~ (e1 = e0)
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | REDUCE: (38), (667) imply:
% 64.25/9.42 | | | | | | | | | | | (670) op(all_4_2, all_4_2) = e0
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.42 | | | | | | | | | | |
% 64.25/9.42 | | | | | | | | | | | Case 1:
% 64.25/9.42 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | (671) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.25/9.43 | | | | | | | | | | | | (438), (439), (440), (637), (643), (671),
% 64.25/9.43 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.43 | | | | | | | | | | | | #159.
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | (672) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.43 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | BETA: splitting (672) gives:
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | | (673) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.43 | | | | | | | | | | | | | (440), (636), (670), (673), (function-axioms) are
% 64.25/9.43 | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | | (674) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.25/9.43 | | | | | | | | | | | | | (439), (440), (662), (674), (function-axioms) are
% 64.25/9.43 | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 64.25/9.43 | | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | (675) all_26_0 = e1
% 64.25/9.43 | | | | | | | | | (676) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | COMBINE_EQS: (597), (675) imply:
% 64.25/9.43 | | | | | | | | | (677) all_4_0 = e1
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | SIMP: (677) implies:
% 64.25/9.43 | | | | | | | | | (678) all_4_0 = e1
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | REDUCE: (634), (678) imply:
% 64.25/9.43 | | | | | | | | | (679) ~ (e2 = e1)
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | REDUCE: (38), (678) imply:
% 64.25/9.43 | | | | | | | | | (680) op(all_4_2, all_4_2) = e1
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | (681) ~ (all_28_0 = e2)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | REDUCE: (626), (681) imply:
% 64.25/9.43 | | | | | | | | | | (682) ~ (all_6_0 = e2)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (683) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (60),
% 64.25/9.43 | | | | | | | | | | | (62), (153), (154), (155), (239), (383), (438),
% 64.25/9.43 | | | | | | | | | | | (439), (440), (444), (643), (680), (683),
% 64.25/9.43 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.43 | | | | | | | | | | | #134.
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (684) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.43 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (43), (51), (153), (155),
% 64.25/9.43 | | | | | | | | | | | (239), (383), (438), (440), (444), (635), (639),
% 64.25/9.43 | | | | | | | | | | | (680), (682), (684), (function-axioms) are
% 64.25/9.43 | | | | | | | | | | | inconsistent by sub-proof #130.
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | (685) all_28_0 = e2
% 64.25/9.43 | | | | | | | | | | (686) ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | COMBINE_EQS: (626), (685) imply:
% 64.25/9.43 | | | | | | | | | | (687) all_6_0 = e2
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | SIMP: (687) implies:
% 64.25/9.43 | | | | | | | | | | (688) all_6_0 = e2
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | REDUCE: (635), (688) imply:
% 64.25/9.43 | | | | | | | | | | (689) ~ (e3 = e2)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | REDUCE: (43), (688) imply:
% 64.25/9.43 | | | | | | | | | | (690) op(all_6_2, all_6_2) = e2
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (691) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (60),
% 64.25/9.43 | | | | | | | | | | | (62), (153), (154), (155), (239), (383), (438),
% 64.25/9.43 | | | | | | | | | | | (439), (440), (444), (643), (680), (691),
% 64.25/9.43 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.43 | | | | | | | | | | | #129.
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (692) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.43 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (37), (42), (51), (153),
% 64.25/9.43 | | | | | | | | | | | (154), (155), (168), (213), (214), (237), (238),
% 64.25/9.43 | | | | | | | | | | | (272), (315), (317), (328), (363), (367), (383),
% 64.25/9.43 | | | | | | | | | | | (418), (432), (438), (439), (440), (447), (460),
% 64.25/9.43 | | | | | | | | | | | (469), (476), (477), (480), (599), (625), (676),
% 64.25/9.43 | | | | | | | | | | | (680), (686), (690), (692), (function-axioms) are
% 64.25/9.43 | | | | | | | | | | | inconsistent by sub-proof #125.
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | End of split
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | (693) all_22_0 = e3
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | COMBINE_EQS: (559), (693) imply:
% 64.25/9.43 | | | | | | | | (694) all_14_0 = e3
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | SIMP: (694) implies:
% 64.25/9.43 | | | | | | | | (695) all_14_0 = e3
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | COMBINE_EQS: (632), (695) imply:
% 64.25/9.43 | | | | | | | | (696) all_44_0 = e3
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | REDUCE: (62), (695) imply:
% 64.25/9.43 | | | | | | | | (697) op(all_14_2, all_14_2) = e3
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | BETA: splitting (91) gives:
% 64.25/9.43 | | | | | | | |
% 64.25/9.43 | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | (698) ~ (all_26_0 = e1)
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | REDUCE: (597), (698) imply:
% 64.25/9.43 | | | | | | | | | (699) ~ (all_4_0 = e1)
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.43 | | | | | | | | |
% 64.25/9.43 | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | (700) ~ (all_28_0 = e2)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | REDUCE: (626), (700) imply:
% 64.25/9.43 | | | | | | | | | | (701) ~ (all_6_0 = e2)
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.43 | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (702) ~ (all_34_0 = e0)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REDUCE: (585), (702) imply:
% 64.25/9.43 | | | | | | | | | | | (703) ~ (all_4_0 = e0)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | (704) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | ALPHA: (704) implies:
% 64.25/9.43 | | | | | | | | | | | | (705) all_52_1 = e2
% 64.25/9.43 | | | | | | | | | | | | (706) ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | COMBINE_EQS: (439), (705) imply:
% 64.25/9.43 | | | | | | | | | | | | (707) all_14_2 = e2
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | SIMP: (707) implies:
% 64.25/9.43 | | | | | | | | | | | | (708) all_14_2 = e2
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (38), (43), (51), (60), (153),
% 64.25/9.43 | | | | | | | | | | | | (154), (155), (383), (438), (440), (634), (697),
% 64.25/9.43 | | | | | | | | | | | | (701), (705), (706), (708), (function-axioms) are
% 64.25/9.43 | | | | | | | | | | | | inconsistent by sub-proof #120.
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | (709) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.43 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (38), (43), (51), (60), (153),
% 64.25/9.43 | | | | | | | | | | | | (154), (383), (438), (439), (440), (639), (699),
% 64.25/9.43 | | | | | | | | | | | | (703), (709), (function-axioms) are inconsistent
% 64.25/9.43 | | | | | | | | | | | | by sub-proof #168.
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | End of split
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | Case 2:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | (710) all_34_0 = e0
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | COMBINE_EQS: (585), (710) imply:
% 64.25/9.43 | | | | | | | | | | | (711) all_4_0 = e0
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | SIMP: (711) implies:
% 64.25/9.43 | | | | | | | | | | | (712) all_4_0 = e0
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REDUCE: (634), (712) imply:
% 64.25/9.43 | | | | | | | | | | | (713) ~ (e2 = e0)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REDUCE: (699), (712) imply:
% 64.25/9.43 | | | | | | | | | | | (714) ~ (e1 = e0)
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | REDUCE: (38), (712) imply:
% 64.25/9.43 | | | | | | | | | | | (715) op(all_4_2, all_4_2) = e0
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.43 | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | Case 1:
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | (716) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.43 | | | | | | | | | | | |
% 64.25/9.43 | | | | | | | | | | | | ALPHA: (716) implies:
% 64.25/9.43 | | | | | | | | | | | | (717) all_52_1 = e2
% 64.25/9.44 | | | | | | | | | | | | (718) ~ (all_52_0 = e1)
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | COMBINE_EQS: (439), (717) imply:
% 64.25/9.44 | | | | | | | | | | | | (719) all_14_2 = e2
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (38), (43), (51), (60), (153),
% 64.25/9.44 | | | | | | | | | | | | (154), (155), (383), (438), (440), (634), (697),
% 64.25/9.44 | | | | | | | | | | | | (701), (717), (718), (719), (function-axioms) are
% 64.25/9.44 | | | | | | | | | | | | inconsistent by sub-proof #120.
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | (720) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.44 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (43), (51), (53), (154), (239),
% 64.25/9.44 | | | | | | | | | | | | (383), (438), (440), (444), (635), (636), (639),
% 64.25/9.44 | | | | | | | | | | | | (701), (715), (720), (function-axioms) are
% 64.25/9.44 | | | | | | | | | | | | inconsistent by sub-proof #160.
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | (721) all_28_0 = e2
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | COMBINE_EQS: (626), (721) imply:
% 64.25/9.44 | | | | | | | | | | (722) all_6_0 = e2
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | SIMP: (722) implies:
% 64.25/9.44 | | | | | | | | | | (723) all_6_0 = e2
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | COMBINE_EQS: (630), (723) imply:
% 64.25/9.44 | | | | | | | | | | (724) all_38_0 = e2
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | REDUCE: (635), (723) imply:
% 64.25/9.44 | | | | | | | | | | (725) ~ (e3 = e2)
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | REDUCE: (43), (723) imply:
% 64.25/9.44 | | | | | | | | | | (726) op(all_6_2, all_6_2) = e2
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.44 | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | (727) ~ (all_34_0 = e0)
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | REDUCE: (585), (727) imply:
% 64.25/9.44 | | | | | | | | | | | (728) ~ (all_4_0 = e0)
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | BETA: splitting (119) gives:
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | (729) ~ (all_38_0 = e2)
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | REDUCE: (724), (729) imply:
% 64.25/9.44 | | | | | | | | | | | | (730) $false
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | CLOSE: (730) is inconsistent.
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | (731) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | BETA: splitting (133) gives:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | (732) ~ (all_44_0 = e3)
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | REDUCE: (696), (732) imply:
% 64.25/9.44 | | | | | | | | | | | | | (733) $false
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | CLOSE: (733) is inconsistent.
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | (734) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | (735) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | ALPHA: (735) implies:
% 64.25/9.44 | | | | | | | | | | | | | | (736) all_52_1 = e2
% 64.25/9.44 | | | | | | | | | | | | | | (737) ~ (all_52_0 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | COMBINE_EQS: (439), (736) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (738) all_14_2 = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | COMBINE_EQS: (437), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (739) all_44_2 = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (461), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (740) ~ (all_54_1 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (463), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (741) ~ (all_54_4 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (469), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (742) ~ (all_54_9 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (471), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (743) ~ (all_54_13 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (440), (737) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (744) ~ (all_10_2 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (697), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (745) op(e2, e2) = e3
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (61), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (746) op(e2, e1) = all_14_1
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (60), (738) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (747) op(e1, e1) = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (38), (41), (42), (51), (153),
% 64.25/9.44 | | | | | | | | | | | | | | (154), (155), (165), (182), (191), (192), (194),
% 64.25/9.44 | | | | | | | | | | | | | | (206), (211), (236), (240), (244), (247), (269),
% 64.25/9.44 | | | | | | | | | | | | | | (280), (292), (296), (300), (311), (334), (346),
% 64.25/9.44 | | | | | | | | | | | | | | (351), (353), (362), (383), (436), (438), (440),
% 64.25/9.44 | | | | | | | | | | | | | | (447), (456), (475), (481), (483), (629), (631),
% 64.25/9.44 | | | | | | | | | | | | | | (634), (731), (734), (736), (739), (740), (741),
% 64.25/9.44 | | | | | | | | | | | | | | (742), (743), (744), (745), (746), (747),
% 64.25/9.44 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.44 | | | | | | | | | | | | | | #112.
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | (748) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.44 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | BETA: splitting (748) gives:
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | | (749) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.25/9.44 | | | | | | | | | | | | | | | (440), (699), (728), (749), (function-axioms) are
% 64.25/9.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #111.
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | | (750) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.25/9.44 | | | | | | | | | | | | | | | (439), (440), (726), (750), (function-axioms) are
% 64.25/9.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #110.
% 64.25/9.44 | | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | End of split
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | (751) all_34_0 = e0
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | COMBINE_EQS: (585), (751) imply:
% 64.25/9.44 | | | | | | | | | | | (752) all_4_0 = e0
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | SIMP: (752) implies:
% 64.25/9.44 | | | | | | | | | | | (753) all_4_0 = e0
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | REDUCE: (634), (753) imply:
% 64.25/9.44 | | | | | | | | | | | (754) ~ (e2 = e0)
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | REDUCE: (699), (753) imply:
% 64.25/9.44 | | | | | | | | | | | (755) ~ (e1 = e0)
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | REDUCE: (38), (753) imply:
% 64.25/9.44 | | | | | | | | | | | (756) op(all_4_2, all_4_2) = e0
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | BETA: splitting (119) gives:
% 64.25/9.44 | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | (757) ~ (all_38_0 = e2)
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | REDUCE: (724), (757) imply:
% 64.25/9.44 | | | | | | | | | | | | (758) $false
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | CLOSE: (758) is inconsistent.
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | (759) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | BETA: splitting (133) gives:
% 64.25/9.44 | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | (760) ~ (all_44_0 = e3)
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | REDUCE: (696), (760) imply:
% 64.25/9.44 | | | | | | | | | | | | | (761) $false
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | CLOSE: (761) is inconsistent.
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | Case 2:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | (762) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.44 | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | Case 1:
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | (763) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | ALPHA: (763) implies:
% 64.25/9.44 | | | | | | | | | | | | | | (764) all_52_1 = e2
% 64.25/9.44 | | | | | | | | | | | | | | (765) ~ (all_52_0 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | COMBINE_EQS: (439), (764) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (766) all_14_2 = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | SIMP: (766) implies:
% 64.25/9.44 | | | | | | | | | | | | | | (767) all_14_2 = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | COMBINE_EQS: (437), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (768) all_44_2 = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (461), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (769) ~ (all_54_1 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (463), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (770) ~ (all_54_4 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (469), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (771) ~ (all_54_9 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (471), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (772) ~ (all_54_13 = e2)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (440), (765) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (773) ~ (all_10_2 = e1)
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (697), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (774) op(e2, e2) = e3
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (61), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (775) op(e2, e1) = all_14_1
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REDUCE: (60), (767) imply:
% 64.25/9.44 | | | | | | | | | | | | | | (776) op(e1, e1) = e2
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.44 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (38), (41), (42), (51), (153),
% 64.25/9.44 | | | | | | | | | | | | | | (154), (155), (165), (182), (191), (192), (194),
% 64.25/9.44 | | | | | | | | | | | | | | (206), (211), (236), (240), (244), (247), (269),
% 64.25/9.44 | | | | | | | | | | | | | | (280), (292), (296), (300), (311), (334), (346),
% 64.25/9.44 | | | | | | | | | | | | | | (351), (353), (362), (383), (436), (438), (440),
% 64.25/9.44 | | | | | | | | | | | | | | (447), (456), (475), (481), (483), (629), (631),
% 64.25/9.44 | | | | | | | | | | | | | | (634), (759), (762), (764), (768), (769), (770),
% 64.25/9.44 | | | | | | | | | | | | | | (771), (772), (773), (774), (775), (776),
% 64.25/9.44 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.44 | | | | | | | | | | | | | | #112.
% 64.25/9.44 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | (777) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.45 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | BETA: splitting (777) gives:
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | (778) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.45 | | | | | | | | | | | | | | | (440), (636), (756), (778), (function-axioms) are
% 64.25/9.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | (779) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.25/9.45 | | | | | | | | | | | | | | | (439), (440), (726), (779), (function-axioms) are
% 64.25/9.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | (780) all_26_0 = e1
% 64.25/9.45 | | | | | | | | | (781) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | COMBINE_EQS: (597), (780) imply:
% 64.25/9.45 | | | | | | | | | (782) all_4_0 = e1
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | SIMP: (782) implies:
% 64.25/9.45 | | | | | | | | | (783) all_4_0 = e1
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | REDUCE: (634), (783) imply:
% 64.25/9.45 | | | | | | | | | (784) ~ (e2 = e1)
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | REDUCE: (38), (783) imply:
% 64.25/9.45 | | | | | | | | | (785) op(all_4_2, all_4_2) = e1
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.45 | | | | | | | | |
% 64.25/9.45 | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | (786) ~ (all_28_0 = e2)
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | REDUCE: (626), (786) imply:
% 64.25/9.45 | | | | | | | | | | (787) ~ (all_6_0 = e2)
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | (788) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | ALPHA: (788) implies:
% 64.25/9.45 | | | | | | | | | | | (789) all_52_1 = e2
% 64.25/9.45 | | | | | | | | | | | (790) ~ (all_52_0 = e1)
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | COMBINE_EQS: (439), (789) imply:
% 64.25/9.45 | | | | | | | | | | | (791) all_14_2 = e2
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | REDUCE: (440), (790) imply:
% 64.25/9.45 | | | | | | | | | | | (792) ~ (all_10_2 = e1)
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | REDUCE: (697), (791) imply:
% 64.25/9.45 | | | | | | | | | | | (793) op(e2, e2) = e3
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | REDUCE: (60), (791) imply:
% 64.25/9.45 | | | | | | | | | | | (794) op(e1, e1) = e2
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 64.25/9.45 | | | | | | | | | | | e2, e2, simplifying with (51), (793) gives:
% 64.25/9.45 | | | | | | | | | | | (795) all_10_2 = e3
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | COMBINE_EQS: (440), (795) imply:
% 64.25/9.45 | | | | | | | | | | | (796) all_52_0 = e3
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | BETA: splitting (153) gives:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | (797) all_52_0 = e0 & ~ (all_52_3 = e2)
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | ALPHA: (797) implies:
% 64.25/9.45 | | | | | | | | | | | | (798) all_52_0 = e0
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (154), (155), (438),
% 64.25/9.45 | | | | | | | | | | | | (785), (789), (794), (798), (function-axioms) are
% 64.25/9.45 | | | | | | | | | | | | inconsistent by sub-proof #144.
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | (799) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 =
% 64.25/9.45 | | | | | | | | | | | | e0 & ~ (all_52_3 = e3))
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | BETA: splitting (799) gives:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | (800) all_52_1 = e0 & ~ (all_52_3 = e1)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REF_CLOSE: (5), (789), (800) are inconsistent by sub-proof
% 64.25/9.45 | | | | | | | | | | | | | #179.
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | (801) all_52_2 = e0 & ~ (all_52_3 = e3)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | ALPHA: (801) implies:
% 64.25/9.45 | | | | | | | | | | | | | (802) all_52_2 = e0
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REF_CLOSE: (4), (8), (43), (154), (383), (787), (794), (796),
% 64.25/9.45 | | | | | | | | | | | | | (802), (function-axioms) are inconsistent by
% 64.25/9.45 | | | | | | | | | | | | | sub-proof #121.
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | (803) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.45 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (43), (51), (153), (155),
% 64.25/9.45 | | | | | | | | | | | (239), (383), (438), (440), (444), (635), (639),
% 64.25/9.45 | | | | | | | | | | | (785), (787), (803), (function-axioms) are
% 64.25/9.45 | | | | | | | | | | | inconsistent by sub-proof #130.
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | End of split
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | (804) all_28_0 = e2
% 64.25/9.45 | | | | | | | | | | (805) ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | COMBINE_EQS: (626), (804) imply:
% 64.25/9.45 | | | | | | | | | | (806) all_6_0 = e2
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | SIMP: (806) implies:
% 64.25/9.45 | | | | | | | | | | (807) all_6_0 = e2
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | COMBINE_EQS: (630), (807) imply:
% 64.25/9.45 | | | | | | | | | | (808) all_38_0 = e2
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | REDUCE: (635), (807) imply:
% 64.25/9.45 | | | | | | | | | | (809) ~ (e3 = e2)
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | REDUCE: (43), (807) imply:
% 64.25/9.45 | | | | | | | | | | (810) op(all_6_2, all_6_2) = e2
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | BETA: splitting (119) gives:
% 64.25/9.45 | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | (811) ~ (all_38_0 = e2)
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | REDUCE: (808), (811) imply:
% 64.25/9.45 | | | | | | | | | | | (812) $false
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | CLOSE: (812) is inconsistent.
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | (813) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | BETA: splitting (133) gives:
% 64.25/9.45 | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | (814) ~ (all_44_0 = e3)
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | REDUCE: (696), (814) imply:
% 64.25/9.45 | | | | | | | | | | | | (815) $false
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | CLOSE: (815) is inconsistent.
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | (816) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.45 | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | (817) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | ALPHA: (817) implies:
% 64.25/9.45 | | | | | | | | | | | | | (818) all_52_1 = e2
% 64.25/9.45 | | | | | | | | | | | | | (819) ~ (all_52_0 = e1)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | COMBINE_EQS: (439), (818) imply:
% 64.25/9.45 | | | | | | | | | | | | | (820) all_14_2 = e2
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | SIMP: (820) implies:
% 64.25/9.45 | | | | | | | | | | | | | (821) all_14_2 = e2
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | COMBINE_EQS: (437), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (822) all_44_2 = e2
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (461), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (823) ~ (all_54_1 = e2)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (463), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (824) ~ (all_54_4 = e2)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (469), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (825) ~ (all_54_9 = e2)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (471), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (826) ~ (all_54_13 = e2)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (440), (819) imply:
% 64.25/9.45 | | | | | | | | | | | | | (827) ~ (all_10_2 = e1)
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (697), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (828) op(e2, e2) = e3
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (61), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (829) op(e2, e1) = all_14_1
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | REDUCE: (60), (821) imply:
% 64.25/9.45 | | | | | | | | | | | | | (830) op(e1, e1) = e2
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | BETA: splitting (816) gives:
% 64.25/9.45 | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | (831) ~ (all_44_1 = e0)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | REDUCE: (631), (831) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (832) ~ (all_14_1 = e0)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_9,
% 64.25/9.45 | | | | | | | | | | | | | | all_14_1, e1, e2, simplifying with (211), (829)
% 64.25/9.45 | | | | | | | | | | | | | | gives:
% 64.25/9.45 | | | | | | | | | | | | | | (833) all_54_9 = all_14_1
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 64.25/9.45 | | | | | | | | | | | | | | e2, e2, simplifying with (51), (828) gives:
% 64.25/9.45 | | | | | | | | | | | | | | (834) all_10_2 = e3
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | COMBINE_EQS: (440), (834) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (835) all_52_0 = e3
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | COMBINE_EQS: (353), (833) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (836) all_56_9 = all_14_1
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | COMBINE_EQS: (447), (834) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (837) all_58_6 = e3
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | REDUCE: (192), (833) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (838) ~ (all_54_1 = all_14_1)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | REDUCE: (165), (833) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (839) ~ (all_54_13 = all_14_1)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | SIMP: (839) implies:
% 64.25/9.45 | | | | | | | | | | | | | | (840) ~ (all_54_13 = all_14_1)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | REDUCE: (475), (833), (834) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (841) ~ (all_14_1 = e3)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | REDUCE: (825), (833) imply:
% 64.25/9.45 | | | | | | | | | | | | | | (842) ~ (all_14_1 = e2)
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 64.25/9.45 | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | (843) all_56_9 = e3
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | REF_CLOSE: (836), (841), (843) are inconsistent by sub-proof
% 64.25/9.45 | | | | | | | | | | | | | | | #119.
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | Case 2:
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | (844) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 64.25/9.45 | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | Case 1:
% 64.25/9.45 | | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | | (845) all_52_0 = e0 & ~ (all_52_3 = e2)
% 64.25/9.45 | | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | | ALPHA: (845) implies:
% 64.25/9.45 | | | | | | | | | | | | | | | | (846) all_52_0 = e0
% 64.25/9.45 | | | | | | | | | | | | | | | |
% 64.25/9.45 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (154), (155), (438),
% 64.25/9.45 | | | | | | | | | | | | | | | | (785), (818), (830), (846), (function-axioms) are
% 64.25/9.45 | | | | | | | | | | | | | | | | inconsistent by sub-proof #144.
% 64.25/9.45 | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | (847) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 =
% 64.25/9.46 | | | | | | | | | | | | | | | | e0 & ~ (all_52_3 = e3))
% 64.25/9.46 | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | BETA: splitting (847) gives:
% 64.25/9.46 | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | (848) all_52_1 = e0 & ~ (all_52_3 = e1)
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (818), (848) are inconsistent by sub-proof
% 64.25/9.46 | | | | | | | | | | | | | | | | | #179.
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | (849) all_52_2 = e0 & ~ (all_52_3 = e3)
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 64.25/9.46 | | | | | | | | | | | | | | | | | (850) all_52_2 = e0
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | COMBINE_EQS: (438), (850) imply:
% 64.25/9.46 | | | | | | | | | | | | | | | | | (851) all_4_2 = e0
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | SIMP: (851) implies:
% 64.25/9.46 | | | | | | | | | | | | | | | | | (852) all_4_2 = e0
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | REDUCE: (481), (852) imply:
% 64.25/9.46 | | | | | | | | | | | | | | | | | (853) ~ (all_54_13 = e0)
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | REDUCE: (483), (852) imply:
% 64.25/9.46 | | | | | | | | | | | | | | | | | (854) ~ (all_54_15 = e0)
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (41), (42), (154), (155), (182), (191),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (194), (206), (236), (244), (247), (269), (280),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (292), (296), (300), (311), (334), (346), (351),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (362), (383), (436), (456), (629), (813), (818),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (823), (824), (826), (832), (835), (836), (837),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (838), (840), (842), (844), (850), (853), (854),
% 64.25/9.46 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.46 | | | | | | | | | | | | | | | | | #113.
% 64.25/9.46 | | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | (855) ~ (all_44_2 = e2)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (822), (855) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (856) $false
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | CLOSE: (856) is inconsistent.
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | (857) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.46 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.46 | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | BETA: splitting (857) gives:
% 64.25/9.46 | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | (858) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | ALPHA: (858) implies:
% 64.25/9.46 | | | | | | | | | | | | | | (859) all_52_2 = e2
% 64.25/9.46 | | | | | | | | | | | | | | (860) ~ (all_52_0 = e3)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | COMBINE_EQS: (438), (859) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (861) all_4_2 = e2
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | SIMP: (861) implies:
% 64.25/9.46 | | | | | | | | | | | | | | (862) all_4_2 = e2
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | COMBINE_EQS: (418), (862) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (863) all_26_2 = e2
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (477), (862) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (864) ~ (all_54_10 = e2)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (480), (862) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (865) ~ (all_54_12 = e2)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (440), (860) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (866) ~ (all_10_2 = e3)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (785), (862) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (867) op(e2, e2) = e1
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REDUCE: (37), (862) imply:
% 64.25/9.46 | | | | | | | | | | | | | | (868) op(e2, e3) = all_4_1
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (42), (51), (153), (155), (168),
% 64.25/9.46 | | | | | | | | | | | | | | (213), (214), (237), (238), (272), (315), (317),
% 64.25/9.46 | | | | | | | | | | | | | | (328), (363), (367), (383), (432), (439), (440),
% 64.25/9.46 | | | | | | | | | | | | | | (447), (460), (469), (476), (599), (625), (781),
% 64.25/9.46 | | | | | | | | | | | | | | (805), (859), (863), (864), (865), (866), (867),
% 64.25/9.46 | | | | | | | | | | | | | | (868), (function-axioms) are inconsistent by
% 64.25/9.46 | | | | | | | | | | | | | | sub-proof #126.
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | (869) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.25/9.46 | | | | | | | | | | | | | | (439), (440), (810), (869), (function-axioms) are
% 64.25/9.46 | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 64.25/9.46 | | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | End of split
% 64.25/9.46 | | | | | | | |
% 64.25/9.46 | | | | | | | End of split
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | Case 2:
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | | (870) all_20_0 = e2
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | | COMBINE_EQS: (615), (870) imply:
% 64.25/9.46 | | | | | | | (871) all_14_0 = e2
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | | REDUCE: (62), (871) imply:
% 64.25/9.46 | | | | | | | (872) op(all_14_2, all_14_2) = e2
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | | BETA: splitting (91) gives:
% 64.25/9.46 | | | | | | |
% 64.25/9.46 | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | |
% 64.25/9.46 | | | | | | | | (873) ~ (all_26_0 = e1)
% 64.25/9.46 | | | | | | | |
% 64.25/9.46 | | | | | | | | REDUCE: (597), (873) imply:
% 64.25/9.46 | | | | | | | | (874) ~ (all_4_0 = e1)
% 64.25/9.46 | | | | | | | |
% 64.25/9.46 | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.46 | | | | | | | |
% 64.25/9.46 | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | (875) ~ (all_28_0 = e2)
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | REDUCE: (626), (875) imply:
% 64.25/9.46 | | | | | | | | | (876) ~ (all_6_0 = e2)
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | (877) ~ (all_34_0 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (38), (43), (51), (60), (152),
% 64.25/9.46 | | | | | | | | | | (153), (154), (155), (383), (438), (439), (440),
% 64.25/9.46 | | | | | | | | | | (585), (639), (872), (874), (877),
% 64.25/9.46 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.46 | | | | | | | | | | #105.
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | (878) all_34_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | COMBINE_EQS: (585), (878) imply:
% 64.25/9.46 | | | | | | | | | | (879) all_4_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | SIMP: (879) implies:
% 64.25/9.46 | | | | | | | | | | (880) all_4_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (634), (880) imply:
% 64.25/9.46 | | | | | | | | | | (881) ~ (e2 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (874), (880) imply:
% 64.25/9.46 | | | | | | | | | | (882) ~ (e1 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (38), (880) imply:
% 64.25/9.46 | | | | | | | | | | (883) op(all_4_2, all_4_2) = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | (884) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.46 | | | | | | | | | | | (439), (440), (872), (884), (function-axioms) are
% 64.25/9.46 | | | | | | | | | | | inconsistent by sub-proof #104.
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | (885) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.46 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (43), (51), (53), (154), (239),
% 64.25/9.46 | | | | | | | | | | | (383), (438), (440), (444), (635), (636), (639),
% 64.25/9.46 | | | | | | | | | | | (876), (883), (885), (function-axioms) are
% 64.25/9.46 | | | | | | | | | | | inconsistent by sub-proof #160.
% 64.25/9.46 | | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | End of split
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | (886) all_28_0 = e2
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | COMBINE_EQS: (626), (886) imply:
% 64.25/9.46 | | | | | | | | | (887) all_6_0 = e2
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | SIMP: (887) implies:
% 64.25/9.46 | | | | | | | | | (888) all_6_0 = e2
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | REDUCE: (635), (888) imply:
% 64.25/9.46 | | | | | | | | | (889) ~ (e3 = e2)
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | REDUCE: (43), (888) imply:
% 64.25/9.46 | | | | | | | | | (890) op(all_6_2, all_6_2) = e2
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.46 | | | | | | | | |
% 64.25/9.46 | | | | | | | | | Case 1:
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | (891) ~ (all_34_0 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (38), (43), (51), (60), (152),
% 64.25/9.46 | | | | | | | | | | (153), (154), (155), (383), (438), (439), (440),
% 64.25/9.46 | | | | | | | | | | (585), (639), (872), (874), (891),
% 64.25/9.46 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.46 | | | | | | | | | | #105.
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | Case 2:
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | (892) all_34_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | COMBINE_EQS: (585), (892) imply:
% 64.25/9.46 | | | | | | | | | | (893) all_4_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | SIMP: (893) implies:
% 64.25/9.46 | | | | | | | | | | (894) all_4_0 = e0
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (634), (894) imply:
% 64.25/9.46 | | | | | | | | | | (895) ~ (e2 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (874), (894) imply:
% 64.25/9.46 | | | | | | | | | | (896) ~ (e1 = e0)
% 64.25/9.46 | | | | | | | | | |
% 64.25/9.46 | | | | | | | | | | REDUCE: (38), (894) imply:
% 64.25/9.47 | | | | | | | | | | (897) op(all_4_2, all_4_2) = e0
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (898) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.47 | | | | | | | | | | | (439), (440), (872), (898), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | | inconsistent by sub-proof #107.
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (899) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.47 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | BETA: splitting (899) gives:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (900) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.47 | | | | | | | | | | | | (440), (636), (897), (900), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | | | inconsistent by sub-proof #158.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (901) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.25/9.47 | | | | | | | | | | | | (439), (440), (890), (901), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | | | inconsistent by sub-proof #149.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | End of split
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | (902) all_26_0 = e1
% 64.25/9.47 | | | | | | | | (903) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | COMBINE_EQS: (597), (902) imply:
% 64.25/9.47 | | | | | | | | (904) all_4_0 = e1
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | SIMP: (904) implies:
% 64.25/9.47 | | | | | | | | (905) all_4_0 = e1
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | REDUCE: (38), (905) imply:
% 64.25/9.47 | | | | | | | | (906) op(all_4_2, all_4_2) = e1
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | BETA: splitting (96) gives:
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | (907) ~ (all_28_0 = e2)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (626), (907) imply:
% 64.25/9.47 | | | | | | | | | (908) ~ (all_6_0 = e2)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (909) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.47 | | | | | | | | | | (439), (440), (872), (909), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | inconsistent by sub-proof #104.
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (910) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.47 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (43), (51), (153), (155),
% 64.25/9.47 | | | | | | | | | | (239), (383), (438), (440), (444), (635), (639),
% 64.25/9.47 | | | | | | | | | | (906), (908), (910), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | inconsistent by sub-proof #130.
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | (911) all_28_0 = e2
% 64.25/9.47 | | | | | | | | | (912) ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | COMBINE_EQS: (626), (911) imply:
% 64.25/9.47 | | | | | | | | | (913) all_6_0 = e2
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | SIMP: (913) implies:
% 64.25/9.47 | | | | | | | | | (914) all_6_0 = e2
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (635), (914) imply:
% 64.25/9.47 | | | | | | | | | (915) ~ (e3 = e2)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (43), (914) imply:
% 64.25/9.47 | | | | | | | | | (916) op(all_6_2, all_6_2) = e2
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (917) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.47 | | | | | | | | | | (439), (440), (872), (917), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | inconsistent by sub-proof #107.
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (918) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.47 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (37), (42), (51), (153),
% 64.25/9.47 | | | | | | | | | | (154), (155), (168), (213), (214), (237), (238),
% 64.25/9.47 | | | | | | | | | | (272), (315), (317), (328), (363), (367), (383),
% 64.25/9.47 | | | | | | | | | | (418), (432), (438), (439), (440), (447), (460),
% 64.25/9.47 | | | | | | | | | | (469), (476), (477), (480), (599), (625), (903),
% 64.25/9.47 | | | | | | | | | | (906), (912), (916), (918), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | inconsistent by sub-proof #125.
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | End of split
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | End of split
% 64.25/9.47 | | | | | | |
% 64.25/9.47 | | | | | | End of split
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | Case 2:
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | (919) all_16_0 = e1
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | COMBINE_EQS: (539), (919) imply:
% 64.25/9.47 | | | | | | (920) all_6_0 = e1
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | SIMP: (920) implies:
% 64.25/9.47 | | | | | | (921) all_6_0 = e1
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | REDUCE: (635), (921) imply:
% 64.25/9.47 | | | | | | (922) ~ (e3 = e1)
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | REDUCE: (43), (921) imply:
% 64.25/9.47 | | | | | | (923) op(all_6_2, all_6_2) = e1
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | BETA: splitting (77) gives:
% 64.25/9.47 | | | | | |
% 64.25/9.47 | | | | | | Case 1:
% 64.25/9.47 | | | | | | |
% 64.25/9.47 | | | | | | | (924) ~ (all_20_0 = e2)
% 64.25/9.47 | | | | | | |
% 64.25/9.47 | | | | | | | REDUCE: (615), (924) imply:
% 64.25/9.47 | | | | | | | (925) ~ (all_14_0 = e2)
% 64.25/9.47 | | | | | | |
% 64.25/9.47 | | | | | | | BETA: splitting (82) gives:
% 64.25/9.47 | | | | | | |
% 64.25/9.47 | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | (926) ~ (all_22_0 = e3)
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | REDUCE: (559), (926) imply:
% 64.25/9.47 | | | | | | | | (927) ~ (all_14_0 = e3)
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | BETA: splitting (91) gives:
% 64.25/9.47 | | | | | | | |
% 64.25/9.47 | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | (928) ~ (all_26_0 = e1)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (597), (928) imply:
% 64.25/9.47 | | | | | | | | | (929) ~ (all_4_0 = e1)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (930) ~ (all_34_0 = e0)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REDUCE: (585), (930) imply:
% 64.25/9.47 | | | | | | | | | | (931) ~ (all_4_0 = e0)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (932) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.25/9.47 | | | | | | | | | | | (438), (439), (440), (637), (927), (932),
% 64.25/9.47 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.47 | | | | | | | | | | | #159.
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (933) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.47 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | BETA: splitting (933) gives:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (934) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.25/9.47 | | | | | | | | | | | | (440), (929), (931), (934), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | | | inconsistent by sub-proof #173.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (935) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.47 | | | | | | | | | | | | (383), (438), (440), (634), (923), (935),
% 64.25/9.47 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.47 | | | | | | | | | | | | #99.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (936) all_34_0 = e0
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | COMBINE_EQS: (585), (936) imply:
% 64.25/9.47 | | | | | | | | | | (937) all_4_0 = e0
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | SIMP: (937) implies:
% 64.25/9.47 | | | | | | | | | | (938) all_4_0 = e0
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REDUCE: (634), (938) imply:
% 64.25/9.47 | | | | | | | | | | (939) ~ (e2 = e0)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REDUCE: (929), (938) imply:
% 64.25/9.47 | | | | | | | | | | (940) ~ (e1 = e0)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | REDUCE: (38), (938) imply:
% 64.25/9.47 | | | | | | | | | | (941) op(all_4_2, all_4_2) = e0
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (942) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.25/9.47 | | | | | | | | | | | (438), (439), (440), (637), (927), (942),
% 64.25/9.47 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.47 | | | | | | | | | | | #165.
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | (943) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.47 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | BETA: splitting (943) gives:
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (944) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.47 | | | | | | | | | | | | (440), (636), (941), (944), (function-axioms) are
% 64.25/9.47 | | | | | | | | | | | | inconsistent by sub-proof #162.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | (945) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.47 | | | | | | | | | | | | (383), (438), (440), (634), (923), (945),
% 64.25/9.47 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.47 | | | | | | | | | | | | #98.
% 64.25/9.47 | | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | End of split
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | Case 2:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | (946) all_26_0 = e1
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | COMBINE_EQS: (597), (946) imply:
% 64.25/9.47 | | | | | | | | | (947) all_4_0 = e1
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | SIMP: (947) implies:
% 64.25/9.47 | | | | | | | | | (948) all_4_0 = e1
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (634), (948) imply:
% 64.25/9.47 | | | | | | | | | (949) ~ (e2 = e1)
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | REDUCE: (38), (948) imply:
% 64.25/9.47 | | | | | | | | | (950) op(all_4_2, all_4_2) = e1
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.47 | | | | | | | | |
% 64.25/9.47 | | | | | | | | | Case 1:
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.47 | | | | | | | | | | (951) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.47 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (60),
% 64.25/9.48 | | | | | | | | | | (62), (153), (154), (155), (239), (383), (438),
% 64.25/9.48 | | | | | | | | | | (439), (440), (444), (927), (950), (951),
% 64.25/9.48 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | #134.
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (952) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.48 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | BETA: splitting (952) gives:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (953) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | ALPHA: (953) implies:
% 64.25/9.48 | | | | | | | | | | | (954) all_52_2 = e2
% 64.25/9.48 | | | | | | | | | | | (955) ~ (all_52_0 = e3)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | COMBINE_EQS: (438), (954) imply:
% 64.25/9.48 | | | | | | | | | | | (956) all_4_2 = e2
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (51), (153), (155),
% 64.25/9.48 | | | | | | | | | | | (383), (440), (923), (950), (954), (955), (956),
% 64.25/9.48 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | | #95.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (957) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.48 | | | | | | | | | | | (383), (438), (440), (634), (923), (957),
% 64.25/9.48 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | | #98.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | End of split
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | (958) all_22_0 = e3
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | COMBINE_EQS: (559), (958) imply:
% 64.25/9.48 | | | | | | | | (959) all_14_0 = e3
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | SIMP: (959) implies:
% 64.25/9.48 | | | | | | | | (960) all_14_0 = e3
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | REDUCE: (62), (960) imply:
% 64.25/9.48 | | | | | | | | (961) op(all_14_2, all_14_2) = e3
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | BETA: splitting (91) gives:
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | (962) ~ (all_26_0 = e1)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (597), (962) imply:
% 64.25/9.48 | | | | | | | | | (963) ~ (all_4_0 = e1)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (964) ~ (all_34_0 = e0)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REDUCE: (585), (964) imply:
% 64.25/9.48 | | | | | | | | | | (965) ~ (all_4_0 = e0)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (966) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (38), (51), (60), (153),
% 64.25/9.48 | | | | | | | | | | | (154), (155), (383), (438), (439), (440), (634),
% 64.25/9.48 | | | | | | | | | | | (923), (961), (966), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | | inconsistent by sub-proof #93.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (967) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.48 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | BETA: splitting (967) gives:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | (968) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.25/9.48 | | | | | | | | | | | | (440), (963), (965), (968), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | | | inconsistent by sub-proof #173.
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | (969) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.48 | | | | | | | | | | | | (383), (438), (440), (634), (923), (969),
% 64.25/9.48 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | | | #99.
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (970) all_34_0 = e0
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | COMBINE_EQS: (585), (970) imply:
% 64.25/9.48 | | | | | | | | | | (971) all_4_0 = e0
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | SIMP: (971) implies:
% 64.25/9.48 | | | | | | | | | | (972) all_4_0 = e0
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REDUCE: (634), (972) imply:
% 64.25/9.48 | | | | | | | | | | (973) ~ (e2 = e0)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REDUCE: (963), (972) imply:
% 64.25/9.48 | | | | | | | | | | (974) ~ (e1 = e0)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REDUCE: (38), (972) imply:
% 64.25/9.48 | | | | | | | | | | (975) op(all_4_2, all_4_2) = e0
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (976) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (38), (51), (60), (153),
% 64.25/9.48 | | | | | | | | | | | (154), (155), (383), (438), (439), (440), (634),
% 64.25/9.48 | | | | | | | | | | | (923), (961), (976), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | | inconsistent by sub-proof #93.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (977) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.48 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | BETA: splitting (977) gives:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | (978) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.48 | | | | | | | | | | | | (440), (636), (975), (978), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | | | inconsistent by sub-proof #158.
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | (979) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.48 | | | | | | | | | | | | (383), (438), (440), (634), (923), (979),
% 64.25/9.48 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | | | #99.
% 64.25/9.48 | | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | (980) all_26_0 = e1
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | COMBINE_EQS: (597), (980) imply:
% 64.25/9.48 | | | | | | | | | (981) all_4_0 = e1
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (634), (981) imply:
% 64.25/9.48 | | | | | | | | | (982) ~ (e2 = e1)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (38), (981) imply:
% 64.25/9.48 | | | | | | | | | (983) op(all_4_2, all_4_2) = e1
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (984) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (38), (51), (60), (153),
% 64.25/9.48 | | | | | | | | | | (154), (155), (383), (438), (439), (440), (634),
% 64.25/9.48 | | | | | | | | | | (923), (961), (984), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | inconsistent by sub-proof #93.
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (985) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.48 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 64.25/9.48 | | | | | | | | | | (51), (153), (155), (383), (438), (440), (634),
% 64.25/9.48 | | | | | | | | | | (923), (983), (985), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | inconsistent by sub-proof #92.
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | End of split
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | End of split
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | Case 2:
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | | (986) all_20_0 = e2
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | | COMBINE_EQS: (615), (986) imply:
% 64.25/9.48 | | | | | | | (987) all_14_0 = e2
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | | REDUCE: (62), (987) imply:
% 64.25/9.48 | | | | | | | (988) op(all_14_2, all_14_2) = e2
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | | BETA: splitting (91) gives:
% 64.25/9.48 | | | | | | |
% 64.25/9.48 | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | (989) ~ (all_26_0 = e1)
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | REDUCE: (597), (989) imply:
% 64.25/9.48 | | | | | | | | (990) ~ (all_4_0 = e1)
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | BETA: splitting (110) gives:
% 64.25/9.48 | | | | | | | |
% 64.25/9.48 | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | (991) ~ (all_34_0 = e0)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (585), (991) imply:
% 64.25/9.48 | | | | | | | | | (992) ~ (all_4_0 = e0)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (993) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.48 | | | | | | | | | | (439), (440), (988), (993), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | inconsistent by sub-proof #107.
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (994) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.48 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | BETA: splitting (994) gives:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (995) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.25/9.48 | | | | | | | | | | | (440), (990), (992), (995), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | | inconsistent by sub-proof #173.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | (996) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.48 | | | | | | | | | | | (383), (438), (440), (634), (923), (996),
% 64.25/9.48 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.48 | | | | | | | | | | | #99.
% 64.25/9.48 | | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | End of split
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | (997) all_34_0 = e0
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | COMBINE_EQS: (585), (997) imply:
% 64.25/9.48 | | | | | | | | | (998) all_4_0 = e0
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (634), (998) imply:
% 64.25/9.48 | | | | | | | | | (999) ~ (e2 = e0)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (990), (998) imply:
% 64.25/9.48 | | | | | | | | | (1000) ~ (e1 = e0)
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | REDUCE: (38), (998) imply:
% 64.25/9.48 | | | | | | | | | (1001) op(all_4_2, all_4_2) = e0
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.48 | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 1:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | (1002) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.48 | | | | | | | | | | (439), (440), (988), (1002), (function-axioms) are
% 64.25/9.48 | | | | | | | | | | inconsistent by sub-proof #107.
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.48 | | | | | | | | | Case 2:
% 64.25/9.48 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | (1003) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.49 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | BETA: splitting (1003) gives:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | | (1004) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.25/9.49 | | | | | | | | | | | (440), (636), (1001), (1004), (function-axioms)
% 64.25/9.49 | | | | | | | | | | | are inconsistent by sub-proof #158.
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | | (1005) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (41), (51), (153), (155),
% 64.25/9.49 | | | | | | | | | | | (383), (438), (440), (634), (923), (1005),
% 64.25/9.49 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.25/9.49 | | | | | | | | | | | #99.
% 64.25/9.49 | | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | End of split
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | End of split
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | End of split
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | (1006) all_26_0 = e1
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | COMBINE_EQS: (597), (1006) imply:
% 64.25/9.49 | | | | | | | | (1007) all_4_0 = e1
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (634), (1007) imply:
% 64.25/9.49 | | | | | | | | (1008) ~ (e2 = e1)
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (38), (1007) imply:
% 64.25/9.49 | | | | | | | | (1009) op(all_4_2, all_4_2) = e1
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | (1010) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.25/9.49 | | | | | | | | | (439), (440), (988), (1010), (function-axioms) are
% 64.25/9.49 | | | | | | | | | inconsistent by sub-proof #107.
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | (1011) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.49 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41),
% 64.25/9.49 | | | | | | | | | (51), (153), (155), (383), (438), (440), (634),
% 64.25/9.49 | | | | | | | | | (923), (1009), (1011), (function-axioms) are
% 64.25/9.49 | | | | | | | | | inconsistent by sub-proof #92.
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | End of split
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | End of split
% 64.25/9.49 | | | | | | |
% 64.25/9.49 | | | | | | End of split
% 64.25/9.49 | | | | | |
% 64.25/9.49 | | | | | End of split
% 64.25/9.49 | | | | |
% 64.25/9.49 | | | | Case 2:
% 64.25/9.49 | | | | |
% 64.25/9.49 | | | | | (1012) all_14_0 = e0
% 64.25/9.49 | | | | | (1013) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 64.25/9.49 | | | | |
% 64.25/9.49 | | | | | REDUCE: (62), (1012) imply:
% 64.25/9.49 | | | | | (1014) op(all_14_2, all_14_2) = e0
% 64.25/9.49 | | | | |
% 64.25/9.49 | | | | | BETA: splitting (68) gives:
% 64.25/9.49 | | | | |
% 64.25/9.49 | | | | | Case 1:
% 64.25/9.49 | | | | | |
% 64.25/9.49 | | | | | | (1015) ~ (all_16_0 = e1)
% 64.25/9.49 | | | | | |
% 64.25/9.49 | | | | | | REDUCE: (539), (1015) imply:
% 64.25/9.49 | | | | | | (1016) ~ (all_6_0 = e1)
% 64.25/9.49 | | | | | |
% 64.25/9.49 | | | | | | BETA: splitting (91) gives:
% 64.25/9.49 | | | | | |
% 64.25/9.49 | | | | | | Case 1:
% 64.25/9.49 | | | | | | |
% 64.25/9.49 | | | | | | | (1017) ~ (all_26_0 = e1)
% 64.25/9.49 | | | | | | |
% 64.25/9.49 | | | | | | | REDUCE: (597), (1017) imply:
% 64.25/9.49 | | | | | | | (1018) ~ (all_4_0 = e1)
% 64.25/9.49 | | | | | | |
% 64.25/9.49 | | | | | | | BETA: splitting (110) gives:
% 64.25/9.49 | | | | | | |
% 64.25/9.49 | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | (1019) ~ (all_34_0 = e0)
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (585), (1019) imply:
% 64.25/9.49 | | | | | | | | (1020) ~ (all_4_0 = e0)
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | (1021) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | ALPHA: (1021) implies:
% 64.25/9.49 | | | | | | | | | (1022) all_52_1 = e2
% 64.25/9.49 | | | | | | | | | (1023) ~ (all_52_0 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | COMBINE_EQS: (439), (1022) imply:
% 64.25/9.49 | | | | | | | | | (1024) all_14_2 = e2
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | SIMP: (1024) implies:
% 64.25/9.49 | | | | | | | | | (1025) all_14_2 = e2
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (51), (60), (154), (155),
% 64.25/9.49 | | | | | | | | | (383), (438), (440), (634), (1013), (1014), (1022),
% 64.25/9.49 | | | | | | | | | (1023), (1025), (function-axioms) are inconsistent
% 64.25/9.49 | | | | | | | | | by sub-proof #90.
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | (1026) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.25/9.49 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | BETA: splitting (1026) gives:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | (1027) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (51), (153),
% 64.25/9.49 | | | | | | | | | | (154), (155), (438), (439), (440), (1014), (1018),
% 64.25/9.49 | | | | | | | | | | (1027), (function-axioms) are inconsistent by
% 64.25/9.49 | | | | | | | | | | sub-proof #83.
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | (1028) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | REF_CLOSE: (4), (6), (38), (43), (51), (60), (153), (154),
% 64.25/9.49 | | | | | | | | | | (383), (438), (439), (440), (1016), (1020),
% 64.25/9.49 | | | | | | | | | | (1028), (function-axioms) are inconsistent by
% 64.25/9.49 | | | | | | | | | | sub-proof #106.
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | End of split
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | End of split
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | (1029) all_34_0 = e0
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | COMBINE_EQS: (585), (1029) imply:
% 64.25/9.49 | | | | | | | | (1030) all_4_0 = e0
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (634), (1030) imply:
% 64.25/9.49 | | | | | | | | (1031) ~ (e2 = e0)
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (1018), (1030) imply:
% 64.25/9.49 | | | | | | | | (1032) ~ (e1 = e0)
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | REDUCE: (38), (1030) imply:
% 64.25/9.49 | | | | | | | | (1033) op(all_4_2, all_4_2) = e0
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | BETA: splitting (152) gives:
% 64.25/9.49 | | | | | | | |
% 64.25/9.49 | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | (1034) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | ALPHA: (1034) implies:
% 64.25/9.49 | | | | | | | | | (1035) all_52_1 = e2
% 64.25/9.49 | | | | | | | | | (1036) ~ (all_52_0 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | COMBINE_EQS: (439), (1035) imply:
% 64.25/9.49 | | | | | | | | | (1037) all_14_2 = e2
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REDUCE: (440), (1036) imply:
% 64.25/9.49 | | | | | | | | | (1038) ~ (all_10_2 = e1)
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REDUCE: (1014), (1037) imply:
% 64.25/9.49 | | | | | | | | | (1039) op(e2, e2) = e0
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | REDUCE: (60), (1037) imply:
% 64.25/9.49 | | | | | | | | | (1040) op(e1, e1) = e2
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 64.25/9.49 | | | | | | | | | e2, e2, simplifying with (51), (1039) gives:
% 64.25/9.49 | | | | | | | | | (1041) all_10_2 = e0
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | COMBINE_EQS: (440), (1041) imply:
% 64.25/9.49 | | | | | | | | | (1042) all_52_0 = e0
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | BETA: splitting (155) gives:
% 64.25/9.49 | | | | | | | | |
% 64.25/9.49 | | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | (1043) all_52_0 = e3 & ~ (all_52_2 = e2)
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | REF_CLOSE: (7), (1042), (1043) are inconsistent by sub-proof
% 64.25/9.49 | | | | | | | | | | #148.
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | Case 2:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | (1044) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 =
% 64.25/9.49 | | | | | | | | | | e3 & ~ (all_52_2 = e0))
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | BETA: splitting (1044) gives:
% 64.25/9.49 | | | | | | | | | |
% 64.25/9.49 | | | | | | | | | | Case 1:
% 64.25/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | (1045) all_52_1 = e3 & ~ (all_52_2 = e1)
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | REF_CLOSE: (9), (1035), (1045) are inconsistent by sub-proof
% 64.65/9.49 | | | | | | | | | | | #147.
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | Case 2:
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | (1046) all_52_3 = e3 & ~ (all_52_2 = e0)
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | ALPHA: (1046) implies:
% 64.65/9.49 | | | | | | | | | | | (1047) all_52_3 = e3
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | BETA: splitting (154) gives:
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | Case 1:
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | (1048) all_52_0 = e1 & ~ (all_52_1 = e2)
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | REF_CLOSE: (4), (1042), (1048) are inconsistent by sub-proof
% 64.65/9.49 | | | | | | | | | | | | #164.
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | Case 2:
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | (1049) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 =
% 64.65/9.49 | | | | | | | | | | | | e1 & ~ (all_52_1 = e0))
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | BETA: splitting (1049) gives:
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | Case 1:
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | (1050) all_52_2 = e1 & ~ (all_52_1 = e3)
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | ALPHA: (1050) implies:
% 64.65/9.49 | | | | | | | | | | | | | (1051) all_52_2 = e1
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | COMBINE_EQS: (438), (1051) imply:
% 64.65/9.49 | | | | | | | | | | | | | (1052) all_4_2 = e1
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | SIMP: (1052) implies:
% 64.65/9.49 | | | | | | | | | | | | | (1053) all_4_2 = e1
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | REDUCE: (1033), (1053) imply:
% 64.65/9.49 | | | | | | | | | | | | | (1054) op(e1, e1) = e0
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e1,
% 64.65/9.49 | | | | | | | | | | | | | e1, simplifying with (1040), (1054) gives:
% 64.65/9.49 | | | | | | | | | | | | | (1055) e2 = e0
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | REDUCE: (5), (1055) imply:
% 64.65/9.49 | | | | | | | | | | | | | (1056) $false
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | CLOSE: (1056) is inconsistent.
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | Case 2:
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | (1057) all_52_3 = e1 & ~ (all_52_1 = e0)
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | | REF_CLOSE: (8), (1047), (1057) are inconsistent by sub-proof
% 64.65/9.49 | | | | | | | | | | | | | #145.
% 64.65/9.49 | | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | | End of split
% 64.65/9.49 | | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | | End of split
% 64.65/9.49 | | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | End of split
% 64.65/9.49 | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | End of split
% 64.65/9.49 | | | | | | | | |
% 64.65/9.49 | | | | | | | | Case 2:
% 64.65/9.49 | | | | | | | | |
% 64.65/9.49 | | | | | | | | | (1058) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.65/9.49 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.65/9.49 | | | | | | | | |
% 64.65/9.49 | | | | | | | | | BETA: splitting (1058) gives:
% 64.65/9.49 | | | | | | | | |
% 64.65/9.49 | | | | | | | | | Case 1:
% 64.65/9.49 | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | (1059) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.65/9.49 | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.65/9.49 | | | | | | | | | | (440), (636), (1033), (1059), (function-axioms)
% 64.65/9.49 | | | | | | | | | | are inconsistent by sub-proof #158.
% 64.65/9.49 | | | | | | | | | |
% 64.65/9.49 | | | | | | | | | Case 2:
% 64.65/9.49 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | (1060) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | ALPHA: (1060) implies:
% 64.65/9.50 | | | | | | | | | | (1061) all_52_3 = e2
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | COMBINE_EQS: (383), (1061) imply:
% 64.65/9.50 | | | | | | | | | | (1062) all_6_2 = e2
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | REDUCE: (41), (1062) imply:
% 64.65/9.50 | | | | | | | | | | (1063) op(e0, e0) = e2
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (153), (154), (155),
% 64.65/9.50 | | | | | | | | | | (438), (439), (1014), (1033), (1061), (1063),
% 64.65/9.50 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.65/9.50 | | | | | | | | | | #79.
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | End of split
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | End of split
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | End of split
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | Case 2:
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | (1064) all_26_0 = e1
% 64.65/9.50 | | | | | | | (1065) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | COMBINE_EQS: (597), (1064) imply:
% 64.65/9.50 | | | | | | | (1066) all_4_0 = e1
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | SIMP: (1066) implies:
% 64.65/9.50 | | | | | | | (1067) all_4_0 = e1
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | REDUCE: (634), (1067) imply:
% 64.65/9.50 | | | | | | | (1068) ~ (e2 = e1)
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | REDUCE: (38), (1067) imply:
% 64.65/9.50 | | | | | | | (1069) op(all_4_2, all_4_2) = e1
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | BETA: splitting (152) gives:
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | Case 1:
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | (1070) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | ALPHA: (1070) implies:
% 64.65/9.50 | | | | | | | | (1071) all_52_1 = e2
% 64.65/9.50 | | | | | | | | (1072) ~ (all_52_0 = e1)
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | COMBINE_EQS: (439), (1071) imply:
% 64.65/9.50 | | | | | | | | (1073) all_14_2 = e2
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (51), (60), (154), (155), (383),
% 64.65/9.50 | | | | | | | | (438), (440), (634), (1013), (1014), (1071), (1072),
% 64.65/9.50 | | | | | | | | (1073), (function-axioms) are inconsistent by
% 64.65/9.50 | | | | | | | | sub-proof #90.
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | Case 2:
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | (1074) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.65/9.50 | | | | | | | | & ~ (all_52_0 = e0))
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | BETA: splitting (1074) gives:
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | Case 1:
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | (1075) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | ALPHA: (1075) implies:
% 64.65/9.50 | | | | | | | | | (1076) all_52_2 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | COMBINE_EQS: (438), (1076) imply:
% 64.65/9.50 | | | | | | | | | (1077) all_4_2 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | SIMP: (1077) implies:
% 64.65/9.50 | | | | | | | | | (1078) all_4_2 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | COMBINE_EQS: (418), (1078) imply:
% 64.65/9.50 | | | | | | | | | (1079) all_26_2 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | REDUCE: (1069), (1078) imply:
% 64.65/9.50 | | | | | | | | | (1080) op(e2, e2) = e1
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | REDUCE: (36), (1078) imply:
% 64.65/9.50 | | | | | | | | | (1081) op(e3, e3) = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | BETA: splitting (1065) gives:
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | Case 1:
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.65/9.50 | | | | | | | | | | e2, e2, simplifying with (51), (1080) gives:
% 64.65/9.50 | | | | | | | | | | (1082) all_10_2 = e1
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | COMBINE_EQS: (440), (1082) imply:
% 64.65/9.50 | | | | | | | | | | (1083) all_52_0 = e1
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (41), (153), (154),
% 64.65/9.50 | | | | | | | | | | (155), (383), (439), (1014), (1076), (1081),
% 64.65/9.50 | | | | | | | | | | (1083), (function-axioms) are inconsistent by
% 64.65/9.50 | | | | | | | | | | sub-proof #78.
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | Case 2:
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | (1084) ~ (all_26_2 = e2)
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | REDUCE: (1079), (1084) imply:
% 64.65/9.50 | | | | | | | | | | (1085) $false
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | | CLOSE: (1085) is inconsistent.
% 64.65/9.50 | | | | | | | | | |
% 64.65/9.50 | | | | | | | | | End of split
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | Case 2:
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | (1086) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | ALPHA: (1086) implies:
% 64.65/9.50 | | | | | | | | | (1087) all_52_3 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | COMBINE_EQS: (383), (1087) imply:
% 64.65/9.50 | | | | | | | | | (1088) all_6_2 = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | REDUCE: (43), (1088) imply:
% 64.65/9.50 | | | | | | | | | (1089) op(e2, e2) = all_6_0
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | REDUCE: (41), (1088) imply:
% 64.65/9.50 | | | | | | | | | (1090) op(e0, e0) = e2
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (60), (153),
% 64.65/9.50 | | | | | | | | | (154), (155), (438), (439), (440), (1014), (1016),
% 64.65/9.50 | | | | | | | | | (1069), (1087), (1089), (1090), (function-axioms)
% 64.65/9.50 | | | | | | | | | are inconsistent by sub-proof #75.
% 64.65/9.50 | | | | | | | | |
% 64.65/9.50 | | | | | | | | End of split
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | End of split
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | End of split
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | Case 2:
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | (1091) all_16_0 = e1
% 64.65/9.50 | | | | | | (1092) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | COMBINE_EQS: (539), (1091) imply:
% 64.65/9.50 | | | | | | (1093) all_6_0 = e1
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | SIMP: (1093) implies:
% 64.65/9.50 | | | | | | (1094) all_6_0 = e1
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | REDUCE: (635), (1094) imply:
% 64.65/9.50 | | | | | | (1095) ~ (e3 = e1)
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | REDUCE: (43), (1094) imply:
% 64.65/9.50 | | | | | | (1096) op(all_6_2, all_6_2) = e1
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | BETA: splitting (91) gives:
% 64.65/9.50 | | | | | |
% 64.65/9.50 | | | | | | Case 1:
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | (1097) ~ (all_26_0 = e1)
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | REDUCE: (597), (1097) imply:
% 64.65/9.50 | | | | | | | (1098) ~ (all_4_0 = e1)
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | BETA: splitting (152) gives:
% 64.65/9.50 | | | | | | |
% 64.65/9.50 | | | | | | | Case 1:
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | (1099) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.65/9.50 | | | | | | | |
% 64.65/9.50 | | | | | | | | ALPHA: (1099) implies:
% 64.65/9.50 | | | | | | | | (1100) all_52_1 = e2
% 64.65/9.50 | | | | | | | | (1101) ~ (all_52_0 = e1)
% 64.65/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | COMBINE_EQS: (439), (1100) imply:
% 64.69/9.50 | | | | | | | | (1102) all_14_2 = e2
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | SIMP: (1102) implies:
% 64.69/9.50 | | | | | | | | (1103) all_14_2 = e2
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | REDUCE: (440), (1101) imply:
% 64.69/9.50 | | | | | | | | (1104) ~ (all_10_2 = e1)
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | REDUCE: (1014), (1103) imply:
% 64.69/9.50 | | | | | | | | (1105) op(e2, e2) = e0
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | REDUCE: (60), (1103) imply:
% 64.69/9.50 | | | | | | | | (1106) op(e1, e1) = e2
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | REF_CLOSE: (7), (8), (9), (38), (51), (154), (155), (383),
% 64.69/9.50 | | | | | | | | (438), (440), (634), (1013), (1100), (1103), (1104),
% 64.69/9.50 | | | | | | | | (1105), (1106), (function-axioms) are inconsistent by
% 64.69/9.50 | | | | | | | | sub-proof #91.
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | Case 2:
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | (1107) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.69/9.50 | | | | | | | | & ~ (all_52_0 = e0))
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | BETA: splitting (1107) gives:
% 64.69/9.50 | | | | | | | |
% 64.69/9.50 | | | | | | | | Case 1:
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | (1108) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (51), (153),
% 64.69/9.50 | | | | | | | | | (154), (155), (438), (439), (440), (1014), (1098),
% 64.69/9.50 | | | | | | | | | (1108), (function-axioms) are inconsistent by
% 64.69/9.50 | | | | | | | | | sub-proof #83.
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | Case 2:
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | (1109) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | ALPHA: (1109) implies:
% 64.69/9.50 | | | | | | | | | (1110) all_52_3 = e2
% 64.69/9.50 | | | | | | | | | (1111) ~ (all_52_0 = e0)
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | COMBINE_EQS: (383), (1110) imply:
% 64.69/9.50 | | | | | | | | | (1112) all_6_2 = e2
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | REDUCE: (440), (1111) imply:
% 64.69/9.50 | | | | | | | | | (1113) ~ (all_10_2 = e0)
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | REDUCE: (1096), (1112) imply:
% 64.69/9.50 | | | | | | | | | (1114) op(e2, e2) = e1
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | REDUCE: (41), (1112) imply:
% 64.69/9.50 | | | | | | | | | (1115) op(e0, e0) = e2
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.69/9.50 | | | | | | | | | e2, e2, simplifying with (51), (1114) gives:
% 64.69/9.50 | | | | | | | | | (1116) all_10_2 = e1
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | COMBINE_EQS: (440), (1116) imply:
% 64.69/9.50 | | | | | | | | | (1117) all_52_0 = e1
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | BETA: splitting (155) gives:
% 64.69/9.50 | | | | | | | | |
% 64.69/9.50 | | | | | | | | | Case 1:
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | (1118) all_52_0 = e3 & ~ (all_52_2 = e2)
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | ALPHA: (1118) implies:
% 64.69/9.50 | | | | | | | | | | (1119) all_52_0 = e3
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (153), (154), (439),
% 64.69/9.50 | | | | | | | | | | (1014), (1110), (1115), (1119), (function-axioms)
% 64.69/9.50 | | | | | | | | | | are inconsistent by sub-proof #80.
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | Case 2:
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | (1120) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 =
% 64.69/9.50 | | | | | | | | | | e3 & ~ (all_52_2 = e0))
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | BETA: splitting (1120) gives:
% 64.69/9.50 | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | Case 1:
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | (1121) all_52_1 = e3 & ~ (all_52_2 = e1)
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | ALPHA: (1121) implies:
% 64.69/9.50 | | | | | | | | | | | (1122) all_52_1 = e3
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | COMBINE_EQS: (439), (1122) imply:
% 64.69/9.50 | | | | | | | | | | | (1123) all_14_2 = e3
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | REF_CLOSE: (4), (7), (38), (153), (438), (634), (1115),
% 64.69/9.50 | | | | | | | | | | | (1117), (1122), (function-axioms) are inconsistent
% 64.69/9.50 | | | | | | | | | | | by sub-proof #101.
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | Case 2:
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | (1124) all_52_3 = e3 & ~ (all_52_2 = e0)
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.50 | | | | | | | | | | | REF_CLOSE: (9), (1110), (1124) are inconsistent by sub-proof
% 64.69/9.50 | | | | | | | | | | | #74.
% 64.69/9.50 | | | | | | | | | | |
% 64.69/9.51 | | | | | | | | | | End of split
% 64.69/9.51 | | | | | | | | | |
% 64.69/9.51 | | | | | | | | | End of split
% 64.69/9.51 | | | | | | | | |
% 64.69/9.51 | | | | | | | | End of split
% 64.69/9.51 | | | | | | | |
% 64.69/9.51 | | | | | | | End of split
% 64.69/9.51 | | | | | | |
% 64.69/9.51 | | | | | | Case 2:
% 64.69/9.51 | | | | | | |
% 64.69/9.51 | | | | | | | (1125) all_26_0 = e1
% 64.69/9.51 | | | | | | |
% 64.69/9.51 | | | | | | | COMBINE_EQS: (597), (1125) imply:
% 64.71/9.51 | | | | | | | (1126) all_4_0 = e1
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | SIMP: (1126) implies:
% 64.71/9.51 | | | | | | | (1127) all_4_0 = e1
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | REDUCE: (634), (1127) imply:
% 64.71/9.51 | | | | | | | (1128) ~ (e2 = e1)
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | REDUCE: (38), (1127) imply:
% 64.71/9.51 | | | | | | | (1129) op(all_4_2, all_4_2) = e1
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | BETA: splitting (152) gives:
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | (1130) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (60), (154), (155), (438),
% 64.71/9.51 | | | | | | | | (439), (440), (1013), (1014), (1129), (1130),
% 64.71/9.51 | | | | | | | | (function-axioms) are inconsistent by sub-proof #72.
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | (1131) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.71/9.51 | | | | | | | | & ~ (all_52_0 = e0))
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | BETA: splitting (1131) gives:
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | (1132) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | ALPHA: (1132) implies:
% 64.71/9.51 | | | | | | | | | (1133) all_52_2 = e2
% 64.71/9.51 | | | | | | | | | (1134) ~ (all_52_0 = e3)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | COMBINE_EQS: (438), (1133) imply:
% 64.71/9.51 | | | | | | | | | (1135) all_4_2 = e2
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (440), (1134) imply:
% 64.71/9.51 | | | | | | | | | (1136) ~ (all_10_2 = e3)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (1129), (1135) imply:
% 64.71/9.51 | | | | | | | | | (1137) op(e2, e2) = e1
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (36), (1135) imply:
% 64.71/9.51 | | | | | | | | | (1138) op(e3, e3) = e2
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.71/9.51 | | | | | | | | | e2, e2, simplifying with (51), (1137) gives:
% 64.71/9.51 | | | | | | | | | (1139) all_10_2 = e1
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | COMBINE_EQS: (440), (1139) imply:
% 64.71/9.51 | | | | | | | | | (1140) all_52_0 = e1
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (41), (153), (154), (155),
% 64.71/9.51 | | | | | | | | | (383), (439), (1014), (1133), (1138), (1140),
% 64.71/9.51 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.51 | | | | | | | | | #78.
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | (1141) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | ALPHA: (1141) implies:
% 64.71/9.51 | | | | | | | | | (1142) all_52_3 = e2
% 64.71/9.51 | | | | | | | | | (1143) ~ (all_52_0 = e0)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | COMBINE_EQS: (383), (1142) imply:
% 64.71/9.51 | | | | | | | | | (1144) all_6_2 = e2
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | COMBINE_EQS: (398), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1145) all_16_2 = e2
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (450), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1146) ~ (all_54_1 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (452), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1147) ~ (all_54_2 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (456), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1148) ~ (all_54_4 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (458), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1149) ~ (all_54_8 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (460), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1150) ~ (all_54_12 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (440), (1143) imply:
% 64.71/9.51 | | | | | | | | | (1151) ~ (all_10_2 = e0)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (1096), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1152) op(e2, e2) = e1
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (42), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1153) op(e2, e0) = all_6_1
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (41), (1144) imply:
% 64.71/9.51 | | | | | | | | | (1154) op(e0, e0) = e2
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (51), (153), (154), (155),
% 64.71/9.51 | | | | | | | | | (160), (168), (170), (174), (175), (180), (181),
% 64.71/9.51 | | | | | | | | | (182), (183), (185), (188), (189), (195), (210),
% 64.71/9.51 | | | | | | | | | (235), (237), (241), (242), (243), (244), (245),
% 64.71/9.51 | | | | | | | | | (247), (268), (270), (274), (275), (278), (294),
% 64.71/9.51 | | | | | | | | | (296), (300), (311), (315), (317), (328), (334),
% 64.71/9.51 | | | | | | | | | (346), (351), (355), (359), (361), (363), (369),
% 64.71/9.51 | | | | | | | | | (371), (438), (439), (440), (447), (448), (461),
% 64.71/9.51 | | | | | | | | | (462), (463), (467), (469), (472), (474), (479),
% 64.71/9.51 | | | | | | | | | (483), (596), (1014), (1092), (1129), (1142),
% 64.71/9.51 | | | | | | | | | (1145), (1146), (1147), (1148), (1149), (1150),
% 64.71/9.51 | | | | | | | | | (1151), (1152), (1153), (1154), (function-axioms)
% 64.71/9.51 | | | | | | | | | are inconsistent by sub-proof #66.
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | End of split
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | End of split
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | End of split
% 64.71/9.51 | | | | | |
% 64.71/9.51 | | | | | End of split
% 64.71/9.51 | | | | |
% 64.71/9.51 | | | | End of split
% 64.71/9.51 | | | |
% 64.71/9.51 | | | Case 2:
% 64.71/9.51 | | | |
% 64.71/9.51 | | | | (1155) all_10_0 = e1
% 64.71/9.51 | | | |
% 64.71/9.51 | | | | COMBINE_EQS: (628), (1155) imply:
% 64.71/9.51 | | | | (1156) all_30_0 = e1
% 64.71/9.51 | | | |
% 64.71/9.51 | | | | REDUCE: (53), (1155) imply:
% 64.71/9.51 | | | | (1157) op(all_10_2, all_10_2) = e1
% 64.71/9.51 | | | |
% 64.71/9.51 | | | | BETA: splitting (63) gives:
% 64.71/9.51 | | | |
% 64.71/9.51 | | | | Case 1:
% 64.71/9.51 | | | | |
% 64.71/9.51 | | | | | (1158) ~ (all_14_0 = e0)
% 64.71/9.51 | | | | |
% 64.71/9.51 | | | | | BETA: splitting (68) gives:
% 64.71/9.51 | | | | |
% 64.71/9.51 | | | | | Case 1:
% 64.71/9.51 | | | | | |
% 64.71/9.51 | | | | | | (1159) ~ (all_16_0 = e1)
% 64.71/9.51 | | | | | |
% 64.71/9.51 | | | | | | REDUCE: (539), (1159) imply:
% 64.71/9.51 | | | | | | (1160) ~ (all_6_0 = e1)
% 64.71/9.51 | | | | | |
% 64.71/9.51 | | | | | | BETA: splitting (82) gives:
% 64.71/9.51 | | | | | |
% 64.71/9.51 | | | | | | Case 1:
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | (1161) ~ (all_22_0 = e3)
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | REDUCE: (559), (1161) imply:
% 64.71/9.51 | | | | | | | (1162) ~ (all_14_0 = e3)
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | BETA: splitting (91) gives:
% 64.71/9.51 | | | | | | |
% 64.71/9.51 | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | (1163) ~ (all_26_0 = e1)
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | REDUCE: (597), (1163) imply:
% 64.71/9.51 | | | | | | | | (1164) ~ (all_4_0 = e1)
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | BETA: splitting (96) gives:
% 64.71/9.51 | | | | | | | |
% 64.71/9.51 | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | (1165) ~ (all_28_0 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | REDUCE: (626), (1165) imply:
% 64.71/9.51 | | | | | | | | | (1166) ~ (all_6_0 = e2)
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.51 | | | | | | | | |
% 64.71/9.51 | | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | (1167) ~ (all_30_0 = e1)
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | REDUCE: (1156), (1167) imply:
% 64.71/9.51 | | | | | | | | | | (1168) $false
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | CLOSE: (1168) is inconsistent.
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | (1169) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.51 | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | (1170) ~ (all_34_0 = e0)
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | REDUCE: (585), (1170) imply:
% 64.71/9.51 | | | | | | | | | | | (1171) ~ (all_4_0 = e0)
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (38), (43), (51), (60),
% 64.71/9.51 | | | | | | | | | | | (62), (152), (153), (154), (155), (383), (438),
% 64.71/9.51 | | | | | | | | | | | (439), (440), (1158), (1160), (1162), (1164),
% 64.71/9.51 | | | | | | | | | | | (1171), (function-axioms) are inconsistent by
% 64.71/9.51 | | | | | | | | | | | sub-proof #167.
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | (1172) all_34_0 = e0
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | COMBINE_EQS: (585), (1172) imply:
% 64.71/9.51 | | | | | | | | | | | (1173) all_4_0 = e0
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | COMBINE_EQS: (633), (1173) imply:
% 64.71/9.51 | | | | | | | | | | | (1174) all_50_0 = e0
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | REDUCE: (634), (1173) imply:
% 64.71/9.51 | | | | | | | | | | | (1175) ~ (e2 = e0)
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | REDUCE: (1164), (1173) imply:
% 64.71/9.51 | | | | | | | | | | | (1176) ~ (e1 = e0)
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | REDUCE: (38), (1173) imply:
% 64.71/9.51 | | | | | | | | | | | (1177) op(all_4_2, all_4_2) = e0
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.51 | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | (1178) ~ (all_50_0 = e0)
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | REDUCE: (1174), (1178) imply:
% 64.71/9.51 | | | | | | | | | | | | (1179) $false
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | CLOSE: (1179) is inconsistent.
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | (1180) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.51 | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | (1181) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.71/9.51 | | | | | | | | | | | | | (438), (439), (440), (1158), (1162), (1181),
% 64.71/9.51 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.51 | | | | | | | | | | | | | #159.
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | Case 2:
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | (1182) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.51 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | BETA: splitting (1182) gives:
% 64.71/9.51 | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | Case 1:
% 64.71/9.51 | | | | | | | | | | | | | |
% 64.71/9.51 | | | | | | | | | | | | | | (1183) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.51 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.52 | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.52 | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.52 | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.52 | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.52 | | | | | | | | | | | | | | (1169), (1177), (1180), (1183), (function-axioms)
% 64.71/9.52 | | | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | (1184) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | ALPHA: (1184) implies:
% 64.71/9.52 | | | | | | | | | | | | | | (1185) all_52_3 = e2
% 64.71/9.52 | | | | | | | | | | | | | | (1186) ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | COMBINE_EQS: (383), (1185) imply:
% 64.71/9.52 | | | | | | | | | | | | | | (1187) all_6_2 = e2
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | REF_CLOSE: (43), (51), (239), (440), (444), (635), (1160),
% 64.71/9.52 | | | | | | | | | | | | | | (1166), (1186), (1187), (function-axioms) are
% 64.71/9.52 | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | (1188) all_28_0 = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | COMBINE_EQS: (626), (1188) imply:
% 64.71/9.52 | | | | | | | | | (1189) all_6_0 = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | REDUCE: (635), (1189) imply:
% 64.71/9.52 | | | | | | | | | (1190) ~ (e3 = e2)
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | REDUCE: (43), (1189) imply:
% 64.71/9.52 | | | | | | | | | (1191) op(all_6_2, all_6_2) = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1192) ~ (all_30_0 = e1)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REDUCE: (1156), (1192) imply:
% 64.71/9.52 | | | | | | | | | | (1193) $false
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | CLOSE: (1193) is inconsistent.
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1194) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1195) ~ (all_34_0 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REDUCE: (585), (1195) imply:
% 64.71/9.52 | | | | | | | | | | | (1196) ~ (all_4_0 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (38), (43), (51), (60),
% 64.71/9.52 | | | | | | | | | | | (62), (152), (153), (154), (155), (383), (438),
% 64.71/9.52 | | | | | | | | | | | (439), (440), (1158), (1160), (1162), (1164),
% 64.71/9.52 | | | | | | | | | | | (1196), (function-axioms) are inconsistent by
% 64.71/9.52 | | | | | | | | | | | sub-proof #167.
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1197) all_34_0 = e0
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | COMBINE_EQS: (585), (1197) imply:
% 64.71/9.52 | | | | | | | | | | | (1198) all_4_0 = e0
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | COMBINE_EQS: (633), (1198) imply:
% 64.71/9.52 | | | | | | | | | | | (1199) all_50_0 = e0
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REDUCE: (634), (1198) imply:
% 64.71/9.52 | | | | | | | | | | | (1200) ~ (e2 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REDUCE: (1164), (1198) imply:
% 64.71/9.52 | | | | | | | | | | | (1201) ~ (e1 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REDUCE: (38), (1198) imply:
% 64.71/9.52 | | | | | | | | | | | (1202) op(all_4_2, all_4_2) = e0
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | (1203) ~ (all_50_0 = e0)
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | REDUCE: (1199), (1203) imply:
% 64.71/9.52 | | | | | | | | | | | | (1204) $false
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | CLOSE: (1204) is inconsistent.
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | (1205) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | (1206) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.71/9.52 | | | | | | | | | | | | | (438), (439), (440), (1158), (1162), (1206),
% 64.71/9.52 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.52 | | | | | | | | | | | | | #165.
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | (1207) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.52 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | BETA: splitting (1207) gives:
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | (1208) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.52 | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.52 | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.52 | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.52 | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.52 | | | | | | | | | | | | | | (1194), (1202), (1205), (1208), (function-axioms)
% 64.71/9.52 | | | | | | | | | | | | | | are inconsistent by sub-proof #62.
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | (1209) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.71/9.52 | | | | | | | | | | | | | | (439), (440), (1191), (1209), (function-axioms)
% 64.71/9.52 | | | | | | | | | | | | | | are inconsistent by sub-proof #110.
% 64.71/9.52 | | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | End of split
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | (1210) all_26_0 = e1
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | COMBINE_EQS: (597), (1210) imply:
% 64.71/9.52 | | | | | | | | (1211) all_4_0 = e1
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | SIMP: (1211) implies:
% 64.71/9.52 | | | | | | | | (1212) all_4_0 = e1
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | REDUCE: (634), (1212) imply:
% 64.71/9.52 | | | | | | | | (1213) ~ (e2 = e1)
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | REDUCE: (38), (1212) imply:
% 64.71/9.52 | | | | | | | | (1214) op(all_4_2, all_4_2) = e1
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | BETA: splitting (96) gives:
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | (1215) ~ (all_28_0 = e2)
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | REDUCE: (626), (1215) imply:
% 64.71/9.52 | | | | | | | | | (1216) ~ (all_6_0 = e2)
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1217) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (60),
% 64.71/9.52 | | | | | | | | | | (62), (153), (154), (155), (239), (383), (438),
% 64.71/9.52 | | | | | | | | | | (439), (440), (444), (1162), (1214), (1217),
% 64.71/9.52 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.52 | | | | | | | | | | #129.
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1218) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.52 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | BETA: splitting (1218) gives:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1219) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.52 | | | | | | | | | | | (1157), (1214), (1219), (function-axioms) are
% 64.71/9.52 | | | | | | | | | | | inconsistent by sub-proof #58.
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1220) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | ALPHA: (1220) implies:
% 64.71/9.52 | | | | | | | | | | | (1221) all_52_3 = e2
% 64.71/9.52 | | | | | | | | | | | (1222) ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | COMBINE_EQS: (383), (1221) imply:
% 64.71/9.52 | | | | | | | | | | | (1223) all_6_2 = e2
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REF_CLOSE: (43), (51), (239), (440), (444), (635), (1160),
% 64.71/9.52 | | | | | | | | | | | (1216), (1222), (1223), (function-axioms) are
% 64.71/9.52 | | | | | | | | | | | inconsistent by sub-proof #161.
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | (1224) all_28_0 = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | COMBINE_EQS: (626), (1224) imply:
% 64.71/9.52 | | | | | | | | | (1225) all_6_0 = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | REDUCE: (635), (1225) imply:
% 64.71/9.52 | | | | | | | | | (1226) ~ (e3 = e2)
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | REDUCE: (43), (1225) imply:
% 64.71/9.52 | | | | | | | | | (1227) op(all_6_2, all_6_2) = e2
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1228) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | ALPHA: (1228) implies:
% 64.71/9.52 | | | | | | | | | | (1229) all_52_1 = e2
% 64.71/9.52 | | | | | | | | | | (1230) ~ (all_52_0 = e1)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | COMBINE_EQS: (439), (1229) imply:
% 64.71/9.52 | | | | | | | | | | (1231) all_14_2 = e2
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REDUCE: (440), (1230) imply:
% 64.71/9.52 | | | | | | | | | | (1232) ~ (all_10_2 = e1)
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REDUCE: (62), (1231) imply:
% 64.71/9.52 | | | | | | | | | | (1233) op(e2, e2) = all_14_0
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REDUCE: (60), (1231) imply:
% 64.71/9.52 | | | | | | | | | | (1234) op(e1, e1) = e2
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (153),
% 64.71/9.52 | | | | | | | | | | (154), (155), (239), (383), (438), (440), (444),
% 64.71/9.52 | | | | | | | | | | (1162), (1214), (1229), (1232), (1233), (1234),
% 64.71/9.52 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.52 | | | | | | | | | | #136.
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | (1235) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.52 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | BETA: splitting (1235) gives:
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 1:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1236) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.52 | | | | | | | | | | | (1157), (1214), (1236), (function-axioms) are
% 64.71/9.52 | | | | | | | | | | | inconsistent by sub-proof #57.
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | Case 2:
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | (1237) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.71/9.52 | | | | | | | | | | | (439), (440), (1227), (1237), (function-axioms)
% 64.71/9.52 | | | | | | | | | | | are inconsistent by sub-proof #110.
% 64.71/9.52 | | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | | |
% 64.71/9.52 | | | | | | | | | End of split
% 64.71/9.52 | | | | | | | | |
% 64.71/9.52 | | | | | | | | End of split
% 64.71/9.52 | | | | | | | |
% 64.71/9.52 | | | | | | | End of split
% 64.71/9.52 | | | | | | |
% 64.71/9.53 | | | | | | Case 2:
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | (1238) all_22_0 = e3
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | COMBINE_EQS: (559), (1238) imply:
% 64.71/9.53 | | | | | | | (1239) all_14_0 = e3
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | COMBINE_EQS: (632), (1239) imply:
% 64.71/9.53 | | | | | | | (1240) all_44_0 = e3
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | REDUCE: (62), (1239) imply:
% 64.71/9.53 | | | | | | | (1241) op(all_14_2, all_14_2) = e3
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | BETA: splitting (91) gives:
% 64.71/9.53 | | | | | | |
% 64.71/9.53 | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | (1242) ~ (all_26_0 = e1)
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | REDUCE: (597), (1242) imply:
% 64.71/9.53 | | | | | | | | (1243) ~ (all_4_0 = e1)
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | (1244) ~ (all_30_0 = e1)
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | REDUCE: (1156), (1244) imply:
% 64.71/9.53 | | | | | | | | | (1245) $false
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | CLOSE: (1245) is inconsistent.
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | (1246) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | BETA: splitting (96) gives:
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | (1247) ~ (all_28_0 = e2)
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | REDUCE: (626), (1247) imply:
% 64.71/9.53 | | | | | | | | | | (1248) ~ (all_6_0 = e2)
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | (1249) ~ (all_34_0 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (43), (51), (60),
% 64.71/9.53 | | | | | | | | | | | (152), (153), (154), (383), (438), (439), (440),
% 64.71/9.53 | | | | | | | | | | | (585), (1157), (1160), (1241), (1243), (1249),
% 64.71/9.53 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.53 | | | | | | | | | | | #53.
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | (1250) all_34_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | COMBINE_EQS: (585), (1250) imply:
% 64.71/9.53 | | | | | | | | | | | (1251) all_4_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | COMBINE_EQS: (633), (1251) imply:
% 64.71/9.53 | | | | | | | | | | | (1252) all_50_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (634), (1251) imply:
% 64.71/9.53 | | | | | | | | | | | (1253) ~ (e2 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (1243), (1251) imply:
% 64.71/9.53 | | | | | | | | | | | (1254) ~ (e1 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (38), (1251) imply:
% 64.71/9.53 | | | | | | | | | | | (1255) op(all_4_2, all_4_2) = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | (1256) ~ (all_44_0 = e3)
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | REDUCE: (1240), (1256) imply:
% 64.71/9.53 | | | | | | | | | | | | (1257) $false
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | CLOSE: (1257) is inconsistent.
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | (1258) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | (1259) ~ (all_50_0 = e0)
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | REDUCE: (1252), (1259) imply:
% 64.71/9.53 | | | | | | | | | | | | | (1260) $false
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | CLOSE: (1260) is inconsistent.
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | (1261) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | (1262) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | ALPHA: (1262) implies:
% 64.71/9.53 | | | | | | | | | | | | | | (1263) all_52_1 = e2
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | COMBINE_EQS: (439), (1263) imply:
% 64.71/9.53 | | | | | | | | | | | | | | (1264) all_14_2 = e2
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | COMBINE_EQS: (437), (1264) imply:
% 64.71/9.53 | | | | | | | | | | | | | | (1265) all_44_2 = e2
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | REDUCE: (1241), (1264) imply:
% 64.71/9.53 | | | | | | | | | | | | | | (1266) op(e2, e2) = e3
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (438), (440),
% 64.71/9.53 | | | | | | | | | | | | | | (1157), (1258), (1263), (1265), (1266),
% 64.71/9.53 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.53 | | | | | | | | | | | | | | #52.
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | (1267) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.53 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | BETA: splitting (1267) gives:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | (1268) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.53 | | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.53 | | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.53 | | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.53 | | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.53 | | | | | | | | | | | | | | | (1246), (1255), (1261), (1268), (function-axioms)
% 64.71/9.53 | | | | | | | | | | | | | | | are inconsistent by sub-proof #62.
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | (1269) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | ALPHA: (1269) implies:
% 64.71/9.53 | | | | | | | | | | | | | | | (1270) all_52_3 = e2
% 64.71/9.53 | | | | | | | | | | | | | | | (1271) ~ (all_52_0 = e0)
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | COMBINE_EQS: (383), (1270) imply:
% 64.71/9.53 | | | | | | | | | | | | | | | (1272) all_6_2 = e2
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | REF_CLOSE: (43), (51), (239), (440), (444), (635), (1160),
% 64.71/9.53 | | | | | | | | | | | | | | | (1248), (1271), (1272), (function-axioms) are
% 64.71/9.53 | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | (1273) all_28_0 = e2
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | COMBINE_EQS: (626), (1273) imply:
% 64.71/9.53 | | | | | | | | | | (1274) all_6_0 = e2
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | SIMP: (1274) implies:
% 64.71/9.53 | | | | | | | | | | (1275) all_6_0 = e2
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | REDUCE: (635), (1275) imply:
% 64.71/9.53 | | | | | | | | | | (1276) ~ (e3 = e2)
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | REDUCE: (43), (1275) imply:
% 64.71/9.53 | | | | | | | | | | (1277) op(all_6_2, all_6_2) = e2
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | (1278) ~ (all_34_0 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (38), (43), (51), (60),
% 64.71/9.53 | | | | | | | | | | | (152), (153), (154), (383), (438), (439), (440),
% 64.71/9.53 | | | | | | | | | | | (585), (1157), (1160), (1241), (1243), (1278),
% 64.71/9.53 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.53 | | | | | | | | | | | #53.
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | (1279) all_34_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | COMBINE_EQS: (585), (1279) imply:
% 64.71/9.53 | | | | | | | | | | | (1280) all_4_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | SIMP: (1280) implies:
% 64.71/9.53 | | | | | | | | | | | (1281) all_4_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | COMBINE_EQS: (633), (1281) imply:
% 64.71/9.53 | | | | | | | | | | | (1282) all_50_0 = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (634), (1281) imply:
% 64.71/9.53 | | | | | | | | | | | (1283) ~ (e2 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (1243), (1281) imply:
% 64.71/9.53 | | | | | | | | | | | (1284) ~ (e1 = e0)
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | REDUCE: (38), (1281) imply:
% 64.71/9.53 | | | | | | | | | | | (1285) op(all_4_2, all_4_2) = e0
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | (1286) ~ (all_44_0 = e3)
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | REDUCE: (1240), (1286) imply:
% 64.71/9.53 | | | | | | | | | | | | (1287) $false
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | CLOSE: (1287) is inconsistent.
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | (1288) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | (1289) ~ (all_50_0 = e0)
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | REDUCE: (1282), (1289) imply:
% 64.71/9.53 | | | | | | | | | | | | | (1290) $false
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | CLOSE: (1290) is inconsistent.
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | (1291) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | (1292) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.53 | | | | | | | | | | | | | | (439), (440), (1157), (1241), (1288), (1292),
% 64.71/9.53 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.53 | | | | | | | | | | | | | | #51.
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | (1293) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.53 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | BETA: splitting (1293) gives:
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | Case 1:
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | (1294) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.53 | | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.53 | | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.53 | | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.53 | | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.53 | | | | | | | | | | | | | | | (1246), (1285), (1291), (1294), (function-axioms)
% 64.71/9.53 | | | | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | (1295) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.71/9.53 | | | | | | | | | | | | | | | (439), (440), (1277), (1295), (function-axioms)
% 64.71/9.53 | | | | | | | | | | | | | | | are inconsistent by sub-proof #110.
% 64.71/9.53 | | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | | |
% 64.71/9.53 | | | | | | | | | End of split
% 64.71/9.53 | | | | | | | | |
% 64.71/9.53 | | | | | | | | End of split
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | Case 2:
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | (1296) all_26_0 = e1
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | COMBINE_EQS: (597), (1296) imply:
% 64.71/9.53 | | | | | | | | (1297) all_4_0 = e1
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | REDUCE: (38), (1297) imply:
% 64.71/9.53 | | | | | | | | (1298) op(all_4_2, all_4_2) = e1
% 64.71/9.53 | | | | | | | |
% 64.71/9.53 | | | | | | | | BETA: splitting (96) gives:
% 64.71/9.53 | | | | | | | |
% 64.71/9.54 | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | (1299) ~ (all_28_0 = e2)
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | REDUCE: (626), (1299) imply:
% 64.71/9.54 | | | | | | | | | (1300) ~ (all_6_0 = e2)
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1301) ~ (all_44_0 = e3)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | REDUCE: (1240), (1301) imply:
% 64.71/9.54 | | | | | | | | | | (1302) $false
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | CLOSE: (1302) is inconsistent.
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1303) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1304) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.54 | | | | | | | | | | | (439), (440), (1157), (1241), (1303), (1304),
% 64.71/9.54 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | #50.
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1305) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.54 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | BETA: splitting (1305) gives:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1306) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.54 | | | | | | | | | | | | (1157), (1298), (1306), (function-axioms) are
% 64.71/9.54 | | | | | | | | | | | | inconsistent by sub-proof #57.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1307) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | ALPHA: (1307) implies:
% 64.71/9.54 | | | | | | | | | | | | (1308) all_52_3 = e2
% 64.71/9.54 | | | | | | | | | | | | (1309) ~ (all_52_0 = e0)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | COMBINE_EQS: (383), (1308) imply:
% 64.71/9.54 | | | | | | | | | | | | (1310) all_6_2 = e2
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REF_CLOSE: (43), (51), (239), (440), (444), (635), (1160),
% 64.71/9.54 | | | | | | | | | | | | (1300), (1309), (1310), (function-axioms) are
% 64.71/9.54 | | | | | | | | | | | | inconsistent by sub-proof #161.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | (1311) all_28_0 = e2
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | COMBINE_EQS: (626), (1311) imply:
% 64.71/9.54 | | | | | | | | | (1312) all_6_0 = e2
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | SIMP: (1312) implies:
% 64.71/9.54 | | | | | | | | | (1313) all_6_0 = e2
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | REDUCE: (635), (1313) imply:
% 64.71/9.54 | | | | | | | | | (1314) ~ (e3 = e2)
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | REDUCE: (43), (1313) imply:
% 64.71/9.54 | | | | | | | | | (1315) op(all_6_2, all_6_2) = e2
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1316) ~ (all_44_0 = e3)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | REDUCE: (1240), (1316) imply:
% 64.71/9.54 | | | | | | | | | | (1317) $false
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | CLOSE: (1317) is inconsistent.
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1318) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1319) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.54 | | | | | | | | | | | (439), (440), (1157), (1241), (1318), (1319),
% 64.71/9.54 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | #51.
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1320) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.54 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | BETA: splitting (1320) gives:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1321) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.54 | | | | | | | | | | | | (1157), (1298), (1321), (function-axioms) are
% 64.71/9.54 | | | | | | | | | | | | inconsistent by sub-proof #58.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1322) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 64.71/9.54 | | | | | | | | | | | | (439), (440), (1315), (1322), (function-axioms)
% 64.71/9.54 | | | | | | | | | | | | are inconsistent by sub-proof #110.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | End of split
% 64.71/9.54 | | | | | | | |
% 64.71/9.54 | | | | | | | End of split
% 64.71/9.54 | | | | | | |
% 64.71/9.54 | | | | | | End of split
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | Case 2:
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | (1323) all_16_0 = e1
% 64.71/9.54 | | | | | | (1324) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | COMBINE_EQS: (539), (1323) imply:
% 64.71/9.54 | | | | | | (1325) all_6_0 = e1
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | SIMP: (1325) implies:
% 64.71/9.54 | | | | | | (1326) all_6_0 = e1
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | REDUCE: (635), (1326) imply:
% 64.71/9.54 | | | | | | (1327) ~ (e3 = e1)
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | REDUCE: (43), (1326) imply:
% 64.71/9.54 | | | | | | (1328) op(all_6_2, all_6_2) = e1
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | BETA: splitting (77) gives:
% 64.71/9.54 | | | | | |
% 64.71/9.54 | | | | | | Case 1:
% 64.71/9.54 | | | | | | |
% 64.71/9.54 | | | | | | | (1329) ~ (all_20_0 = e2)
% 64.71/9.54 | | | | | | |
% 64.71/9.54 | | | | | | | REDUCE: (615), (1329) imply:
% 64.71/9.54 | | | | | | | (1330) ~ (all_14_0 = e2)
% 64.71/9.54 | | | | | | |
% 64.71/9.54 | | | | | | | BETA: splitting (82) gives:
% 64.71/9.54 | | | | | | |
% 64.71/9.54 | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | |
% 64.71/9.54 | | | | | | | | (1331) ~ (all_22_0 = e3)
% 64.71/9.54 | | | | | | | |
% 64.71/9.54 | | | | | | | | REDUCE: (559), (1331) imply:
% 64.71/9.54 | | | | | | | | (1332) ~ (all_14_0 = e3)
% 64.71/9.54 | | | | | | | |
% 64.71/9.54 | | | | | | | | BETA: splitting (91) gives:
% 64.71/9.54 | | | | | | | |
% 64.71/9.54 | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | (1333) ~ (all_26_0 = e1)
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | REDUCE: (597), (1333) imply:
% 64.71/9.54 | | | | | | | | | (1334) ~ (all_4_0 = e1)
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1335) ~ (all_30_0 = e1)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | REDUCE: (1156), (1335) imply:
% 64.71/9.54 | | | | | | | | | | (1336) $false
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | CLOSE: (1336) is inconsistent.
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | (1337) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1338) ~ (all_34_0 = e0)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REDUCE: (585), (1338) imply:
% 64.71/9.54 | | | | | | | | | | | (1339) ~ (all_4_0 = e0)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1340) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.71/9.54 | | | | | | | | | | | | (438), (439), (440), (1158), (1332), (1340),
% 64.71/9.54 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | | #159.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1341) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.54 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | BETA: splitting (1341) gives:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | (1342) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.71/9.54 | | | | | | | | | | | | | (440), (1334), (1339), (1342), (function-axioms)
% 64.71/9.54 | | | | | | | | | | | | | are inconsistent by sub-proof #111.
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | (1343) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.54 | | | | | | | | | | | | | (440), (1157), (1324), (1328), (1343),
% 64.71/9.54 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | | | #48.
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | (1344) all_34_0 = e0
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | COMBINE_EQS: (585), (1344) imply:
% 64.71/9.54 | | | | | | | | | | | (1345) all_4_0 = e0
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | COMBINE_EQS: (633), (1345) imply:
% 64.71/9.54 | | | | | | | | | | | (1346) all_50_0 = e0
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REDUCE: (634), (1345) imply:
% 64.71/9.54 | | | | | | | | | | | (1347) ~ (e2 = e0)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REDUCE: (1334), (1345) imply:
% 64.71/9.54 | | | | | | | | | | | (1348) ~ (e1 = e0)
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | REDUCE: (38), (1345) imply:
% 64.71/9.54 | | | | | | | | | | | (1349) op(all_4_2, all_4_2) = e0
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1350) ~ (all_50_0 = e0)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | REDUCE: (1346), (1350) imply:
% 64.71/9.54 | | | | | | | | | | | | (1351) $false
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | CLOSE: (1351) is inconsistent.
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | (1352) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | (1353) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 64.71/9.54 | | | | | | | | | | | | | (438), (439), (440), (1158), (1332), (1353),
% 64.71/9.54 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | | | #165.
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | (1354) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.54 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | BETA: splitting (1354) gives:
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | Case 1:
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | | (1355) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.54 | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.54 | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.54 | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.54 | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.54 | | | | | | | | | | | | | | (1337), (1349), (1352), (1355), (function-axioms)
% 64.71/9.54 | | | | | | | | | | | | | | are inconsistent by sub-proof #62.
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | | (1356) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.54 | | | | | | | | | | | | | | (440), (1157), (1324), (1328), (1356),
% 64.71/9.54 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.54 | | | | | | | | | | | | | | #48.
% 64.71/9.54 | | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | | |
% 64.71/9.54 | | | | | | | | | End of split
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | Case 2:
% 64.71/9.54 | | | | | | | | |
% 64.71/9.54 | | | | | | | | | (1357) all_26_0 = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | COMBINE_EQS: (597), (1357) imply:
% 64.71/9.55 | | | | | | | | | (1358) all_4_0 = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | REDUCE: (634), (1358) imply:
% 64.71/9.55 | | | | | | | | | (1359) ~ (e2 = e1)
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | REDUCE: (38), (1358) imply:
% 64.71/9.55 | | | | | | | | | (1360) op(all_4_2, all_4_2) = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1361) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (41), (51), (60),
% 64.71/9.55 | | | | | | | | | | (62), (153), (154), (155), (239), (383), (438),
% 64.71/9.55 | | | | | | | | | | (439), (440), (444), (1332), (1360), (1361),
% 64.71/9.55 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | #134.
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1362) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.55 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | BETA: splitting (1362) gives:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1363) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.55 | | | | | | | | | | | (1157), (1360), (1363), (function-axioms) are
% 64.71/9.55 | | | | | | | | | | | inconsistent by sub-proof #57.
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1364) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | ALPHA: (1364) implies:
% 64.71/9.55 | | | | | | | | | | | (1365) all_52_3 = e2
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | COMBINE_EQS: (383), (1365) imply:
% 64.71/9.55 | | | | | | | | | | | (1366) all_6_2 = e2
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | COMBINE_EQS: (398), (1366) imply:
% 64.71/9.55 | | | | | | | | | | | (1367) all_16_2 = e2
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REDUCE: (1328), (1366) imply:
% 64.71/9.55 | | | | | | | | | | | (1368) op(e2, e2) = e1
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (439), (440), (1157),
% 64.71/9.55 | | | | | | | | | | | (1324), (1365), (1367), (1368), (function-axioms)
% 64.71/9.55 | | | | | | | | | | | are inconsistent by sub-proof #49.
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | End of split
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | (1369) all_22_0 = e3
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | COMBINE_EQS: (559), (1369) imply:
% 64.71/9.55 | | | | | | | | (1370) all_14_0 = e3
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | COMBINE_EQS: (632), (1370) imply:
% 64.71/9.55 | | | | | | | | (1371) all_44_0 = e3
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | REDUCE: (62), (1370) imply:
% 64.71/9.55 | | | | | | | | (1372) op(all_14_2, all_14_2) = e3
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | BETA: splitting (91) gives:
% 64.71/9.55 | | | | | | | |
% 64.71/9.55 | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | (1373) ~ (all_26_0 = e1)
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | REDUCE: (597), (1373) imply:
% 64.71/9.55 | | | | | | | | | (1374) ~ (all_4_0 = e1)
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1375) ~ (all_30_0 = e1)
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | REDUCE: (1156), (1375) imply:
% 64.71/9.55 | | | | | | | | | | (1376) $false
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | CLOSE: (1376) is inconsistent.
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1377) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1378) ~ (all_34_0 = e0)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REDUCE: (585), (1378) imply:
% 64.71/9.55 | | | | | | | | | | | (1379) ~ (all_4_0 = e0)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1380) ~ (all_44_0 = e3)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | REDUCE: (1371), (1380) imply:
% 64.71/9.55 | | | | | | | | | | | | (1381) $false
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | CLOSE: (1381) is inconsistent.
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1382) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | (1383) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.55 | | | | | | | | | | | | | (439), (440), (1157), (1372), (1382), (1383),
% 64.71/9.55 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | | | | #50.
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | (1384) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.55 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | BETA: splitting (1384) gives:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | (1385) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.71/9.55 | | | | | | | | | | | | | | (440), (1374), (1379), (1385), (function-axioms)
% 64.71/9.55 | | | | | | | | | | | | | | are inconsistent by sub-proof #173.
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | (1386) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.55 | | | | | | | | | | | | | | (440), (1157), (1324), (1328), (1386),
% 64.71/9.55 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | | | | | #48.
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1387) all_34_0 = e0
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | COMBINE_EQS: (585), (1387) imply:
% 64.71/9.55 | | | | | | | | | | | (1388) all_4_0 = e0
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | SIMP: (1388) implies:
% 64.71/9.55 | | | | | | | | | | | (1389) all_4_0 = e0
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | COMBINE_EQS: (633), (1389) imply:
% 64.71/9.55 | | | | | | | | | | | (1390) all_50_0 = e0
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REDUCE: (634), (1389) imply:
% 64.71/9.55 | | | | | | | | | | | (1391) ~ (e2 = e0)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REDUCE: (1374), (1389) imply:
% 64.71/9.55 | | | | | | | | | | | (1392) ~ (e1 = e0)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REDUCE: (38), (1389) imply:
% 64.71/9.55 | | | | | | | | | | | (1393) op(all_4_2, all_4_2) = e0
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1394) ~ (all_44_0 = e3)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | REDUCE: (1371), (1394) imply:
% 64.71/9.55 | | | | | | | | | | | | (1395) $false
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | CLOSE: (1395) is inconsistent.
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1396) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | (1397) ~ (all_50_0 = e0)
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | REDUCE: (1390), (1397) imply:
% 64.71/9.55 | | | | | | | | | | | | | (1398) $false
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | CLOSE: (1398) is inconsistent.
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | (1399) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | (1400) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.55 | | | | | | | | | | | | | | (439), (440), (1157), (1372), (1396), (1400),
% 64.71/9.55 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | | | | | #51.
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | (1401) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.55 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | BETA: splitting (1401) gives:
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | | (1402) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.55 | | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.55 | | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.55 | | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.55 | | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.55 | | | | | | | | | | | | | | | (1377), (1393), (1399), (1402), (function-axioms)
% 64.71/9.55 | | | | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | | (1403) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.55 | | | | | | | | | | | | | | | (440), (1157), (1324), (1328), (1403),
% 64.71/9.55 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | | | | | | #48.
% 64.71/9.55 | | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | End of split
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | (1404) all_26_0 = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | COMBINE_EQS: (597), (1404) imply:
% 64.71/9.55 | | | | | | | | | (1405) all_4_0 = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | SIMP: (1405) implies:
% 64.71/9.55 | | | | | | | | | (1406) all_4_0 = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | REDUCE: (38), (1406) imply:
% 64.71/9.55 | | | | | | | | | (1407) op(all_4_2, all_4_2) = e1
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.55 | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1408) ~ (all_44_0 = e3)
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | REDUCE: (1371), (1408) imply:
% 64.71/9.55 | | | | | | | | | | (1409) $false
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | CLOSE: (1409) is inconsistent.
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | (1410) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.55 | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1411) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 64.71/9.55 | | | | | | | | | | | (439), (440), (1157), (1372), (1410), (1411),
% 64.71/9.55 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.55 | | | | | | | | | | | #51.
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | (1412) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.55 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | BETA: splitting (1412) gives:
% 64.71/9.55 | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 1:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1413) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.55 | | | | | | | | | | | | (1157), (1407), (1413), (function-axioms) are
% 64.71/9.55 | | | | | | | | | | | | inconsistent by sub-proof #58.
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | Case 2:
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | (1414) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.55 | | | | | | | | | | | |
% 64.71/9.55 | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.55 | | | | | | | | | | | | (440), (1157), (1324), (1328), (1414),
% 64.71/9.56 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.56 | | | | | | | | | | | | #48.
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | End of split
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | End of split
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | Case 2:
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | (1415) all_20_0 = e2
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | COMBINE_EQS: (615), (1415) imply:
% 64.71/9.56 | | | | | | | (1416) all_14_0 = e2
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | SIMP: (1416) implies:
% 64.71/9.56 | | | | | | | (1417) all_14_0 = e2
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | REDUCE: (62), (1417) imply:
% 64.71/9.56 | | | | | | | (1418) op(all_14_2, all_14_2) = e2
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | BETA: splitting (91) gives:
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | (1419) ~ (all_26_0 = e1)
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | REDUCE: (597), (1419) imply:
% 64.71/9.56 | | | | | | | | (1420) ~ (all_4_0 = e1)
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | (1421) ~ (all_30_0 = e1)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | REDUCE: (1156), (1421) imply:
% 64.71/9.56 | | | | | | | | | (1422) $false
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | CLOSE: (1422) is inconsistent.
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | (1423) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1424) ~ (all_34_0 = e0)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REDUCE: (585), (1424) imply:
% 64.71/9.56 | | | | | | | | | | (1425) ~ (all_4_0 = e0)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | (1426) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.71/9.56 | | | | | | | | | | | (439), (440), (1418), (1426), (function-axioms)
% 64.71/9.56 | | | | | | | | | | | are inconsistent by sub-proof #104.
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | (1427) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.56 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | BETA: splitting (1427) gives:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | (1428) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.71/9.56 | | | | | | | | | | | | (440), (1420), (1425), (1428), (function-axioms)
% 64.71/9.56 | | | | | | | | | | | | are inconsistent by sub-proof #173.
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | (1429) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.56 | | | | | | | | | | | | (440), (1157), (1324), (1328), (1429),
% 64.71/9.56 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.56 | | | | | | | | | | | | #48.
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1430) all_34_0 = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | COMBINE_EQS: (585), (1430) imply:
% 64.71/9.56 | | | | | | | | | | (1431) all_4_0 = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | SIMP: (1431) implies:
% 64.71/9.56 | | | | | | | | | | (1432) all_4_0 = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | COMBINE_EQS: (633), (1432) imply:
% 64.71/9.56 | | | | | | | | | | (1433) all_50_0 = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REDUCE: (634), (1432) imply:
% 64.71/9.56 | | | | | | | | | | (1434) ~ (e2 = e0)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REDUCE: (1420), (1432) imply:
% 64.71/9.56 | | | | | | | | | | (1435) ~ (e1 = e0)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REDUCE: (38), (1432) imply:
% 64.71/9.56 | | | | | | | | | | (1436) op(all_4_2, all_4_2) = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | (1437) ~ (all_50_0 = e0)
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | REDUCE: (1433), (1437) imply:
% 64.71/9.56 | | | | | | | | | | | (1438) $false
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | CLOSE: (1438) is inconsistent.
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | (1439) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | (1440) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383),
% 64.71/9.56 | | | | | | | | | | | | (439), (440), (1418), (1440), (function-axioms)
% 64.71/9.56 | | | | | | | | | | | | are inconsistent by sub-proof #107.
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | (1441) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.56 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | BETA: splitting (1441) gives:
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | | (1442) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.56 | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.56 | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.56 | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.56 | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.56 | | | | | | | | | | | | | (1423), (1436), (1439), (1442), (function-axioms)
% 64.71/9.56 | | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | | (1443) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.56 | | | | | | | | | | | | | (440), (1157), (1324), (1328), (1443),
% 64.71/9.56 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.56 | | | | | | | | | | | | | #48.
% 64.71/9.56 | | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | End of split
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | (1444) all_26_0 = e1
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | COMBINE_EQS: (597), (1444) imply:
% 64.71/9.56 | | | | | | | | (1445) all_4_0 = e1
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | SIMP: (1445) implies:
% 64.71/9.56 | | | | | | | | (1446) all_4_0 = e1
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | REDUCE: (38), (1446) imply:
% 64.71/9.56 | | | | | | | | (1447) op(all_4_2, all_4_2) = e1
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | (1448) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | ALPHA: (1448) implies:
% 64.71/9.56 | | | | | | | | | (1449) all_52_1 = e2
% 64.71/9.56 | | | | | | | | | (1450) ~ (all_52_0 = e1)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | COMBINE_EQS: (439), (1449) imply:
% 64.71/9.56 | | | | | | | | | (1451) all_14_2 = e2
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | SIMP: (1451) implies:
% 64.71/9.56 | | | | | | | | | (1452) all_14_2 = e2
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (51), (60), (153), (154),
% 64.71/9.56 | | | | | | | | | (155), (383), (438), (440), (1418), (1447), (1449),
% 64.71/9.56 | | | | | | | | | (1450), (1452), (function-axioms) are inconsistent
% 64.71/9.56 | | | | | | | | | by sub-proof #47.
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | (1453) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.56 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | BETA: splitting (1453) gives:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1454) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REF_CLOSE: (4), (5), (51), (60), (153), (438), (439), (440),
% 64.71/9.56 | | | | | | | | | | (1157), (1447), (1454), (function-axioms) are
% 64.71/9.56 | | | | | | | | | | inconsistent by sub-proof #58.
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1455) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REF_CLOSE: (8), (9), (51), (60), (155), (383), (398), (439),
% 64.71/9.56 | | | | | | | | | | (440), (1157), (1324), (1328), (1455),
% 64.71/9.56 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.56 | | | | | | | | | | #48.
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | End of split
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | End of split
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | End of split
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | End of split
% 64.71/9.56 | | | | | |
% 64.71/9.56 | | | | | End of split
% 64.71/9.56 | | | | |
% 64.71/9.56 | | | | Case 2:
% 64.71/9.56 | | | | |
% 64.71/9.56 | | | | | (1456) all_14_0 = e0
% 64.71/9.56 | | | | | (1457) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 64.71/9.56 | | | | |
% 64.71/9.56 | | | | | REDUCE: (62), (1456) imply:
% 64.71/9.56 | | | | | (1458) op(all_14_2, all_14_2) = e0
% 64.71/9.56 | | | | |
% 64.71/9.56 | | | | | BETA: splitting (68) gives:
% 64.71/9.56 | | | | |
% 64.71/9.56 | | | | | Case 1:
% 64.71/9.56 | | | | | |
% 64.71/9.56 | | | | | | (1459) ~ (all_16_0 = e1)
% 64.71/9.56 | | | | | |
% 64.71/9.56 | | | | | | REDUCE: (539), (1459) imply:
% 64.71/9.56 | | | | | | (1460) ~ (all_6_0 = e1)
% 64.71/9.56 | | | | | |
% 64.71/9.56 | | | | | | BETA: splitting (91) gives:
% 64.71/9.56 | | | | | |
% 64.71/9.56 | | | | | | Case 1:
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | (1461) ~ (all_26_0 = e1)
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | REDUCE: (597), (1461) imply:
% 64.71/9.56 | | | | | | | (1462) ~ (all_4_0 = e1)
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | BETA: splitting (101) gives:
% 64.71/9.56 | | | | | | |
% 64.71/9.56 | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | (1463) ~ (all_30_0 = e1)
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | REDUCE: (1156), (1463) imply:
% 64.71/9.56 | | | | | | | | (1464) $false
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | CLOSE: (1464) is inconsistent.
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | (1465) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.56 | | | | | | | |
% 64.71/9.56 | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | (1466) ~ (all_34_0 = e0)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | REDUCE: (585), (1466) imply:
% 64.71/9.56 | | | | | | | | | (1467) ~ (all_4_0 = e0)
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.56 | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1468) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | ALPHA: (1468) implies:
% 64.71/9.56 | | | | | | | | | | (1469) all_52_1 = e2
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | COMBINE_EQS: (439), (1469) imply:
% 64.71/9.56 | | | | | | | | | | (1470) all_14_2 = e2
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | SIMP: (1470) implies:
% 64.71/9.56 | | | | | | | | | | (1471) all_14_2 = e2
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REDUCE: (1458), (1471) imply:
% 64.71/9.56 | | | | | | | | | | (1472) op(e2, e2) = e0
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | REF_CLOSE: (7), (8), (9), (41), (51), (155), (383), (440),
% 64.71/9.56 | | | | | | | | | | (1157), (1457), (1469), (1471), (1472),
% 64.71/9.56 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.56 | | | | | | | | | | #46.
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | Case 2:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | (1473) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.56 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | BETA: splitting (1473) gives:
% 64.71/9.56 | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | Case 1:
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | (1474) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | ALPHA: (1474) implies:
% 64.71/9.56 | | | | | | | | | | | (1475) all_52_2 = e2
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | COMBINE_EQS: (438), (1475) imply:
% 64.71/9.56 | | | | | | | | | | | (1476) all_4_2 = e2
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.56 | | | | | | | | | | | SIMP: (1476) implies:
% 64.71/9.56 | | | | | | | | | | | (1477) all_4_2 = e2
% 64.71/9.56 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (51), (153),
% 64.71/9.57 | | | | | | | | | | | (154), (155), (439), (440), (1458), (1462),
% 64.71/9.57 | | | | | | | | | | | (1475), (1477), (function-axioms) are inconsistent
% 64.71/9.57 | | | | | | | | | | | by sub-proof #84.
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | (1478) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | ALPHA: (1478) implies:
% 64.71/9.57 | | | | | | | | | | | (1479) all_52_3 = e2
% 64.71/9.57 | | | | | | | | | | | (1480) ~ (all_52_0 = e0)
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | COMBINE_EQS: (383), (1479) imply:
% 64.71/9.57 | | | | | | | | | | | (1481) all_6_2 = e2
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | SIMP: (1481) implies:
% 64.71/9.57 | | | | | | | | | | | (1482) all_6_2 = e2
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | REDUCE: (440), (1480) imply:
% 64.71/9.57 | | | | | | | | | | | (1483) ~ (all_10_2 = e0)
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | REDUCE: (43), (1482) imply:
% 64.71/9.57 | | | | | | | | | | | (1484) op(e2, e2) = all_6_0
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | REF_CLOSE: (4), (6), (38), (51), (60), (153), (154), (438),
% 64.71/9.57 | | | | | | | | | | | (439), (440), (1460), (1467), (1479), (1483),
% 64.71/9.57 | | | | | | | | | | | (1484), (function-axioms) are inconsistent by
% 64.71/9.57 | | | | | | | | | | | sub-proof #170.
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | (1485) all_34_0 = e0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | COMBINE_EQS: (585), (1485) imply:
% 64.71/9.57 | | | | | | | | | (1486) all_4_0 = e0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | SIMP: (1486) implies:
% 64.71/9.57 | | | | | | | | | (1487) all_4_0 = e0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | COMBINE_EQS: (633), (1487) imply:
% 64.71/9.57 | | | | | | | | | (1488) all_50_0 = e0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (634), (1487) imply:
% 64.71/9.57 | | | | | | | | | (1489) ~ (e2 = e0)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (1462), (1487) imply:
% 64.71/9.57 | | | | | | | | | (1490) ~ (e1 = e0)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (38), (1487) imply:
% 64.71/9.57 | | | | | | | | | (1491) op(all_4_2, all_4_2) = e0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | BETA: splitting (146) gives:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | (1492) ~ (all_50_0 = e0)
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | REDUCE: (1488), (1492) imply:
% 64.71/9.57 | | | | | | | | | | (1493) $false
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | CLOSE: (1493) is inconsistent.
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | (1494) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | (1495) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (41), (51), (155), (383), (439),
% 64.71/9.57 | | | | | | | | | | | (440), (1157), (1457), (1458), (1495),
% 64.71/9.57 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.57 | | | | | | | | | | | #45.
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | (1496) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.57 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | BETA: splitting (1496) gives:
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | (1497) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 64.71/9.57 | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 64.71/9.57 | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 64.71/9.57 | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 64.71/9.57 | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 64.71/9.57 | | | | | | | | | | | | (1465), (1491), (1494), (1497), (function-axioms)
% 64.71/9.57 | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | (1498) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | ALPHA: (1498) implies:
% 64.71/9.57 | | | | | | | | | | | | (1499) all_52_3 = e2
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | COMBINE_EQS: (383), (1499) imply:
% 64.71/9.57 | | | | | | | | | | | | (1500) all_6_2 = e2
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | REDUCE: (41), (1500) imply:
% 64.71/9.57 | | | | | | | | | | | | (1501) op(e0, e0) = e2
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (153), (154), (155),
% 64.71/9.57 | | | | | | | | | | | | (438), (439), (1458), (1491), (1499), (1501),
% 64.71/9.57 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.57 | | | | | | | | | | | | #79.
% 64.71/9.57 | | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | End of split
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | End of split
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | Case 2:
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | (1502) all_26_0 = e1
% 64.71/9.57 | | | | | | | (1503) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | COMBINE_EQS: (597), (1502) imply:
% 64.71/9.57 | | | | | | | (1504) all_4_0 = e1
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | SIMP: (1504) implies:
% 64.71/9.57 | | | | | | | (1505) all_4_0 = e1
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | REDUCE: (634), (1505) imply:
% 64.71/9.57 | | | | | | | (1506) ~ (e2 = e1)
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | REDUCE: (38), (1505) imply:
% 64.71/9.57 | | | | | | | (1507) op(all_4_2, all_4_2) = e1
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | BETA: splitting (152) gives:
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | (1508) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | REF_CLOSE: (7), (8), (9), (41), (51), (155), (383), (439),
% 64.71/9.57 | | | | | | | | (440), (1157), (1457), (1458), (1508),
% 64.71/9.57 | | | | | | | | (function-axioms) are inconsistent by sub-proof #45.
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | (1509) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.71/9.57 | | | | | | | | & ~ (all_52_0 = e0))
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | BETA: splitting (1509) gives:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | (1510) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | ALPHA: (1510) implies:
% 64.71/9.57 | | | | | | | | | (1511) all_52_2 = e2
% 64.71/9.57 | | | | | | | | | (1512) ~ (all_52_0 = e3)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | COMBINE_EQS: (438), (1511) imply:
% 64.71/9.57 | | | | | | | | | (1513) all_4_2 = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | COMBINE_EQS: (418), (1513) imply:
% 64.71/9.57 | | | | | | | | | (1514) all_26_2 = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (440), (1512) imply:
% 64.71/9.57 | | | | | | | | | (1515) ~ (all_10_2 = e3)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (1507), (1513) imply:
% 64.71/9.57 | | | | | | | | | (1516) op(e2, e2) = e1
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (36), (1513) imply:
% 64.71/9.57 | | | | | | | | | (1517) op(e3, e3) = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | BETA: splitting (1503) gives:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.71/9.57 | | | | | | | | | | e2, e2, simplifying with (51), (1516) gives:
% 64.71/9.57 | | | | | | | | | | (1518) all_10_2 = e1
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (60), (153), (154), (155),
% 64.71/9.57 | | | | | | | | | | (439), (1157), (1458), (1511), (1515), (1517),
% 64.71/9.57 | | | | | | | | | | (1518), (function-axioms) are inconsistent by
% 64.71/9.57 | | | | | | | | | | sub-proof #44.
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | (1519) ~ (all_26_2 = e2)
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | REDUCE: (1514), (1519) imply:
% 64.71/9.57 | | | | | | | | | | (1520) $false
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | | CLOSE: (1520) is inconsistent.
% 64.71/9.57 | | | | | | | | | |
% 64.71/9.57 | | | | | | | | | End of split
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | (1521) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | ALPHA: (1521) implies:
% 64.71/9.57 | | | | | | | | | (1522) all_52_3 = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | COMBINE_EQS: (383), (1522) imply:
% 64.71/9.57 | | | | | | | | | (1523) all_6_2 = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (43), (1523) imply:
% 64.71/9.57 | | | | | | | | | (1524) op(e2, e2) = all_6_0
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REDUCE: (41), (1523) imply:
% 64.71/9.57 | | | | | | | | | (1525) op(e0, e0) = e2
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (60), (153),
% 64.71/9.57 | | | | | | | | | (154), (155), (438), (439), (440), (1458), (1460),
% 64.71/9.57 | | | | | | | | | (1507), (1522), (1524), (1525), (function-axioms)
% 64.71/9.57 | | | | | | | | | are inconsistent by sub-proof #75.
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | End of split
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | End of split
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | End of split
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | Case 2:
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | (1526) all_16_0 = e1
% 64.71/9.57 | | | | | | (1527) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | COMBINE_EQS: (539), (1526) imply:
% 64.71/9.57 | | | | | | (1528) all_6_0 = e1
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | SIMP: (1528) implies:
% 64.71/9.57 | | | | | | (1529) all_6_0 = e1
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | REDUCE: (635), (1529) imply:
% 64.71/9.57 | | | | | | (1530) ~ (e3 = e1)
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | REDUCE: (43), (1529) imply:
% 64.71/9.57 | | | | | | (1531) op(all_6_2, all_6_2) = e1
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | BETA: splitting (91) gives:
% 64.71/9.57 | | | | | |
% 64.71/9.57 | | | | | | Case 1:
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | (1532) ~ (all_26_0 = e1)
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | REDUCE: (597), (1532) imply:
% 64.71/9.57 | | | | | | | (1533) ~ (all_4_0 = e1)
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | BETA: splitting (152) gives:
% 64.71/9.57 | | | | | | |
% 64.71/9.57 | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | (1534) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | ALPHA: (1534) implies:
% 64.71/9.57 | | | | | | | | (1535) all_52_1 = e2
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | COMBINE_EQS: (439), (1535) imply:
% 64.71/9.57 | | | | | | | | (1536) all_14_2 = e2
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | REDUCE: (1458), (1536) imply:
% 64.71/9.57 | | | | | | | | (1537) op(e2, e2) = e0
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | REF_CLOSE: (7), (8), (9), (41), (51), (155), (383), (440),
% 64.71/9.57 | | | | | | | | (1157), (1457), (1535), (1536), (1537),
% 64.71/9.57 | | | | | | | | (function-axioms) are inconsistent by sub-proof #46.
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | (1538) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.71/9.57 | | | | | | | | & ~ (all_52_0 = e0))
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | BETA: splitting (1538) gives:
% 64.71/9.57 | | | | | | | |
% 64.71/9.57 | | | | | | | | Case 1:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | (1539) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (38), (51), (153),
% 64.71/9.57 | | | | | | | | | (154), (155), (438), (439), (440), (1458), (1533),
% 64.71/9.57 | | | | | | | | | (1539), (function-axioms) are inconsistent by
% 64.71/9.57 | | | | | | | | | sub-proof #83.
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | Case 2:
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | (1540) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.57 | | | | | | | | |
% 64.71/9.57 | | | | | | | | | ALPHA: (1540) implies:
% 64.71/9.58 | | | | | | | | | (1541) all_52_3 = e2
% 64.71/9.58 | | | | | | | | | (1542) ~ (all_52_0 = e0)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | COMBINE_EQS: (383), (1541) imply:
% 64.71/9.58 | | | | | | | | | (1543) all_6_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | COMBINE_EQS: (398), (1543) imply:
% 64.71/9.58 | | | | | | | | | (1544) all_16_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (440), (1542) imply:
% 64.71/9.58 | | | | | | | | | (1545) ~ (all_10_2 = e0)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (1531), (1543) imply:
% 64.71/9.58 | | | | | | | | | (1546) op(e2, e2) = e1
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (41), (1543) imply:
% 64.71/9.58 | | | | | | | | | (1547) op(e0, e0) = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | BETA: splitting (1527) gives:
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.71/9.58 | | | | | | | | | | e2, e2, simplifying with (51), (1546) gives:
% 64.71/9.58 | | | | | | | | | | (1548) all_10_2 = e1
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (1157), (1548) imply:
% 64.71/9.58 | | | | | | | | | | (1549) op(e1, e1) = e1
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (60), (153), (154),
% 64.71/9.58 | | | | | | | | | | (155), (439), (1458), (1541), (1547), (1549),
% 64.71/9.58 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.58 | | | | | | | | | | #76.
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | (1550) ~ (all_16_2 = e2)
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (1544), (1550) imply:
% 64.71/9.58 | | | | | | | | | | (1551) $false
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | CLOSE: (1551) is inconsistent.
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | End of split
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | End of split
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | End of split
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | Case 2:
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | (1552) all_26_0 = e1
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | COMBINE_EQS: (597), (1552) imply:
% 64.71/9.58 | | | | | | | (1553) all_4_0 = e1
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | SIMP: (1553) implies:
% 64.71/9.58 | | | | | | | (1554) all_4_0 = e1
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | REDUCE: (634), (1554) imply:
% 64.71/9.58 | | | | | | | (1555) ~ (e2 = e1)
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | REDUCE: (38), (1554) imply:
% 64.71/9.58 | | | | | | | (1556) op(all_4_2, all_4_2) = e1
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | BETA: splitting (152) gives:
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | (1557) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (60), (154), (155), (438),
% 64.71/9.58 | | | | | | | | (439), (440), (1457), (1458), (1556), (1557),
% 64.71/9.58 | | | | | | | | (function-axioms) are inconsistent by sub-proof #72.
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | (1558) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.71/9.58 | | | | | | | | & ~ (all_52_0 = e0))
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | BETA: splitting (1558) gives:
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | (1559) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | ALPHA: (1559) implies:
% 64.71/9.58 | | | | | | | | | (1560) all_52_2 = e2
% 64.71/9.58 | | | | | | | | | (1561) ~ (all_52_0 = e3)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | COMBINE_EQS: (438), (1560) imply:
% 64.71/9.58 | | | | | | | | | (1562) all_4_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | SIMP: (1562) implies:
% 64.71/9.58 | | | | | | | | | (1563) all_4_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (440), (1561) imply:
% 64.71/9.58 | | | | | | | | | (1564) ~ (all_10_2 = e3)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (1556), (1563) imply:
% 64.71/9.58 | | | | | | | | | (1565) op(e2, e2) = e1
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (36), (1563) imply:
% 64.71/9.58 | | | | | | | | | (1566) op(e3, e3) = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 64.71/9.58 | | | | | | | | | e2, e2, simplifying with (51), (1565) gives:
% 64.71/9.58 | | | | | | | | | (1567) all_10_2 = e1
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (60), (153), (154), (155),
% 64.71/9.58 | | | | | | | | | (439), (1157), (1458), (1560), (1564), (1566),
% 64.71/9.58 | | | | | | | | | (1567), (function-axioms) are inconsistent by
% 64.71/9.58 | | | | | | | | | sub-proof #44.
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | (1568) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | ALPHA: (1568) implies:
% 64.71/9.58 | | | | | | | | | (1569) all_52_3 = e2
% 64.71/9.58 | | | | | | | | | (1570) ~ (all_52_0 = e0)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | COMBINE_EQS: (383), (1569) imply:
% 64.71/9.58 | | | | | | | | | (1571) all_6_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | SIMP: (1571) implies:
% 64.71/9.58 | | | | | | | | | (1572) all_6_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | COMBINE_EQS: (398), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1573) all_16_2 = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (450), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1574) ~ (all_54_1 = e2)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (452), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1575) ~ (all_54_2 = e2)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (456), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1576) ~ (all_54_4 = e2)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (458), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1577) ~ (all_54_8 = e2)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (460), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1578) ~ (all_54_12 = e2)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (440), (1570) imply:
% 64.71/9.58 | | | | | | | | | (1579) ~ (all_10_2 = e0)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (1531), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1580) op(e2, e2) = e1
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (42), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1581) op(e2, e0) = all_6_1
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (41), (1572) imply:
% 64.71/9.58 | | | | | | | | | (1582) op(e0, e0) = e2
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (51), (153), (154), (155),
% 64.71/9.58 | | | | | | | | | (160), (168), (170), (174), (175), (180), (181),
% 64.71/9.58 | | | | | | | | | (182), (183), (185), (188), (189), (195), (210),
% 64.71/9.58 | | | | | | | | | (235), (237), (241), (242), (243), (244), (245),
% 64.71/9.58 | | | | | | | | | (247), (268), (270), (274), (275), (278), (294),
% 64.71/9.58 | | | | | | | | | (296), (300), (311), (315), (317), (328), (334),
% 64.71/9.58 | | | | | | | | | (346), (351), (355), (359), (361), (363), (369),
% 64.71/9.58 | | | | | | | | | (371), (438), (439), (440), (447), (448), (461),
% 64.71/9.58 | | | | | | | | | (462), (463), (467), (469), (472), (474), (479),
% 64.71/9.58 | | | | | | | | | (483), (596), (1458), (1527), (1556), (1569),
% 64.71/9.58 | | | | | | | | | (1573), (1574), (1575), (1576), (1577), (1578),
% 64.71/9.58 | | | | | | | | | (1579), (1580), (1581), (1582), (function-axioms)
% 64.71/9.58 | | | | | | | | | are inconsistent by sub-proof #66.
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | End of split
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | End of split
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | End of split
% 64.71/9.58 | | | | | |
% 64.71/9.58 | | | | | End of split
% 64.71/9.58 | | | | |
% 64.71/9.58 | | | | End of split
% 64.71/9.58 | | | |
% 64.71/9.58 | | | End of split
% 64.71/9.58 | | |
% 64.71/9.58 | | Case 2:
% 64.71/9.58 | | |
% 64.71/9.58 | | | (1583) all_6_0 = e3
% 64.71/9.58 | | |
% 64.71/9.58 | | | COMBINE_EQS: (622), (1583) imply:
% 64.71/9.58 | | | (1584) all_8_0 = e3
% 64.71/9.58 | | |
% 64.71/9.58 | | | REDUCE: (43), (1583) imply:
% 64.71/9.58 | | | (1585) op(all_6_2, all_6_2) = e3
% 64.71/9.58 | | |
% 64.71/9.58 | | | BETA: splitting (49) gives:
% 64.71/9.58 | | |
% 64.71/9.58 | | | Case 1:
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | (1586) ~ (all_8_0 = e3)
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | REDUCE: (1584), (1586) imply:
% 64.71/9.58 | | | | (1587) $false
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | CLOSE: (1587) is inconsistent.
% 64.71/9.58 | | | |
% 64.71/9.58 | | | Case 2:
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | (1588) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | BETA: splitting (54) gives:
% 64.71/9.58 | | | |
% 64.71/9.58 | | | | Case 1:
% 64.71/9.58 | | | | |
% 64.71/9.58 | | | | | (1589) ~ (all_10_0 = e1)
% 64.71/9.58 | | | | |
% 64.71/9.58 | | | | | BETA: splitting (63) gives:
% 64.71/9.58 | | | | |
% 64.71/9.58 | | | | | Case 1:
% 64.71/9.58 | | | | | |
% 64.71/9.58 | | | | | | (1590) ~ (all_14_0 = e0)
% 64.71/9.58 | | | | | |
% 64.71/9.58 | | | | | | BETA: splitting (77) gives:
% 64.71/9.58 | | | | | |
% 64.71/9.58 | | | | | | Case 1:
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | (1591) ~ (all_20_0 = e2)
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | REDUCE: (615), (1591) imply:
% 64.71/9.58 | | | | | | | (1592) ~ (all_14_0 = e2)
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | BETA: splitting (82) gives:
% 64.71/9.58 | | | | | | |
% 64.71/9.58 | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | (1593) ~ (all_22_0 = e3)
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | REDUCE: (559), (1593) imply:
% 64.71/9.58 | | | | | | | | (1594) ~ (all_14_0 = e3)
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | BETA: splitting (91) gives:
% 64.71/9.58 | | | | | | | |
% 64.71/9.58 | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | (1595) ~ (all_26_0 = e1)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | REDUCE: (597), (1595) imply:
% 64.71/9.58 | | | | | | | | | (1596) ~ (all_4_0 = e1)
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.58 | | | | | | | | |
% 64.71/9.58 | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | (1597) ~ (all_34_0 = e0)
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (585), (1597) imply:
% 64.71/9.58 | | | | | | | | | | (1598) ~ (all_4_0 = e0)
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | (1599) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 64.71/9.58 | | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 64.71/9.58 | | | | | | | | | | | (440), (444), (1585), (1594), (1599),
% 64.71/9.58 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.58 | | | | | | | | | | | #41.
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | (1600) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.58 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | BETA: splitting (1600) gives:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | | (1601) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.71/9.58 | | | | | | | | | | | | (440), (1596), (1598), (1601), (function-axioms)
% 64.71/9.58 | | | | | | | | | | | | are inconsistent by sub-proof #173.
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | | (1602) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.58 | | | | | | | | | | | | (440), (1585), (1589), (1602), (function-axioms)
% 64.71/9.58 | | | | | | | | | | | | are inconsistent by sub-proof #39.
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | End of split
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | End of split
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | (1603) all_34_0 = e0
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | COMBINE_EQS: (585), (1603) imply:
% 64.71/9.58 | | | | | | | | | | (1604) all_4_0 = e0
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (634), (1604) imply:
% 64.71/9.58 | | | | | | | | | | (1605) ~ (e2 = e0)
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (1596), (1604) imply:
% 64.71/9.58 | | | | | | | | | | (1606) ~ (e1 = e0)
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | REDUCE: (38), (1604) imply:
% 64.71/9.58 | | | | | | | | | | (1607) op(all_4_2, all_4_2) = e0
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.58 | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | (1608) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 64.71/9.58 | | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 64.71/9.58 | | | | | | | | | | | (440), (444), (1585), (1594), (1608),
% 64.71/9.58 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.58 | | | | | | | | | | | #38.
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | Case 2:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | (1609) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.58 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | BETA: splitting (1609) gives:
% 64.71/9.58 | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | Case 1:
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.58 | | | | | | | | | | | | (1610) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.58 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | (440), (1589), (1607), (1610), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | are inconsistent by sub-proof #162.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1611) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | (440), (1585), (1589), (1611), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | (1612) all_26_0 = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | COMBINE_EQS: (597), (1612) imply:
% 64.71/9.59 | | | | | | | | | (1613) all_4_0 = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | REDUCE: (634), (1613) imply:
% 64.71/9.59 | | | | | | | | | (1614) ~ (e2 = e1)
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | REDUCE: (38), (1613) imply:
% 64.71/9.59 | | | | | | | | | (1615) op(all_4_2, all_4_2) = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1616) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 64.71/9.59 | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 64.71/9.59 | | | | | | | | | | (440), (444), (1585), (1594), (1616),
% 64.71/9.59 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.59 | | | | | | | | | | #38.
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1617) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.59 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | BETA: splitting (1617) gives:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1618) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 64.71/9.59 | | | | | | | | | | | (383), (438), (440), (1585), (1615), (1618),
% 64.71/9.59 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.59 | | | | | | | | | | | #34.
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1619) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | (440), (1585), (1589), (1619), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | End of split
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | (1620) all_22_0 = e3
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | COMBINE_EQS: (559), (1620) imply:
% 64.71/9.59 | | | | | | | | (1621) all_14_0 = e3
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | COMBINE_EQS: (632), (1621) imply:
% 64.71/9.59 | | | | | | | | (1622) all_44_0 = e3
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | REDUCE: (62), (1621) imply:
% 64.71/9.59 | | | | | | | | (1623) op(all_14_2, all_14_2) = e3
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | BETA: splitting (91) gives:
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | (1624) ~ (all_26_0 = e1)
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | REDUCE: (597), (1624) imply:
% 64.71/9.59 | | | | | | | | | (1625) ~ (all_4_0 = e1)
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1626) ~ (all_34_0 = e0)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REDUCE: (585), (1626) imply:
% 64.71/9.59 | | | | | | | | | | (1627) ~ (all_4_0 = e0)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1628) ~ (all_44_0 = e3)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | REDUCE: (1622), (1628) imply:
% 64.71/9.59 | | | | | | | | | | | (1629) $false
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | CLOSE: (1629) is inconsistent.
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1630) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1631) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | ALPHA: (1631) implies:
% 64.71/9.59 | | | | | | | | | | | | (1632) all_52_1 = e2
% 64.71/9.59 | | | | | | | | | | | | (1633) ~ (all_52_0 = e1)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | COMBINE_EQS: (439), (1632) imply:
% 64.71/9.59 | | | | | | | | | | | | (1634) all_14_2 = e2
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | COMBINE_EQS: (437), (1634) imply:
% 64.71/9.59 | | | | | | | | | | | | (1635) all_44_2 = e2
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REDUCE: (463), (1634) imply:
% 64.71/9.59 | | | | | | | | | | | | (1636) ~ (all_54_4 = e2)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REDUCE: (440), (1633) imply:
% 64.71/9.59 | | | | | | | | | | | | (1637) ~ (all_10_2 = e1)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REDUCE: (1623), (1634) imply:
% 64.71/9.59 | | | | | | | | | | | | (1638) op(e2, e2) = e3
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REDUCE: (61), (1634) imply:
% 64.71/9.59 | | | | | | | | | | | | (1639) op(e2, e1) = all_14_1
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REDUCE: (60), (1634) imply:
% 64.71/9.59 | | | | | | | | | | | | (1640) op(e1, e1) = e2
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (154),
% 64.71/9.59 | | | | | | | | | | | | (155), (168), (180), (181), (211), (237), (244),
% 64.71/9.59 | | | | | | | | | | | | (272), (315), (317), (328), (346), (363), (383),
% 64.71/9.59 | | | | | | | | | | | | (438), (440), (447), (456), (458), (460), (477),
% 64.71/9.59 | | | | | | | | | | | | (631), (1585), (1630), (1632), (1635), (1636),
% 64.71/9.59 | | | | | | | | | | | | (1637), (1638), (1639), (1640), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | are inconsistent by sub-proof #33.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1641) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.59 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | BETA: splitting (1641) gives:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | (1642) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 64.71/9.59 | | | | | | | | | | | | | (440), (1625), (1627), (1642), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | | are inconsistent by sub-proof #173.
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | (1643) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | | (440), (1585), (1589), (1643), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1644) all_34_0 = e0
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | COMBINE_EQS: (585), (1644) imply:
% 64.71/9.59 | | | | | | | | | | (1645) all_4_0 = e0
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | SIMP: (1645) implies:
% 64.71/9.59 | | | | | | | | | | (1646) all_4_0 = e0
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REDUCE: (634), (1646) imply:
% 64.71/9.59 | | | | | | | | | | (1647) ~ (e2 = e0)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REDUCE: (1625), (1646) imply:
% 64.71/9.59 | | | | | | | | | | (1648) ~ (e1 = e0)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REDUCE: (38), (1646) imply:
% 64.71/9.59 | | | | | | | | | | (1649) op(all_4_2, all_4_2) = e0
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1650) ~ (all_44_0 = e3)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | REDUCE: (1622), (1650) imply:
% 64.71/9.59 | | | | | | | | | | | (1651) $false
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | CLOSE: (1651) is inconsistent.
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1652) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1653) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 64.71/9.59 | | | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 64.71/9.59 | | | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 64.71/9.59 | | | | | | | | | | | | (383), (437), (438), (439), (440), (447), (456),
% 64.71/9.59 | | | | | | | | | | | | (458), (460), (463), (477), (631), (1585), (1623),
% 64.71/9.59 | | | | | | | | | | | | (1652), (1653), (function-axioms) are inconsistent
% 64.71/9.59 | | | | | | | | | | | | by sub-proof #31.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1654) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.59 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | BETA: splitting (1654) gives:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | (1655) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | | (440), (1589), (1649), (1655), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | | are inconsistent by sub-proof #162.
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | (1656) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | | (440), (1585), (1589), (1656), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.59 | | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | (1657) all_26_0 = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | COMBINE_EQS: (597), (1657) imply:
% 64.71/9.59 | | | | | | | | | (1658) all_4_0 = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | REDUCE: (634), (1658) imply:
% 64.71/9.59 | | | | | | | | | (1659) ~ (e2 = e1)
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | REDUCE: (38), (1658) imply:
% 64.71/9.59 | | | | | | | | | (1660) op(all_4_2, all_4_2) = e1
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | BETA: splitting (133) gives:
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1661) ~ (all_44_0 = e3)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | REDUCE: (1622), (1661) imply:
% 64.71/9.59 | | | | | | | | | | (1662) $false
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | CLOSE: (1662) is inconsistent.
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | (1663) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1664) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 64.71/9.59 | | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 64.71/9.59 | | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 64.71/9.59 | | | | | | | | | | | (383), (437), (438), (439), (440), (447), (456),
% 64.71/9.59 | | | | | | | | | | | (458), (460), (463), (477), (631), (1585), (1623),
% 64.71/9.59 | | | | | | | | | | | (1663), (1664), (function-axioms) are inconsistent
% 64.71/9.59 | | | | | | | | | | | by sub-proof #31.
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | (1665) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.59 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | BETA: splitting (1665) gives:
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1666) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 64.71/9.59 | | | | | | | | | | | | (383), (438), (440), (1585), (1660), (1666),
% 64.71/9.59 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.59 | | | | | | | | | | | | #34.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | Case 2:
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | (1667) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.59 | | | | | | | | | | | | (440), (1585), (1589), (1667), (function-axioms)
% 64.71/9.59 | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.59 | | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | | |
% 64.71/9.59 | | | | | | | | | End of split
% 64.71/9.59 | | | | | | | | |
% 64.71/9.59 | | | | | | | | End of split
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | End of split
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | Case 2:
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | (1668) all_20_0 = e2
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | COMBINE_EQS: (615), (1668) imply:
% 64.71/9.59 | | | | | | | (1669) all_14_0 = e2
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | SIMP: (1669) implies:
% 64.71/9.59 | | | | | | | (1670) all_14_0 = e2
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | REDUCE: (62), (1670) imply:
% 64.71/9.59 | | | | | | | (1671) op(all_14_2, all_14_2) = e2
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | BETA: splitting (91) gives:
% 64.71/9.59 | | | | | | |
% 64.71/9.59 | | | | | | | Case 1:
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | (1672) ~ (all_26_0 = e1)
% 64.71/9.59 | | | | | | | |
% 64.71/9.59 | | | | | | | | REDUCE: (597), (1672) imply:
% 64.71/9.60 | | | | | | | | (1673) ~ (all_4_0 = e1)
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | (1674) ~ (all_34_0 = e0)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REDUCE: (585), (1674) imply:
% 64.71/9.60 | | | | | | | | | (1675) ~ (all_4_0 = e0)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1676) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (51), (153), (154),
% 64.71/9.60 | | | | | | | | | | (155), (383), (438), (439), (440), (1585), (1671),
% 64.71/9.60 | | | | | | | | | | (1676), (function-axioms) are inconsistent by
% 64.71/9.60 | | | | | | | | | | sub-proof #29.
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1677) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.60 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (38), (51), (60), (153),
% 64.71/9.60 | | | | | | | | | | (154), (383), (438), (439), (440), (1585), (1673),
% 64.71/9.60 | | | | | | | | | | (1675), (1677), (function-axioms) are inconsistent
% 64.71/9.60 | | | | | | | | | | by sub-proof #27.
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | End of split
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | (1678) all_34_0 = e0
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | COMBINE_EQS: (585), (1678) imply:
% 64.71/9.60 | | | | | | | | | (1679) all_4_0 = e0
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | SIMP: (1679) implies:
% 64.71/9.60 | | | | | | | | | (1680) all_4_0 = e0
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REDUCE: (1673), (1680) imply:
% 64.71/9.60 | | | | | | | | | (1681) ~ (e1 = e0)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REDUCE: (38), (1680) imply:
% 64.71/9.60 | | | | | | | | | (1682) op(all_4_2, all_4_2) = e0
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | BETA: splitting (152) gives:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1683) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (51), (153), (154),
% 64.71/9.60 | | | | | | | | | | (155), (383), (438), (439), (440), (1585), (1671),
% 64.71/9.60 | | | | | | | | | | (1683), (function-axioms) are inconsistent by
% 64.71/9.60 | | | | | | | | | | sub-proof #26.
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1684) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 64.71/9.60 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | BETA: splitting (1684) gives:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | | (1685) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | | REF_CLOSE: (4), (6), (41), (51), (53), (154), (383), (438),
% 64.71/9.60 | | | | | | | | | | | (440), (1589), (1682), (1685), (function-axioms)
% 64.71/9.60 | | | | | | | | | | | are inconsistent by sub-proof #158.
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | | (1686) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.60 | | | | | | | | | | | (440), (1585), (1589), (1686), (function-axioms)
% 64.71/9.60 | | | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.60 | | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | End of split
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | End of split
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | End of split
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | (1687) all_26_0 = e1
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (42), (51),
% 64.71/9.60 | | | | | | | | (60), (152), (153), (154), (155), (210), (273),
% 64.71/9.60 | | | | | | | | (315), (317), (328), (383), (431), (438), (439),
% 64.71/9.60 | | | | | | | | (440), (447), (469), (477), (597), (624), (634),
% 64.71/9.60 | | | | | | | | (1585), (1588), (1671), (1687), (function-axioms) are
% 64.71/9.60 | | | | | | | | inconsistent by sub-proof #21.
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | End of split
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | End of split
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | Case 2:
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | (1688) all_14_0 = e0
% 64.71/9.60 | | | | | | (1689) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | REDUCE: (62), (1688) imply:
% 64.71/9.60 | | | | | | (1690) op(all_14_2, all_14_2) = e0
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | BETA: splitting (91) gives:
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | Case 1:
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | (1691) ~ (all_26_0 = e1)
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (51),
% 64.71/9.60 | | | | | | | (152), (153), (154), (155), (383), (438), (439), (440),
% 64.71/9.60 | | | | | | | (597), (1585), (1689), (1690), (1691),
% 64.71/9.60 | | | | | | | (function-axioms) are inconsistent by sub-proof #19.
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | Case 2:
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | (1692) all_26_0 = e1
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | COMBINE_EQS: (597), (1692) imply:
% 64.71/9.60 | | | | | | | (1693) all_4_0 = e1
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | SIMP: (1693) implies:
% 64.71/9.60 | | | | | | | (1694) all_4_0 = e1
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | REDUCE: (634), (1694) imply:
% 64.71/9.60 | | | | | | | (1695) ~ (e2 = e1)
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | REDUCE: (38), (1694) imply:
% 64.71/9.60 | | | | | | | (1696) op(all_4_2, all_4_2) = e1
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | BETA: splitting (152) gives:
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | (1697) all_52_1 = e2 & ~ (all_52_0 = e1)
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | ALPHA: (1697) implies:
% 64.71/9.60 | | | | | | | | (1698) all_52_1 = e2
% 64.71/9.60 | | | | | | | | (1699) ~ (all_52_0 = e1)
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | COMBINE_EQS: (439), (1698) imply:
% 64.71/9.60 | | | | | | | | (1700) all_14_2 = e2
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (60), (154), (155), (438),
% 64.71/9.60 | | | | | | | | (440), (1689), (1690), (1696), (1698), (1699),
% 64.71/9.60 | | | | | | | | (1700), (function-axioms) are inconsistent by
% 64.71/9.60 | | | | | | | | sub-proof #73.
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | (1701) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 64.71/9.60 | | | | | | | | & ~ (all_52_0 = e0))
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | BETA: splitting (1701) gives:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | (1702) all_52_2 = e2 & ~ (all_52_0 = e3)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 64.71/9.60 | | | | | | | | | (383), (438), (440), (1585), (1696), (1702),
% 64.71/9.60 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 64.71/9.60 | | | | | | | | | #34.
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | (1703) all_52_3 = e2 & ~ (all_52_0 = e0)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 64.71/9.60 | | | | | | | | | (440), (1585), (1589), (1703), (function-axioms)
% 64.71/9.60 | | | | | | | | | are inconsistent by sub-proof #37.
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | End of split
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | End of split
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | End of split
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | End of split
% 64.71/9.60 | | | | |
% 64.71/9.60 | | | | Case 2:
% 64.71/9.60 | | | | |
% 64.71/9.60 | | | | | (1704) all_10_0 = e1
% 64.71/9.60 | | | | | (1705) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 64.71/9.60 | | | | |
% 64.71/9.60 | | | | | COMBINE_EQS: (628), (1704) imply:
% 64.71/9.60 | | | | | (1706) all_30_0 = e1
% 64.71/9.60 | | | | |
% 64.71/9.60 | | | | | BETA: splitting (63) gives:
% 64.71/9.60 | | | | |
% 64.71/9.60 | | | | | Case 1:
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | (1707) ~ (all_14_0 = e0)
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | BETA: splitting (77) gives:
% 64.71/9.60 | | | | | |
% 64.71/9.60 | | | | | | Case 1:
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | (1708) ~ (all_20_0 = e2)
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | REDUCE: (615), (1708) imply:
% 64.71/9.60 | | | | | | | (1709) ~ (all_14_0 = e2)
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | BETA: splitting (82) gives:
% 64.71/9.60 | | | | | | |
% 64.71/9.60 | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | (1710) ~ (all_22_0 = e3)
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | REDUCE: (559), (1710) imply:
% 64.71/9.60 | | | | | | | | (1711) ~ (all_14_0 = e3)
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | BETA: splitting (91) gives:
% 64.71/9.60 | | | | | | | |
% 64.71/9.60 | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | (1712) ~ (all_26_0 = e1)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | REDUCE: (597), (1712) imply:
% 64.71/9.60 | | | | | | | | | (1713) ~ (all_4_0 = e1)
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | BETA: splitting (101) gives:
% 64.71/9.60 | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 1:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1714) ~ (all_30_0 = e1)
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | REDUCE: (1706), (1714) imply:
% 64.71/9.60 | | | | | | | | | | (1715) $false
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | CLOSE: (1715) is inconsistent.
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | Case 2:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | (1716) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | BETA: splitting (110) gives:
% 64.71/9.60 | | | | | | | | | |
% 64.71/9.60 | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | (1717) ~ (all_34_0 = e0)
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | REDUCE: (585), (1717) imply:
% 65.12/9.60 | | | | | | | | | | | (1718) ~ (all_4_0 = e0)
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | (1719) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 65.12/9.60 | | | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 65.12/9.60 | | | | | | | | | | | | (440), (444), (1585), (1711), (1719),
% 65.12/9.60 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.60 | | | | | | | | | | | | #38.
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | Case 2:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | (1720) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.60 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | BETA: splitting (1720) gives:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | (1721) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (38), (51), (153), (154), (438), (439),
% 65.12/9.60 | | | | | | | | | | | | | (440), (1713), (1718), (1721), (function-axioms)
% 65.12/9.60 | | | | | | | | | | | | | are inconsistent by sub-proof #173.
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | Case 2:
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | (1722) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | ALPHA: (1722) implies:
% 65.12/9.60 | | | | | | | | | | | | | (1723) all_52_3 = e2
% 65.12/9.60 | | | | | | | | | | | | | (1724) ~ (all_52_0 = e0)
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | COMBINE_EQS: (383), (1723) imply:
% 65.12/9.60 | | | | | | | | | | | | | (1725) all_6_2 = e2
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | SIMP: (1725) implies:
% 65.12/9.60 | | | | | | | | | | | | | (1726) all_6_2 = e2
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (38), (51), (60), (153), (154),
% 65.12/9.60 | | | | | | | | | | | | | (438), (439), (440), (1585), (1718), (1723),
% 65.12/9.60 | | | | | | | | | | | | | (1724), (1726), (function-axioms) are inconsistent
% 65.12/9.60 | | | | | | | | | | | | | by sub-proof #28.
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | End of split
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | End of split
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | Case 2:
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | (1727) all_34_0 = e0
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | COMBINE_EQS: (585), (1727) imply:
% 65.12/9.60 | | | | | | | | | | | (1728) all_4_0 = e0
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | SIMP: (1728) implies:
% 65.12/9.60 | | | | | | | | | | | (1729) all_4_0 = e0
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | COMBINE_EQS: (633), (1729) imply:
% 65.12/9.60 | | | | | | | | | | | (1730) all_50_0 = e0
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | REDUCE: (634), (1729) imply:
% 65.12/9.60 | | | | | | | | | | | (1731) ~ (e2 = e0)
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | REDUCE: (1713), (1729) imply:
% 65.12/9.60 | | | | | | | | | | | (1732) ~ (e1 = e0)
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | REDUCE: (38), (1729) imply:
% 65.12/9.60 | | | | | | | | | | | (1733) op(all_4_2, all_4_2) = e0
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | BETA: splitting (146) gives:
% 65.12/9.60 | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | (1734) ~ (all_50_0 = e0)
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | REDUCE: (1730), (1734) imply:
% 65.12/9.60 | | | | | | | | | | | | (1735) $false
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | CLOSE: (1735) is inconsistent.
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | Case 2:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | (1736) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.60 | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | (1737) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 65.12/9.60 | | | | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 65.12/9.60 | | | | | | | | | | | | | (440), (444), (1585), (1711), (1737),
% 65.12/9.60 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.60 | | | | | | | | | | | | | #41.
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | Case 2:
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | (1738) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.60 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | BETA: splitting (1738) gives:
% 65.12/9.60 | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | Case 1:
% 65.12/9.60 | | | | | | | | | | | | | |
% 65.12/9.60 | | | | | | | | | | | | | | (1739) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.60 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 65.12/9.61 | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 65.12/9.61 | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 65.12/9.61 | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 65.12/9.61 | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 65.12/9.61 | | | | | | | | | | | | | | (1716), (1733), (1736), (1739), (function-axioms)
% 65.12/9.61 | | | | | | | | | | | | | | are inconsistent by sub-proof #63.
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | (1740) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (52), (153), (154),
% 65.12/9.61 | | | | | | | | | | | | | | (158), (160), (168), (180), (181), (182), (192),
% 65.12/9.61 | | | | | | | | | | | | | | (210), (216), (235), (237), (241), (243), (244),
% 65.12/9.61 | | | | | | | | | | | | | | (247), (267), (273), (276), (282), (292), (294),
% 65.12/9.61 | | | | | | | | | | | | | | (300), (315), (317), (328), (330), (332), (334),
% 65.12/9.61 | | | | | | | | | | | | | | (346), (351), (355), (359), (361), (363), (383),
% 65.12/9.61 | | | | | | | | | | | | | | (431), (438), (439), (440), (447), (448), (450),
% 65.12/9.61 | | | | | | | | | | | | | | (456), (458), (460), (461), (467), (473), (474),
% 65.12/9.61 | | | | | | | | | | | | | | (477), (480), (483), (624), (1585), (1588),
% 65.12/9.61 | | | | | | | | | | | | | | (1705), (1740), (function-axioms) are inconsistent
% 65.12/9.61 | | | | | | | | | | | | | | by sub-proof #15.
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | (1741) all_26_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | COMBINE_EQS: (597), (1741) imply:
% 65.12/9.61 | | | | | | | | | (1742) all_4_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | SIMP: (1742) implies:
% 65.12/9.61 | | | | | | | | | (1743) all_4_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | REDUCE: (634), (1743) imply:
% 65.12/9.61 | | | | | | | | | (1744) ~ (e2 = e1)
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | REDUCE: (38), (1743) imply:
% 65.12/9.61 | | | | | | | | | (1745) op(all_4_2, all_4_2) = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | (1746) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 65.12/9.61 | | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 65.12/9.61 | | | | | | | | | | (440), (444), (1585), (1711), (1746),
% 65.12/9.61 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.61 | | | | | | | | | | #41.
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | (1747) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.61 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | BETA: splitting (1747) gives:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | (1748) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 65.12/9.61 | | | | | | | | | | | (383), (438), (440), (1585), (1745), (1748),
% 65.12/9.61 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.61 | | | | | | | | | | | #34.
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | (1749) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (60), (153), (154),
% 65.12/9.61 | | | | | | | | | | | (210), (273), (315), (317), (328), (383), (431),
% 65.12/9.61 | | | | | | | | | | | (438), (439), (440), (447), (469), (477), (624),
% 65.12/9.61 | | | | | | | | | | | (1585), (1588), (1745), (1749), (function-axioms)
% 65.12/9.61 | | | | | | | | | | | are inconsistent by sub-proof #22.
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | End of split
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | (1750) all_22_0 = e3
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | COMBINE_EQS: (559), (1750) imply:
% 65.12/9.61 | | | | | | | | (1751) all_14_0 = e3
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | SIMP: (1751) implies:
% 65.12/9.61 | | | | | | | | (1752) all_14_0 = e3
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | COMBINE_EQS: (632), (1752) imply:
% 65.12/9.61 | | | | | | | | (1753) all_44_0 = e3
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | REDUCE: (62), (1752) imply:
% 65.12/9.61 | | | | | | | | (1754) op(all_14_2, all_14_2) = e3
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | BETA: splitting (91) gives:
% 65.12/9.61 | | | | | | | |
% 65.12/9.61 | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | (1755) ~ (all_26_0 = e1)
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | REDUCE: (597), (1755) imply:
% 65.12/9.61 | | | | | | | | | (1756) ~ (all_4_0 = e1)
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | BETA: splitting (101) gives:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | (1757) ~ (all_30_0 = e1)
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | REDUCE: (1706), (1757) imply:
% 65.12/9.61 | | | | | | | | | | (1758) $false
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | CLOSE: (1758) is inconsistent.
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | (1759) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | BETA: splitting (110) gives:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | (1760) ~ (all_34_0 = e0)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REDUCE: (585), (1760) imply:
% 65.12/9.61 | | | | | | | | | | | (1761) ~ (all_4_0 = e0)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | BETA: splitting (133) gives:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | (1762) ~ (all_44_0 = e3)
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | REDUCE: (1753), (1762) imply:
% 65.12/9.61 | | | | | | | | | | | | (1763) $false
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | CLOSE: (1763) is inconsistent.
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | (1764) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | (1765) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | ALPHA: (1765) implies:
% 65.12/9.61 | | | | | | | | | | | | | (1766) all_52_1 = e2
% 65.12/9.61 | | | | | | | | | | | | | (1767) ~ (all_52_0 = e1)
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | COMBINE_EQS: (439), (1766) imply:
% 65.12/9.61 | | | | | | | | | | | | | (1768) all_14_2 = e2
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | COMBINE_EQS: (437), (1768) imply:
% 65.12/9.61 | | | | | | | | | | | | | (1769) all_44_2 = e2
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 65.12/9.61 | | | | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 65.12/9.61 | | | | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 65.12/9.61 | | | | | | | | | | | | | (383), (438), (440), (447), (456), (458), (460),
% 65.12/9.61 | | | | | | | | | | | | | (463), (477), (631), (1585), (1754), (1764),
% 65.12/9.61 | | | | | | | | | | | | | (1766), (1767), (1768), (1769), (function-axioms)
% 65.12/9.61 | | | | | | | | | | | | | are inconsistent by sub-proof #32.
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | (1770) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.61 | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (38), (51), (60), (153),
% 65.12/9.61 | | | | | | | | | | | | | (154), (383), (438), (439), (440), (1585), (1756),
% 65.12/9.61 | | | | | | | | | | | | | (1761), (1770), (function-axioms) are inconsistent
% 65.12/9.61 | | | | | | | | | | | | | by sub-proof #27.
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | (1771) all_34_0 = e0
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | COMBINE_EQS: (585), (1771) imply:
% 65.12/9.61 | | | | | | | | | | | (1772) all_4_0 = e0
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | SIMP: (1772) implies:
% 65.12/9.61 | | | | | | | | | | | (1773) all_4_0 = e0
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | COMBINE_EQS: (633), (1773) imply:
% 65.12/9.61 | | | | | | | | | | | (1774) all_50_0 = e0
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REDUCE: (634), (1773) imply:
% 65.12/9.61 | | | | | | | | | | | (1775) ~ (e2 = e0)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REDUCE: (1756), (1773) imply:
% 65.12/9.61 | | | | | | | | | | | (1776) ~ (e1 = e0)
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | REDUCE: (38), (1773) imply:
% 65.12/9.61 | | | | | | | | | | | (1777) op(all_4_2, all_4_2) = e0
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | BETA: splitting (133) gives:
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | (1778) ~ (all_44_0 = e3)
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | REDUCE: (1753), (1778) imply:
% 65.12/9.61 | | | | | | | | | | | | (1779) $false
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | CLOSE: (1779) is inconsistent.
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | (1780) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | BETA: splitting (146) gives:
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | (1781) ~ (all_50_0 = e0)
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | REDUCE: (1774), (1781) imply:
% 65.12/9.61 | | | | | | | | | | | | | (1782) $false
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | CLOSE: (1782) is inconsistent.
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | (1783) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | (1784) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 65.12/9.61 | | | | | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 65.12/9.61 | | | | | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 65.12/9.61 | | | | | | | | | | | | | | (383), (437), (438), (439), (440), (447), (456),
% 65.12/9.61 | | | | | | | | | | | | | | (458), (460), (463), (477), (631), (1585), (1754),
% 65.12/9.61 | | | | | | | | | | | | | | (1780), (1784), (function-axioms) are inconsistent
% 65.12/9.61 | | | | | | | | | | | | | | by sub-proof #31.
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | (1785) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.61 | | | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | BETA: splitting (1785) gives:
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | (1786) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (37), (51), (52), (154), (155), (188),
% 65.12/9.61 | | | | | | | | | | | | | | | (190), (194), (195), (204), (213), (238), (245),
% 65.12/9.61 | | | | | | | | | | | | | | | (246), (247), (336), (351), (360), (367), (371),
% 65.12/9.61 | | | | | | | | | | | | | | | (383), (433), (438), (439), (440), (450), (452),
% 65.12/9.61 | | | | | | | | | | | | | | | (454), (461), (462), (476), (477), (527), (627),
% 65.12/9.61 | | | | | | | | | | | | | | | (1759), (1777), (1783), (1786), (function-axioms)
% 65.12/9.61 | | | | | | | | | | | | | | | are inconsistent by sub-proof #62.
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | (1787) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | ALPHA: (1787) implies:
% 65.12/9.61 | | | | | | | | | | | | | | | (1788) all_52_3 = e2
% 65.12/9.61 | | | | | | | | | | | | | | | (1789) ~ (all_52_0 = e0)
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | COMBINE_EQS: (383), (1788) imply:
% 65.12/9.61 | | | | | | | | | | | | | | | (1790) all_6_2 = e2
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | SIMP: (1790) implies:
% 65.12/9.61 | | | | | | | | | | | | | | | (1791) all_6_2 = e2
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | COMBINE_EQS: (431), (1791) imply:
% 65.12/9.61 | | | | | | | | | | | | | | | (1792) all_8_2 = e2
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (52), (153), (154),
% 65.12/9.61 | | | | | | | | | | | | | | | (158), (160), (168), (180), (181), (182), (192),
% 65.12/9.61 | | | | | | | | | | | | | | | (210), (216), (235), (237), (241), (243), (244),
% 65.12/9.61 | | | | | | | | | | | | | | | (247), (267), (273), (276), (282), (292), (294),
% 65.12/9.61 | | | | | | | | | | | | | | | (300), (315), (317), (328), (330), (332), (334),
% 65.12/9.61 | | | | | | | | | | | | | | | (346), (351), (355), (359), (361), (363), (438),
% 65.12/9.61 | | | | | | | | | | | | | | | (439), (440), (447), (448), (450), (456), (458),
% 65.12/9.61 | | | | | | | | | | | | | | | (460), (461), (467), (473), (474), (477), (480),
% 65.12/9.61 | | | | | | | | | | | | | | | (483), (624), (1585), (1588), (1705), (1788),
% 65.12/9.61 | | | | | | | | | | | | | | | (1789), (1791), (1792), (function-axioms) are
% 65.12/9.61 | | | | | | | | | | | | | | | inconsistent by sub-proof #16.
% 65.12/9.61 | | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | End of split
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | Case 2:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | (1793) all_26_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | COMBINE_EQS: (597), (1793) imply:
% 65.12/9.61 | | | | | | | | | (1794) all_4_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | SIMP: (1794) implies:
% 65.12/9.61 | | | | | | | | | (1795) all_4_0 = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | REDUCE: (634), (1795) imply:
% 65.12/9.61 | | | | | | | | | (1796) ~ (e2 = e1)
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | REDUCE: (38), (1795) imply:
% 65.12/9.61 | | | | | | | | | (1797) op(all_4_2, all_4_2) = e1
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | BETA: splitting (133) gives:
% 65.12/9.61 | | | | | | | | |
% 65.12/9.61 | | | | | | | | | Case 1:
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | (1798) ~ (all_44_0 = e3)
% 65.12/9.61 | | | | | | | | | |
% 65.12/9.61 | | | | | | | | | | REDUCE: (1753), (1798) imply:
% 65.12/9.62 | | | | | | | | | | (1799) $false
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | CLOSE: (1799) is inconsistent.
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | (1800) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1801) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 65.12/9.62 | | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 65.12/9.62 | | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 65.12/9.62 | | | | | | | | | | | (383), (437), (438), (439), (440), (447), (456),
% 65.12/9.62 | | | | | | | | | | | (458), (460), (463), (477), (631), (1585), (1754),
% 65.12/9.62 | | | | | | | | | | | (1800), (1801), (function-axioms) are inconsistent
% 65.12/9.62 | | | | | | | | | | | by sub-proof #31.
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1802) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.62 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | BETA: splitting (1802) gives:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | (1803) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 65.12/9.62 | | | | | | | | | | | | (383), (438), (440), (1585), (1797), (1803),
% 65.12/9.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.62 | | | | | | | | | | | | #25.
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | (1804) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | ALPHA: (1804) implies:
% 65.12/9.62 | | | | | | | | | | | | (1805) all_52_3 = e2
% 65.12/9.62 | | | | | | | | | | | | (1806) ~ (all_52_0 = e0)
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | COMBINE_EQS: (383), (1805) imply:
% 65.12/9.62 | | | | | | | | | | | | (1807) all_6_2 = e2
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | SIMP: (1807) implies:
% 65.12/9.62 | | | | | | | | | | | | (1808) all_6_2 = e2
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | COMBINE_EQS: (431), (1808) imply:
% 65.12/9.62 | | | | | | | | | | | | (1809) all_8_2 = e2
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (60), (153), (154),
% 65.12/9.62 | | | | | | | | | | | | (210), (273), (315), (317), (328), (438), (439),
% 65.12/9.62 | | | | | | | | | | | | (440), (447), (469), (477), (624), (1585), (1588),
% 65.12/9.62 | | | | | | | | | | | | (1797), (1805), (1806), (1808), (1809),
% 65.12/9.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.62 | | | | | | | | | | | | #23.
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | End of split
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | End of split
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | Case 2:
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | (1810) all_20_0 = e2
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | COMBINE_EQS: (615), (1810) imply:
% 65.12/9.62 | | | | | | | (1811) all_14_0 = e2
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | SIMP: (1811) implies:
% 65.12/9.62 | | | | | | | (1812) all_14_0 = e2
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | REDUCE: (62), (1812) imply:
% 65.12/9.62 | | | | | | | (1813) op(all_14_2, all_14_2) = e2
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | BETA: splitting (91) gives:
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | (1814) ~ (all_26_0 = e1)
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | REDUCE: (597), (1814) imply:
% 65.12/9.62 | | | | | | | | (1815) ~ (all_4_0 = e1)
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | BETA: splitting (101) gives:
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | (1816) ~ (all_30_0 = e1)
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | REDUCE: (1706), (1816) imply:
% 65.12/9.62 | | | | | | | | | (1817) $false
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | CLOSE: (1817) is inconsistent.
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | (1818) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | BETA: splitting (110) gives:
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | (1819) ~ (all_34_0 = e0)
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | REDUCE: (585), (1819) imply:
% 65.12/9.62 | | | | | | | | | | (1820) ~ (all_4_0 = e0)
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1821) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (51), (153), (154),
% 65.12/9.62 | | | | | | | | | | | (155), (383), (438), (439), (440), (1585), (1813),
% 65.12/9.62 | | | | | | | | | | | (1821), (function-axioms) are inconsistent by
% 65.12/9.62 | | | | | | | | | | | sub-proof #29.
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1822) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.62 | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (38), (51), (60), (153),
% 65.12/9.62 | | | | | | | | | | | (154), (383), (438), (439), (440), (1585), (1815),
% 65.12/9.62 | | | | | | | | | | | (1820), (1822), (function-axioms) are inconsistent
% 65.12/9.62 | | | | | | | | | | | by sub-proof #27.
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | (1823) all_34_0 = e0
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | COMBINE_EQS: (585), (1823) imply:
% 65.12/9.62 | | | | | | | | | | (1824) all_4_0 = e0
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | COMBINE_EQS: (633), (1824) imply:
% 65.12/9.62 | | | | | | | | | | (1825) all_50_0 = e0
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | REDUCE: (1815), (1824) imply:
% 65.12/9.62 | | | | | | | | | | (1826) ~ (e1 = e0)
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | REDUCE: (38), (1824) imply:
% 65.12/9.62 | | | | | | | | | | (1827) op(all_4_2, all_4_2) = e0
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | BETA: splitting (146) gives:
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1828) ~ (all_50_0 = e0)
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | REDUCE: (1825), (1828) imply:
% 65.12/9.62 | | | | | | | | | | | (1829) $false
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | CLOSE: (1829) is inconsistent.
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | (1830) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | (1831) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (51), (153), (154),
% 65.12/9.62 | | | | | | | | | | | | (155), (383), (438), (439), (440), (1585), (1813),
% 65.12/9.62 | | | | | | | | | | | | (1831), (function-axioms) are inconsistent by
% 65.12/9.62 | | | | | | | | | | | | sub-proof #29.
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | (1832) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.62 | | | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | BETA: splitting (1832) gives:
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | (1833) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | ALPHA: (1833) implies:
% 65.12/9.62 | | | | | | | | | | | | | (1834) all_52_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | COMBINE_EQS: (438), (1834) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1835) all_4_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | SIMP: (1835) implies:
% 65.12/9.62 | | | | | | | | | | | | | (1836) all_4_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | COMBINE_EQS: (336), (1836) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1837) all_50_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (462), (1836) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1838) ~ (all_54_2 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (477), (1836) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1839) ~ (all_54_10 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (1827), (1836) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1840) op(e2, e2) = e0
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (37), (1836) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1841) op(e2, e3) = all_4_1
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (51), (52), (154), (155), (188), (190),
% 65.12/9.62 | | | | | | | | | | | | | (194), (195), (204), (213), (238), (245), (246),
% 65.12/9.62 | | | | | | | | | | | | | (247), (351), (360), (367), (371), (383), (433),
% 65.12/9.62 | | | | | | | | | | | | | (439), (440), (450), (452), (454), (461), (476),
% 65.12/9.62 | | | | | | | | | | | | | (527), (627), (1818), (1830), (1834), (1837),
% 65.12/9.62 | | | | | | | | | | | | | (1838), (1839), (1840), (1841), (function-axioms)
% 65.12/9.62 | | | | | | | | | | | | | are inconsistent by sub-proof #65.
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | (1842) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | ALPHA: (1842) implies:
% 65.12/9.62 | | | | | | | | | | | | | (1843) all_52_3 = e2
% 65.12/9.62 | | | | | | | | | | | | | (1844) ~ (all_52_0 = e0)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | COMBINE_EQS: (383), (1843) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1845) all_6_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | SIMP: (1845) implies:
% 65.12/9.62 | | | | | | | | | | | | | (1846) all_6_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | COMBINE_EQS: (431), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1847) all_8_2 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | COMBINE_EQS: (292), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1848) all_58_0 = e2
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (450), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1849) ~ (all_54_1 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (456), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1850) ~ (all_54_4 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (458), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1851) ~ (all_54_8 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (460), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1852) ~ (all_54_12 = e2)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (440), (1844) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1853) ~ (all_10_2 = e0)
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (1585), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1854) op(e2, e2) = e3
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REDUCE: (42), (1846) imply:
% 65.12/9.62 | | | | | | | | | | | | | (1855) op(e2, e0) = all_6_1
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (51), (52), (153), (154), (158),
% 65.12/9.62 | | | | | | | | | | | | | (160), (168), (180), (181), (182), (192), (210),
% 65.12/9.62 | | | | | | | | | | | | | (216), (235), (237), (241), (243), (244), (247),
% 65.12/9.62 | | | | | | | | | | | | | (267), (273), (276), (282), (294), (300), (315),
% 65.12/9.62 | | | | | | | | | | | | | (317), (328), (330), (332), (334), (346), (351),
% 65.12/9.62 | | | | | | | | | | | | | (355), (359), (361), (363), (438), (439), (440),
% 65.12/9.62 | | | | | | | | | | | | | (447), (448), (461), (467), (473), (474), (477),
% 65.12/9.62 | | | | | | | | | | | | | (480), (483), (624), (1588), (1705), (1843),
% 65.12/9.62 | | | | | | | | | | | | | (1847), (1848), (1849), (1850), (1851), (1852),
% 65.12/9.62 | | | | | | | | | | | | | (1853), (1854), (1855), (function-axioms) are
% 65.12/9.62 | | | | | | | | | | | | | inconsistent by sub-proof #17.
% 65.12/9.62 | | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | | |
% 65.12/9.62 | | | | | | | | | End of split
% 65.12/9.62 | | | | | | | | |
% 65.12/9.62 | | | | | | | | End of split
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | (1856) all_26_0 = e1
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (38), (42), (51),
% 65.12/9.62 | | | | | | | | (60), (152), (153), (154), (155), (210), (273),
% 65.12/9.62 | | | | | | | | (315), (317), (328), (383), (431), (438), (439),
% 65.12/9.62 | | | | | | | | (440), (447), (469), (477), (597), (624), (634),
% 65.12/9.62 | | | | | | | | (1585), (1588), (1813), (1856), (function-axioms) are
% 65.12/9.62 | | | | | | | | inconsistent by sub-proof #21.
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | End of split
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | End of split
% 65.12/9.62 | | | | | |
% 65.12/9.62 | | | | | Case 2:
% 65.12/9.62 | | | | | |
% 65.12/9.62 | | | | | | (1857) all_14_0 = e0
% 65.12/9.62 | | | | | | (1858) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.12/9.62 | | | | | |
% 65.12/9.62 | | | | | | REDUCE: (62), (1857) imply:
% 65.12/9.62 | | | | | | (1859) op(all_14_2, all_14_2) = e0
% 65.12/9.62 | | | | | |
% 65.12/9.62 | | | | | | BETA: splitting (91) gives:
% 65.12/9.62 | | | | | |
% 65.12/9.62 | | | | | | Case 1:
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | (1860) ~ (all_26_0 = e1)
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (38), (41), (51),
% 65.12/9.62 | | | | | | | (152), (153), (154), (155), (383), (438), (439), (440),
% 65.12/9.62 | | | | | | | (597), (1585), (1858), (1859), (1860),
% 65.12/9.62 | | | | | | | (function-axioms) are inconsistent by sub-proof #19.
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | Case 2:
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | (1861) all_26_0 = e1
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | COMBINE_EQS: (597), (1861) imply:
% 65.12/9.62 | | | | | | | (1862) all_4_0 = e1
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | SIMP: (1862) implies:
% 65.12/9.62 | | | | | | | (1863) all_4_0 = e1
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | REDUCE: (634), (1863) imply:
% 65.12/9.62 | | | | | | | (1864) ~ (e2 = e1)
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | REDUCE: (38), (1863) imply:
% 65.12/9.62 | | | | | | | (1865) op(all_4_2, all_4_2) = e1
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.62 | | | | | | |
% 65.12/9.62 | | | | | | | Case 1:
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | (1866) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | ALPHA: (1866) implies:
% 65.12/9.62 | | | | | | | | (1867) all_52_1 = e2
% 65.12/9.62 | | | | | | | | (1868) ~ (all_52_0 = e1)
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | COMBINE_EQS: (439), (1867) imply:
% 65.12/9.62 | | | | | | | | (1869) all_14_2 = e2
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | | REF_CLOSE: (7), (8), (9), (36), (51), (154), (155), (383),
% 65.12/9.62 | | | | | | | | (438), (440), (1585), (1858), (1859), (1867), (1868),
% 65.12/9.62 | | | | | | | | (1869), (function-axioms) are inconsistent by
% 65.12/9.62 | | | | | | | | sub-proof #14.
% 65.12/9.62 | | | | | | | |
% 65.12/9.62 | | | | | | | Case 2:
% 65.12/9.62 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1870) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.63 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | BETA: splitting (1870) gives:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1871) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (153), (155),
% 65.12/9.63 | | | | | | | | | (383), (438), (440), (1585), (1865), (1871),
% 65.12/9.63 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.63 | | | | | | | | | #25.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1872) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (60), (153), (154),
% 65.12/9.63 | | | | | | | | | (210), (273), (315), (317), (328), (383), (431),
% 65.12/9.63 | | | | | | | | | (438), (439), (440), (447), (469), (477), (624),
% 65.12/9.63 | | | | | | | | | (1585), (1588), (1865), (1872), (function-axioms)
% 65.12/9.63 | | | | | | | | | are inconsistent by sub-proof #22.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | End of split
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | End of split
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | End of split
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | End of split
% 65.12/9.63 | | | | |
% 65.12/9.63 | | | | End of split
% 65.12/9.63 | | | |
% 65.12/9.63 | | | End of split
% 65.12/9.63 | | |
% 65.12/9.63 | | End of split
% 65.12/9.63 | |
% 65.12/9.63 | Case 2:
% 65.12/9.63 | |
% 65.12/9.63 | | (1873) all_4_0 = e2
% 65.12/9.63 | | (1874) ~ (all_4_1 = e1) | ~ (all_4_2 = e0)
% 65.12/9.63 | |
% 65.12/9.63 | | COMBINE_EQS: (530), (1873) imply:
% 65.12/9.63 | | (1875) all_42_0 = e2
% 65.12/9.63 | |
% 65.12/9.63 | | REDUCE: (38), (1873) imply:
% 65.12/9.63 | | (1876) op(all_4_2, all_4_2) = e2
% 65.12/9.63 | |
% 65.12/9.63 | | BETA: splitting (44) gives:
% 65.12/9.63 | |
% 65.12/9.63 | | Case 1:
% 65.12/9.63 | | |
% 65.12/9.63 | | | (1877) ~ (all_6_0 = e3)
% 65.12/9.63 | | |
% 65.12/9.63 | | | BETA: splitting (63) gives:
% 65.12/9.63 | | |
% 65.12/9.63 | | | Case 1:
% 65.12/9.63 | | | |
% 65.12/9.63 | | | | (1878) ~ (all_14_0 = e0)
% 65.12/9.63 | | | |
% 65.12/9.63 | | | | BETA: splitting (68) gives:
% 65.12/9.63 | | | |
% 65.12/9.63 | | | | Case 1:
% 65.12/9.63 | | | | |
% 65.12/9.63 | | | | | (1879) ~ (all_16_0 = e1)
% 65.12/9.63 | | | | |
% 65.12/9.63 | | | | | REDUCE: (539), (1879) imply:
% 65.12/9.63 | | | | | (1880) ~ (all_6_0 = e1)
% 65.12/9.63 | | | | |
% 65.12/9.63 | | | | | BETA: splitting (82) gives:
% 65.12/9.63 | | | | |
% 65.12/9.63 | | | | | Case 1:
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | (1881) ~ (all_22_0 = e3)
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | REDUCE: (559), (1881) imply:
% 65.12/9.63 | | | | | | (1882) ~ (all_14_0 = e3)
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | BETA: splitting (96) gives:
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | Case 1:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | (1883) ~ (all_28_0 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (626), (1883) imply:
% 65.12/9.63 | | | | | | | (1884) ~ (all_6_0 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1885) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 65.12/9.63 | | | | | | | | (438), (439), (440), (1878), (1882), (1885),
% 65.12/9.63 | | | | | | | | (function-axioms) are inconsistent by sub-proof #159.
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1886) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.63 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | BETA: splitting (1886) gives:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1887) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.63 | | | | | | | | | (1876), (1887), (function-axioms) are inconsistent
% 65.12/9.63 | | | | | | | | | by sub-proof #12.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1888) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (43), (51), (239), (383), (440), (444), (1877),
% 65.12/9.63 | | | | | | | | | (1880), (1884), (1888), (function-axioms) are
% 65.12/9.63 | | | | | | | | | inconsistent by sub-proof #11.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | End of split
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | End of split
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | Case 2:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | (1889) all_28_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | COMBINE_EQS: (626), (1889) imply:
% 65.12/9.63 | | | | | | | (1890) all_6_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | SIMP: (1890) implies:
% 65.12/9.63 | | | | | | | (1891) all_6_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (1877), (1891) imply:
% 65.12/9.63 | | | | | | | (1892) ~ (e3 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (43), (1891) imply:
% 65.12/9.63 | | | | | | | (1893) op(all_6_2, all_6_2) = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1894) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 65.12/9.63 | | | | | | | | (438), (439), (440), (1878), (1882), (1894),
% 65.12/9.63 | | | | | | | | (function-axioms) are inconsistent by sub-proof #165.
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1895) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.63 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | BETA: splitting (1895) gives:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1896) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.63 | | | | | | | | | (1876), (1896), (function-axioms) are inconsistent
% 65.12/9.63 | | | | | | | | | by sub-proof #10.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1897) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 65.12/9.63 | | | | | | | | | (439), (440), (1893), (1897), (function-axioms) are
% 65.12/9.63 | | | | | | | | | inconsistent by sub-proof #110.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | End of split
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | End of split
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | End of split
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | Case 2:
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | (1898) all_22_0 = e3
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | COMBINE_EQS: (559), (1898) imply:
% 65.12/9.63 | | | | | | (1899) all_14_0 = e3
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | SIMP: (1899) implies:
% 65.12/9.63 | | | | | | (1900) all_14_0 = e3
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | COMBINE_EQS: (632), (1900) imply:
% 65.12/9.63 | | | | | | (1901) all_44_0 = e3
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | REDUCE: (62), (1900) imply:
% 65.12/9.63 | | | | | | (1902) op(all_14_2, all_14_2) = e3
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | BETA: splitting (96) gives:
% 65.12/9.63 | | | | | |
% 65.12/9.63 | | | | | | Case 1:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | (1903) ~ (all_28_0 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (626), (1903) imply:
% 65.12/9.63 | | | | | | | (1904) ~ (all_6_0 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | BETA: splitting (133) gives:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1905) ~ (all_44_0 = e3)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | REDUCE: (1901), (1905) imply:
% 65.12/9.63 | | | | | | | | (1906) $false
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | CLOSE: (1906) is inconsistent.
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1907) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1908) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | ALPHA: (1908) implies:
% 65.12/9.63 | | | | | | | | | (1909) all_52_1 = e2
% 65.12/9.63 | | | | | | | | | (1910) ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | COMBINE_EQS: (439), (1909) imply:
% 65.12/9.63 | | | | | | | | | (1911) all_14_2 = e2
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | SIMP: (1911) implies:
% 65.12/9.63 | | | | | | | | | (1912) all_14_2 = e2
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | COMBINE_EQS: (437), (1912) imply:
% 65.12/9.63 | | | | | | | | | (1913) all_44_2 = e2
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REDUCE: (440), (1910) imply:
% 65.12/9.63 | | | | | | | | | (1914) ~ (all_10_2 = e1)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REDUCE: (1902), (1912) imply:
% 65.12/9.63 | | | | | | | | | (1915) op(e2, e2) = e3
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REDUCE: (60), (1912) imply:
% 65.12/9.63 | | | | | | | | | (1916) op(e1, e1) = e2
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | BETA: splitting (1907) gives:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 65.12/9.63 | | | | | | | | | | e2, e2, simplifying with (51), (1915) gives:
% 65.12/9.63 | | | | | | | | | | (1917) all_10_2 = e3
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | COMBINE_EQS: (440), (1917) imply:
% 65.12/9.63 | | | | | | | | | | (1918) all_52_0 = e3
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (43), (153), (154), (383),
% 65.12/9.63 | | | | | | | | | | (1904), (1909), (1916), (1918), (function-axioms)
% 65.12/9.63 | | | | | | | | | | are inconsistent by sub-proof #9.
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | (1919) ~ (all_44_2 = e2)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (1913), (1919) imply:
% 65.12/9.63 | | | | | | | | | | (1920) $false
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | CLOSE: (1920) is inconsistent.
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | End of split
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1921) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.63 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | BETA: splitting (1921) gives:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | (1922) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.63 | | | | | | | | | | (1876), (1922), (function-axioms) are inconsistent
% 65.12/9.63 | | | | | | | | | | by sub-proof #10.
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | (1923) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | ALPHA: (1923) implies:
% 65.12/9.63 | | | | | | | | | | (1924) all_52_3 = e2
% 65.12/9.63 | | | | | | | | | | (1925) ~ (all_52_0 = e0)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | COMBINE_EQS: (383), (1924) imply:
% 65.12/9.63 | | | | | | | | | | (1926) all_6_2 = e2
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REF_CLOSE: (43), (51), (239), (440), (444), (1877), (1880),
% 65.12/9.63 | | | | | | | | | | (1904), (1925), (1926), (function-axioms) are
% 65.12/9.63 | | | | | | | | | | inconsistent by sub-proof #161.
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | End of split
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | End of split
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | End of split
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | Case 2:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | (1927) all_28_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | COMBINE_EQS: (626), (1927) imply:
% 65.12/9.63 | | | | | | | (1928) all_6_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | COMBINE_EQS: (630), (1928) imply:
% 65.12/9.63 | | | | | | | (1929) all_38_0 = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (1877), (1928) imply:
% 65.12/9.63 | | | | | | | (1930) ~ (e3 = e2)
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | REDUCE: (43), (1928) imply:
% 65.12/9.63 | | | | | | | (1931) op(all_6_2, all_6_2) = e2
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | BETA: splitting (119) gives:
% 65.12/9.63 | | | | | | |
% 65.12/9.63 | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1932) ~ (all_38_0 = e2)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | REDUCE: (1929), (1932) imply:
% 65.12/9.63 | | | | | | | | (1933) $false
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | CLOSE: (1933) is inconsistent.
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | (1934) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | BETA: splitting (133) gives:
% 65.12/9.63 | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1935) ~ (all_44_0 = e3)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | REDUCE: (1901), (1935) imply:
% 65.12/9.63 | | | | | | | | | (1936) $false
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | CLOSE: (1936) is inconsistent.
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | Case 2:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | (1937) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.63 | | | | | | | | |
% 65.12/9.63 | | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | (1938) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | ALPHA: (1938) implies:
% 65.12/9.63 | | | | | | | | | | (1939) all_52_1 = e2
% 65.12/9.63 | | | | | | | | | | (1940) ~ (all_52_0 = e1)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | COMBINE_EQS: (439), (1939) imply:
% 65.12/9.63 | | | | | | | | | | (1941) all_14_2 = e2
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | COMBINE_EQS: (437), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1942) all_44_2 = e2
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (461), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1943) ~ (all_54_1 = e2)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (463), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1944) ~ (all_54_4 = e2)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (469), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1945) ~ (all_54_9 = e2)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (471), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1946) ~ (all_54_13 = e2)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (440), (1940) imply:
% 65.12/9.63 | | | | | | | | | | (1947) ~ (all_10_2 = e1)
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (1902), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1948) op(e2, e2) = e3
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | REDUCE: (61), (1941) imply:
% 65.12/9.63 | | | | | | | | | | (1949) op(e2, e1) = all_14_1
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | BETA: splitting (1937) gives:
% 65.12/9.63 | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | (1950) ~ (all_44_1 = e0)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | REDUCE: (631), (1950) imply:
% 65.12/9.63 | | | | | | | | | | | (1951) ~ (all_14_1 = e0)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_9,
% 65.12/9.63 | | | | | | | | | | | all_14_1, e1, e2, simplifying with (211), (1949)
% 65.12/9.63 | | | | | | | | | | | gives:
% 65.12/9.63 | | | | | | | | | | | (1952) all_54_9 = all_14_1
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 65.12/9.63 | | | | | | | | | | | e2, e2, simplifying with (51), (1948) gives:
% 65.12/9.63 | | | | | | | | | | | (1953) all_10_2 = e3
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | COMBINE_EQS: (440), (1953) imply:
% 65.12/9.63 | | | | | | | | | | | (1954) all_52_0 = e3
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | COMBINE_EQS: (353), (1952) imply:
% 65.12/9.63 | | | | | | | | | | | (1955) all_56_9 = all_14_1
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | COMBINE_EQS: (447), (1953) imply:
% 65.12/9.63 | | | | | | | | | | | (1956) all_58_6 = e3
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | REDUCE: (192), (1952) imply:
% 65.12/9.63 | | | | | | | | | | | (1957) ~ (all_54_1 = all_14_1)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | REDUCE: (165), (1952) imply:
% 65.12/9.63 | | | | | | | | | | | (1958) ~ (all_54_13 = all_14_1)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | SIMP: (1958) implies:
% 65.12/9.63 | | | | | | | | | | | (1959) ~ (all_54_13 = all_14_1)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | REDUCE: (475), (1952), (1953) imply:
% 65.12/9.63 | | | | | | | | | | | (1960) ~ (all_14_1 = e3)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | REDUCE: (1945), (1952) imply:
% 65.12/9.63 | | | | | | | | | | | (1961) ~ (all_14_1 = e2)
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | BETA: splitting (153) gives:
% 65.12/9.63 | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | Case 1:
% 65.12/9.63 | | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | | (1962) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.12/9.63 | | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | | ALPHA: (1962) implies:
% 65.12/9.63 | | | | | | | | | | | | (1963) all_52_0 = e0
% 65.12/9.63 | | | | | | | | | | | |
% 65.12/9.63 | | | | | | | | | | | | REF_CLOSE: (7), (1954), (1963) are inconsistent by sub-proof
% 65.12/9.63 | | | | | | | | | | | | #124.
% 65.12/9.63 | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | (1964) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 =
% 65.12/9.64 | | | | | | | | | | | | e0 & ~ (all_52_3 = e3))
% 65.12/9.64 | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | BETA: splitting (1964) gives:
% 65.12/9.64 | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | (1965) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | REF_CLOSE: (5), (1939), (1965) are inconsistent by sub-proof
% 65.12/9.64 | | | | | | | | | | | | | #179.
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | (1966) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | ALPHA: (1966) implies:
% 65.12/9.64 | | | | | | | | | | | | | (1967) all_52_2 = e0
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | COMBINE_EQS: (438), (1967) imply:
% 65.12/9.64 | | | | | | | | | | | | | (1968) all_4_2 = e0
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | SIMP: (1968) implies:
% 65.12/9.64 | | | | | | | | | | | | | (1969) all_4_2 = e0
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | REDUCE: (481), (1969) imply:
% 65.12/9.64 | | | | | | | | | | | | | (1970) ~ (all_54_13 = e0)
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | REDUCE: (483), (1969) imply:
% 65.12/9.64 | | | | | | | | | | | | | (1971) ~ (all_54_15 = e0)
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | (1972) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | ALPHA: (1972) implies:
% 65.12/9.64 | | | | | | | | | | | | | | (1973) all_52_0 = e1
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | REF_CLOSE: (8), (1954), (1973) are inconsistent by sub-proof
% 65.12/9.64 | | | | | | | | | | | | | | #122.
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | (1974) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 =
% 65.12/9.64 | | | | | | | | | | | | | | e1 & ~ (all_52_1 = e0))
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | BETA: splitting (1974) gives:
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | (1975) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | ALPHA: (1975) implies:
% 65.12/9.64 | | | | | | | | | | | | | | | (1976) all_52_2 = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | REF_CLOSE: (4), (1967), (1976) are inconsistent by sub-proof
% 65.12/9.64 | | | | | | | | | | | | | | | #152.
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | (1977) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | ALPHA: (1977) implies:
% 65.12/9.64 | | | | | | | | | | | | | | | (1978) all_52_3 = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | COMBINE_EQS: (383), (1978) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1979) all_6_2 = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | COMBINE_EQS: (436), (1979) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1980) all_38_2 = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1979) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1981) all_58_0 = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | REDUCE: (456), (1979) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1982) ~ (all_54_4 = e1)
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | REDUCE: (42), (1979) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1983) op(e1, e0) = all_6_1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | REDUCE: (41), (1979) imply:
% 65.12/9.64 | | | | | | | | | | | | | | | (1984) op(e0, e0) = e1
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | | (1985) all_56_9 = e3
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | | REF_CLOSE: (1955), (1960), (1985) are inconsistent by
% 65.12/9.64 | | | | | | | | | | | | | | | | sub-proof #119.
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | | (1986) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (155), (182), (191), (194), (206),
% 65.12/9.64 | | | | | | | | | | | | | | | | (236), (244), (247), (269), (280), (296), (300),
% 65.12/9.64 | | | | | | | | | | | | | | | | (311), (334), (346), (351), (362), (383), (629),
% 65.12/9.64 | | | | | | | | | | | | | | | | (1934), (1939), (1943), (1944), (1946), (1951),
% 65.12/9.64 | | | | | | | | | | | | | | | | (1954), (1955), (1956), (1957), (1959), (1961),
% 65.12/9.64 | | | | | | | | | | | | | | | | (1970), (1971), (1980), (1981), (1982), (1983),
% 65.12/9.64 | | | | | | | | | | | | | | | | (1984), (1986), (function-axioms) are inconsistent
% 65.12/9.64 | | | | | | | | | | | | | | | | by sub-proof #114.
% 65.12/9.64 | | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | (1987) ~ (all_44_2 = e2)
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | REDUCE: (1942), (1987) imply:
% 65.12/9.64 | | | | | | | | | | | (1988) $false
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | CLOSE: (1988) is inconsistent.
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | (1989) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.64 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.64 | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | BETA: splitting (1989) gives:
% 65.12/9.64 | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | (1990) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.64 | | | | | | | | | | | (1876), (1990), (function-axioms) are inconsistent
% 65.12/9.64 | | | | | | | | | | | by sub-proof #12.
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | (1991) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 65.12/9.64 | | | | | | | | | | | (439), (440), (1931), (1991), (function-axioms)
% 65.12/9.64 | | | | | | | | | | | are inconsistent by sub-proof #110.
% 65.12/9.64 | | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | | |
% 65.12/9.64 | | | | | | | | | End of split
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | End of split
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | End of split
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | End of split
% 65.12/9.64 | | | | | |
% 65.12/9.64 | | | | | End of split
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | Case 2:
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | (1992) all_16_0 = e1
% 65.12/9.64 | | | | | (1993) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | COMBINE_EQS: (539), (1992) imply:
% 65.12/9.64 | | | | | (1994) all_6_0 = e1
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | SIMP: (1994) implies:
% 65.12/9.64 | | | | | (1995) all_6_0 = e1
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | REDUCE: (1877), (1995) imply:
% 65.12/9.64 | | | | | (1996) ~ (e3 = e1)
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | REDUCE: (43), (1995) imply:
% 65.12/9.64 | | | | | (1997) op(all_6_2, all_6_2) = e1
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | BETA: splitting (77) gives:
% 65.12/9.64 | | | | |
% 65.12/9.64 | | | | | Case 1:
% 65.12/9.64 | | | | | |
% 65.12/9.64 | | | | | | (1998) ~ (all_20_0 = e2)
% 65.12/9.64 | | | | | |
% 65.12/9.64 | | | | | | REDUCE: (615), (1998) imply:
% 65.12/9.64 | | | | | | (1999) ~ (all_14_0 = e2)
% 65.12/9.64 | | | | | |
% 65.12/9.64 | | | | | | BETA: splitting (82) gives:
% 65.12/9.64 | | | | | |
% 65.12/9.64 | | | | | | Case 1:
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | (2000) ~ (all_22_0 = e3)
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | REDUCE: (559), (2000) imply:
% 65.12/9.64 | | | | | | | (2001) ~ (all_14_0 = e3)
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | (2002) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | REF_CLOSE: (5), (8), (9), (51), (62), (153), (154), (155),
% 65.12/9.64 | | | | | | | | (438), (439), (440), (1878), (2001), (2002),
% 65.12/9.64 | | | | | | | | (function-axioms) are inconsistent by sub-proof #159.
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | (2003) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.64 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | BETA: splitting (2003) gives:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2004) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.64 | | | | | | | | | (1876), (2004), (function-axioms) are inconsistent
% 65.12/9.64 | | | | | | | | | by sub-proof #10.
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2005) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | ALPHA: (2005) implies:
% 65.12/9.64 | | | | | | | | | (2006) all_52_3 = e2
% 65.12/9.64 | | | | | | | | | (2007) ~ (all_52_0 = e0)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | COMBINE_EQS: (383), (2006) imply:
% 65.12/9.64 | | | | | | | | | (2008) all_6_2 = e2
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | COMBINE_EQS: (398), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2009) all_16_2 = e2
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | COMBINE_EQS: (292), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2010) all_58_0 = e2
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REDUCE: (452), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2011) ~ (all_54_2 = e2)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REDUCE: (456), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2012) ~ (all_54_4 = e2)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REDUCE: (440), (2007) imply:
% 65.12/9.64 | | | | | | | | | (2013) ~ (all_10_2 = e0)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REDUCE: (1997), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2014) op(e2, e2) = e1
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REDUCE: (42), (2008) imply:
% 65.12/9.64 | | | | | | | | | (2015) op(e2, e0) = all_6_1
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (7), (8), (9), (37), (51), (153), (155), (160),
% 65.12/9.64 | | | | | | | | | (167), (171), (180), (182), (183), (186), (192),
% 65.12/9.64 | | | | | | | | | (205), (210), (235), (238), (240), (243), (244),
% 65.12/9.64 | | | | | | | | | (265), (266), (269), (271), (279), (281), (283),
% 65.12/9.64 | | | | | | | | | (294), (296), (298), (300), (311), (313), (315),
% 65.12/9.64 | | | | | | | | | (328), (330), (334), (346), (353), (359), (361),
% 65.12/9.64 | | | | | | | | | (367), (438), (439), (440), (446), (447), (462),
% 65.12/9.64 | | | | | | | | | (463), (467), (469), (473), (475), (476), (477),
% 65.12/9.64 | | | | | | | | | (479), (480), (483), (596), (1874), (1993), (2006),
% 65.12/9.64 | | | | | | | | | (2009), (2010), (2011), (2012), (2013), (2014),
% 65.12/9.64 | | | | | | | | | (2015), (function-axioms) are inconsistent by
% 65.12/9.64 | | | | | | | | | sub-proof #8.
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | End of split
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | End of split
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | Case 2:
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | (2016) all_22_0 = e3
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | COMBINE_EQS: (559), (2016) imply:
% 65.12/9.64 | | | | | | | (2017) all_14_0 = e3
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | REDUCE: (62), (2017) imply:
% 65.12/9.64 | | | | | | | (2018) op(all_14_2, all_14_2) = e3
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.64 | | | | | | |
% 65.12/9.64 | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | (2019) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | ALPHA: (2019) implies:
% 65.12/9.64 | | | | | | | | (2020) all_52_1 = e2
% 65.12/9.64 | | | | | | | | (2021) ~ (all_52_0 = e1)
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | COMBINE_EQS: (439), (2020) imply:
% 65.12/9.64 | | | | | | | | (2022) all_14_2 = e2
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | SIMP: (2022) implies:
% 65.12/9.64 | | | | | | | | (2023) all_14_2 = e2
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | REDUCE: (440), (2021) imply:
% 65.12/9.64 | | | | | | | | (2024) ~ (all_10_2 = e1)
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | REDUCE: (2018), (2023) imply:
% 65.12/9.64 | | | | | | | | (2025) op(e2, e2) = e3
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | REDUCE: (60), (2023) imply:
% 65.12/9.64 | | | | | | | | (2026) op(e1, e1) = e2
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 65.12/9.64 | | | | | | | | e2, e2, simplifying with (51), (2025) gives:
% 65.12/9.64 | | | | | | | | (2027) all_10_2 = e3
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | COMBINE_EQS: (440), (2027) imply:
% 65.12/9.64 | | | | | | | | (2028) all_52_0 = e3
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | BETA: splitting (153) gives:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2029) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | ALPHA: (2029) implies:
% 65.12/9.64 | | | | | | | | | (2030) all_52_0 = e0
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (7), (2028), (2030) are inconsistent by sub-proof
% 65.12/9.64 | | | | | | | | | #124.
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2031) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 =
% 65.12/9.64 | | | | | | | | | e0 & ~ (all_52_3 = e3))
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (154), (383), (1997), (2020),
% 65.12/9.64 | | | | | | | | | (2026), (2028), (2031), (function-axioms) are
% 65.12/9.64 | | | | | | | | | inconsistent by sub-proof #94.
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | End of split
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | (2032) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.64 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | BETA: splitting (2032) gives:
% 65.12/9.64 | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 1:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2033) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.64 | | | | | | | | | (1876), (2033), (function-axioms) are inconsistent
% 65.12/9.64 | | | | | | | | | by sub-proof #10.
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | Case 2:
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | (2034) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.64 | | | | | | | | |
% 65.12/9.64 | | | | | | | | | REF_CLOSE: (7), (8), (9), (37), (42), (51), (153), (155),
% 65.12/9.64 | | | | | | | | | (160), (167), (171), (180), (182), (183), (186),
% 65.12/9.64 | | | | | | | | | (192), (205), (210), (235), (238), (240), (243),
% 65.12/9.64 | | | | | | | | | (244), (265), (266), (269), (271), (279), (281),
% 65.12/9.64 | | | | | | | | | (283), (292), (294), (296), (298), (300), (311),
% 65.12/9.64 | | | | | | | | | (313), (315), (328), (330), (334), (346), (353),
% 65.12/9.64 | | | | | | | | | (359), (361), (367), (383), (398), (438), (439),
% 65.12/9.64 | | | | | | | | | (440), (446), (447), (452), (456), (462), (463),
% 65.12/9.64 | | | | | | | | | (467), (469), (473), (475), (476), (477), (479),
% 65.12/9.65 | | | | | | | | | (480), (483), (596), (1874), (1993), (1997),
% 65.12/9.65 | | | | | | | | | (2034), (function-axioms) are inconsistent by
% 65.12/9.65 | | | | | | | | | sub-proof #7.
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | End of split
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | End of split
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | End of split
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | Case 2:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | (2035) all_20_0 = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | COMBINE_EQS: (615), (2035) imply:
% 65.12/9.65 | | | | | | (2036) all_14_0 = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | REDUCE: (62), (2036) imply:
% 65.12/9.65 | | | | | | (2037) op(all_14_2, all_14_2) = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | BETA: splitting (152) gives:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | Case 1:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | (2038) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | REF_CLOSE: (4), (5), (9), (51), (153), (154), (155), (383), (439),
% 65.12/9.65 | | | | | | | (440), (2037), (2038), (function-axioms) are
% 65.12/9.65 | | | | | | | inconsistent by sub-proof #104.
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | Case 2:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | (2039) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 &
% 65.12/9.65 | | | | | | | ~ (all_52_0 = e0))
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | BETA: splitting (2039) gives:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | (2040) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.65 | | | | | | | | (1876), (2040), (function-axioms) are inconsistent by
% 65.12/9.65 | | | | | | | | sub-proof #12.
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | (2041) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | ALPHA: (2041) implies:
% 65.12/9.65 | | | | | | | | (2042) all_52_3 = e2
% 65.12/9.65 | | | | | | | | (2043) ~ (all_52_0 = e0)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | COMBINE_EQS: (383), (2042) imply:
% 65.12/9.65 | | | | | | | | (2044) all_6_2 = e2
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (440), (2043) imply:
% 65.12/9.65 | | | | | | | | (2045) ~ (all_10_2 = e0)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (1997), (2044) imply:
% 65.12/9.65 | | | | | | | | (2046) op(e2, e2) = e1
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e1,
% 65.12/9.65 | | | | | | | | e2, e2, simplifying with (51), (2046) gives:
% 65.12/9.65 | | | | | | | | (2047) all_10_2 = e1
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | COMBINE_EQS: (440), (2047) imply:
% 65.12/9.65 | | | | | | | | (2048) all_52_0 = e1
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | BETA: splitting (155) gives:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2049) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REF_CLOSE: (8), (2048), (2049) are inconsistent by sub-proof
% 65.12/9.65 | | | | | | | | | #132.
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2050) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 =
% 65.12/9.65 | | | | | | | | | e3 & ~ (all_52_2 = e0))
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | BETA: splitting (2050) gives:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | (2051) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | ALPHA: (2051) implies:
% 65.12/9.65 | | | | | | | | | | (2052) all_52_1 = e3
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | COMBINE_EQS: (439), (2052) imply:
% 65.12/9.65 | | | | | | | | | | (2053) all_14_2 = e3
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | SIMP: (2053) implies:
% 65.12/9.65 | | | | | | | | | | (2054) all_14_2 = e3
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | REDUCE: (2037), (2054) imply:
% 65.12/9.65 | | | | | | | | | | (2055) op(e3, e3) = e2
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | BETA: splitting (153) gives:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | (2056) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | ALPHA: (2056) implies:
% 65.12/9.65 | | | | | | | | | | | (2057) all_52_0 = e0
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | REF_CLOSE: (4), (2048), (2057) are inconsistent by sub-proof
% 65.12/9.65 | | | | | | | | | | | #133.
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | (2058) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 =
% 65.12/9.65 | | | | | | | | | | | e0 & ~ (all_52_3 = e3))
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | BETA: splitting (2058) gives:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | (2059) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (155), (383), (1997), (2048),
% 65.12/9.65 | | | | | | | | | | | | (2055), (2059), (function-axioms) are inconsistent
% 65.12/9.65 | | | | | | | | | | | | by sub-proof #96.
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | (2060) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | ALPHA: (2060) implies:
% 65.12/9.65 | | | | | | | | | | | | (2061) all_52_2 = e0
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | COMBINE_EQS: (438), (2061) imply:
% 65.12/9.65 | | | | | | | | | | | | (2062) all_4_2 = e0
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REDUCE: (36), (2062) imply:
% 65.12/9.65 | | | | | | | | | | | | (2063) op(e3, e3) = e0
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REF_CLOSE: (5), (2055), (2063), (function-axioms) are
% 65.12/9.65 | | | | | | | | | | | | inconsistent by sub-proof #89.
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | (2064) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | REF_CLOSE: (9), (2042), (2064) are inconsistent by sub-proof
% 65.12/9.65 | | | | | | | | | | #153.
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | End of split
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | End of split
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | End of split
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | End of split
% 65.12/9.65 | | | | |
% 65.12/9.65 | | | | End of split
% 65.12/9.65 | | | |
% 65.12/9.65 | | | Case 2:
% 65.12/9.65 | | | |
% 65.12/9.65 | | | | (2065) all_14_0 = e0
% 65.12/9.65 | | | | (2066) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.12/9.65 | | | |
% 65.12/9.65 | | | | REDUCE: (62), (2065) imply:
% 65.12/9.65 | | | | (2067) op(all_14_2, all_14_2) = e0
% 65.12/9.65 | | | |
% 65.12/9.65 | | | | BETA: splitting (68) gives:
% 65.12/9.65 | | | |
% 65.12/9.65 | | | | Case 1:
% 65.12/9.65 | | | | |
% 65.12/9.65 | | | | | (2068) ~ (all_16_0 = e1)
% 65.12/9.65 | | | | |
% 65.12/9.65 | | | | | REDUCE: (539), (2068) imply:
% 65.12/9.65 | | | | | (2069) ~ (all_6_0 = e1)
% 65.12/9.65 | | | | |
% 65.12/9.65 | | | | | BETA: splitting (96) gives:
% 65.12/9.65 | | | | |
% 65.12/9.65 | | | | | Case 1:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | (2070) ~ (all_28_0 = e2)
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | REDUCE: (626), (2070) imply:
% 65.12/9.65 | | | | | | (2071) ~ (all_6_0 = e2)
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | BETA: splitting (128) gives:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | Case 1:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | (2072) ~ (all_42_0 = e2)
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | REDUCE: (1875), (2072) imply:
% 65.12/9.65 | | | | | | | (2073) $false
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | CLOSE: (2073) is inconsistent.
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | Case 2:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | (2074) ~ (all_42_1 = e0) | ~ (all_42_2 = e1)
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | (2075) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | ALPHA: (2075) implies:
% 65.12/9.65 | | | | | | | | (2076) all_52_1 = e2
% 65.12/9.65 | | | | | | | | (2077) ~ (all_52_0 = e1)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | COMBINE_EQS: (439), (2076) imply:
% 65.12/9.65 | | | | | | | | (2078) all_14_2 = e2
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | SIMP: (2078) implies:
% 65.12/9.65 | | | | | | | | (2079) all_14_2 = e2
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | COMBINE_EQS: (448), (2079) imply:
% 65.12/9.65 | | | | | | | | (2080) all_58_2 = e2
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (465), (2079) imply:
% 65.12/9.65 | | | | | | | | (2081) ~ (all_54_6 = e2)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (469), (2079) imply:
% 65.12/9.65 | | | | | | | | (2082) ~ (all_54_9 = e2)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (440), (2077) imply:
% 65.12/9.65 | | | | | | | | (2083) ~ (all_10_2 = e1)
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (2067), (2079) imply:
% 65.12/9.65 | | | | | | | | (2084) op(e2, e2) = e0
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (61), (2079) imply:
% 65.12/9.65 | | | | | | | | (2085) op(e2, e1) = all_14_1
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | REDUCE: (60), (2079) imply:
% 65.12/9.65 | | | | | | | | (2086) op(e1, e1) = e2
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | BETA: splitting (2066) gives:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2087) ~ (all_14_1 = e3)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_9,
% 65.12/9.65 | | | | | | | | | all_14_1, e1, e2, simplifying with (211), (2085)
% 65.12/9.65 | | | | | | | | | gives:
% 65.12/9.65 | | | | | | | | | (2088) all_54_9 = all_14_1
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 65.12/9.65 | | | | | | | | | e2, e2, simplifying with (51), (2084) gives:
% 65.12/9.65 | | | | | | | | | (2089) all_10_2 = e0
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | COMBINE_EQS: (440), (2089) imply:
% 65.12/9.65 | | | | | | | | | (2090) all_52_0 = e0
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | COMBINE_EQS: (353), (2088) imply:
% 65.12/9.65 | | | | | | | | | (2091) all_56_9 = all_14_1
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | COMBINE_EQS: (447), (2089) imply:
% 65.12/9.65 | | | | | | | | | (2092) all_58_6 = e0
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | COMBINE_EQS: (317), (2088) imply:
% 65.12/9.65 | | | | | | | | | (2093) all_58_4 = all_14_1
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REDUCE: (475), (2088), (2089) imply:
% 65.12/9.65 | | | | | | | | | (2094) ~ (all_14_1 = e0)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REDUCE: (2082), (2088) imply:
% 65.12/9.65 | | | | | | | | | (2095) ~ (all_14_1 = e2)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REDUCE: (2083), (2089) imply:
% 65.12/9.65 | | | | | | | | | (2096) ~ (e1 = e0)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | BETA: splitting (240) gives:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | (2097) all_56_9 = e3
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | REF_CLOSE: (2087), (2091), (2097) are inconsistent by
% 65.12/9.65 | | | | | | | | | | sub-proof #119.
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | (2098) ~ (all_56_9 = e3)
% 65.12/9.65 | | | | | | | | | | (2099) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | BETA: splitting (155) gives:
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | (2100) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | ALPHA: (2100) implies:
% 65.12/9.65 | | | | | | | | | | | (2101) all_52_0 = e3
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (43), (153), (154), (383),
% 65.12/9.65 | | | | | | | | | | | (2071), (2076), (2086), (2101), (function-axioms)
% 65.12/9.65 | | | | | | | | | | | are inconsistent by sub-proof #9.
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | (2102) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 =
% 65.12/9.65 | | | | | | | | | | | e3 & ~ (all_52_2 = e0))
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | BETA: splitting (2102) gives:
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | (2103) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REF_CLOSE: (9), (2076), (2103) are inconsistent by sub-proof
% 65.12/9.65 | | | | | | | | | | | | #147.
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | (2104) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | ALPHA: (2104) implies:
% 65.12/9.65 | | | | | | | | | | | | (2105) all_52_3 = e3
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | COMBINE_EQS: (383), (2105) imply:
% 65.12/9.65 | | | | | | | | | | | | (2106) all_6_2 = e3
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REDUCE: (450), (2106) imply:
% 65.12/9.65 | | | | | | | | | | | | (2107) ~ (all_54_1 = e3)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REDUCE: (454), (2106) imply:
% 65.12/9.65 | | | | | | | | | | | | (2108) ~ (all_54_3 = e3)
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (37), (154), (158), (175), (209),
% 65.12/9.65 | | | | | | | | | | | | (242), (271), (277), (294), (296), (311), (332),
% 65.12/9.65 | | | | | | | | | | | | (334), (369), (399), (438), (472), (567), (2074),
% 65.12/9.65 | | | | | | | | | | | | (2076), (2080), (2081), (2087), (2090), (2091),
% 65.12/9.65 | | | | | | | | | | | | (2092), (2093), (2094), (2095), (2099), (2105),
% 65.12/9.65 | | | | | | | | | | | | (2107), (2108), (function-axioms) are inconsistent
% 65.12/9.65 | | | | | | | | | | | | by sub-proof #6.
% 65.12/9.65 | | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | | |
% 65.12/9.65 | | | | | | | | | End of split
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2109) ~ (all_14_2 = e2)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REDUCE: (2079), (2109) imply:
% 65.12/9.65 | | | | | | | | | (2110) $false
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | CLOSE: (2110) is inconsistent.
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | End of split
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | (2111) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.65 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | BETA: splitting (2111) gives:
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 1:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2112) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | ALPHA: (2112) implies:
% 65.12/9.65 | | | | | | | | | (2113) all_52_2 = e2
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | COMBINE_EQS: (438), (2113) imply:
% 65.12/9.65 | | | | | | | | | (2114) all_4_2 = e2
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | SIMP: (2114) implies:
% 65.12/9.65 | | | | | | | | | (2115) all_4_2 = e2
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (153),
% 65.12/9.65 | | | | | | | | | (154), (155), (383), (439), (440), (1876), (2067),
% 65.12/9.65 | | | | | | | | | (2113), (2115), (function-axioms) are inconsistent
% 65.12/9.65 | | | | | | | | | by sub-proof #4.
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | Case 2:
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | (2116) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | | REF_CLOSE: (43), (51), (239), (383), (440), (444), (1877),
% 65.12/9.65 | | | | | | | | | (2069), (2071), (2116), (function-axioms) are
% 65.12/9.65 | | | | | | | | | inconsistent by sub-proof #11.
% 65.12/9.65 | | | | | | | | |
% 65.12/9.65 | | | | | | | | End of split
% 65.12/9.65 | | | | | | | |
% 65.12/9.65 | | | | | | | End of split
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | End of split
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | Case 2:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | (2117) all_28_0 = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | COMBINE_EQS: (626), (2117) imply:
% 65.12/9.65 | | | | | | (2118) all_6_0 = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | SIMP: (2118) implies:
% 65.12/9.65 | | | | | | (2119) all_6_0 = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | REDUCE: (1877), (2119) imply:
% 65.12/9.65 | | | | | | (2120) ~ (e3 = e2)
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | REDUCE: (43), (2119) imply:
% 65.12/9.65 | | | | | | (2121) op(all_6_2, all_6_2) = e2
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | BETA: splitting (152) gives:
% 65.12/9.65 | | | | | |
% 65.12/9.65 | | | | | | Case 1:
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | (2122) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | ALPHA: (2122) implies:
% 65.12/9.65 | | | | | | | (2123) all_52_1 = e2
% 65.12/9.65 | | | | | | | (2124) ~ (all_52_0 = e1)
% 65.12/9.65 | | | | | | |
% 65.12/9.65 | | | | | | | COMBINE_EQS: (439), (2123) imply:
% 65.12/9.65 | | | | | | | (2125) all_14_2 = e2
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (440), (2124) imply:
% 65.12/9.66 | | | | | | | (2126) ~ (all_10_2 = e1)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (2067), (2125) imply:
% 65.12/9.66 | | | | | | | (2127) op(e2, e2) = e0
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 65.12/9.66 | | | | | | | e2, e2, simplifying with (51), (2127) gives:
% 65.12/9.66 | | | | | | | (2128) all_10_2 = e0
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | COMBINE_EQS: (440), (2128) imply:
% 65.12/9.66 | | | | | | | (2129) all_52_0 = e0
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (2126), (2128) imply:
% 65.12/9.66 | | | | | | | (2130) ~ (e1 = e0)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | BETA: splitting (155) gives:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2131) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REF_CLOSE: (7), (2129), (2131) are inconsistent by sub-proof
% 65.12/9.66 | | | | | | | | #148.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2132) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3
% 65.12/9.66 | | | | | | | | & ~ (all_52_2 = e0))
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | BETA: splitting (2132) gives:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | (2133) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | REF_CLOSE: (9), (2123), (2133) are inconsistent by sub-proof
% 65.12/9.66 | | | | | | | | | #147.
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | (2134) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | ALPHA: (2134) implies:
% 65.12/9.66 | | | | | | | | | (2135) all_52_3 = e3
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | COMBINE_EQS: (383), (2135) imply:
% 65.12/9.66 | | | | | | | | | (2136) all_6_2 = e3
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | SIMP: (2136) implies:
% 65.12/9.66 | | | | | | | | | (2137) all_6_2 = e3
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | REDUCE: (2121), (2137) imply:
% 65.12/9.66 | | | | | | | | | (2138) op(e3, e3) = e2
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | BETA: splitting (154) gives:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | (2139) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | REF_CLOSE: (4), (2129), (2139) are inconsistent by sub-proof
% 65.12/9.66 | | | | | | | | | | #164.
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | (2140) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 =
% 65.12/9.66 | | | | | | | | | | e1 & ~ (all_52_1 = e0))
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | BETA: splitting (2140) gives:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | (2141) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | ALPHA: (2141) implies:
% 65.12/9.66 | | | | | | | | | | | (2142) all_52_2 = e1
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | COMBINE_EQS: (438), (2142) imply:
% 65.12/9.66 | | | | | | | | | | | (2143) all_4_2 = e1
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | SIMP: (2143) implies:
% 65.12/9.66 | | | | | | | | | | | (2144) all_4_2 = e1
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | REDUCE: (36), (2144) imply:
% 65.12/9.66 | | | | | | | | | | | (2145) op(e3, e3) = e1
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | REF_CLOSE: (6), (2138), (2145), (function-axioms) are
% 65.12/9.66 | | | | | | | | | | | inconsistent by sub-proof #97.
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | (2146) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | ALPHA: (2146) implies:
% 65.12/9.66 | | | | | | | | | | | (2147) all_52_3 = e1
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (155), (439), (2067), (2129),
% 65.12/9.66 | | | | | | | | | | | (2138), (2147), (function-axioms) are inconsistent
% 65.12/9.66 | | | | | | | | | | | by sub-proof #88.
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | End of split
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | End of split
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | End of split
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | End of split
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | Case 2:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | (2148) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 &
% 65.12/9.66 | | | | | | | ~ (all_52_0 = e0))
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | BETA: splitting (2148) gives:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2149) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (153),
% 65.12/9.66 | | | | | | | | (154), (155), (383), (438), (439), (440), (1876),
% 65.12/9.66 | | | | | | | | (2067), (2149), (function-axioms) are inconsistent by
% 65.12/9.66 | | | | | | | | sub-proof #3.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2150) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REF_CLOSE: (4), (6), (9), (51), (153), (154), (155), (383),
% 65.12/9.66 | | | | | | | | (439), (440), (2121), (2150), (function-axioms) are
% 65.12/9.66 | | | | | | | | inconsistent by sub-proof #110.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | End of split
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | End of split
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | End of split
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | Case 2:
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | (2151) all_16_0 = e1
% 65.12/9.66 | | | | | (2152) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | COMBINE_EQS: (539), (2151) imply:
% 65.12/9.66 | | | | | (2153) all_6_0 = e1
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | REDUCE: (1877), (2153) imply:
% 65.12/9.66 | | | | | (2154) ~ (e3 = e1)
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | REDUCE: (43), (2153) imply:
% 65.12/9.66 | | | | | (2155) op(all_6_2, all_6_2) = e1
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | BETA: splitting (128) gives:
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | Case 1:
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | (2156) ~ (all_42_0 = e2)
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | REDUCE: (1875), (2156) imply:
% 65.12/9.66 | | | | | | (2157) $false
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | CLOSE: (2157) is inconsistent.
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | Case 2:
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | (2158) ~ (all_42_1 = e0) | ~ (all_42_2 = e1)
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | BETA: splitting (152) gives:
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | Case 1:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | (2159) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | ALPHA: (2159) implies:
% 65.12/9.66 | | | | | | | (2160) all_52_1 = e2
% 65.12/9.66 | | | | | | | (2161) ~ (all_52_0 = e1)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | COMBINE_EQS: (439), (2160) imply:
% 65.12/9.66 | | | | | | | (2162) all_14_2 = e2
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | COMBINE_EQS: (448), (2162) imply:
% 65.12/9.66 | | | | | | | (2163) all_58_2 = e2
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (465), (2162) imply:
% 65.12/9.66 | | | | | | | (2164) ~ (all_54_6 = e2)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (469), (2162) imply:
% 65.12/9.66 | | | | | | | (2165) ~ (all_54_9 = e2)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (440), (2161) imply:
% 65.12/9.66 | | | | | | | (2166) ~ (all_10_2 = e1)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (2067), (2162) imply:
% 65.12/9.66 | | | | | | | (2167) op(e2, e2) = e0
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (61), (2162) imply:
% 65.12/9.66 | | | | | | | (2168) op(e2, e1) = all_14_1
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | BETA: splitting (2066) gives:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2169) ~ (all_14_1 = e3)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_9,
% 65.12/9.66 | | | | | | | | all_14_1, e1, e2, simplifying with (211), (2168)
% 65.12/9.66 | | | | | | | | gives:
% 65.12/9.66 | | | | | | | | (2170) all_54_9 = all_14_1
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 65.12/9.66 | | | | | | | | e2, e2, simplifying with (51), (2167) gives:
% 65.12/9.66 | | | | | | | | (2171) all_10_2 = e0
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | COMBINE_EQS: (440), (2171) imply:
% 65.12/9.66 | | | | | | | | (2172) all_52_0 = e0
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | COMBINE_EQS: (353), (2170) imply:
% 65.12/9.66 | | | | | | | | (2173) all_56_9 = all_14_1
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | COMBINE_EQS: (447), (2171) imply:
% 65.12/9.66 | | | | | | | | (2174) all_58_6 = e0
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | COMBINE_EQS: (317), (2170) imply:
% 65.12/9.66 | | | | | | | | (2175) all_58_4 = all_14_1
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REDUCE: (475), (2170), (2171) imply:
% 65.12/9.66 | | | | | | | | (2176) ~ (all_14_1 = e0)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REDUCE: (2165), (2170) imply:
% 65.12/9.66 | | | | | | | | (2177) ~ (all_14_1 = e2)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REDUCE: (2166), (2171) imply:
% 65.12/9.66 | | | | | | | | (2178) ~ (e1 = e0)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | BETA: splitting (155) gives:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | (2179) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | REF_CLOSE: (7), (2172), (2179) are inconsistent by sub-proof
% 65.12/9.66 | | | | | | | | | #148.
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | (2180) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 =
% 65.12/9.66 | | | | | | | | | e3 & ~ (all_52_2 = e0))
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | BETA: splitting (2180) gives:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | (2181) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | REF_CLOSE: (9), (2160), (2181) are inconsistent by sub-proof
% 65.12/9.66 | | | | | | | | | | #147.
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | (2182) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | ALPHA: (2182) implies:
% 65.12/9.66 | | | | | | | | | | (2183) all_52_3 = e3
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | COMBINE_EQS: (383), (2183) imply:
% 65.12/9.66 | | | | | | | | | | (2184) all_6_2 = e3
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | SIMP: (2184) implies:
% 65.12/9.66 | | | | | | | | | | (2185) all_6_2 = e3
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | REDUCE: (450), (2185) imply:
% 65.12/9.66 | | | | | | | | | | (2186) ~ (all_54_1 = e3)
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | REDUCE: (454), (2185) imply:
% 65.12/9.66 | | | | | | | | | | (2187) ~ (all_54_3 = e3)
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | BETA: splitting (240) gives:
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | (2188) all_56_9 = e3
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | REF_CLOSE: (2169), (2173), (2188) are inconsistent by
% 65.12/9.66 | | | | | | | | | | | sub-proof #119.
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | (2189) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (37), (154), (158), (175), (209),
% 65.12/9.66 | | | | | | | | | | | (242), (271), (277), (294), (296), (311), (332),
% 65.12/9.66 | | | | | | | | | | | (334), (369), (399), (438), (472), (567), (2158),
% 65.12/9.66 | | | | | | | | | | | (2160), (2163), (2164), (2169), (2172), (2173),
% 65.12/9.66 | | | | | | | | | | | (2174), (2175), (2176), (2177), (2183), (2186),
% 65.12/9.66 | | | | | | | | | | | (2187), (2189), (function-axioms) are inconsistent
% 65.12/9.66 | | | | | | | | | | | by sub-proof #6.
% 65.12/9.66 | | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | | End of split
% 65.12/9.66 | | | | | | | | | |
% 65.12/9.66 | | | | | | | | | End of split
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | End of split
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2190) ~ (all_14_2 = e2)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REDUCE: (2162), (2190) imply:
% 65.12/9.66 | | | | | | | | (2191) $false
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | CLOSE: (2191) is inconsistent.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | End of split
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | Case 2:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | (2192) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 &
% 65.12/9.66 | | | | | | | ~ (all_52_0 = e0))
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | BETA: splitting (2192) gives:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2193) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (41), (51), (153),
% 65.12/9.66 | | | | | | | | (154), (155), (383), (438), (439), (440), (1876),
% 65.12/9.66 | | | | | | | | (2067), (2193), (function-axioms) are inconsistent by
% 65.12/9.66 | | | | | | | | sub-proof #3.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | Case 2:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2194) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REF_CLOSE: (7), (8), (9), (37), (42), (51), (153), (155), (160),
% 65.12/9.66 | | | | | | | | (167), (171), (180), (182), (183), (186), (192),
% 65.12/9.66 | | | | | | | | (205), (210), (235), (238), (240), (243), (244),
% 65.12/9.66 | | | | | | | | (265), (266), (269), (271), (279), (281), (283),
% 65.12/9.66 | | | | | | | | (292), (294), (296), (298), (300), (311), (313),
% 65.12/9.66 | | | | | | | | (315), (328), (330), (334), (346), (353), (359),
% 65.12/9.66 | | | | | | | | (361), (367), (383), (398), (438), (439), (440),
% 65.12/9.66 | | | | | | | | (446), (447), (452), (456), (462), (463), (467),
% 65.12/9.66 | | | | | | | | (469), (473), (475), (476), (477), (479), (480),
% 65.12/9.66 | | | | | | | | (483), (596), (1874), (2152), (2155), (2194),
% 65.12/9.66 | | | | | | | | (function-axioms) are inconsistent by sub-proof #7.
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | End of split
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | End of split
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | End of split
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | End of split
% 65.12/9.66 | | | |
% 65.12/9.66 | | | End of split
% 65.12/9.66 | | |
% 65.12/9.66 | | Case 2:
% 65.12/9.66 | | |
% 65.12/9.66 | | | (2195) all_6_0 = e3
% 65.12/9.66 | | |
% 65.12/9.66 | | | COMBINE_EQS: (622), (2195) imply:
% 65.12/9.66 | | | (2196) all_8_0 = e3
% 65.12/9.66 | | |
% 65.12/9.66 | | | REDUCE: (43), (2195) imply:
% 65.12/9.66 | | | (2197) op(all_6_2, all_6_2) = e3
% 65.12/9.66 | | |
% 65.12/9.66 | | | BETA: splitting (49) gives:
% 65.12/9.66 | | |
% 65.12/9.66 | | | Case 1:
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | (2198) ~ (all_8_0 = e3)
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | REDUCE: (2196), (2198) imply:
% 65.12/9.66 | | | | (2199) $false
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | CLOSE: (2199) is inconsistent.
% 65.12/9.66 | | | |
% 65.12/9.66 | | | Case 2:
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | (2200) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | BETA: splitting (54) gives:
% 65.12/9.66 | | | |
% 65.12/9.66 | | | | Case 1:
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | (2201) ~ (all_10_0 = e1)
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | BETA: splitting (63) gives:
% 65.12/9.66 | | | | |
% 65.12/9.66 | | | | | Case 1:
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | (2202) ~ (all_14_0 = e0)
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | BETA: splitting (77) gives:
% 65.12/9.66 | | | | | |
% 65.12/9.66 | | | | | | Case 1:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | (2203) ~ (all_20_0 = e2)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | REDUCE: (615), (2203) imply:
% 65.12/9.66 | | | | | | | (2204) ~ (all_14_0 = e2)
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | BETA: splitting (82) gives:
% 65.12/9.66 | | | | | | |
% 65.12/9.66 | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | (2205) ~ (all_22_0 = e3)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | REDUCE: (559), (2205) imply:
% 65.12/9.66 | | | | | | | | (2206) ~ (all_14_0 = e3)
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.66 | | | | | | | |
% 65.12/9.66 | | | | | | | | Case 1:
% 65.12/9.66 | | | | | | | | |
% 65.12/9.66 | | | | | | | | | (2207) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.66 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 65.12/9.67 | | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 65.12/9.67 | | | | | | | | | (440), (444), (2197), (2206), (2207),
% 65.12/9.67 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.67 | | | | | | | | | #38.
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2208) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.67 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | BETA: splitting (2208) gives:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2209) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.67 | | | | | | | | | | (1876), (2209), (function-axioms) are inconsistent
% 65.12/9.67 | | | | | | | | | | by sub-proof #12.
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2210) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 65.12/9.67 | | | | | | | | | | (440), (2197), (2201), (2210), (function-axioms)
% 65.12/9.67 | | | | | | | | | | are inconsistent by sub-proof #39.
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | End of split
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | End of split
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2211) all_22_0 = e3
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | COMBINE_EQS: (559), (2211) imply:
% 65.12/9.67 | | | | | | | | (2212) all_14_0 = e3
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | SIMP: (2212) implies:
% 65.12/9.67 | | | | | | | | (2213) all_14_0 = e3
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | COMBINE_EQS: (632), (2213) imply:
% 65.12/9.67 | | | | | | | | (2214) all_44_0 = e3
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REDUCE: (62), (2213) imply:
% 65.12/9.67 | | | | | | | | (2215) op(all_14_2, all_14_2) = e3
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | BETA: splitting (133) gives:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2216) ~ (all_44_0 = e3)
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REDUCE: (2214), (2216) imply:
% 65.12/9.67 | | | | | | | | | (2217) $false
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | CLOSE: (2217) is inconsistent.
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2218) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2219) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (51), (60), (61), (153),
% 65.12/9.67 | | | | | | | | | | (154), (155), (168), (180), (181), (211), (237),
% 65.12/9.67 | | | | | | | | | | (244), (272), (315), (317), (328), (346), (363),
% 65.12/9.67 | | | | | | | | | | (383), (437), (438), (439), (440), (447), (456),
% 65.12/9.67 | | | | | | | | | | (458), (460), (463), (477), (631), (2197), (2215),
% 65.12/9.67 | | | | | | | | | | (2218), (2219), (function-axioms) are inconsistent
% 65.12/9.67 | | | | | | | | | | by sub-proof #31.
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2220) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.67 | | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | BETA: splitting (2220) gives:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | | (2221) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (438), (439), (440),
% 65.12/9.67 | | | | | | | | | | | (1876), (2221), (function-axioms) are inconsistent
% 65.12/9.67 | | | | | | | | | | | by sub-proof #12.
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | | (2222) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 65.12/9.67 | | | | | | | | | | | (440), (2197), (2201), (2222), (function-axioms)
% 65.12/9.67 | | | | | | | | | | | are inconsistent by sub-proof #39.
% 65.12/9.67 | | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | End of split
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | End of split
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | End of split
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | End of split
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | Case 2:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | (2223) all_20_0 = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | COMBINE_EQS: (615), (2223) imply:
% 65.12/9.67 | | | | | | | (2224) all_14_0 = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | SIMP: (2224) implies:
% 65.12/9.67 | | | | | | | (2225) all_14_0 = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | REDUCE: (62), (2225) imply:
% 65.12/9.67 | | | | | | | (2226) op(all_14_2, all_14_2) = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2227) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (51), (153), (154), (155),
% 65.12/9.67 | | | | | | | | (383), (438), (439), (440), (2197), (2226), (2227),
% 65.12/9.67 | | | | | | | | (function-axioms) are inconsistent by sub-proof #26.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2228) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.67 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | BETA: splitting (2228) gives:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2229) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | ALPHA: (2229) implies:
% 65.12/9.67 | | | | | | | | | (2230) all_52_2 = e2
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | COMBINE_EQS: (438), (2230) imply:
% 65.12/9.67 | | | | | | | | | (2231) all_4_2 = e2
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REDUCE: (1876), (2231) imply:
% 65.12/9.67 | | | | | | | | | (2232) op(e2, e2) = e2
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REF_CLOSE: (5), (6), (51), (153), (154), (439), (440), (2230),
% 65.12/9.67 | | | | | | | | | (2232), (function-axioms) are inconsistent by
% 65.12/9.67 | | | | | | | | | sub-proof #13.
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2233) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 65.12/9.67 | | | | | | | | | (440), (2197), (2201), (2233), (function-axioms)
% 65.12/9.67 | | | | | | | | | are inconsistent by sub-proof #37.
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | End of split
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | End of split
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | End of split
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | Case 2:
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | (2234) all_14_0 = e0
% 65.12/9.67 | | | | | | (2235) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | REDUCE: (62), (2234) imply:
% 65.12/9.67 | | | | | | (2236) op(all_14_2, all_14_2) = e0
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | BETA: splitting (152) gives:
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | Case 1:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | (2237) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | ALPHA: (2237) implies:
% 65.12/9.67 | | | | | | | (2238) all_52_1 = e2
% 65.12/9.67 | | | | | | | (2239) ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | COMBINE_EQS: (439), (2238) imply:
% 65.12/9.67 | | | | | | | (2240) all_14_2 = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | SIMP: (2240) implies:
% 65.12/9.67 | | | | | | | (2241) all_14_2 = e2
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | REF_CLOSE: (7), (8), (9), (36), (51), (154), (155), (383), (438),
% 65.12/9.67 | | | | | | | (440), (2197), (2235), (2236), (2238), (2239), (2241),
% 65.12/9.67 | | | | | | | (function-axioms) are inconsistent by sub-proof #14.
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | Case 2:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | (2242) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 &
% 65.12/9.67 | | | | | | | ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | BETA: splitting (2242) gives:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2243) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | ALPHA: (2243) implies:
% 65.12/9.67 | | | | | | | | (2244) all_52_2 = e2
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | COMBINE_EQS: (438), (2244) imply:
% 65.12/9.67 | | | | | | | | (2245) all_4_2 = e2
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REDUCE: (1876), (2245) imply:
% 65.12/9.67 | | | | | | | | (2246) op(e2, e2) = e2
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REDUCE: (36), (2245) imply:
% 65.12/9.67 | | | | | | | | (2247) op(e3, e3) = e2
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (41), (51), (153), (154),
% 65.12/9.67 | | | | | | | | (155), (383), (439), (440), (2236), (2244), (2246),
% 65.12/9.67 | | | | | | | | (2247), (function-axioms) are inconsistent by
% 65.12/9.67 | | | | | | | | sub-proof #5.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2248) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REF_CLOSE: (6), (8), (36), (51), (53), (154), (383), (438),
% 65.12/9.67 | | | | | | | | (440), (2197), (2201), (2248), (function-axioms) are
% 65.12/9.67 | | | | | | | | inconsistent by sub-proof #37.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | End of split
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | End of split
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | End of split
% 65.12/9.67 | | | | |
% 65.12/9.67 | | | | Case 2:
% 65.12/9.67 | | | | |
% 65.12/9.67 | | | | | (2249) all_10_0 = e1
% 65.12/9.67 | | | | | (2250) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 65.12/9.67 | | | | |
% 65.12/9.67 | | | | | REDUCE: (53), (2249) imply:
% 65.12/9.67 | | | | | (2251) op(all_10_2, all_10_2) = e1
% 65.12/9.67 | | | | |
% 65.12/9.67 | | | | | BETA: splitting (63) gives:
% 65.12/9.67 | | | | |
% 65.12/9.67 | | | | | Case 1:
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | (2252) ~ (all_14_0 = e0)
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | BETA: splitting (82) gives:
% 65.12/9.67 | | | | | |
% 65.12/9.67 | | | | | | Case 1:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | (2253) ~ (all_22_0 = e3)
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | REDUCE: (559), (2253) imply:
% 65.12/9.67 | | | | | | | (2254) ~ (all_14_0 = e3)
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | BETA: splitting (152) gives:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2255) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (62),
% 65.12/9.67 | | | | | | | | (153), (154), (155), (239), (383), (438), (439),
% 65.12/9.67 | | | | | | | | (440), (444), (2197), (2254), (2255),
% 65.12/9.67 | | | | | | | | (function-axioms) are inconsistent by sub-proof #38.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2256) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2
% 65.12/9.67 | | | | | | | | & ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (42), (51), (52),
% 65.12/9.67 | | | | | | | | (153), (154), (155), (158), (160), (168), (180),
% 65.12/9.67 | | | | | | | | (181), (182), (192), (210), (216), (235), (237),
% 65.12/9.67 | | | | | | | | (241), (243), (244), (247), (267), (273), (276),
% 65.12/9.67 | | | | | | | | (282), (292), (294), (300), (315), (317), (328),
% 65.12/9.67 | | | | | | | | (330), (332), (334), (346), (351), (355), (359),
% 65.12/9.67 | | | | | | | | (361), (363), (383), (431), (438), (439), (440),
% 65.12/9.67 | | | | | | | | (447), (448), (450), (456), (458), (460), (461),
% 65.12/9.67 | | | | | | | | (467), (473), (474), (477), (480), (483), (624),
% 65.12/9.67 | | | | | | | | (1876), (2197), (2200), (2250), (2251), (2256),
% 65.12/9.67 | | | | | | | | (function-axioms) are inconsistent by sub-proof #1.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | End of split
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | Case 2:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | (2257) all_22_0 = e3
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | COMBINE_EQS: (559), (2257) imply:
% 65.12/9.67 | | | | | | | (2258) all_14_0 = e3
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | COMBINE_EQS: (632), (2258) imply:
% 65.12/9.67 | | | | | | | (2259) all_44_0 = e3
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | REDUCE: (62), (2258) imply:
% 65.12/9.67 | | | | | | | (2260) op(all_14_2, all_14_2) = e3
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | BETA: splitting (133) gives:
% 65.12/9.67 | | | | | | |
% 65.12/9.67 | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2261) ~ (all_44_0 = e3)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | REDUCE: (2259), (2261) imply:
% 65.12/9.67 | | | | | | | | (2262) $false
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | CLOSE: (2262) is inconsistent.
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | (2263) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | BETA: splitting (152) gives:
% 65.12/9.67 | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2264) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (437), (438),
% 65.12/9.67 | | | | | | | | | (439), (440), (2251), (2260), (2263), (2264),
% 65.12/9.67 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 65.12/9.67 | | | | | | | | | #50.
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | (2265) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 =
% 65.12/9.67 | | | | | | | | | e2 & ~ (all_52_0 = e0))
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | BETA: splitting (2265) gives:
% 65.12/9.67 | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 1:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2266) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | ALPHA: (2266) implies:
% 65.12/9.67 | | | | | | | | | | (2267) all_52_2 = e2
% 65.12/9.67 | | | | | | | | | | (2268) ~ (all_52_0 = e3)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | COMBINE_EQS: (438), (2267) imply:
% 65.12/9.67 | | | | | | | | | | (2269) all_4_2 = e2
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | SIMP: (2269) implies:
% 65.12/9.67 | | | | | | | | | | (2270) all_4_2 = e2
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (51), (153), (155), (383),
% 65.12/9.67 | | | | | | | | | | (440), (1876), (2197), (2251), (2267), (2268),
% 65.12/9.67 | | | | | | | | | | (2270), (function-axioms) are inconsistent by
% 65.12/9.67 | | | | | | | | | | sub-proof #2.
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | Case 2:
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.67 | | | | | | | | | | (2271) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.67 | | | | | | | | | |
% 65.12/9.68 | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (51), (52), (153), (154),
% 65.12/9.68 | | | | | | | | | | (158), (160), (168), (180), (181), (182), (192),
% 65.12/9.68 | | | | | | | | | | (210), (216), (235), (237), (241), (243), (244),
% 65.12/9.68 | | | | | | | | | | (247), (267), (273), (276), (282), (292), (294),
% 65.12/9.68 | | | | | | | | | | (300), (315), (317), (328), (330), (332), (334),
% 65.12/9.68 | | | | | | | | | | (346), (351), (355), (359), (361), (363), (383),
% 65.12/9.68 | | | | | | | | | | (431), (438), (439), (440), (447), (448), (450),
% 65.12/9.68 | | | | | | | | | | (456), (458), (460), (461), (467), (473), (474),
% 65.12/9.68 | | | | | | | | | | (477), (480), (483), (624), (2197), (2200),
% 65.12/9.68 | | | | | | | | | | (2250), (2271), (function-axioms) are inconsistent
% 65.12/9.68 | | | | | | | | | | by sub-proof #15.
% 65.12/9.68 | | | | | | | | | |
% 65.12/9.68 | | | | | | | | | End of split
% 65.12/9.68 | | | | | | | | |
% 65.12/9.68 | | | | | | | | End of split
% 65.12/9.68 | | | | | | | |
% 65.12/9.68 | | | | | | | End of split
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | End of split
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | Case 2:
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | | (2272) all_14_0 = e0
% 65.12/9.68 | | | | | | (2273) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | | REDUCE: (62), (2272) imply:
% 65.12/9.68 | | | | | | (2274) op(all_14_2, all_14_2) = e0
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | | BETA: splitting (152) gives:
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | | Case 1:
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | | (2275) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | | REF_CLOSE: (7), (8), (9), (41), (51), (155), (383), (439), (440),
% 65.12/9.68 | | | | | | | (2251), (2273), (2274), (2275), (function-axioms) are
% 65.12/9.68 | | | | | | | inconsistent by sub-proof #45.
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | Case 2:
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | | (2276) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 &
% 65.12/9.68 | | | | | | | ~ (all_52_0 = e0))
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (42), (51), (52), (153),
% 65.12/9.68 | | | | | | | (154), (155), (158), (160), (168), (180), (181), (182),
% 65.12/9.68 | | | | | | | (192), (210), (216), (235), (237), (241), (243), (244),
% 65.12/9.68 | | | | | | | (247), (267), (273), (276), (282), (292), (294), (300),
% 65.12/9.68 | | | | | | | (315), (317), (328), (330), (332), (334), (346), (351),
% 65.12/9.68 | | | | | | | (355), (359), (361), (363), (383), (431), (438), (439),
% 65.12/9.68 | | | | | | | (440), (447), (448), (450), (456), (458), (460), (461),
% 65.12/9.68 | | | | | | | (467), (473), (474), (477), (480), (483), (624),
% 65.12/9.68 | | | | | | | (1876), (2197), (2200), (2250), (2251), (2276),
% 65.12/9.68 | | | | | | | (function-axioms) are inconsistent by sub-proof #1.
% 65.12/9.68 | | | | | | |
% 65.12/9.68 | | | | | | End of split
% 65.12/9.68 | | | | | |
% 65.12/9.68 | | | | | End of split
% 65.12/9.68 | | | | |
% 65.12/9.68 | | | | End of split
% 65.12/9.68 | | | |
% 65.12/9.68 | | | End of split
% 65.12/9.68 | | |
% 65.12/9.68 | | End of split
% 65.12/9.68 | |
% 65.12/9.68 | End of split
% 65.12/9.68 |
% 65.12/9.68 End of proof
% 65.12/9.68
% 65.12/9.68 Sub-proof #1 shows that the following formulas are inconsistent:
% 65.12/9.68 ----------------------------------------------------------------
% 65.12/9.68 (1) ~ (all_54_4 = all_6_2)
% 65.12/9.68 (2) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 65.12/9.68 e0))
% 65.12/9.68 (3) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 65.12/9.68 (4) all_52_2 = all_4_2
% 65.12/9.68 (5) all_58_9 = all_54_15
% 65.12/9.68 (6) op(e3, e2) = all_54_15
% 65.12/9.68 (7) ~ (all_54_1 = all_14_2)
% 65.12/9.68 (8) ~ (all_54_7 = all_10_2)
% 65.12/9.68 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.12/9.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.12/9.68 (10) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.12/9.68 (11) ~ (all_54_4 = all_54_8)
% 65.12/9.68 (12) all_58_13 = all_54_10
% 65.12/9.68 (13) op(e2, e0) = all_54_8
% 65.12/9.68 (14) ~ (all_54_8 = all_54_12)
% 65.12/9.68 (15) ~ (all_54_1 = all_54_9)
% 65.12/9.68 (16) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.12/9.68 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.12/9.68 (17) all_56_4 = all_54_4
% 65.12/9.68 (18) op(all_6_2, e0) = all_6_1
% 65.12/9.68 (19) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.12/9.68 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.12/9.68 (20) ~ (e3 = e1)
% 65.12/9.68 (21) op(e2, e2) = all_10_2
% 65.12/9.68 (22) all_56_1 = all_54_1
% 65.12/9.68 (23) all_56_8 = all_54_8
% 65.12/9.68 (24) all_8_1 = all_6_1
% 65.12/9.68 (25) all_58_0 = all_6_2
% 65.12/9.68 (26) all_52_1 = all_14_2
% 65.12/9.68 (27) ~ (all_54_8 = all_6_2)
% 65.12/9.68 (28) all_8_2 = all_6_2
% 65.12/9.68 (29) op(all_10_2, all_10_2) = e1
% 65.12/9.68 (30) all_58_4 = all_54_9
% 65.12/9.68 (31) ~ (all_54_12 = all_4_2)
% 65.12/9.68 (32) ~ (e3 = e0)
% 65.12/9.68 (33) ~ (e1 = e0)
% 65.12/9.68 (34) ~ (all_54_8 = all_10_2)
% 65.12/9.68 (35) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0
% 65.12/9.68 (36) all_58_6 = all_10_2
% 65.12/9.68 (37) ~ (all_54_4 = all_54_7)
% 65.12/9.68 (38) ~ (all_54_13 = all_54_15)
% 65.12/9.68 (39) op(e3, e3) = all_4_2
% 65.12/9.68 (40) all_56_12 = all_54_12
% 65.12/9.68 (41) all_58_2 = all_14_2
% 65.12/9.68 (42) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.12/9.68 (43) all_56_6 = all_54_7
% 65.12/9.68 (44) op(all_6_2, all_6_2) = e3
% 65.12/9.68 (45) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.12/9.68 (46) ~ (all_54_10 = all_4_2)
% 65.12/9.68 (47) ~ (all_54_15 = all_4_2)
% 65.12/9.68 (48) ~ (e2 = e0)
% 65.12/9.68 (49) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.12/9.68 (50) ~ (e2 = e1)
% 65.12/9.68 (51) all_58_1 = all_54_4
% 65.12/9.68 (52) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.12/9.68 (53) ~ (all_54_1 = all_6_2)
% 65.12/9.68 (54) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 65.12/9.68 (55) all_52_3 = all_6_2
% 65.12/9.68 (56) op(all_10_2, e2) = all_10_1
% 65.12/9.68 (57) all_52_0 = all_10_2
% 65.12/9.68 (58) all_58_11 = all_54_12
% 65.12/9.68 (59) all_58_3 = all_54_1
% 65.12/9.68 (60) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.12/9.68 (61) all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 65.12/9.68 (62) all_58_5 = all_54_8
% 65.12/9.68 (63) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.12/9.68 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.12/9.68 (64) all_58_10 = all_54_13
% 65.12/9.68 (65) op(all_4_2, all_4_2) = e2
% 65.12/9.68 (66) ~ (all_54_7 = all_14_2)
% 65.12/9.68 (67) ~ (all_54_4 = all_54_12)
% 65.12/9.68 (68) ~ (all_54_12 = all_6_2)
% 65.12/9.68 (69) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.12/9.68 (70) ~ (all_54_12 = all_54_15)
% 65.12/9.68 (71) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.12/9.68 (72) all_56_14 = all_54_15
% 65.12/9.68
% 65.12/9.68 Begin of proof
% 65.12/9.68 |
% 65.12/9.68 | BETA: splitting (2) gives:
% 65.12/9.68 |
% 65.12/9.68 | Case 1:
% 65.12/9.68 | |
% 65.12/9.68 | | (73) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.68 | |
% 65.12/9.68 | | ALPHA: (73) implies:
% 65.12/9.68 | | (74) all_52_2 = e2
% 65.12/9.68 | | (75) ~ (all_52_0 = e3)
% 65.12/9.68 | |
% 65.12/9.68 | | COMBINE_EQS: (4), (74) imply:
% 65.12/9.68 | | (76) all_4_2 = e2
% 65.12/9.68 | |
% 65.12/9.68 | | REF_CLOSE: (9), (16), (21), (29), (32), (33), (39), (44), (48), (55), (57),
% 65.12/9.68 | | (63), (65), (74), (75), (76) are inconsistent by sub-proof #2.
% 65.12/9.68 | |
% 65.12/9.68 | Case 2:
% 65.12/9.68 | |
% 65.12/9.68 | | (77) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.12/9.68 | |
% 65.12/9.68 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.12/9.68 | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 65.12/9.68 | | (26), (27), (28), (30), (31), (33), (34), (35), (36), (37), (38),
% 65.12/9.68 | | (40), (41), (42), (43), (44), (45), (46), (47), (49), (50), (51),
% 65.12/9.68 | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 65.12/9.68 | | (63), (64), (66), (67), (68), (69), (70), (71), (72), (77) are
% 65.12/9.68 | | inconsistent by sub-proof #15.
% 65.12/9.68 | |
% 65.12/9.68 | End of split
% 65.12/9.68 |
% 65.12/9.68 End of proof
% 65.12/9.68
% 65.12/9.68 Sub-proof #2 shows that the following formulas are inconsistent:
% 65.12/9.68 ----------------------------------------------------------------
% 65.12/9.68 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.12/9.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.12/9.68 (2) ~ (all_52_0 = e3)
% 65.12/9.68 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.12/9.68 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.12/9.68 (4) op(e2, e2) = all_10_2
% 65.12/9.68 (5) op(all_10_2, all_10_2) = e1
% 65.12/9.68 (6) ~ (e3 = e0)
% 65.12/9.68 (7) ~ (e1 = e0)
% 65.12/9.68 (8) all_4_2 = e2
% 65.12/9.68 (9) op(e3, e3) = all_4_2
% 65.12/9.68 (10) op(all_6_2, all_6_2) = e3
% 65.12/9.68 (11) ~ (e2 = e0)
% 65.12/9.68 (12) all_52_3 = all_6_2
% 65.12/9.68 (13) all_52_0 = all_10_2
% 65.12/9.68 (14) all_52_2 = e2
% 65.12/9.68 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.12/9.68 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.12/9.68 (16) op(all_4_2, all_4_2) = e2
% 65.12/9.68
% 65.12/9.68 Begin of proof
% 65.12/9.68 |
% 65.12/9.68 | REDUCE: (2), (13) imply:
% 65.12/9.68 | (17) ~ (all_10_2 = e3)
% 65.12/9.68 |
% 65.12/9.68 | REDUCE: (8), (16) imply:
% 65.12/9.68 | (18) op(e2, e2) = e2
% 65.12/9.68 |
% 65.12/9.68 | REDUCE: (8), (9) imply:
% 65.12/9.68 | (19) op(e3, e3) = e2
% 65.12/9.68 |
% 65.12/9.68 | GROUND_INST: instantiating (1) with all_10_2, e2, e2, e2, simplifying with
% 65.12/9.68 | (4), (18) gives:
% 65.12/9.68 | (20) all_10_2 = e2
% 65.12/9.68 |
% 65.12/9.68 | REDUCE: (17), (20) imply:
% 65.12/9.68 | (21) ~ (e3 = e2)
% 65.12/9.68 |
% 65.12/9.68 | SIMP: (21) implies:
% 65.12/9.68 | (22) ~ (e3 = e2)
% 65.12/9.69 |
% 65.12/9.69 | REDUCE: (5), (20) imply:
% 65.12/9.69 | (23) op(e2, e2) = e1
% 65.12/9.69 |
% 65.12/9.69 | REF_CLOSE: (1), (3), (4), (6), (7), (10), (11), (12), (13), (14), (15), (17),
% 65.12/9.69 | (19), (22), (23) are inconsistent by sub-proof #36.
% 65.12/9.69 |
% 65.12/9.69 End of proof
% 65.12/9.69
% 65.12/9.69 Sub-proof #3 shows that the following formulas are inconsistent:
% 65.12/9.69 ----------------------------------------------------------------
% 65.12/9.69 (1) all_52_2 = all_4_2
% 65.12/9.69 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.12/9.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.12/9.69 (3) op(e0, e0) = all_6_2
% 65.12/9.69 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.12/9.69 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.12/9.69 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.12/9.69 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.12/9.69 (6) ~ (e3 = e1)
% 65.12/9.69 (7) op(e2, e2) = all_10_2
% 65.12/9.69 (8) all_52_1 = all_14_2
% 65.12/9.69 (9) ~ (e3 = e0)
% 65.12/9.69 (10) ~ (e1 = e0)
% 65.12/9.69 (11) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.12/9.69 (12) op(e3, e3) = all_4_2
% 65.12/9.69 (13) ~ (e2 = e0)
% 65.12/9.69 (14) ~ (e2 = e1)
% 65.12/9.69 (15) all_52_3 = all_6_2
% 65.12/9.69 (16) all_52_0 = all_10_2
% 65.12/9.69 (17) op(all_14_2, all_14_2) = e0
% 65.12/9.69 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.12/9.69 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.12/9.69 (19) op(all_4_2, all_4_2) = e2
% 65.12/9.69
% 65.12/9.69 Begin of proof
% 65.12/9.69 |
% 65.12/9.69 | ALPHA: (11) implies:
% 65.12/9.69 | (20) all_52_2 = e2
% 65.12/9.69 |
% 65.12/9.69 | COMBINE_EQS: (1), (20) imply:
% 65.12/9.69 | (21) all_4_2 = e2
% 65.12/9.69 |
% 65.12/9.69 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 65.12/9.69 | (15), (16), (17), (18), (19), (20), (21) are inconsistent by
% 65.12/9.69 | sub-proof #4.
% 65.12/9.69 |
% 65.12/9.69 End of proof
% 65.12/9.69
% 65.12/9.69 Sub-proof #4 shows that the following formulas are inconsistent:
% 65.12/9.69 ----------------------------------------------------------------
% 65.12/9.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.12/9.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.12/9.69 (2) op(e0, e0) = all_6_2
% 65.12/9.69 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.12/9.69 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.12/9.69 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.12/9.69 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.12/9.69 (5) ~ (e3 = e1)
% 65.12/9.69 (6) op(e2, e2) = all_10_2
% 65.12/9.69 (7) all_52_1 = all_14_2
% 65.12/9.69 (8) ~ (e3 = e0)
% 65.12/9.69 (9) ~ (e1 = e0)
% 65.12/9.69 (10) all_4_2 = e2
% 65.12/9.69 (11) op(e3, e3) = all_4_2
% 65.12/9.69 (12) ~ (e2 = e0)
% 65.12/9.69 (13) ~ (e2 = e1)
% 65.12/9.69 (14) all_52_3 = all_6_2
% 65.12/9.69 (15) all_52_0 = all_10_2
% 65.12/9.69 (16) all_52_2 = e2
% 65.12/9.69 (17) op(all_14_2, all_14_2) = e0
% 65.12/9.69 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.12/9.69 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.12/9.69 (19) op(all_4_2, all_4_2) = e2
% 65.12/9.69
% 65.12/9.69 Begin of proof
% 65.12/9.69 |
% 65.12/9.69 | REDUCE: (10), (19) imply:
% 65.12/9.69 | (20) op(e2, e2) = e2
% 65.12/9.69 |
% 65.12/9.69 | REDUCE: (10), (11) imply:
% 65.12/9.69 | (21) op(e3, e3) = e2
% 65.12/9.69 |
% 65.12/9.69 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 65.12/9.69 | (15), (16), (17), (18), (20), (21) are inconsistent by sub-proof
% 65.12/9.69 | #5.
% 65.12/9.69 |
% 65.12/9.69 End of proof
% 65.12/9.69
% 65.12/9.69 Sub-proof #5 shows that the following formulas are inconsistent:
% 65.12/9.69 ----------------------------------------------------------------
% 65.12/9.69 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.12/9.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.12/9.69 (2) op(e0, e0) = all_6_2
% 65.12/9.69 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.12/9.69 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.12/9.69 (4) op(e2, e2) = e2
% 65.12/9.69 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.12/9.69 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.12/9.69 (6) ~ (e3 = e1)
% 65.12/9.69 (7) op(e2, e2) = all_10_2
% 65.12/9.69 (8) all_52_1 = all_14_2
% 65.12/9.69 (9) ~ (e3 = e0)
% 65.12/9.69 (10) ~ (e1 = e0)
% 65.12/9.69 (11) op(e3, e3) = e2
% 65.12/9.69 (12) ~ (e2 = e0)
% 65.12/9.69 (13) ~ (e2 = e1)
% 65.12/9.69 (14) all_52_3 = all_6_2
% 65.12/9.69 (15) all_52_0 = all_10_2
% 65.12/9.69 (16) all_52_2 = e2
% 65.12/9.69 (17) op(all_14_2, all_14_2) = e0
% 65.12/9.69 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.12/9.69 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.12/9.69
% 65.12/9.69 Begin of proof
% 65.12/9.69 |
% 65.12/9.69 | GROUND_INST: instantiating (1) with all_10_2, e2, e2, e2, simplifying with
% 65.12/9.69 | (4), (7) gives:
% 65.12/9.69 | (19) all_10_2 = e2
% 65.12/9.69 |
% 65.12/9.69 | COMBINE_EQS: (15), (19) imply:
% 65.12/9.69 | (20) all_52_0 = e2
% 65.12/9.69 |
% 65.12/9.69 | BETA: splitting (5) gives:
% 65.12/9.69 |
% 65.12/9.69 | Case 1:
% 65.12/9.69 | |
% 65.12/9.69 | | (21) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.12/9.69 | |
% 65.12/9.69 | | ALPHA: (21) implies:
% 65.12/9.69 | | (22) all_52_0 = e1
% 65.12/9.69 | |
% 65.12/9.69 | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 65.12/9.69 | | (16), (17), (18), (22) are inconsistent by sub-proof #78.
% 65.12/9.69 | |
% 65.12/9.69 | Case 2:
% 65.12/9.69 | |
% 65.12/9.69 | | (23) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 65.12/9.69 | | = e0))
% 65.12/9.69 | |
% 65.12/9.69 | | BETA: splitting (23) gives:
% 65.12/9.69 | |
% 65.12/9.69 | | Case 1:
% 65.12/9.69 | | |
% 65.12/9.69 | | | (24) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.12/9.69 | | |
% 65.12/9.69 | | | ALPHA: (24) implies:
% 65.12/9.69 | | | (25) all_52_2 = e1
% 65.12/9.69 | | |
% 65.12/9.69 | | | COMBINE_EQS: (16), (25) imply:
% 65.12/9.69 | | | (26) e2 = e1
% 65.12/9.69 | | |
% 65.12/9.69 | | | COMBINE_EQS: (20), (26) imply:
% 65.12/9.69 | | | (27) all_52_0 = e1
% 65.12/9.69 | | |
% 65.12/9.69 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13),
% 65.12/9.69 | | | (14), (16), (17), (18), (27) are inconsistent by sub-proof #78.
% 65.12/9.69 | | |
% 65.12/9.69 | | Case 2:
% 65.12/9.69 | | |
% 65.12/9.69 | | | (28) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.12/9.69 | | |
% 65.12/9.69 | | | ALPHA: (28) implies:
% 65.12/9.69 | | | (29) ~ (all_52_1 = e0)
% 65.12/9.69 | | |
% 65.12/9.69 | | | REDUCE: (8), (29) imply:
% 65.12/9.69 | | | (30) ~ (all_14_2 = e0)
% 65.12/9.69 | | |
% 65.12/9.69 | | | BETA: splitting (18) gives:
% 65.12/9.69 | | |
% 65.12/9.69 | | | Case 1:
% 65.12/9.69 | | | |
% 65.12/9.69 | | | | (31) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.12/9.69 | | | |
% 65.12/9.69 | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 65.12/9.69 | | | | (17), (31) are inconsistent by sub-proof #87.
% 65.12/9.69 | | | |
% 65.49/9.69 | | | Case 2:
% 65.49/9.69 | | | |
% 65.49/9.69 | | | | (32) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.49/9.69 | | | | (all_52_3 = e3))
% 65.49/9.69 | | | |
% 65.49/9.69 | | | | REF_CLOSE: (8), (12), (16), (30), (32) are inconsistent by sub-proof
% 65.49/9.69 | | | | #86.
% 65.49/9.69 | | | |
% 65.49/9.69 | | | End of split
% 65.49/9.69 | | |
% 65.49/9.69 | | End of split
% 65.49/9.69 | |
% 65.49/9.69 | End of split
% 65.49/9.69 |
% 65.49/9.69 End of proof
% 65.49/9.69
% 65.49/9.69 Sub-proof #6 shows that the following formulas are inconsistent:
% 65.49/9.69 ----------------------------------------------------------------
% 65.49/9.69 (1) ~ (all_14_1 = e0)
% 65.49/9.69 (2) all_42_1 = all_4_1
% 65.49/9.69 (3) all_52_2 = all_4_2
% 65.49/9.69 (4) all_58_9 = all_54_15
% 65.49/9.69 (5) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 65.49/9.69 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.69 (7) all_52_3 = e3
% 65.49/9.69 (8) all_58_2 = e3 | all_58_3 = e3 | all_58_4 = e3 | all_58_10 = e3
% 65.49/9.69 (9) all_58_6 = e0
% 65.49/9.69 (10) all_58_2 = e2
% 65.49/9.69 (11) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.69 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.69 (12) ~ (e3 = e1)
% 65.49/9.69 (13) all_56_7 = all_54_6
% 65.49/9.69 (14) all_58_8 = all_54_3
% 65.49/9.69 (15) ~ (all_54_6 = e2)
% 65.49/9.69 (16) ~ (e3 = e0)
% 65.49/9.69 (17) ~ (e1 = e0)
% 65.49/9.69 (18) ~ (all_14_1 = e2)
% 65.49/9.69 (19) all_58_7 = all_54_7
% 65.49/9.69 (20) ~ (all_54_13 = all_54_15)
% 65.49/9.69 (21) ~ (all_54_6 = all_4_2)
% 65.49/9.69 (22) all_52_0 = e0
% 65.49/9.69 (23) ~ (all_14_1 = e3)
% 65.49/9.69 (24) op(e1, e3) = all_54_6
% 65.49/9.69 (25) op(all_4_2, e3) = all_4_1
% 65.49/9.69 (26) all_42_2 = all_4_2
% 65.49/9.69 (27) ~ (all_54_3 = e3)
% 65.49/9.69 (28) all_58_4 = all_14_1
% 65.49/9.69 (29) all_56_9 = all_14_1
% 65.49/9.69 (30) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.49/9.69 (31) ~ (all_42_1 = e0) | ~ (all_42_2 = e1)
% 65.49/9.69 (32) all_58_3 = all_54_1
% 65.49/9.69 (33) all_52_1 = e2
% 65.49/9.69 (34) all_58_10 = all_54_13
% 65.49/9.70 (35) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 65.49/9.70 (36) ~ (all_54_6 = all_54_7)
% 65.49/9.70 (37) ~ (all_54_1 = e3)
% 65.49/9.70
% 65.49/9.70 Begin of proof
% 65.49/9.70 |
% 65.49/9.70 | BETA: splitting (11) gives:
% 65.49/9.70 |
% 65.49/9.70 | Case 1:
% 65.49/9.70 | |
% 65.49/9.70 | | (38) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.49/9.70 | |
% 65.49/9.70 | | ALPHA: (38) implies:
% 65.49/9.70 | | (39) all_52_0 = e1
% 65.49/9.70 | |
% 65.49/9.70 | | REF_CLOSE: (17), (22), (39) are inconsistent by sub-proof #133.
% 65.49/9.70 | |
% 65.49/9.70 | Case 2:
% 65.49/9.70 | |
% 65.49/9.70 | | (40) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 65.49/9.70 | | = e0))
% 65.49/9.70 | |
% 65.49/9.70 | | BETA: splitting (40) gives:
% 65.49/9.70 | |
% 65.49/9.70 | | Case 1:
% 65.49/9.70 | | |
% 65.49/9.70 | | | (41) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.49/9.70 | | |
% 65.49/9.70 | | | ALPHA: (41) implies:
% 65.49/9.70 | | | (42) all_52_2 = e1
% 65.49/9.70 | | | (43) ~ (all_52_1 = e3)
% 65.49/9.70 | | |
% 65.49/9.70 | | | COMBINE_EQS: (3), (42) imply:
% 65.49/9.70 | | | (44) all_4_2 = e1
% 65.49/9.70 | | |
% 65.49/9.70 | | | COMBINE_EQS: (26), (44) imply:
% 65.49/9.70 | | | (45) all_42_2 = e1
% 65.49/9.70 | | |
% 65.49/9.70 | | | REDUCE: (21), (44) imply:
% 65.49/9.70 | | | (46) ~ (all_54_6 = e1)
% 65.49/9.70 | | |
% 65.49/9.70 | | | REDUCE: (33), (43) imply:
% 65.49/9.70 | | | (47) ~ (e3 = e2)
% 65.49/9.70 | | |
% 65.49/9.70 | | | SIMP: (47) implies:
% 65.49/9.70 | | | (48) ~ (e3 = e2)
% 65.49/9.70 | | |
% 65.49/9.70 | | | REDUCE: (25), (44) imply:
% 65.49/9.70 | | | (49) op(e1, e3) = all_4_1
% 65.49/9.70 | | |
% 65.49/9.70 | | | BETA: splitting (8) gives:
% 65.49/9.70 | | |
% 65.49/9.70 | | | Case 1:
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | (50) all_58_2 = e3
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | COMBINE_EQS: (10), (50) imply:
% 65.49/9.70 | | | | (51) e3 = e2
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | REDUCE: (48), (51) imply:
% 65.49/9.70 | | | | (52) $false
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | CLOSE: (52) is inconsistent.
% 65.49/9.70 | | | |
% 65.49/9.70 | | | Case 2:
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | (53) all_58_3 = e3 | all_58_4 = e3 | all_58_10 = e3
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | BETA: splitting (30) gives:
% 65.49/9.70 | | | |
% 65.49/9.70 | | | | Case 1:
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | (54) all_56_9 = e2
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | COMBINE_EQS: (29), (54) imply:
% 65.49/9.70 | | | | | (55) all_14_1 = e2
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | SIMP: (55) implies:
% 65.49/9.70 | | | | | (56) all_14_1 = e2
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | REDUCE: (18), (56) imply:
% 65.49/9.70 | | | | | (57) $false
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | CLOSE: (57) is inconsistent.
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | Case 2:
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | (58) all_56_9 = e1 | all_56_9 = e0
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | BETA: splitting (31) gives:
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | | Case 1:
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | (59) ~ (all_42_1 = e0)
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | REDUCE: (2), (59) imply:
% 65.49/9.70 | | | | | | (60) ~ (all_4_1 = e0)
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | BETA: splitting (58) gives:
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | Case 1:
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | (61) all_56_9 = e1
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | COMBINE_EQS: (29), (61) imply:
% 65.49/9.70 | | | | | | | (62) all_14_1 = e1
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | SIMP: (62) implies:
% 65.49/9.70 | | | | | | | (63) all_14_1 = e1
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | COMBINE_EQS: (28), (63) imply:
% 65.49/9.70 | | | | | | | (64) all_58_4 = e1
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | REDUCE: (23), (63) imply:
% 65.49/9.70 | | | | | | | (65) ~ (e3 = e1)
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | BETA: splitting (53) gives:
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | (66) all_58_3 = e3
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | COMBINE_EQS: (32), (66) imply:
% 65.49/9.70 | | | | | | | | (67) all_54_1 = e3
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | REDUCE: (37), (67) imply:
% 65.49/9.70 | | | | | | | | (68) $false
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | CLOSE: (68) is inconsistent.
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | (69) all_58_4 = e3 | all_58_10 = e3
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | BETA: splitting (69) gives:
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | (70) all_58_4 = e3
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | COMBINE_EQS: (64), (70) imply:
% 65.49/9.70 | | | | | | | | | (71) e3 = e1
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | SIMP: (71) implies:
% 65.49/9.70 | | | | | | | | | (72) e3 = e1
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | REDUCE: (12), (72) imply:
% 65.49/9.70 | | | | | | | | | (73) $false
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | CLOSE: (73) is inconsistent.
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | (74) all_58_10 = e3
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | COMBINE_EQS: (34), (74) imply:
% 65.49/9.70 | | | | | | | | | (75) all_54_13 = e3
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | REDUCE: (20), (75) imply:
% 65.49/9.70 | | | | | | | | | (76) ~ (all_54_15 = e3)
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | SIMP: (76) implies:
% 65.49/9.70 | | | | | | | | | (77) ~ (all_54_15 = e3)
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | BETA: splitting (35) gives:
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | (78) all_58_6 = e3
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | COMBINE_EQS: (9), (78) imply:
% 65.49/9.70 | | | | | | | | | | (79) e3 = e0
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | REDUCE: (16), (79) imply:
% 65.49/9.70 | | | | | | | | | | (80) $false
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | CLOSE: (80) is inconsistent.
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | (81) all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | BETA: splitting (81) gives:
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | (82) all_58_7 = e3
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | COMBINE_EQS: (19), (82) imply:
% 65.49/9.70 | | | | | | | | | | | (83) all_54_7 = e3
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | REDUCE: (36), (83) imply:
% 65.49/9.70 | | | | | | | | | | | (84) ~ (all_54_6 = e3)
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | BETA: splitting (5) gives:
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | (85) all_56_7 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | COMBINE_EQS: (13), (85) imply:
% 65.49/9.70 | | | | | | | | | | | | (86) all_54_6 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | SIMP: (86) implies:
% 65.49/9.70 | | | | | | | | | | | | (87) all_54_6 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | REDUCE: (84), (87) imply:
% 65.49/9.70 | | | | | | | | | | | | (88) $false
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | CLOSE: (88) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | (89) all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | BETA: splitting (89) gives:
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | (90) all_56_7 = e2
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | COMBINE_EQS: (13), (90) imply:
% 65.49/9.70 | | | | | | | | | | | | | (91) all_54_6 = e2
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | REDUCE: (15), (91) imply:
% 65.49/9.70 | | | | | | | | | | | | | (92) $false
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | CLOSE: (92) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | (93) all_56_7 = e1 | all_56_7 = e0
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | (94) all_56_7 = e1
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | COMBINE_EQS: (13), (94) imply:
% 65.49/9.70 | | | | | | | | | | | | | | (95) all_54_6 = e1
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | REDUCE: (46), (95) imply:
% 65.49/9.70 | | | | | | | | | | | | | | (96) $false
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | CLOSE: (96) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | (97) all_56_7 = e0
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | COMBINE_EQS: (13), (97) imply:
% 65.49/9.70 | | | | | | | | | | | | | | (98) all_54_6 = e0
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | REDUCE: (24), (98) imply:
% 65.49/9.70 | | | | | | | | | | | | | | (99) op(e1, e3) = e0
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, all_4_1, e3, e1,
% 65.49/9.70 | | | | | | | | | | | | | | simplifying with (49), (99) gives:
% 65.49/9.70 | | | | | | | | | | | | | | (100) all_4_1 = e0
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | REDUCE: (60), (100) imply:
% 65.49/9.70 | | | | | | | | | | | | | | (101) $false
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | | CLOSE: (101) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | (102) all_58_8 = e3 | all_58_9 = e3
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | BETA: splitting (102) gives:
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | Case 1:
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | (103) all_58_8 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | COMBINE_EQS: (14), (103) imply:
% 65.49/9.70 | | | | | | | | | | | | (104) all_54_3 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | REDUCE: (27), (104) imply:
% 65.49/9.70 | | | | | | | | | | | | (105) $false
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | CLOSE: (105) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | Case 2:
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | (106) all_58_9 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | COMBINE_EQS: (4), (106) imply:
% 65.49/9.70 | | | | | | | | | | | | (107) all_54_15 = e3
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | REDUCE: (77), (107) imply:
% 65.49/9.70 | | | | | | | | | | | | (108) $false
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | | CLOSE: (108) is inconsistent.
% 65.49/9.70 | | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | | |
% 65.49/9.70 | | | | | | | | | End of split
% 65.49/9.70 | | | | | | | | |
% 65.49/9.70 | | | | | | | | End of split
% 65.49/9.70 | | | | | | | |
% 65.49/9.70 | | | | | | | End of split
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | Case 2:
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | (109) all_56_9 = e0
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | COMBINE_EQS: (29), (109) imply:
% 65.49/9.70 | | | | | | | (110) all_14_1 = e0
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | SIMP: (110) implies:
% 65.49/9.70 | | | | | | | (111) all_14_1 = e0
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | REDUCE: (1), (111) imply:
% 65.49/9.70 | | | | | | | (112) $false
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | | CLOSE: (112) is inconsistent.
% 65.49/9.70 | | | | | | |
% 65.49/9.70 | | | | | | End of split
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | Case 2:
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | (113) ~ (all_42_2 = e1)
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | REDUCE: (45), (113) imply:
% 65.49/9.70 | | | | | | (114) $false
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | | CLOSE: (114) is inconsistent.
% 65.49/9.70 | | | | | |
% 65.49/9.70 | | | | | End of split
% 65.49/9.70 | | | | |
% 65.49/9.70 | | | | End of split
% 65.49/9.70 | | | |
% 65.49/9.70 | | | End of split
% 65.49/9.70 | | |
% 65.49/9.70 | | Case 2:
% 65.49/9.70 | | |
% 65.49/9.70 | | | (115) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.49/9.70 | | |
% 65.49/9.70 | | | REF_CLOSE: (7), (12), (115) are inconsistent by sub-proof #145.
% 65.49/9.70 | | |
% 65.49/9.70 | | End of split
% 65.49/9.70 | |
% 65.49/9.70 | End of split
% 65.49/9.70 |
% 65.49/9.70 End of proof
% 65.49/9.70
% 65.49/9.70 Sub-proof #7 shows that the following formulas are inconsistent:
% 65.49/9.70 ----------------------------------------------------------------
% 65.49/9.70 (1) ~ (all_54_4 = all_6_2)
% 65.49/9.70 (2) ~ (all_54_2 = all_6_2)
% 65.49/9.70 (3) ~ (all_54_4 = all_54_6)
% 65.49/9.70 (4) all_52_2 = all_4_2
% 65.49/9.70 (5) all_58_9 = all_54_15
% 65.49/9.70 (6) ~ (all_54_7 = all_10_2)
% 65.49/9.70 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.70 (8) ~ (all_54_9 = all_54_10)
% 65.49/9.70 (9) all_58_13 = all_54_10
% 65.49/9.70 (10) all_58_12 = all_4_2
% 65.49/9.70 (11) op(e2, e0) = all_54_8
% 65.49/9.70 (12) ~ (all_54_1 = all_54_9)
% 65.49/9.70 (13) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.70 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.70 (14) all_56_4 = all_54_4
% 65.49/9.70 (15) all_58_0 = e3 | all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3
% 65.49/9.70 (16) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.49/9.70 (17) op(all_6_2, e0) = all_6_1
% 65.49/9.70 (18) ~ (all_4_1 = e1) | ~ (all_4_2 = e0)
% 65.49/9.70 (19) ~ (e3 = e1)
% 65.49/9.70 (20) op(e2, e2) = all_10_2
% 65.49/9.70 (21) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0
% 65.49/9.70 (22) all_58_0 = e1 | all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1
% 65.49/9.70 (23) all_16_2 = all_6_2
% 65.49/9.70 (24) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.49/9.70 (25) all_58_0 = all_6_2
% 65.49/9.70 (26) all_58_8 = all_54_3
% 65.49/9.70 (27) all_52_1 = all_14_2
% 65.49/9.70 (28) ~ (all_54_3 = all_54_7)
% 65.49/9.70 (29) all_56_9 = all_54_9
% 65.49/9.70 (30) ~ (all_54_12 = all_4_2)
% 65.49/9.70 (31) ~ (e3 = e0)
% 65.49/9.70 (32) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 65.49/9.70 (33) all_58_7 = all_54_7
% 65.49/9.70 (34) ~ (all_54_2 = all_4_2)
% 65.49/9.70 (35) all_58_6 = all_10_2
% 65.49/9.70 (36) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 65.49/9.70 (37) ~ (all_54_4 = all_54_7)
% 65.49/9.70 (38) all_58_14 = all_54_6
% 65.49/9.70 (39) ~ (all_54_9 = all_14_2)
% 65.49/9.70 (40) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.70 (41) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.49/9.70 (42) all_56_6 = all_54_7
% 65.49/9.70 (43) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.70 (44) ~ (all_54_10 = all_4_2)
% 65.49/9.70 (45) ~ (all_54_15 = all_4_2)
% 65.49/9.70 (46) op(all_4_2, e3) = all_4_1
% 65.49/9.70 (47) all_58_1 = all_54_4
% 65.49/9.70 (48) all_52_3 = all_6_2
% 65.49/9.70 (49) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.70 (50) all_52_0 = all_10_2
% 65.49/9.70 (51) all_58_11 = all_54_12
% 65.49/9.71 (52) ~ (all_54_10 = all_10_2)
% 65.49/9.71 (53) all_58_3 = all_54_1
% 65.49/9.71 (54) all_16_1 = all_6_1
% 65.49/9.71 (55) op(e0, e3) = all_54_2
% 65.49/9.71 (56) all_56_11 = all_54_10
% 65.49/9.71 (57) op(all_6_2, all_6_2) = e1
% 65.49/9.71 (58) ~ (e3 = e2)
% 65.49/9.71 (59) all_58_5 = all_54_8
% 65.49/9.71 (60) ~ (all_54_9 = all_10_2)
% 65.49/9.71 (61) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.71 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.71 (62) ~ (all_54_15 = all_10_2)
% 65.49/9.71 (63) ~ (all_54_4 = all_14_2)
% 65.49/9.71 (64) ~ (all_54_7 = all_54_15)
% 65.49/9.71 (65) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 65.49/9.71 (66) ~ (all_54_7 = all_14_2)
% 65.49/9.71 (67) ~ (all_54_4 = all_54_12)
% 65.49/9.71 (68) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 65.49/9.71 (69) ~ (all_54_12 = all_54_15)
% 65.49/9.71 (70) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.71 (71) all_58_15 = all_54_2
% 65.49/9.71 (72) all_56_14 = all_54_15
% 65.49/9.71
% 65.49/9.71 Begin of proof
% 65.49/9.71 |
% 65.49/9.71 | ALPHA: (49) implies:
% 65.49/9.71 | (73) all_52_3 = e2
% 65.49/9.71 | (74) ~ (all_52_0 = e0)
% 65.49/9.71 |
% 65.49/9.71 | COMBINE_EQS: (48), (73) imply:
% 65.49/9.71 | (75) all_6_2 = e2
% 65.49/9.71 |
% 65.49/9.71 | COMBINE_EQS: (23), (75) imply:
% 65.49/9.71 | (76) all_16_2 = e2
% 65.49/9.71 |
% 65.49/9.71 | COMBINE_EQS: (25), (75) imply:
% 65.49/9.71 | (77) all_58_0 = e2
% 65.49/9.71 |
% 65.49/9.71 | REDUCE: (2), (75) imply:
% 65.49/9.71 | (78) ~ (all_54_2 = e2)
% 65.49/9.71 |
% 65.49/9.71 | REDUCE: (1), (75) imply:
% 65.49/9.71 | (79) ~ (all_54_4 = e2)
% 65.49/9.71 |
% 65.49/9.71 | REDUCE: (50), (74) imply:
% 65.49/9.71 | (80) ~ (all_10_2 = e0)
% 65.49/9.71 |
% 65.49/9.71 | REDUCE: (57), (75) imply:
% 65.49/9.71 | (81) op(e2, e2) = e1
% 65.49/9.71 |
% 65.49/9.71 | REDUCE: (17), (75) imply:
% 65.49/9.71 | (82) op(e2, e0) = all_6_1
% 65.49/9.71 |
% 65.49/9.71 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 65.49/9.71 | (15), (16), (18), (19), (20), (21), (22), (24), (26), (27), (28),
% 65.49/9.71 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 65.49/9.71 | (40), (41), (42), (43), (44), (45), (46), (47), (50), (51), (52),
% 65.49/9.71 | (53), (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 65.49/9.71 | (65), (66), (67), (68), (69), (70), (71), (72), (73), (76), (77),
% 65.49/9.71 | (78), (79), (80), (81), (82) are inconsistent by sub-proof #8.
% 65.49/9.71 |
% 65.49/9.71 End of proof
% 65.49/9.71
% 65.49/9.71 Sub-proof #8 shows that the following formulas are inconsistent:
% 65.49/9.71 ----------------------------------------------------------------
% 65.49/9.71 (1) ~ (all_10_2 = e0)
% 65.49/9.71 (2) ~ (all_54_4 = all_54_6)
% 65.49/9.71 (3) all_52_2 = all_4_2
% 65.49/9.71 (4) op(e2, e2) = e1
% 65.49/9.71 (5) all_58_9 = all_54_15
% 65.49/9.71 (6) ~ (all_54_7 = all_10_2)
% 65.49/9.71 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.71 (8) ~ (all_54_4 = e2)
% 65.49/9.71 (9) ~ (all_54_9 = all_54_10)
% 65.49/9.71 (10) op(e2, e0) = all_6_1
% 65.49/9.71 (11) all_58_13 = all_54_10
% 65.49/9.71 (12) all_58_12 = all_4_2
% 65.49/9.71 (13) op(e2, e0) = all_54_8
% 65.49/9.71 (14) ~ (all_54_1 = all_54_9)
% 65.49/9.71 (15) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.71 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.71 (16) all_56_4 = all_54_4
% 65.49/9.71 (17) all_58_0 = e3 | all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3
% 65.49/9.71 (18) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.49/9.71 (19) ~ (all_54_2 = e2)
% 65.49/9.71 (20) ~ (all_4_1 = e1) | ~ (all_4_2 = e0)
% 65.49/9.71 (21) ~ (e3 = e1)
% 65.49/9.71 (22) op(e2, e2) = all_10_2
% 65.49/9.71 (23) all_58_0 = e0 | all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0
% 65.49/9.71 (24) all_58_0 = e1 | all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1
% 65.49/9.71 (25) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.49/9.71 (26) all_58_8 = all_54_3
% 65.49/9.71 (27) all_52_1 = all_14_2
% 65.49/9.71 (28) ~ (all_54_3 = all_54_7)
% 65.49/9.71 (29) all_56_9 = all_54_9
% 65.49/9.71 (30) ~ (all_54_12 = all_4_2)
% 65.49/9.71 (31) ~ (e3 = e0)
% 65.49/9.71 (32) all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 65.49/9.71 (33) all_58_7 = all_54_7
% 65.49/9.71 (34) ~ (all_54_2 = all_4_2)
% 65.49/9.71 (35) all_58_6 = all_10_2
% 65.49/9.71 (36) all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 65.49/9.71 (37) ~ (all_54_4 = all_54_7)
% 65.49/9.71 (38) all_58_14 = all_54_6
% 65.49/9.71 (39) ~ (all_54_9 = all_14_2)
% 65.49/9.71 (40) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.71 (41) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.49/9.71 (42) all_56_6 = all_54_7
% 65.49/9.71 (43) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.71 (44) ~ (all_54_10 = all_4_2)
% 65.49/9.71 (45) all_52_3 = e2
% 65.49/9.71 (46) ~ (all_54_15 = all_4_2)
% 65.49/9.71 (47) op(all_4_2, e3) = all_4_1
% 65.49/9.71 (48) all_58_1 = all_54_4
% 65.49/9.71 (49) all_52_0 = all_10_2
% 65.49/9.71 (50) all_58_11 = all_54_12
% 65.49/9.71 (51) ~ (all_54_10 = all_10_2)
% 65.49/9.71 (52) all_16_2 = e2
% 65.49/9.71 (53) all_58_3 = all_54_1
% 65.49/9.71 (54) all_16_1 = all_6_1
% 65.49/9.71 (55) op(e0, e3) = all_54_2
% 65.49/9.71 (56) all_56_11 = all_54_10
% 65.49/9.71 (57) ~ (e3 = e2)
% 65.49/9.71 (58) all_58_5 = all_54_8
% 65.49/9.71 (59) ~ (all_54_9 = all_10_2)
% 65.49/9.71 (60) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.71 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.71 (61) ~ (all_54_15 = all_10_2)
% 65.49/9.71 (62) ~ (all_54_4 = all_14_2)
% 65.49/9.71 (63) ~ (all_54_7 = all_54_15)
% 65.49/9.71 (64) all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 65.49/9.71 (65) all_58_0 = e2
% 65.49/9.71 (66) ~ (all_54_7 = all_14_2)
% 65.49/9.71 (67) ~ (all_54_4 = all_54_12)
% 65.49/9.71 (68) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 65.49/9.71 (69) ~ (all_54_12 = all_54_15)
% 65.49/9.71 (70) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.71 (71) all_58_15 = all_54_2
% 65.49/9.71 (72) all_56_14 = all_54_15
% 65.49/9.71
% 65.49/9.71 Begin of proof
% 65.49/9.71 |
% 65.49/9.71 | BETA: splitting (18) gives:
% 65.49/9.71 |
% 65.49/9.71 | Case 1:
% 65.49/9.71 | |
% 65.49/9.71 | | (73) ~ (all_16_1 = e3)
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (54), (73) imply:
% 65.49/9.71 | | (74) ~ (all_6_1 = e3)
% 65.49/9.71 | |
% 65.49/9.71 | | GROUND_INST: instantiating (7) with all_54_8, all_6_1, e0, e2, simplifying
% 65.49/9.71 | | with (10), (13) gives:
% 65.49/9.71 | | (75) all_54_8 = all_6_1
% 65.49/9.71 | |
% 65.49/9.71 | | GROUND_INST: instantiating (7) with all_10_2, e1, e2, e2, simplifying with
% 65.49/9.71 | | (4), (22) gives:
% 65.49/9.71 | | (76) all_10_2 = e1
% 65.49/9.71 | |
% 65.49/9.71 | | COMBINE_EQS: (49), (76) imply:
% 65.49/9.71 | | (77) all_52_0 = e1
% 65.49/9.71 | |
% 65.49/9.71 | | COMBINE_EQS: (35), (76) imply:
% 65.49/9.71 | | (78) all_58_6 = e1
% 65.49/9.71 | |
% 65.49/9.71 | | COMBINE_EQS: (58), (75) imply:
% 65.49/9.71 | | (79) all_58_5 = all_6_1
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (6), (76) imply:
% 65.49/9.71 | | (80) ~ (all_54_7 = e1)
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (59), (76) imply:
% 65.49/9.71 | | (81) ~ (all_54_9 = e1)
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (51), (76) imply:
% 65.49/9.71 | | (82) ~ (all_54_10 = e1)
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (61), (76) imply:
% 65.49/9.71 | | (83) ~ (all_54_15 = e1)
% 65.49/9.71 | |
% 65.49/9.71 | | REDUCE: (1), (76) imply:
% 65.49/9.71 | | (84) ~ (e1 = e0)
% 65.49/9.71 | |
% 65.49/9.71 | | BETA: splitting (15) gives:
% 65.49/9.71 | |
% 65.49/9.71 | | Case 1:
% 65.49/9.71 | | |
% 65.49/9.71 | | | (85) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.49/9.71 | | |
% 65.49/9.71 | | | ALPHA: (85) implies:
% 65.49/9.71 | | | (86) all_52_0 = e3
% 65.49/9.71 | | |
% 65.49/9.71 | | | REF_CLOSE: (21), (77), (86) are inconsistent by sub-proof #122.
% 65.49/9.71 | | |
% 65.49/9.71 | | Case 2:
% 65.49/9.71 | | |
% 65.49/9.71 | | | (87) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 65.49/9.71 | | | (all_52_2 = e0))
% 65.49/9.71 | | |
% 65.49/9.71 | | | BETA: splitting (87) gives:
% 65.49/9.71 | | |
% 65.49/9.71 | | | Case 1:
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | (88) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | ALPHA: (88) implies:
% 65.49/9.71 | | | | (89) all_52_1 = e3
% 65.49/9.71 | | | | (90) ~ (all_52_2 = e1)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | COMBINE_EQS: (27), (89) imply:
% 65.49/9.71 | | | | (91) all_14_2 = e3
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | REDUCE: (62), (91) imply:
% 65.49/9.71 | | | | (92) ~ (all_54_4 = e3)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | REDUCE: (66), (91) imply:
% 65.49/9.71 | | | | (93) ~ (all_54_7 = e3)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | REDUCE: (39), (91) imply:
% 65.49/9.71 | | | | (94) ~ (all_54_9 = e3)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | REDUCE: (3), (90) imply:
% 65.49/9.71 | | | | (95) ~ (all_4_2 = e1)
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | BETA: splitting (17) gives:
% 65.49/9.71 | | | |
% 65.49/9.71 | | | | Case 1:
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | (96) all_58_0 = e3
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | COMBINE_EQS: (65), (96) imply:
% 65.49/9.71 | | | | | (97) e3 = e2
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | SIMP: (97) implies:
% 65.49/9.71 | | | | | (98) e3 = e2
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | REDUCE: (57), (98) imply:
% 65.49/9.71 | | | | | (99) $false
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | CLOSE: (99) is inconsistent.
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | Case 2:
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | (100) all_58_1 = e3 | all_58_5 = e3 | all_58_11 = e3
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | BETA: splitting (60) gives:
% 65.49/9.71 | | | | |
% 65.49/9.71 | | | | | Case 1:
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | | (101) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | | REF_CLOSE: (77), (84), (101) are inconsistent by sub-proof #103.
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | Case 2:
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | | (102) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.49/9.71 | | | | | | (all_52_3 = e3))
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | | BETA: splitting (102) gives:
% 65.49/9.71 | | | | | |
% 65.49/9.71 | | | | | | Case 1:
% 65.49/9.71 | | | | | | |
% 65.49/9.71 | | | | | | | (103) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.49/9.71 | | | | | | |
% 65.49/9.71 | | | | | | | ALPHA: (103) implies:
% 65.49/9.71 | | | | | | | (104) all_52_1 = e0
% 65.49/9.71 | | | | | | |
% 65.49/9.71 | | | | | | | REF_CLOSE: (31), (89), (104) are inconsistent by sub-proof #102.
% 65.49/9.71 | | | | | | |
% 65.49/9.71 | | | | | | Case 2:
% 65.49/9.71 | | | | | | |
% 65.49/9.71 | | | | | | | (105) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | ALPHA: (105) implies:
% 65.49/9.72 | | | | | | | (106) all_52_2 = e0
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | COMBINE_EQS: (3), (106) imply:
% 65.49/9.72 | | | | | | | (107) all_4_2 = e0
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | COMBINE_EQS: (12), (107) imply:
% 65.49/9.72 | | | | | | | (108) all_58_12 = e0
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (34), (107) imply:
% 65.49/9.72 | | | | | | | (109) ~ (all_54_2 = e0)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (44), (107) imply:
% 65.49/9.72 | | | | | | | (110) ~ (all_54_10 = e0)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (30), (107) imply:
% 65.49/9.72 | | | | | | | (111) ~ (all_54_12 = e0)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (46), (107) imply:
% 65.49/9.72 | | | | | | | (112) ~ (all_54_15 = e0)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (95), (107) imply:
% 65.49/9.72 | | | | | | | (113) ~ (e1 = e0)
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | REDUCE: (47), (107) imply:
% 65.49/9.72 | | | | | | | (114) op(e0, e3) = all_4_1
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | BETA: splitting (20) gives:
% 65.49/9.72 | | | | | | |
% 65.49/9.72 | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | |
% 65.49/9.72 | | | | | | | | (115) ~ (all_4_1 = e1)
% 65.49/9.72 | | | | | | | |
% 65.49/9.72 | | | | | | | | BETA: splitting (100) gives:
% 65.49/9.72 | | | | | | | |
% 65.49/9.72 | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | (116) all_58_1 = e3
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | COMBINE_EQS: (48), (116) imply:
% 65.49/9.72 | | | | | | | | | (117) all_54_4 = e3
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | REDUCE: (92), (117) imply:
% 65.49/9.72 | | | | | | | | | (118) $false
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | CLOSE: (118) is inconsistent.
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | (119) all_58_5 = e3 | all_58_11 = e3
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | BETA: splitting (119) gives:
% 65.49/9.72 | | | | | | | | |
% 65.49/9.72 | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | (120) all_58_5 = e3
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | COMBINE_EQS: (79), (120) imply:
% 65.49/9.72 | | | | | | | | | | (121) all_6_1 = e3
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | REDUCE: (74), (121) imply:
% 65.49/9.72 | | | | | | | | | | (122) $false
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | CLOSE: (122) is inconsistent.
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | (123) all_58_11 = e3
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | COMBINE_EQS: (50), (123) imply:
% 65.49/9.72 | | | | | | | | | | (124) all_54_12 = e3
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | REDUCE: (69), (124) imply:
% 65.49/9.72 | | | | | | | | | | (125) ~ (all_54_15 = e3)
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | SIMP: (125) implies:
% 65.49/9.72 | | | | | | | | | | (126) ~ (all_54_15 = e3)
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | BETA: splitting (40) gives:
% 65.49/9.72 | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | (127) all_56_14 = e3
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | REF_CLOSE: (72), (126), (127) are inconsistent by sub-proof
% 65.49/9.72 | | | | | | | | | | | #71.
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | (128) ~ (all_56_14 = e3)
% 65.49/9.72 | | | | | | | | | | | (129) all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | BETA: splitting (129) gives:
% 65.49/9.72 | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | (130) all_56_14 = e2
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | COMBINE_EQS: (72), (130) imply:
% 65.49/9.72 | | | | | | | | | | | | (131) all_54_15 = e2
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | SIMP: (131) implies:
% 65.49/9.72 | | | | | | | | | | | | (132) all_54_15 = e2
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | COMBINE_EQS: (5), (132) imply:
% 65.49/9.72 | | | | | | | | | | | | (133) all_58_9 = e2
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | REDUCE: (63), (132) imply:
% 65.49/9.72 | | | | | | | | | | | | (134) ~ (all_54_7 = e2)
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | REDUCE: (126), (132) imply:
% 65.49/9.72 | | | | | | | | | | | | (135) ~ (e3 = e2)
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | REDUCE: (83), (132) imply:
% 65.49/9.72 | | | | | | | | | | | | (136) ~ (e2 = e1)
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | REDUCE: (112), (132) imply:
% 65.49/9.72 | | | | | | | | | | | | (137) ~ (e2 = e0)
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | BETA: splitting (24) gives:
% 65.49/9.72 | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | (138) all_58_0 = e1
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | COMBINE_EQS: (65), (138) imply:
% 65.49/9.72 | | | | | | | | | | | | | (139) e2 = e1
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | REDUCE: (136), (139) imply:
% 65.49/9.72 | | | | | | | | | | | | | (140) $false
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | (141) all_58_1 = e1 | all_58_5 = e1 | all_58_11 = e1
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | BETA: splitting (64) gives:
% 65.49/9.72 | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | (142) all_58_6 = e3
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | COMBINE_EQS: (78), (142) imply:
% 65.49/9.72 | | | | | | | | | | | | | | (143) e3 = e1
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | REDUCE: (21), (143) imply:
% 65.49/9.72 | | | | | | | | | | | | | | (144) $false
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | (145) all_58_7 = e3 | all_58_8 = e3 | all_58_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 65.49/9.72 | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | (146) all_58_7 = e3
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | COMBINE_EQS: (33), (146) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | (147) all_54_7 = e3
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | REDUCE: (93), (147) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | (148) $false
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | (149) all_58_8 = e3 | all_58_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 65.49/9.72 | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | (150) all_58_8 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (150) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | (151) all_54_3 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | REDUCE: (28), (151) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | (152) ~ (all_54_7 = e3)
% 65.49/9.72 | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | (153) all_58_0 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (153) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | (154) e2 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | REDUCE: (137), (154) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | (155) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | (156) all_58_3 = e0 | all_58_8 = e0 | all_58_15 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | (157) all_58_3 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (157) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | (158) all_54_1 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | REDUCE: (14), (158) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | (159) ~ (all_54_9 = e0)
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | (160) ~ (all_54_9 = e0)
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | (161) all_58_6 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (84), (161) are inconsistent by sub-proof
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | #128.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | (162) all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | (163) all_56_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (163) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | (164) all_54_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | SIMP: (164) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | (165) all_54_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (165) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | (166) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | (167) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | (168) all_56_6 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (168) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | (169) all_54_7 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (169) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | (170) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | (171) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | (172) all_58_7 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (172) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | (173) all_54_7 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (173) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | (174) ~ (all_54_4 = e0)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | (175) all_56_4 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (175) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | (176) all_54_4 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (176) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | (177) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | (178) ~ (all_56_4 = e3)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | (179) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | (180) all_56_9 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (180) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_9 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (181) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_54_10 = e2)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_54_10 = e2)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_56_11 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (184) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_54_10 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_10 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (186) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_58_13 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_1 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (188) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_54_4 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (189) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_54_6 = e1)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_54_6 = e1)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (189) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (192) ~ (e3 = e1)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_12 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (193) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) e2 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (194) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) e2 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (195) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_58_13 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (198) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) e3 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (199) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_58_8 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (200) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) e3 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (199) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_9 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (203) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_15 = e3
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (204) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_14 = e2 | all_58_15 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_14 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (207) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_54_6 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (208) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_6 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_12 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (210) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e1 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) e1 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (212) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_13 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (215) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) e3 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (216) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_14 = e1 | all_58_15 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_14 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (219) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) e2 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (220) implies:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) e2 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (221) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_15 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (223) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_54_2 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (224) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) op(e0, e3) = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, all_4_1, e3, e0,
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (225) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_4_1 = e1
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (226) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_58_15 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (228) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_54_2 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (229) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_58_1 = e1)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (231) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_54_4 = e1)
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (174), (179), (232) are inconsistent by
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_56_11 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (234) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_10 = e2
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (235) imply:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_56_11 = e1 | all_56_11 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_56_11 = e1
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (238) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_10 = e1
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (239) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_56_11 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (241) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_54_10 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (242) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | (244) all_56_9 = e1 | all_56_9 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_56_9 = e1
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (245) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_54_9 = e1
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (246) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (247) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_56_9 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (248) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_54_9 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (249) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | (250) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_58_7 = e0)
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (251) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_54_7 = e0)
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (80), (134), (171), (252) are inconsistent
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #18.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | (253) all_58_8 = e0 | all_58_15 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 65.49/9.73 | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (254) all_58_8 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (254) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (255) e3 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | REDUCE: (31), (255) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (256) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (257) all_58_15 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (257) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (258) all_54_2 = e0
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | REDUCE: (109), (258) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | (259) $false
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | (260) all_58_9 = e3
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (260) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | (261) e3 = e2
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 65.49/9.73 | | | | | | | | | | | | | | | | (262) e3 = e2
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | REDUCE: (57), (262) imply:
% 65.49/9.73 | | | | | | | | | | | | | | | | (263) $false
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | | CLOSE: (263) is inconsistent.
% 65.49/9.73 | | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | (264) all_56_14 = e1 | all_56_14 = e0
% 65.49/9.73 | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | | REF_CLOSE: (72), (83), (112), (264) are inconsistent by
% 65.49/9.73 | | | | | | | | | | | | sub-proof #70.
% 65.49/9.73 | | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | | |
% 65.49/9.73 | | | | | | | | | End of split
% 65.49/9.73 | | | | | | | | |
% 65.49/9.73 | | | | | | | | End of split
% 65.49/9.73 | | | | | | | |
% 65.49/9.73 | | | | | | | Case 2:
% 65.49/9.73 | | | | | | | |
% 65.49/9.73 | | | | | | | | (265) ~ (all_4_2 = e0)
% 65.49/9.73 | | | | | | | |
% 65.49/9.73 | | | | | | | | REDUCE: (107), (265) imply:
% 65.49/9.73 | | | | | | | | (266) $false
% 65.49/9.73 | | | | | | | |
% 65.49/9.73 | | | | | | | | CLOSE: (266) is inconsistent.
% 65.49/9.73 | | | | | | | |
% 65.49/9.73 | | | | | | | End of split
% 65.49/9.73 | | | | | | |
% 65.49/9.73 | | | | | | End of split
% 65.49/9.73 | | | | | |
% 65.49/9.73 | | | | | End of split
% 65.49/9.73 | | | | |
% 65.49/9.73 | | | | End of split
% 65.49/9.73 | | | |
% 65.49/9.73 | | | Case 2:
% 65.49/9.73 | | | |
% 65.49/9.73 | | | | (267) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.49/9.73 | | | |
% 65.49/9.73 | | | | REF_CLOSE: (45), (57), (267) are inconsistent by sub-proof #74.
% 65.49/9.73 | | | |
% 65.49/9.73 | | | End of split
% 65.49/9.73 | | |
% 65.49/9.73 | | End of split
% 65.49/9.73 | |
% 65.49/9.73 | Case 2:
% 65.49/9.73 | |
% 65.49/9.73 | | (268) ~ (all_16_2 = e2)
% 65.49/9.73 | |
% 65.49/9.73 | | REDUCE: (52), (268) imply:
% 65.49/9.73 | | (269) $false
% 65.49/9.73 | |
% 65.49/9.73 | | CLOSE: (269) is inconsistent.
% 65.49/9.73 | |
% 65.49/9.73 | End of split
% 65.49/9.73 |
% 65.49/9.73 End of proof
% 65.49/9.73
% 65.49/9.73 Sub-proof #9 shows that the following formulas are inconsistent:
% 65.49/9.73 ----------------------------------------------------------------
% 65.49/9.73 (1) op(e1, e1) = e2
% 65.49/9.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.73 (3) all_52_0 = e3
% 65.49/9.73 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.73 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.73 (5) ~ (e3 = e1)
% 65.49/9.73 (6) ~ (all_6_0 = e2)
% 65.49/9.73 (7) ~ (e3 = e0)
% 65.49/9.73 (8) ~ (e1 = e0)
% 65.49/9.73 (9) op(all_6_2, all_6_2) = all_6_0
% 65.49/9.73 (10) ~ (e2 = e0)
% 65.49/9.73 (11) all_52_3 = all_6_2
% 65.49/9.73 (12) all_52_1 = e2
% 65.49/9.73 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.73 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.73
% 65.49/9.73 Begin of proof
% 65.49/9.73 |
% 65.49/9.73 | BETA: splitting (13) gives:
% 65.49/9.73 |
% 65.49/9.73 | Case 1:
% 65.49/9.73 | |
% 65.49/9.73 | | (14) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.49/9.73 | |
% 65.49/9.73 | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #56.
% 65.49/9.73 | |
% 65.49/9.73 | Case 2:
% 65.49/9.73 | |
% 65.49/9.73 | | (15) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.49/9.73 | | = e3))
% 65.49/9.73 | |
% 65.49/9.73 | | BETA: splitting (15) gives:
% 65.49/9.73 | |
% 65.49/9.73 | | Case 1:
% 65.49/9.73 | | |
% 65.49/9.73 | | | (16) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.49/9.73 | | |
% 65.49/9.73 | | | REF_CLOSE: (10), (12), (16) are inconsistent by sub-proof #55.
% 65.49/9.73 | | |
% 65.49/9.73 | | Case 2:
% 65.49/9.73 | | |
% 65.49/9.73 | | | (17) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.49/9.73 | | |
% 65.49/9.73 | | | ALPHA: (17) implies:
% 65.49/9.73 | | | (18) all_52_2 = e0
% 65.49/9.73 | | |
% 65.49/9.73 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (18) are
% 65.49/9.73 | | | inconsistent by sub-proof #121.
% 65.49/9.73 | | |
% 65.49/9.73 | | End of split
% 65.49/9.73 | |
% 65.49/9.73 | End of split
% 65.49/9.73 |
% 65.49/9.73 End of proof
% 65.49/9.73
% 65.49/9.73 Sub-proof #10 shows that the following formulas are inconsistent:
% 65.49/9.73 ----------------------------------------------------------------
% 65.49/9.73 (1) all_52_2 = all_4_2
% 65.49/9.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.73 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.73 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.73 (4) op(e2, e2) = all_10_2
% 65.49/9.73 (5) all_52_1 = all_14_2
% 65.49/9.73 (6) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.49/9.73 (7) ~ (e2 = e0)
% 65.49/9.73 (8) ~ (e2 = e1)
% 65.49/9.73 (9) all_52_0 = all_10_2
% 65.49/9.73 (10) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.73 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.73 (11) op(all_4_2, all_4_2) = e2
% 65.49/9.73
% 65.49/9.73 Begin of proof
% 65.49/9.73 |
% 65.49/9.73 | ALPHA: (6) implies:
% 65.49/9.73 | (12) all_52_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | COMBINE_EQS: (1), (12) imply:
% 65.49/9.73 | (13) all_4_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | REDUCE: (11), (13) imply:
% 65.49/9.73 | (14) op(e2, e2) = e2
% 65.49/9.73 |
% 65.49/9.73 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (14) are
% 65.49/9.73 | inconsistent by sub-proof #13.
% 65.49/9.73 |
% 65.49/9.73 End of proof
% 65.49/9.73
% 65.49/9.73 Sub-proof #11 shows that the following formulas are inconsistent:
% 65.49/9.73 ----------------------------------------------------------------
% 65.49/9.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.73 (2) op(e2, e2) = all_10_2
% 65.49/9.73 (3) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 65.49/9.73 (4) ~ (all_6_0 = e2)
% 65.49/9.73 (5) op(all_6_2, all_6_2) = all_6_0
% 65.49/9.73 (6) ~ (all_6_0 = e3)
% 65.49/9.73 (7) all_52_3 = all_6_2
% 65.49/9.73 (8) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.73 (9) all_52_0 = all_10_2
% 65.49/9.73 (10) all_56_10 = all_10_2
% 65.49/9.73 (11) ~ (all_6_0 = e1)
% 65.49/9.73
% 65.49/9.73 Begin of proof
% 65.49/9.73 |
% 65.49/9.73 | ALPHA: (8) implies:
% 65.49/9.73 | (12) all_52_3 = e2
% 65.49/9.73 | (13) ~ (all_52_0 = e0)
% 65.49/9.73 |
% 65.49/9.73 | COMBINE_EQS: (7), (12) imply:
% 65.49/9.73 | (14) all_6_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | SIMP: (14) implies:
% 65.49/9.73 | (15) all_6_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (13), (15) are
% 65.49/9.73 | inconsistent by sub-proof #161.
% 65.49/9.73 |
% 65.49/9.73 End of proof
% 65.49/9.73
% 65.49/9.73 Sub-proof #12 shows that the following formulas are inconsistent:
% 65.49/9.73 ----------------------------------------------------------------
% 65.49/9.73 (1) all_52_2 = all_4_2
% 65.49/9.73 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.73 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.73 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.73 (4) op(e2, e2) = all_10_2
% 65.49/9.73 (5) all_52_1 = all_14_2
% 65.49/9.73 (6) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.49/9.73 (7) ~ (e2 = e0)
% 65.49/9.73 (8) ~ (e2 = e1)
% 65.49/9.73 (9) all_52_0 = all_10_2
% 65.49/9.73 (10) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.73 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.73 (11) op(all_4_2, all_4_2) = e2
% 65.49/9.73
% 65.49/9.73 Begin of proof
% 65.49/9.73 |
% 65.49/9.73 | ALPHA: (6) implies:
% 65.49/9.73 | (12) all_52_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | COMBINE_EQS: (1), (12) imply:
% 65.49/9.73 | (13) all_4_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | SIMP: (13) implies:
% 65.49/9.73 | (14) all_4_2 = e2
% 65.49/9.73 |
% 65.49/9.73 | REDUCE: (11), (14) imply:
% 65.49/9.73 | (15) op(e2, e2) = e2
% 65.49/9.73 |
% 65.49/9.73 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (15) are
% 65.49/9.73 | inconsistent by sub-proof #13.
% 65.49/9.73 |
% 65.49/9.73 End of proof
% 65.49/9.73
% 65.49/9.73 Sub-proof #13 shows that the following formulas are inconsistent:
% 65.49/9.73 ----------------------------------------------------------------
% 65.49/9.73 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.73 (2) op(e2, e2) = e2
% 65.49/9.73 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.73 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.73 (4) op(e2, e2) = all_10_2
% 65.49/9.73 (5) all_52_1 = all_14_2
% 65.49/9.73 (6) ~ (e2 = e0)
% 65.49/9.73 (7) ~ (e2 = e1)
% 65.49/9.74 (8) all_52_0 = all_10_2
% 65.49/9.74 (9) all_52_2 = e2
% 65.49/9.74 (10) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.74 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.74
% 65.49/9.74 Begin of proof
% 65.49/9.74 |
% 65.49/9.74 | GROUND_INST: instantiating (1) with all_10_2, e2, e2, e2, simplifying with
% 65.49/9.74 | (2), (4) gives:
% 65.49/9.74 | (11) all_10_2 = e2
% 65.49/9.74 |
% 65.49/9.74 | COMBINE_EQS: (8), (11) imply:
% 65.49/9.74 | (12) all_52_0 = e2
% 65.49/9.74 |
% 65.49/9.74 | BETA: splitting (3) gives:
% 65.49/9.74 |
% 65.49/9.74 | Case 1:
% 65.49/9.74 | |
% 65.49/9.74 | | (13) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.49/9.74 | |
% 65.49/9.74 | | REF_CLOSE: (7), (12), (13) are inconsistent by sub-proof #157.
% 65.49/9.74 | |
% 65.49/9.74 | Case 2:
% 65.49/9.74 | |
% 65.49/9.74 | | (14) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 65.49/9.74 | | = e0))
% 65.49/9.74 | |
% 65.49/9.74 | | BETA: splitting (14) gives:
% 65.49/9.74 | |
% 65.49/9.74 | | Case 1:
% 65.49/9.74 | | |
% 65.49/9.74 | | | (15) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.49/9.74 | | |
% 65.49/9.74 | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #175.
% 65.49/9.74 | | |
% 65.49/9.74 | | Case 2:
% 65.49/9.74 | | |
% 65.49/9.74 | | | (16) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.49/9.74 | | |
% 65.49/9.74 | | | ALPHA: (16) implies:
% 65.49/9.74 | | | (17) ~ (all_52_1 = e0)
% 65.49/9.74 | | |
% 65.49/9.74 | | | REDUCE: (5), (17) imply:
% 65.49/9.74 | | | (18) ~ (all_14_2 = e0)
% 65.49/9.74 | | |
% 65.49/9.74 | | | BETA: splitting (10) gives:
% 65.49/9.74 | | |
% 65.49/9.74 | | | Case 1:
% 65.49/9.74 | | | |
% 65.49/9.74 | | | | (19) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.49/9.74 | | | |
% 65.49/9.74 | | | | REF_CLOSE: (6), (12), (19) are inconsistent by sub-proof #156.
% 65.49/9.74 | | | |
% 65.49/9.74 | | | Case 2:
% 65.49/9.74 | | | |
% 65.49/9.74 | | | | (20) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.49/9.74 | | | | (all_52_3 = e3))
% 65.49/9.74 | | | |
% 65.49/9.74 | | | | REF_CLOSE: (5), (6), (9), (18), (20) are inconsistent by sub-proof #86.
% 65.49/9.74 | | | |
% 65.49/9.74 | | | End of split
% 65.49/9.74 | | |
% 65.49/9.74 | | End of split
% 65.49/9.74 | |
% 65.49/9.74 | End of split
% 65.49/9.74 |
% 65.49/9.74 End of proof
% 65.49/9.74
% 65.49/9.74 Sub-proof #14 shows that the following formulas are inconsistent:
% 65.49/9.74 ----------------------------------------------------------------
% 65.49/9.74 (1) ~ (all_52_0 = e1)
% 65.49/9.74 (2) all_52_2 = all_4_2
% 65.49/9.74 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.74 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.74 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.74 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.74 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.74 (6) ~ (e3 = e1)
% 65.49/9.74 (7) op(e2, e2) = all_10_2
% 65.49/9.74 (8) ~ (e3 = e0)
% 65.49/9.74 (9) all_14_2 = e2
% 65.49/9.74 (10) op(e3, e3) = all_4_2
% 65.49/9.74 (11) op(all_6_2, all_6_2) = e3
% 65.49/9.74 (12) all_52_3 = all_6_2
% 65.49/9.74 (13) all_52_0 = all_10_2
% 65.49/9.74 (14) all_52_1 = e2
% 65.49/9.74 (15) ~ (e3 = e2)
% 65.49/9.74 (16) op(all_14_2, all_14_2) = e0
% 65.49/9.74 (17) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.49/9.74
% 65.49/9.74 Begin of proof
% 65.49/9.74 |
% 65.49/9.74 | REDUCE: (1), (13) imply:
% 65.49/9.74 | (18) ~ (all_10_2 = e1)
% 65.49/9.74 |
% 65.49/9.74 | REDUCE: (9), (16) imply:
% 65.49/9.74 | (19) op(e2, e2) = e0
% 65.49/9.74 |
% 65.49/9.74 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.49/9.74 | (14), (15), (17), (18), (19) are inconsistent by sub-proof #20.
% 65.49/9.74 |
% 65.49/9.74 End of proof
% 65.49/9.74
% 65.49/9.74 Sub-proof #15 shows that the following formulas are inconsistent:
% 65.49/9.74 ----------------------------------------------------------------
% 65.49/9.74 (1) ~ (all_54_4 = all_6_2)
% 65.49/9.74 (2) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 65.49/9.74 (3) all_52_2 = all_4_2
% 65.49/9.74 (4) all_58_9 = all_54_15
% 65.49/9.74 (5) op(e3, e2) = all_54_15
% 65.49/9.74 (6) ~ (all_54_1 = all_14_2)
% 65.49/9.74 (7) ~ (all_54_7 = all_10_2)
% 65.49/9.74 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.74 (9) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.49/9.74 (10) ~ (all_54_4 = all_54_8)
% 65.49/9.74 (11) all_58_13 = all_54_10
% 65.49/9.74 (12) op(e2, e0) = all_54_8
% 65.49/9.74 (13) ~ (all_54_8 = all_54_12)
% 65.49/9.74 (14) ~ (all_54_1 = all_54_9)
% 65.49/9.74 (15) all_56_4 = all_54_4
% 65.49/9.74 (16) op(all_6_2, e0) = all_6_1
% 65.49/9.74 (17) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.74 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.74 (18) ~ (e3 = e1)
% 65.49/9.74 (19) op(e2, e2) = all_10_2
% 65.49/9.74 (20) all_56_1 = all_54_1
% 65.49/9.74 (21) all_56_8 = all_54_8
% 65.49/9.74 (22) all_8_1 = all_6_1
% 65.49/9.74 (23) all_58_0 = all_6_2
% 65.49/9.74 (24) all_52_1 = all_14_2
% 65.49/9.74 (25) ~ (all_54_8 = all_6_2)
% 65.49/9.74 (26) all_8_2 = all_6_2
% 65.49/9.74 (27) all_58_4 = all_54_9
% 65.49/9.74 (28) ~ (all_54_12 = all_4_2)
% 65.49/9.74 (29) ~ (e1 = e0)
% 65.49/9.74 (30) ~ (all_54_8 = all_10_2)
% 65.49/9.74 (31) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0
% 65.49/9.74 (32) all_58_6 = all_10_2
% 65.49/9.74 (33) ~ (all_54_4 = all_54_7)
% 65.49/9.74 (34) ~ (all_54_13 = all_54_15)
% 65.49/9.74 (35) all_56_12 = all_54_12
% 65.49/9.74 (36) all_58_2 = all_14_2
% 65.49/9.74 (37) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.74 (38) all_56_6 = all_54_7
% 65.49/9.74 (39) op(all_6_2, all_6_2) = e3
% 65.49/9.74 (40) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.74 (41) ~ (all_54_10 = all_4_2)
% 65.49/9.74 (42) ~ (all_54_15 = all_4_2)
% 65.49/9.74 (43) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.74 (44) ~ (e2 = e1)
% 65.49/9.74 (45) all_58_1 = all_54_4
% 65.49/9.74 (46) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.74 (47) ~ (all_54_1 = all_6_2)
% 65.49/9.74 (48) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 65.49/9.74 (49) all_52_3 = all_6_2
% 65.49/9.74 (50) op(all_10_2, e2) = all_10_1
% 65.49/9.74 (51) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.74 (52) all_52_0 = all_10_2
% 65.49/9.74 (53) all_58_11 = all_54_12
% 65.49/9.74 (54) all_58_3 = all_54_1
% 65.49/9.74 (55) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.49/9.74 (56) all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 65.49/9.74 (57) all_58_5 = all_54_8
% 65.49/9.74 (58) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.74 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.74 (59) all_58_10 = all_54_13
% 65.49/9.74 (60) ~ (all_54_7 = all_14_2)
% 65.49/9.74 (61) ~ (all_54_4 = all_54_12)
% 65.49/9.74 (62) ~ (all_54_12 = all_6_2)
% 65.49/9.74 (63) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.49/9.74 (64) ~ (all_54_12 = all_54_15)
% 65.49/9.74 (65) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.74 (66) all_56_14 = all_54_15
% 65.49/9.74
% 65.49/9.74 Begin of proof
% 65.49/9.74 |
% 65.49/9.74 | ALPHA: (51) implies:
% 65.49/9.74 | (67) all_52_3 = e2
% 65.49/9.74 | (68) ~ (all_52_0 = e0)
% 65.49/9.74 |
% 65.49/9.74 | COMBINE_EQS: (49), (67) imply:
% 65.49/9.74 | (69) all_6_2 = e2
% 65.49/9.74 |
% 65.49/9.74 | COMBINE_EQS: (26), (69) imply:
% 65.49/9.74 | (70) all_8_2 = e2
% 65.49/9.74 |
% 65.49/9.74 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 65.49/9.74 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 65.49/9.74 | (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 65.49/9.74 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 65.49/9.74 | (47), (48), (50), (52), (53), (54), (55), (56), (57), (58), (59),
% 65.49/9.74 | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70)
% 65.49/9.74 | are inconsistent by sub-proof #16.
% 65.49/9.74 |
% 65.49/9.74 End of proof
% 65.49/9.74
% 65.49/9.74 Sub-proof #16 shows that the following formulas are inconsistent:
% 65.49/9.74 ----------------------------------------------------------------
% 65.49/9.74 (1) ~ (all_54_4 = all_6_2)
% 65.49/9.74 (2) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 65.49/9.74 (3) all_52_2 = all_4_2
% 65.49/9.74 (4) all_58_9 = all_54_15
% 65.49/9.74 (5) op(e3, e2) = all_54_15
% 65.49/9.74 (6) ~ (all_54_1 = all_14_2)
% 65.49/9.74 (7) ~ (all_54_7 = all_10_2)
% 65.49/9.74 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.74 (9) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.49/9.74 (10) ~ (all_54_4 = all_54_8)
% 65.49/9.74 (11) all_58_13 = all_54_10
% 65.49/9.74 (12) op(e2, e0) = all_54_8
% 65.49/9.74 (13) ~ (all_54_8 = all_54_12)
% 65.49/9.74 (14) ~ (all_54_1 = all_54_9)
% 65.49/9.74 (15) all_56_4 = all_54_4
% 65.49/9.74 (16) all_6_2 = e2
% 65.49/9.74 (17) op(all_6_2, e0) = all_6_1
% 65.49/9.74 (18) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.74 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.74 (19) ~ (e3 = e1)
% 65.49/9.74 (20) op(e2, e2) = all_10_2
% 65.49/9.74 (21) all_56_1 = all_54_1
% 65.49/9.74 (22) all_56_8 = all_54_8
% 65.49/9.74 (23) all_8_1 = all_6_1
% 65.49/9.74 (24) all_58_0 = all_6_2
% 65.49/9.74 (25) all_52_1 = all_14_2
% 65.49/9.74 (26) ~ (all_54_8 = all_6_2)
% 65.49/9.74 (27) all_8_2 = e2
% 65.49/9.74 (28) all_58_4 = all_54_9
% 65.49/9.74 (29) ~ (all_54_12 = all_4_2)
% 65.49/9.74 (30) ~ (e1 = e0)
% 65.49/9.74 (31) ~ (all_54_8 = all_10_2)
% 65.49/9.75 (32) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0
% 65.49/9.75 (33) all_58_6 = all_10_2
% 65.49/9.75 (34) ~ (all_54_4 = all_54_7)
% 65.49/9.75 (35) ~ (all_54_13 = all_54_15)
% 65.49/9.75 (36) all_56_12 = all_54_12
% 65.49/9.75 (37) all_58_2 = all_14_2
% 65.49/9.75 (38) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.75 (39) ~ (all_52_0 = e0)
% 65.49/9.75 (40) all_56_6 = all_54_7
% 65.49/9.75 (41) op(all_6_2, all_6_2) = e3
% 65.49/9.75 (42) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.75 (43) ~ (all_54_10 = all_4_2)
% 65.49/9.75 (44) all_52_3 = e2
% 65.49/9.75 (45) ~ (all_54_15 = all_4_2)
% 65.49/9.75 (46) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.75 (47) ~ (e2 = e1)
% 65.49/9.75 (48) all_58_1 = all_54_4
% 65.49/9.75 (49) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.75 (50) ~ (all_54_1 = all_6_2)
% 65.49/9.75 (51) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 65.49/9.75 (52) op(all_10_2, e2) = all_10_1
% 65.49/9.75 (53) all_52_0 = all_10_2
% 65.49/9.75 (54) all_58_11 = all_54_12
% 65.49/9.75 (55) all_58_3 = all_54_1
% 65.49/9.75 (56) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.49/9.75 (57) all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 65.49/9.75 (58) all_58_5 = all_54_8
% 65.49/9.75 (59) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.75 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.75 (60) all_58_10 = all_54_13
% 65.49/9.75 (61) ~ (all_54_7 = all_14_2)
% 65.49/9.75 (62) ~ (all_54_4 = all_54_12)
% 65.49/9.75 (63) ~ (all_54_12 = all_6_2)
% 65.49/9.75 (64) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.49/9.75 (65) ~ (all_54_12 = all_54_15)
% 65.49/9.75 (66) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.75 (67) all_56_14 = all_54_15
% 65.49/9.75
% 65.49/9.75 Begin of proof
% 65.49/9.75 |
% 65.49/9.75 | COMBINE_EQS: (16), (24) imply:
% 65.49/9.75 | (68) all_58_0 = e2
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (16), (50) imply:
% 65.49/9.75 | (69) ~ (all_54_1 = e2)
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (1), (16) imply:
% 65.49/9.75 | (70) ~ (all_54_4 = e2)
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (16), (26) imply:
% 65.49/9.75 | (71) ~ (all_54_8 = e2)
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (16), (63) imply:
% 65.49/9.75 | (72) ~ (all_54_12 = e2)
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (39), (53) imply:
% 65.49/9.75 | (73) ~ (all_10_2 = e0)
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (16), (41) imply:
% 65.49/9.75 | (74) op(e2, e2) = e3
% 65.49/9.75 |
% 65.49/9.75 | REDUCE: (16), (17) imply:
% 65.49/9.75 | (75) op(e2, e0) = all_6_1
% 65.49/9.75 |
% 65.49/9.75 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.49/9.75 | (14), (15), (18), (19), (20), (21), (22), (23), (25), (27), (28),
% 65.49/9.75 | (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (40),
% 65.49/9.75 | (42), (43), (44), (45), (46), (47), (48), (49), (51), (52), (53),
% 65.49/9.75 | (54), (55), (56), (57), (58), (59), (60), (61), (62), (64), (65),
% 65.49/9.75 | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75) are
% 65.49/9.75 | inconsistent by sub-proof #17.
% 65.49/9.75 |
% 65.49/9.75 End of proof
% 65.49/9.75
% 65.49/9.75 Sub-proof #17 shows that the following formulas are inconsistent:
% 65.49/9.75 ----------------------------------------------------------------
% 65.49/9.75 (1) ~ (all_10_2 = e0)
% 65.49/9.75 (2) ~ (all_10_1 = e0) | ~ (all_10_2 = e3)
% 65.49/9.75 (3) all_52_2 = all_4_2
% 65.49/9.75 (4) all_58_9 = all_54_15
% 65.49/9.75 (5) op(e3, e2) = all_54_15
% 65.49/9.75 (6) ~ (all_54_1 = all_14_2)
% 65.49/9.75 (7) ~ (all_54_7 = all_10_2)
% 65.49/9.75 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.75 (9) ~ (all_54_4 = e2)
% 65.49/9.75 (10) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.49/9.75 (11) ~ (all_54_4 = all_54_8)
% 65.49/9.75 (12) op(e2, e0) = all_6_1
% 65.49/9.75 (13) all_58_13 = all_54_10
% 65.49/9.75 (14) op(e2, e0) = all_54_8
% 65.49/9.75 (15) ~ (all_54_8 = all_54_12)
% 65.49/9.75 (16) ~ (all_54_1 = all_54_9)
% 65.49/9.75 (17) all_56_4 = all_54_4
% 65.49/9.75 (18) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.75 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.75 (19) ~ (e3 = e1)
% 65.49/9.75 (20) ~ (all_54_8 = e2)
% 65.49/9.75 (21) op(e2, e2) = all_10_2
% 65.49/9.75 (22) all_56_1 = all_54_1
% 65.49/9.75 (23) all_56_8 = all_54_8
% 65.49/9.75 (24) all_8_1 = all_6_1
% 65.49/9.75 (25) all_52_1 = all_14_2
% 65.49/9.75 (26) all_8_2 = e2
% 65.49/9.75 (27) all_58_4 = all_54_9
% 65.49/9.75 (28) ~ (all_54_12 = all_4_2)
% 65.49/9.75 (29) ~ (e1 = e0)
% 65.49/9.75 (30) ~ (all_54_12 = e2)
% 65.49/9.75 (31) ~ (all_54_8 = all_10_2)
% 65.49/9.75 (32) all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0 | all_58_12 = e0
% 65.49/9.75 (33) all_58_6 = all_10_2
% 65.49/9.75 (34) ~ (all_54_4 = all_54_7)
% 65.49/9.75 (35) ~ (all_54_13 = all_54_15)
% 65.49/9.75 (36) op(e2, e2) = e3
% 65.49/9.75 (37) all_56_12 = all_54_12
% 65.49/9.75 (38) all_58_2 = all_14_2
% 65.49/9.75 (39) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.75 (40) ~ (all_54_1 = e2)
% 65.49/9.75 (41) all_56_6 = all_54_7
% 65.49/9.75 (42) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.75 (43) ~ (all_54_10 = all_4_2)
% 65.49/9.75 (44) all_52_3 = e2
% 65.49/9.75 (45) ~ (all_54_15 = all_4_2)
% 65.49/9.75 (46) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.75 (47) ~ (e2 = e1)
% 65.49/9.75 (48) all_58_1 = all_54_4
% 65.49/9.75 (49) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.75 (50) all_58_0 = e2 | all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 65.49/9.75 (51) op(all_10_2, e2) = all_10_1
% 65.49/9.75 (52) all_52_0 = all_10_2
% 65.49/9.75 (53) all_58_11 = all_54_12
% 65.49/9.75 (54) all_58_3 = all_54_1
% 65.49/9.75 (55) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.49/9.75 (56) all_58_2 = e2 | all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 65.49/9.75 (57) all_58_5 = all_54_8
% 65.49/9.75 (58) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.75 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.75 (59) all_58_10 = all_54_13
% 65.49/9.75 (60) all_58_0 = e2
% 65.49/9.75 (61) ~ (all_54_7 = all_14_2)
% 65.49/9.75 (62) ~ (all_54_4 = all_54_12)
% 65.49/9.75 (63) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.49/9.75 (64) ~ (all_54_12 = all_54_15)
% 65.49/9.75 (65) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.75 (66) all_56_14 = all_54_15
% 65.49/9.75
% 65.49/9.75 Begin of proof
% 65.49/9.75 |
% 65.49/9.75 | BETA: splitting (49) gives:
% 65.49/9.75 |
% 65.49/9.75 | Case 1:
% 65.49/9.75 | |
% 65.49/9.75 | | (67) ~ (all_8_1 = e1)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (24), (67) imply:
% 65.49/9.75 | | (68) ~ (all_6_1 = e1)
% 65.49/9.75 | |
% 65.49/9.75 | | GROUND_INST: instantiating (8) with all_54_8, all_6_1, e0, e2, simplifying
% 65.49/9.75 | | with (12), (14) gives:
% 65.49/9.75 | | (69) all_54_8 = all_6_1
% 65.49/9.75 | |
% 65.49/9.75 | | GROUND_INST: instantiating (8) with all_10_2, e3, e2, e2, simplifying with
% 65.49/9.75 | | (21), (36) gives:
% 65.49/9.75 | | (70) all_10_2 = e3
% 65.49/9.75 | |
% 65.49/9.75 | | COMBINE_EQS: (52), (70) imply:
% 65.49/9.75 | | (71) all_52_0 = e3
% 65.49/9.75 | |
% 65.49/9.75 | | COMBINE_EQS: (23), (69) imply:
% 65.49/9.75 | | (72) all_56_8 = all_6_1
% 65.49/9.75 | |
% 65.49/9.75 | | COMBINE_EQS: (33), (70) imply:
% 65.49/9.75 | | (73) all_58_6 = e3
% 65.49/9.75 | |
% 65.49/9.75 | | COMBINE_EQS: (57), (69) imply:
% 65.49/9.75 | | (74) all_58_5 = all_6_1
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (11), (69) imply:
% 65.49/9.75 | | (75) ~ (all_54_4 = all_6_1)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (7), (70) imply:
% 65.49/9.75 | | (76) ~ (all_54_7 = e3)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (15), (69) imply:
% 65.49/9.75 | | (77) ~ (all_54_12 = all_6_1)
% 65.49/9.75 | |
% 65.49/9.75 | | SIMP: (77) implies:
% 65.49/9.75 | | (78) ~ (all_54_12 = all_6_1)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (31), (69), (70) imply:
% 65.49/9.75 | | (79) ~ (all_6_1 = e3)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (20), (69) imply:
% 65.49/9.75 | | (80) ~ (all_6_1 = e2)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (1), (70) imply:
% 65.49/9.75 | | (81) ~ (e3 = e0)
% 65.49/9.75 | |
% 65.49/9.75 | | REDUCE: (51), (70) imply:
% 65.49/9.75 | | (82) op(e3, e2) = all_10_1
% 65.49/9.75 | |
% 65.49/9.75 | | BETA: splitting (18) gives:
% 65.49/9.75 | |
% 65.49/9.75 | | Case 1:
% 65.49/9.75 | | |
% 65.49/9.75 | | | (83) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.49/9.75 | | |
% 65.49/9.75 | | | ALPHA: (83) implies:
% 65.49/9.75 | | | (84) all_52_0 = e1
% 65.49/9.75 | | |
% 65.49/9.75 | | | REF_CLOSE: (19), (71), (84) are inconsistent by sub-proof #122.
% 65.49/9.75 | | |
% 65.49/9.75 | | Case 2:
% 65.49/9.75 | | |
% 65.49/9.75 | | | (85) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 65.49/9.75 | | | (all_52_1 = e0))
% 65.49/9.75 | | |
% 65.49/9.75 | | | BETA: splitting (85) gives:
% 65.49/9.75 | | |
% 65.49/9.75 | | | Case 1:
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | (86) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | ALPHA: (86) implies:
% 65.49/9.75 | | | | (87) all_52_2 = e1
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | COMBINE_EQS: (3), (87) imply:
% 65.49/9.75 | | | | (88) all_4_2 = e1
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | SIMP: (88) implies:
% 65.49/9.75 | | | | (89) all_4_2 = e1
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | REDUCE: (43), (89) imply:
% 65.49/9.75 | | | | (90) ~ (all_54_10 = e1)
% 65.49/9.75 | | | |
% 65.49/9.75 | | | | REDUCE: (28), (89) imply:
% 65.49/9.75 | | | | (91) ~ (all_54_12 = e1)
% 65.49/9.75 | | | |
% 65.49/9.76 | | | | REDUCE: (45), (89) imply:
% 65.49/9.76 | | | | (92) ~ (all_54_15 = e1)
% 65.49/9.76 | | | |
% 65.49/9.76 | | | | BETA: splitting (55) gives:
% 65.49/9.76 | | | |
% 65.49/9.76 | | | | Case 1:
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | (93) all_56_8 = e3
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | COMBINE_EQS: (72), (93) imply:
% 65.49/9.76 | | | | | (94) all_6_1 = e3
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | REDUCE: (79), (94) imply:
% 65.49/9.76 | | | | | (95) $false
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | CLOSE: (95) is inconsistent.
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | Case 2:
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | (96) all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | BETA: splitting (58) gives:
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | | Case 1:
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | (97) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | ALPHA: (97) implies:
% 65.49/9.76 | | | | | | (98) all_52_0 = e0
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | REF_CLOSE: (71), (81), (98) are inconsistent by sub-proof #124.
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | Case 2:
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | (99) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.49/9.76 | | | | | | (all_52_3 = e3))
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | BETA: splitting (99) gives:
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | | Case 1:
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | (100) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | ALPHA: (100) implies:
% 65.49/9.76 | | | | | | | (101) all_52_1 = e0
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | COMBINE_EQS: (25), (101) imply:
% 65.49/9.76 | | | | | | | (102) all_14_2 = e0
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | SIMP: (102) implies:
% 65.49/9.76 | | | | | | | (103) all_14_2 = e0
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | COMBINE_EQS: (38), (103) imply:
% 65.49/9.76 | | | | | | | (104) all_58_2 = e0
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | REDUCE: (6), (103) imply:
% 65.49/9.76 | | | | | | | (105) ~ (all_54_1 = e0)
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | REDUCE: (61), (103) imply:
% 65.49/9.76 | | | | | | | (106) ~ (all_54_7 = e0)
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | BETA: splitting (2) gives:
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | (107) ~ (all_10_1 = e0)
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | BETA: splitting (96) gives:
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | (108) all_56_8 = e2
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | COMBINE_EQS: (72), (108) imply:
% 65.49/9.76 | | | | | | | | | (109) all_6_1 = e2
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | REDUCE: (80), (109) imply:
% 65.49/9.76 | | | | | | | | | (110) $false
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | CLOSE: (110) is inconsistent.
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | (111) ~ (all_56_8 = e2)
% 65.49/9.76 | | | | | | | | | (112) all_56_8 = e1 | all_56_8 = e0
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | BETA: splitting (112) gives:
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | (113) all_56_8 = e1
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | COMBINE_EQS: (72), (113) imply:
% 65.49/9.76 | | | | | | | | | | (114) all_6_1 = e1
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | REDUCE: (68), (114) imply:
% 65.49/9.76 | | | | | | | | | | (115) $false
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | CLOSE: (115) is inconsistent.
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | (116) all_56_8 = e0
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | COMBINE_EQS: (72), (116) imply:
% 65.49/9.76 | | | | | | | | | | (117) all_6_1 = e0
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | REDUCE: (75), (117) imply:
% 65.49/9.76 | | | | | | | | | | (118) ~ (all_54_4 = e0)
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | REDUCE: (78), (117) imply:
% 65.49/9.76 | | | | | | | | | | (119) ~ (all_54_12 = e0)
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | REDUCE: (80), (117) imply:
% 65.49/9.76 | | | | | | | | | | (120) ~ (e2 = e0)
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | SIMP: (120) implies:
% 65.49/9.76 | | | | | | | | | | (121) ~ (e2 = e0)
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | BETA: splitting (46) gives:
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | (122) all_58_4 = e1
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | COMBINE_EQS: (27), (122) imply:
% 65.49/9.76 | | | | | | | | | | | (123) all_54_9 = e1
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | REDUCE: (16), (123) imply:
% 65.49/9.76 | | | | | | | | | | | (124) ~ (all_54_1 = e1)
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | BETA: splitting (10) gives:
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | (125) all_56_1 = e3
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | COMBINE_EQS: (22), (125) imply:
% 65.49/9.76 | | | | | | | | | | | | (126) all_54_1 = e3
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | COMBINE_EQS: (54), (126) imply:
% 65.49/9.76 | | | | | | | | | | | | (127) all_58_3 = e3
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | BETA: splitting (63) gives:
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | (128) all_56_12 = e3
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | COMBINE_EQS: (37), (128) imply:
% 65.49/9.76 | | | | | | | | | | | | | (129) all_54_12 = e3
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | SIMP: (129) implies:
% 65.49/9.76 | | | | | | | | | | | | | (130) all_54_12 = e3
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | REDUCE: (62), (130) imply:
% 65.49/9.76 | | | | | | | | | | | | | (131) ~ (all_54_4 = e3)
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | REDUCE: (64), (130) imply:
% 65.49/9.76 | | | | | | | | | | | | | (132) ~ (all_54_15 = e3)
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | SIMP: (132) implies:
% 65.49/9.76 | | | | | | | | | | | | | (133) ~ (all_54_15 = e3)
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | REDUCE: (30), (130) imply:
% 65.49/9.76 | | | | | | | | | | | | | (134) ~ (e3 = e2)
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | BETA: splitting (56) gives:
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | (135) all_58_2 = e2
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | COMBINE_EQS: (104), (135) imply:
% 65.49/9.76 | | | | | | | | | | | | | | (136) e2 = e0
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | SIMP: (136) implies:
% 65.49/9.76 | | | | | | | | | | | | | | (137) e2 = e0
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | REDUCE: (121), (137) imply:
% 65.49/9.76 | | | | | | | | | | | | | | (138) $false
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | (139) all_58_3 = e2 | all_58_4 = e2 | all_58_10 = e2
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | (140) all_56_4 = e3
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | COMBINE_EQS: (17), (140) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | (141) all_54_4 = e3
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | REDUCE: (131), (141) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | (142) $false
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | (143) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | (144) all_58_3 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (144) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | (145) e3 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | REDUCE: (134), (145) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | (146) $false
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | (147) all_58_4 = e2 | all_58_10 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | (148) all_56_4 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (148) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | (149) all_54_4 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | REDUCE: (9), (149) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | (150) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | (151) ~ (all_56_4 = e2)
% 65.49/9.76 | | | | | | | | | | | | | | | | | (152) all_56_4 = e1 | all_56_4 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (153) all_56_4 = e1
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (153) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (154) all_54_4 = e1
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | REDUCE: (34), (154) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (155) ~ (all_54_7 = e1)
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | SIMP: (155) implies:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (156) ~ (all_54_7 = e1)
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | REDUCE: (9), (154) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (157) ~ (e2 = e1)
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | (158) all_56_6 = e3
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (158) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | (159) all_54_7 = e3
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | REDUCE: (76), (159) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | (160) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | (161) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (162) all_58_9 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (162) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (163) all_54_15 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (163) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (164) op(e3, e2) = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, all_10_1, e2, e3,
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | simplifying with (82), (164) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (165) all_10_1 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (107), (165) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (166) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (167) ~ (all_58_9 = e0)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (167) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | (168) ~ (all_54_15 = e0)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | (169) all_56_14 = e3
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (133), (169) are inconsistent by sub-proof
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | #71.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | (170) all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (171) all_58_4 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (171) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (172) e2 = e1
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | SIMP: (172) implies:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (173) e2 = e1
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (173) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (174) all_58_0 = e1
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (173) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | (175) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | (176) all_58_1 = e2 | all_58_5 = e2 | all_58_11 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | (177) all_58_1 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (177) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | (178) all_54_4 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (178) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | (179) ~ (all_54_7 = e2)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | (180) ~ (all_54_7 = e2)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (106), (156), (161), (180) are inconsistent
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #18.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_5 = e2 | all_58_11 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_58_5 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (182) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_54_8 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (183) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (184) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_58_11 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (185) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_12 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (30), (186) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | (187) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (188) all_58_10 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (188) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (189) all_54_13 = e2
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (189) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_54_15 = e2)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_54_15 = e2)
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (92), (168), (170), (191) are inconsistent
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #69.
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (192) all_56_4 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (192) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (193) all_54_4 = e0
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | REDUCE: (118), (193) imply:
% 65.49/9.76 | | | | | | | | | | | | | | | | | | (194) $false
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 65.49/9.76 | | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | (195) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | | REF_CLOSE: (30), (37), (91), (119), (195) are inconsistent by
% 65.49/9.76 | | | | | | | | | | | | | sub-proof #67.
% 65.49/9.76 | | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | (196) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | | REF_CLOSE: (22), (40), (105), (124), (196) are inconsistent
% 65.49/9.76 | | | | | | | | | | | | by sub-proof #117.
% 65.49/9.76 | | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | (197) all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | | REF_CLOSE: (13), (19), (68), (73), (74), (90), (197) are
% 65.49/9.76 | | | | | | | | | | | inconsistent by sub-proof #24.
% 65.49/9.76 | | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | | |
% 65.49/9.76 | | | | | | | | | End of split
% 65.49/9.76 | | | | | | | | |
% 65.49/9.76 | | | | | | | | End of split
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | Case 2:
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | (198) ~ (all_10_2 = e3)
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | REDUCE: (70), (198) imply:
% 65.49/9.76 | | | | | | | | (199) $false
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | | CLOSE: (199) is inconsistent.
% 65.49/9.76 | | | | | | | |
% 65.49/9.76 | | | | | | | End of split
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | Case 2:
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | (200) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | ALPHA: (200) implies:
% 65.49/9.76 | | | | | | | (201) all_52_2 = e0
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | | REF_CLOSE: (29), (87), (201) are inconsistent by sub-proof #152.
% 65.49/9.76 | | | | | | |
% 65.49/9.76 | | | | | | End of split
% 65.49/9.76 | | | | | |
% 65.49/9.76 | | | | | End of split
% 65.49/9.76 | | | | |
% 65.49/9.76 | | | | End of split
% 65.49/9.76 | | | |
% 65.49/9.76 | | | Case 2:
% 65.49/9.76 | | | |
% 65.49/9.76 | | | | (202) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.49/9.76 | | | |
% 65.49/9.76 | | | | REF_CLOSE: (44), (47), (202) are inconsistent by sub-proof #151.
% 65.49/9.76 | | | |
% 65.49/9.76 | | | End of split
% 65.49/9.76 | | |
% 65.49/9.76 | | End of split
% 65.49/9.76 | |
% 65.49/9.76 | Case 2:
% 65.49/9.76 | |
% 65.49/9.76 | | (203) ~ (all_8_2 = e2)
% 65.49/9.76 | |
% 65.49/9.76 | | REDUCE: (26), (203) imply:
% 65.49/9.76 | | (204) $false
% 65.49/9.76 | |
% 65.49/9.76 | | CLOSE: (204) is inconsistent.
% 65.49/9.76 | |
% 65.49/9.76 | End of split
% 65.49/9.76 |
% 65.49/9.76 End of proof
% 65.49/9.76
% 65.49/9.76 Sub-proof #18 shows that the following formulas are inconsistent:
% 65.49/9.76 ----------------------------------------------------------------
% 65.49/9.76 (1) ~ (all_54_7 = e0)
% 65.49/9.76 (2) ~ (all_54_7 = e1)
% 65.49/9.76 (3) ~ (all_54_7 = e2)
% 65.49/9.76 (4) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.49/9.76 (5) all_56_6 = all_54_7
% 65.49/9.76
% 65.49/9.76 Begin of proof
% 65.49/9.76 |
% 65.49/9.76 | BETA: splitting (4) gives:
% 65.49/9.76 |
% 65.49/9.76 | Case 1:
% 65.49/9.76 | |
% 65.49/9.76 | | (6) all_56_6 = e2
% 65.49/9.76 | |
% 65.49/9.76 | | COMBINE_EQS: (5), (6) imply:
% 65.49/9.76 | | (7) all_54_7 = e2
% 65.49/9.76 | |
% 65.49/9.76 | | REDUCE: (3), (7) imply:
% 65.49/9.76 | | (8) $false
% 65.49/9.76 | |
% 65.49/9.76 | | CLOSE: (8) is inconsistent.
% 65.49/9.76 | |
% 65.49/9.76 | Case 2:
% 65.49/9.76 | |
% 65.49/9.76 | | (9) all_56_6 = e1 | all_56_6 = e0
% 65.49/9.76 | |
% 65.49/9.76 | | BETA: splitting (9) gives:
% 65.49/9.76 | |
% 65.49/9.76 | | Case 1:
% 65.49/9.76 | | |
% 65.49/9.76 | | | (10) all_56_6 = e1
% 65.49/9.76 | | |
% 65.49/9.76 | | | COMBINE_EQS: (5), (10) imply:
% 65.49/9.76 | | | (11) all_54_7 = e1
% 65.49/9.76 | | |
% 65.49/9.76 | | | REDUCE: (2), (11) imply:
% 65.49/9.76 | | | (12) $false
% 65.49/9.76 | | |
% 65.49/9.76 | | | CLOSE: (12) is inconsistent.
% 65.49/9.76 | | |
% 65.49/9.76 | | Case 2:
% 65.49/9.76 | | |
% 65.49/9.76 | | | (13) all_56_6 = e0
% 65.49/9.76 | | |
% 65.49/9.77 | | | COMBINE_EQS: (5), (13) imply:
% 65.49/9.77 | | | (14) all_54_7 = e0
% 65.49/9.77 | | |
% 65.49/9.77 | | | REDUCE: (1), (14) imply:
% 65.49/9.77 | | | (15) $false
% 65.49/9.77 | | |
% 65.49/9.77 | | | CLOSE: (15) is inconsistent.
% 65.49/9.77 | | |
% 65.49/9.77 | | End of split
% 65.49/9.77 | |
% 65.49/9.77 | End of split
% 65.49/9.77 |
% 65.49/9.77 End of proof
% 65.49/9.77
% 65.49/9.77 Sub-proof #19 shows that the following formulas are inconsistent:
% 65.49/9.77 ----------------------------------------------------------------
% 65.49/9.77 (1) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 =
% 65.49/9.77 e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 65.49/9.77 (2) all_52_2 = all_4_2
% 65.49/9.77 (3) op(all_4_2, all_4_2) = all_4_0
% 65.49/9.77 (4) ~ (all_26_0 = e1)
% 65.49/9.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.77 (6) op(e0, e0) = all_6_2
% 65.49/9.77 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.77 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.77 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.77 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.77 (9) ~ (e3 = e1)
% 65.49/9.77 (10) op(e2, e2) = all_10_2
% 65.49/9.77 (11) all_52_1 = all_14_2
% 65.49/9.77 (12) ~ (e3 = e0)
% 65.49/9.77 (13) ~ (e1 = e0)
% 65.49/9.77 (14) all_26_0 = all_4_0
% 65.49/9.77 (15) op(e3, e3) = all_4_2
% 65.49/9.77 (16) op(all_6_2, all_6_2) = e3
% 65.49/9.77 (17) ~ (e2 = e0)
% 65.49/9.77 (18) ~ (e2 = e1)
% 65.49/9.77 (19) all_52_3 = all_6_2
% 65.49/9.77 (20) all_52_0 = all_10_2
% 65.49/9.77 (21) ~ (e3 = e2)
% 65.49/9.77 (22) op(all_14_2, all_14_2) = e0
% 65.49/9.77 (23) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.77 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.77 (24) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.49/9.77
% 65.49/9.77 Begin of proof
% 65.49/9.77 |
% 65.49/9.77 | REDUCE: (4), (14) imply:
% 65.49/9.77 | (25) ~ (all_4_0 = e1)
% 65.49/9.77 |
% 65.49/9.77 | BETA: splitting (1) gives:
% 65.49/9.77 |
% 65.49/9.77 | Case 1:
% 65.49/9.77 | |
% 65.49/9.77 | | (26) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.49/9.77 | |
% 65.49/9.77 | | ALPHA: (26) implies:
% 65.49/9.77 | | (27) all_52_1 = e2
% 65.49/9.77 | | (28) ~ (all_52_0 = e1)
% 65.49/9.77 | |
% 65.49/9.77 | | COMBINE_EQS: (11), (27) imply:
% 65.49/9.77 | | (29) all_14_2 = e2
% 65.49/9.77 | |
% 65.49/9.77 | | REDUCE: (20), (28) imply:
% 65.49/9.77 | | (30) ~ (all_10_2 = e1)
% 65.49/9.77 | |
% 65.49/9.77 | | REDUCE: (22), (29) imply:
% 65.49/9.77 | | (31) op(e2, e2) = e0
% 65.49/9.77 | |
% 65.49/9.77 | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (12), (15), (16), (19), (20),
% 65.49/9.77 | | (21), (24), (27), (29), (30), (31) are inconsistent by sub-proof
% 65.49/9.77 | | #20.
% 65.49/9.77 | |
% 65.49/9.77 | Case 2:
% 65.49/9.77 | |
% 65.49/9.77 | | (32) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0
% 65.49/9.77 | | = e0))
% 65.49/9.77 | |
% 65.49/9.77 | | BETA: splitting (32) gives:
% 65.49/9.77 | |
% 65.49/9.77 | | Case 1:
% 65.49/9.77 | | |
% 65.49/9.77 | | | (33) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.49/9.77 | | |
% 65.49/9.77 | | | ALPHA: (33) implies:
% 65.49/9.77 | | | (34) all_52_2 = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | COMBINE_EQS: (2), (34) imply:
% 65.49/9.77 | | | (35) all_4_2 = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | REDUCE: (3), (35) imply:
% 65.49/9.77 | | | (36) op(e2, e2) = all_4_0
% 65.49/9.77 | | |
% 65.49/9.77 | | | REDUCE: (15), (35) imply:
% 65.49/9.77 | | | (37) op(e3, e3) = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (13), (17), (18), (20),
% 65.49/9.77 | | | (22), (23), (25), (34), (36), (37) are inconsistent by
% 65.49/9.77 | | | sub-proof #85.
% 65.49/9.77 | | |
% 65.49/9.77 | | Case 2:
% 65.49/9.77 | | |
% 65.49/9.77 | | | (38) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.77 | | |
% 65.49/9.77 | | | ALPHA: (38) implies:
% 65.49/9.77 | | | (39) all_52_3 = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | COMBINE_EQS: (19), (39) imply:
% 65.49/9.77 | | | (40) all_6_2 = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | REDUCE: (16), (40) imply:
% 65.49/9.77 | | | (41) op(e2, e2) = e3
% 65.49/9.77 | | |
% 65.49/9.77 | | | REDUCE: (6), (40) imply:
% 65.49/9.77 | | | (42) op(e0, e0) = e2
% 65.49/9.77 | | |
% 65.49/9.77 | | | GROUND_INST: instantiating (5) with all_10_2, e3, e2, e2, simplifying with
% 65.49/9.77 | | | (10), (41) gives:
% 65.49/9.77 | | | (43) all_10_2 = e3
% 65.49/9.77 | | |
% 65.49/9.77 | | | COMBINE_EQS: (20), (43) imply:
% 65.49/9.77 | | | (44) all_52_0 = e3
% 65.49/9.77 | | |
% 65.49/9.77 | | | REF_CLOSE: (5), (8), (9), (11), (12), (13), (17), (18), (22), (23), (39),
% 65.49/9.77 | | | (42), (44) are inconsistent by sub-proof #80.
% 65.49/9.77 | | |
% 65.49/9.77 | | End of split
% 65.49/9.77 | |
% 65.49/9.77 | End of split
% 65.49/9.77 |
% 65.49/9.77 End of proof
% 65.49/9.77
% 65.49/9.77 Sub-proof #20 shows that the following formulas are inconsistent:
% 65.49/9.77 ----------------------------------------------------------------
% 65.49/9.77 (1) all_52_2 = all_4_2
% 65.49/9.77 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.77 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.77 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.77 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.77 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.77 (5) ~ (e3 = e1)
% 65.49/9.77 (6) op(e2, e2) = all_10_2
% 65.49/9.77 (7) ~ (e3 = e0)
% 65.49/9.77 (8) all_14_2 = e2
% 65.49/9.77 (9) op(e3, e3) = all_4_2
% 65.49/9.77 (10) op(all_6_2, all_6_2) = e3
% 65.49/9.77 (11) all_52_3 = all_6_2
% 65.49/9.77 (12) all_52_0 = all_10_2
% 65.49/9.77 (13) all_52_1 = e2
% 65.49/9.77 (14) ~ (e3 = e2)
% 65.49/9.77 (15) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.49/9.77 (16) ~ (all_10_2 = e1)
% 65.49/9.77 (17) op(e2, e2) = e0
% 65.49/9.77
% 65.49/9.77 Begin of proof
% 65.49/9.77 |
% 65.49/9.77 | BETA: splitting (15) gives:
% 65.49/9.77 |
% 65.49/9.77 | Case 1:
% 65.49/9.77 | |
% 65.49/9.77 | |
% 65.49/9.77 | | GROUND_INST: instantiating (2) with all_10_2, e0, e2, e2, simplifying with
% 65.49/9.77 | | (6), (17) gives:
% 65.49/9.77 | | (18) all_10_2 = e0
% 65.49/9.77 | |
% 65.49/9.77 | | COMBINE_EQS: (12), (18) imply:
% 65.49/9.77 | | (19) all_52_0 = e0
% 65.49/9.77 | |
% 65.49/9.77 | | REDUCE: (16), (18) imply:
% 65.49/9.77 | | (20) ~ (e1 = e0)
% 65.49/9.77 | |
% 65.49/9.77 | | SIMP: (20) implies:
% 65.49/9.77 | | (21) ~ (e1 = e0)
% 65.49/9.77 | |
% 65.49/9.77 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (13), (14), (19),
% 65.49/9.77 | | (21) are inconsistent by sub-proof #43.
% 65.49/9.77 | |
% 65.49/9.77 | Case 2:
% 65.49/9.77 | |
% 65.49/9.77 | | (22) ~ (all_14_2 = e2)
% 65.49/9.77 | |
% 65.49/9.77 | | REDUCE: (8), (22) imply:
% 65.49/9.77 | | (23) $false
% 65.49/9.77 | |
% 65.49/9.77 | | CLOSE: (23) is inconsistent.
% 65.49/9.77 | |
% 65.49/9.77 | End of split
% 65.49/9.77 |
% 65.49/9.77 End of proof
% 65.49/9.77
% 65.49/9.77 Sub-proof #21 shows that the following formulas are inconsistent:
% 65.49/9.77 ----------------------------------------------------------------
% 65.49/9.77 (1) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 =
% 65.49/9.77 e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 65.49/9.77 (2) ~ (all_4_0 = e2)
% 65.49/9.77 (3) op(e1, e1) = all_14_2
% 65.49/9.77 (4) op(all_14_2, all_14_2) = e2
% 65.49/9.77 (5) all_52_2 = all_4_2
% 65.49/9.77 (6) op(all_4_2, all_4_2) = all_4_0
% 65.49/9.77 (7) all_26_0 = e1
% 65.49/9.77 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.77 (9) all_58_13 = all_54_10
% 65.49/9.77 (10) op(e2, e0) = all_54_8
% 65.49/9.77 (11) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.77 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.77 (12) op(all_6_2, e0) = all_6_1
% 65.49/9.77 (13) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.77 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.77 (14) ~ (e3 = e1)
% 65.49/9.77 (15) op(e2, e2) = all_10_2
% 65.49/9.77 (16) all_8_1 = all_6_1
% 65.49/9.77 (17) all_52_1 = all_14_2
% 65.49/9.77 (18) all_8_2 = all_6_2
% 65.49/9.77 (19) all_58_4 = all_54_9
% 65.49/9.77 (20) ~ (e3 = e0)
% 65.49/9.77 (21) ~ (e1 = e0)
% 65.49/9.77 (22) all_26_0 = all_4_0
% 65.49/9.77 (23) all_58_6 = all_10_2
% 65.49/9.77 (24) op(e3, e3) = all_4_2
% 65.49/9.77 (25) ~ (all_54_9 = all_14_2)
% 65.49/9.77 (26) op(all_6_2, all_6_2) = e3
% 65.49/9.77 (27) ~ (all_54_10 = all_4_2)
% 65.49/9.77 (28) ~ (e2 = e0)
% 65.49/9.77 (29) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.77 (30) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.77 (31) all_52_3 = all_6_2
% 65.49/9.77 (32) all_52_0 = all_10_2
% 65.49/9.77 (33) ~ (e3 = e2)
% 65.49/9.77 (34) all_58_5 = all_54_8
% 65.49/9.77 (35) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.77 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.77
% 65.49/9.77 Begin of proof
% 65.49/9.77 |
% 65.49/9.77 | COMBINE_EQS: (7), (22) imply:
% 65.49/9.77 | (36) all_4_0 = e1
% 65.49/9.77 |
% 65.49/9.77 | SIMP: (36) implies:
% 65.49/9.77 | (37) all_4_0 = e1
% 65.49/9.77 |
% 65.49/9.77 | REDUCE: (2), (37) imply:
% 65.49/9.77 | (38) ~ (e2 = e1)
% 65.49/9.77 |
% 65.49/9.77 | SIMP: (38) implies:
% 65.49/9.77 | (39) ~ (e2 = e1)
% 65.49/9.77 |
% 65.49/9.77 | REDUCE: (6), (37) imply:
% 65.49/9.77 | (40) op(all_4_2, all_4_2) = e1
% 65.49/9.77 |
% 65.49/9.77 | BETA: splitting (1) gives:
% 65.49/9.77 |
% 65.49/9.77 | Case 1:
% 65.49/9.77 | |
% 65.49/9.77 | | (41) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.49/9.77 | |
% 65.49/9.77 | | ALPHA: (41) implies:
% 65.49/9.77 | | (42) all_52_1 = e2
% 65.49/9.77 | | (43) ~ (all_52_0 = e1)
% 65.49/9.77 | |
% 65.49/9.77 | | COMBINE_EQS: (17), (42) imply:
% 65.49/9.77 | | (44) all_14_2 = e2
% 65.49/9.77 | |
% 65.49/9.77 | | REF_CLOSE: (3), (4), (5), (8), (11), (13), (14), (15), (20), (21), (31),
% 65.49/9.77 | | (32), (33), (35), (40), (42), (43), (44) are inconsistent by
% 65.49/9.77 | | sub-proof #47.
% 65.49/9.77 | |
% 65.49/9.77 | Case 2:
% 65.49/9.77 | |
% 65.49/9.77 | | (45) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0
% 65.49/9.77 | | = e0))
% 65.49/9.77 | |
% 65.49/9.77 | | BETA: splitting (45) gives:
% 65.49/9.77 | |
% 65.49/9.77 | | Case 1:
% 65.49/9.77 | | |
% 65.49/9.77 | | | (46) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.49/9.77 | | |
% 65.49/9.77 | | | REF_CLOSE: (5), (8), (11), (15), (20), (21), (24), (26), (28), (31), (32),
% 65.49/9.77 | | | (33), (35), (40), (46) are inconsistent by sub-proof #25.
% 65.49/9.77 | | |
% 65.49/9.77 | | Case 2:
% 65.49/9.77 | | |
% 65.49/9.77 | | | (47) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.77 | | |
% 65.49/9.78 | | | REF_CLOSE: (3), (5), (8), (9), (10), (12), (13), (14), (15), (16), (17),
% 65.49/9.78 | | | (18), (19), (21), (23), (25), (26), (27), (29), (30), (31),
% 65.49/9.78 | | | (32), (34), (35), (39), (40), (47) are inconsistent by
% 65.49/9.78 | | | sub-proof #22.
% 65.49/9.78 | | |
% 65.49/9.78 | | End of split
% 65.49/9.78 | |
% 65.49/9.78 | End of split
% 65.49/9.78 |
% 65.49/9.78 End of proof
% 65.49/9.78
% 65.49/9.78 Sub-proof #22 shows that the following formulas are inconsistent:
% 65.49/9.78 ----------------------------------------------------------------
% 65.49/9.78 (1) op(e1, e1) = all_14_2
% 65.49/9.78 (2) all_52_2 = all_4_2
% 65.49/9.78 (3) op(all_4_2, all_4_2) = e1
% 65.49/9.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.78 (5) all_58_13 = all_54_10
% 65.49/9.78 (6) op(e2, e0) = all_54_8
% 65.49/9.78 (7) op(all_6_2, e0) = all_6_1
% 65.49/9.78 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.78 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.78 (9) ~ (e3 = e1)
% 65.49/9.78 (10) op(e2, e2) = all_10_2
% 65.49/9.78 (11) all_8_1 = all_6_1
% 65.49/9.78 (12) all_52_1 = all_14_2
% 65.49/9.78 (13) all_8_2 = all_6_2
% 65.49/9.78 (14) all_58_4 = all_54_9
% 65.49/9.78 (15) ~ (e1 = e0)
% 65.49/9.78 (16) all_58_6 = all_10_2
% 65.49/9.78 (17) ~ (all_54_9 = all_14_2)
% 65.49/9.78 (18) op(all_6_2, all_6_2) = e3
% 65.49/9.78 (19) ~ (all_54_10 = all_4_2)
% 65.49/9.78 (20) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.78 (21) ~ (e2 = e1)
% 65.49/9.78 (22) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.78 (23) all_52_3 = all_6_2
% 65.49/9.78 (24) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.49/9.78 (25) all_52_0 = all_10_2
% 65.49/9.78 (26) all_58_5 = all_54_8
% 65.49/9.78 (27) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.78 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.78
% 65.49/9.78 Begin of proof
% 65.49/9.78 |
% 65.49/9.78 | ALPHA: (24) implies:
% 65.49/9.78 | (28) all_52_3 = e2
% 65.49/9.78 | (29) ~ (all_52_0 = e0)
% 65.49/9.78 |
% 65.49/9.78 | COMBINE_EQS: (23), (28) imply:
% 65.49/9.78 | (30) all_6_2 = e2
% 65.49/9.78 |
% 65.49/9.78 | COMBINE_EQS: (13), (30) imply:
% 65.49/9.78 | (31) all_8_2 = e2
% 65.49/9.78 |
% 65.49/9.78 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 65.49/9.78 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (25), (26),
% 65.49/9.78 | (27), (28), (29), (30), (31) are inconsistent by sub-proof #23.
% 65.49/9.78 |
% 65.49/9.78 End of proof
% 65.49/9.78
% 65.49/9.78 Sub-proof #23 shows that the following formulas are inconsistent:
% 65.49/9.78 ----------------------------------------------------------------
% 65.49/9.78 (1) op(e1, e1) = all_14_2
% 65.49/9.78 (2) all_52_2 = all_4_2
% 65.49/9.78 (3) op(all_4_2, all_4_2) = e1
% 65.49/9.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.78 (5) all_58_13 = all_54_10
% 65.49/9.78 (6) op(e2, e0) = all_54_8
% 65.49/9.78 (7) all_6_2 = e2
% 65.49/9.78 (8) op(all_6_2, e0) = all_6_1
% 65.49/9.78 (9) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.78 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.78 (10) ~ (e3 = e1)
% 65.49/9.78 (11) op(e2, e2) = all_10_2
% 65.49/9.78 (12) all_8_1 = all_6_1
% 65.49/9.78 (13) all_52_1 = all_14_2
% 65.49/9.78 (14) all_8_2 = e2
% 65.49/9.78 (15) all_58_4 = all_54_9
% 65.49/9.78 (16) ~ (e1 = e0)
% 65.49/9.78 (17) all_58_6 = all_10_2
% 65.49/9.78 (18) ~ (all_54_9 = all_14_2)
% 65.49/9.78 (19) ~ (all_52_0 = e0)
% 65.49/9.78 (20) op(all_6_2, all_6_2) = e3
% 65.49/9.78 (21) ~ (all_54_10 = all_4_2)
% 65.49/9.78 (22) all_52_3 = e2
% 65.49/9.78 (23) all_58_4 = e1 | all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.78 (24) ~ (e2 = e1)
% 65.49/9.78 (25) ~ (all_8_1 = e1) | ~ (all_8_2 = e2)
% 65.49/9.78 (26) all_52_0 = all_10_2
% 65.49/9.78 (27) all_58_5 = all_54_8
% 65.49/9.78 (28) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.78 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.78
% 65.49/9.78 Begin of proof
% 65.49/9.78 |
% 65.49/9.78 | REDUCE: (19), (26) imply:
% 65.49/9.78 | (29) ~ (all_10_2 = e0)
% 65.49/9.78 |
% 65.49/9.78 | REDUCE: (7), (20) imply:
% 65.49/9.78 | (30) op(e2, e2) = e3
% 65.49/9.78 |
% 65.49/9.78 | REDUCE: (7), (8) imply:
% 65.49/9.78 | (31) op(e2, e0) = all_6_1
% 65.49/9.78 |
% 65.49/9.78 | BETA: splitting (25) gives:
% 65.49/9.78 |
% 65.49/9.78 | Case 1:
% 65.49/9.78 | |
% 65.49/9.78 | | (32) ~ (all_8_1 = e1)
% 65.49/9.78 | |
% 65.49/9.78 | | REDUCE: (12), (32) imply:
% 65.49/9.78 | | (33) ~ (all_6_1 = e1)
% 65.49/9.78 | |
% 65.49/9.78 | | GROUND_INST: instantiating (4) with all_54_8, all_6_1, e0, e2, simplifying
% 65.49/9.78 | | with (6), (31) gives:
% 65.49/9.78 | | (34) all_54_8 = all_6_1
% 65.49/9.78 | |
% 65.49/9.78 | | GROUND_INST: instantiating (4) with all_10_2, e3, e2, e2, simplifying with
% 65.49/9.78 | | (11), (30) gives:
% 65.49/9.78 | | (35) all_10_2 = e3
% 65.49/9.78 | |
% 65.49/9.78 | | COMBINE_EQS: (26), (35) imply:
% 65.49/9.78 | | (36) all_52_0 = e3
% 65.49/9.78 | |
% 65.49/9.78 | | COMBINE_EQS: (17), (35) imply:
% 65.49/9.78 | | (37) all_58_6 = e3
% 65.49/9.78 | |
% 65.49/9.78 | | COMBINE_EQS: (27), (34) imply:
% 65.49/9.78 | | (38) all_58_5 = all_6_1
% 65.49/9.78 | |
% 65.49/9.78 | | REDUCE: (29), (35) imply:
% 65.49/9.78 | | (39) ~ (e3 = e0)
% 65.49/9.78 | |
% 65.49/9.78 | | BETA: splitting (9) gives:
% 65.49/9.78 | |
% 65.49/9.78 | | Case 1:
% 65.49/9.78 | | |
% 65.49/9.78 | | | (40) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.49/9.78 | | |
% 65.49/9.78 | | | ALPHA: (40) implies:
% 65.49/9.78 | | | (41) all_52_0 = e1
% 65.49/9.78 | | |
% 65.49/9.78 | | | REF_CLOSE: (10), (36), (41) are inconsistent by sub-proof #122.
% 65.49/9.78 | | |
% 65.49/9.78 | | Case 2:
% 65.49/9.78 | | |
% 65.49/9.78 | | | (42) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 65.49/9.78 | | | (all_52_1 = e0))
% 65.49/9.78 | | |
% 65.49/9.78 | | | BETA: splitting (42) gives:
% 65.49/9.78 | | |
% 65.49/9.78 | | | Case 1:
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | (43) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | ALPHA: (43) implies:
% 65.49/9.78 | | | | (44) all_52_2 = e1
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | COMBINE_EQS: (2), (44) imply:
% 65.49/9.78 | | | | (45) all_4_2 = e1
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | SIMP: (45) implies:
% 65.49/9.78 | | | | (46) all_4_2 = e1
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | REDUCE: (21), (46) imply:
% 65.49/9.78 | | | | (47) ~ (all_54_10 = e1)
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | REDUCE: (3), (46) imply:
% 65.49/9.78 | | | | (48) op(e1, e1) = e1
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | BETA: splitting (23) gives:
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | Case 1:
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | (49) all_58_4 = e1
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | COMBINE_EQS: (15), (49) imply:
% 65.49/9.78 | | | | | (50) all_54_9 = e1
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | REDUCE: (18), (50) imply:
% 65.49/9.78 | | | | | (51) ~ (all_14_2 = e1)
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | SIMP: (51) implies:
% 65.49/9.78 | | | | | (52) ~ (all_14_2 = e1)
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | BETA: splitting (28) gives:
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | Case 1:
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | (53) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | ALPHA: (53) implies:
% 65.49/9.78 | | | | | | (54) all_52_0 = e0
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | REF_CLOSE: (36), (39), (54) are inconsistent by sub-proof #124.
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | Case 2:
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | (55) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.49/9.78 | | | | | | (all_52_3 = e3))
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | BETA: splitting (55) gives:
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | | Case 1:
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | (56) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | ALPHA: (56) implies:
% 65.49/9.78 | | | | | | | (57) all_52_1 = e0
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | COMBINE_EQS: (13), (57) imply:
% 65.49/9.78 | | | | | | | (58) all_14_2 = e0
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | SIMP: (58) implies:
% 65.49/9.78 | | | | | | | (59) all_14_2 = e0
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | REDUCE: (52), (59) imply:
% 65.49/9.78 | | | | | | | (60) ~ (e1 = e0)
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | REF_CLOSE: (1), (4), (16), (48), (59) are inconsistent by
% 65.49/9.78 | | | | | | | sub-proof #61.
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | Case 2:
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | (61) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | ALPHA: (61) implies:
% 65.49/9.78 | | | | | | | (62) all_52_2 = e0
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | | REF_CLOSE: (16), (44), (62) are inconsistent by sub-proof #152.
% 65.49/9.78 | | | | | | |
% 65.49/9.78 | | | | | | End of split
% 65.49/9.78 | | | | | |
% 65.49/9.78 | | | | | End of split
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | Case 2:
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | (63) all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | | REF_CLOSE: (5), (10), (33), (37), (38), (47), (63) are inconsistent by
% 65.49/9.78 | | | | | sub-proof #24.
% 65.49/9.78 | | | | |
% 65.49/9.78 | | | | End of split
% 65.49/9.78 | | | |
% 65.49/9.78 | | | Case 2:
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | (64) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.49/9.78 | | | |
% 65.49/9.78 | | | | REF_CLOSE: (22), (24), (64) are inconsistent by sub-proof #151.
% 65.49/9.78 | | | |
% 65.49/9.78 | | | End of split
% 65.49/9.78 | | |
% 65.49/9.78 | | End of split
% 65.49/9.78 | |
% 65.49/9.78 | Case 2:
% 65.49/9.78 | |
% 65.49/9.78 | | (65) ~ (all_8_2 = e2)
% 65.49/9.78 | |
% 65.49/9.78 | | REDUCE: (14), (65) imply:
% 65.49/9.78 | | (66) $false
% 65.49/9.78 | |
% 65.49/9.78 | | CLOSE: (66) is inconsistent.
% 65.49/9.78 | |
% 65.49/9.78 | End of split
% 65.49/9.78 |
% 65.49/9.78 End of proof
% 65.49/9.78
% 65.49/9.78 Sub-proof #24 shows that the following formulas are inconsistent:
% 65.49/9.78 ----------------------------------------------------------------
% 65.49/9.78 (1) all_58_13 = all_54_10
% 65.49/9.78 (2) ~ (e3 = e1)
% 65.49/9.78 (3) all_58_5 = e1 | all_58_6 = e1 | all_58_13 = e1
% 65.49/9.78 (4) ~ (all_54_10 = e1)
% 65.49/9.78 (5) all_58_5 = all_6_1
% 65.49/9.78 (6) all_58_6 = e3
% 65.49/9.78 (7) ~ (all_6_1 = e1)
% 65.49/9.78
% 65.49/9.78 Begin of proof
% 65.49/9.78 |
% 65.49/9.78 | BETA: splitting (3) gives:
% 65.49/9.78 |
% 65.49/9.78 | Case 1:
% 65.49/9.78 | |
% 65.49/9.78 | | (8) all_58_5 = e1
% 65.49/9.78 | |
% 65.49/9.78 | | COMBINE_EQS: (5), (8) imply:
% 65.49/9.78 | | (9) all_6_1 = e1
% 65.49/9.78 | |
% 65.49/9.78 | | REDUCE: (7), (9) imply:
% 65.49/9.78 | | (10) $false
% 65.49/9.78 | |
% 65.49/9.78 | | CLOSE: (10) is inconsistent.
% 65.49/9.78 | |
% 65.49/9.78 | Case 2:
% 65.49/9.78 | |
% 65.49/9.78 | | (11) all_58_6 = e1 | all_58_13 = e1
% 65.49/9.78 | |
% 65.49/9.78 | | BETA: splitting (11) gives:
% 65.49/9.78 | |
% 65.49/9.78 | | Case 1:
% 65.49/9.78 | | |
% 65.49/9.78 | | | (12) all_58_6 = e1
% 65.49/9.78 | | |
% 65.49/9.78 | | | COMBINE_EQS: (6), (12) imply:
% 65.49/9.78 | | | (13) e3 = e1
% 65.49/9.78 | | |
% 65.49/9.78 | | | REDUCE: (2), (13) imply:
% 65.49/9.78 | | | (14) $false
% 65.49/9.78 | | |
% 65.49/9.78 | | | CLOSE: (14) is inconsistent.
% 65.49/9.78 | | |
% 65.49/9.78 | | Case 2:
% 65.49/9.78 | | |
% 65.49/9.78 | | | (15) all_58_13 = e1
% 65.49/9.78 | | |
% 65.49/9.78 | | | COMBINE_EQS: (1), (15) imply:
% 65.49/9.78 | | | (16) all_54_10 = e1
% 65.49/9.78 | | |
% 65.49/9.78 | | | REDUCE: (4), (16) imply:
% 65.49/9.78 | | | (17) $false
% 65.49/9.78 | | |
% 65.49/9.78 | | | CLOSE: (17) is inconsistent.
% 65.49/9.78 | | |
% 65.49/9.78 | | End of split
% 65.49/9.78 | |
% 65.49/9.78 | End of split
% 65.49/9.78 |
% 65.49/9.78 End of proof
% 65.49/9.78
% 65.49/9.78 Sub-proof #25 shows that the following formulas are inconsistent:
% 65.49/9.78 ----------------------------------------------------------------
% 65.49/9.78 (1) all_52_2 = all_4_2
% 65.49/9.78 (2) op(all_4_2, all_4_2) = e1
% 65.49/9.78 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.78 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.78 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.78 (5) op(e2, e2) = all_10_2
% 65.49/9.78 (6) ~ (e3 = e0)
% 65.49/9.78 (7) ~ (e1 = e0)
% 65.49/9.78 (8) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.49/9.78 (9) op(e3, e3) = all_4_2
% 65.49/9.78 (10) op(all_6_2, all_6_2) = e3
% 65.49/9.78 (11) ~ (e2 = e0)
% 65.49/9.78 (12) all_52_3 = all_6_2
% 65.49/9.78 (13) all_52_0 = all_10_2
% 65.49/9.78 (14) ~ (e3 = e2)
% 65.49/9.78 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.78 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.78
% 65.49/9.78 Begin of proof
% 65.49/9.79 |
% 65.49/9.79 | ALPHA: (8) implies:
% 65.49/9.79 | (16) all_52_2 = e2
% 65.49/9.79 | (17) ~ (all_52_0 = e3)
% 65.49/9.79 |
% 65.49/9.79 | COMBINE_EQS: (1), (16) imply:
% 65.49/9.79 | (18) all_4_2 = e2
% 65.49/9.79 |
% 65.49/9.79 | SIMP: (18) implies:
% 65.49/9.79 | (19) all_4_2 = e2
% 65.49/9.79 |
% 65.49/9.79 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 65.49/9.79 | (15), (16), (17), (19) are inconsistent by sub-proof #35.
% 65.49/9.79 |
% 65.49/9.79 End of proof
% 65.49/9.79
% 65.49/9.79 Sub-proof #26 shows that the following formulas are inconsistent:
% 65.49/9.79 ----------------------------------------------------------------
% 65.49/9.79 (1) op(all_14_2, all_14_2) = e2
% 65.49/9.79 (2) all_52_2 = all_4_2
% 65.49/9.79 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.79 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.49/9.79 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.49/9.79 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.79 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.49/9.79 (6) ~ (e3 = e1)
% 65.49/9.79 (7) op(e2, e2) = all_10_2
% 65.49/9.79 (8) all_52_1 = all_14_2
% 65.49/9.79 (9) ~ (e3 = e0)
% 65.49/9.79 (10) ~ (e1 = e0)
% 65.49/9.79 (11) op(e3, e3) = all_4_2
% 65.49/9.79 (12) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.49/9.79 (13) op(all_6_2, all_6_2) = e3
% 65.49/9.79 (14) all_52_3 = all_6_2
% 65.49/9.79 (15) all_52_0 = all_10_2
% 65.49/9.79 (16) ~ (e3 = e2)
% 65.49/9.79 (17) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.49/9.79 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.49/9.79
% 65.49/9.79 Begin of proof
% 65.49/9.79 |
% 65.49/9.79 | ALPHA: (12) implies:
% 65.49/9.79 | (18) all_52_1 = e2
% 65.49/9.79 | (19) ~ (all_52_0 = e1)
% 65.49/9.79 |
% 65.49/9.79 | COMBINE_EQS: (8), (18) imply:
% 65.49/9.79 | (20) all_14_2 = e2
% 65.49/9.79 |
% 65.49/9.79 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 65.49/9.79 | (15), (16), (17), (18), (19), (20) are inconsistent by sub-proof
% 65.49/9.79 | #30.
% 65.49/9.79 |
% 65.49/9.79 End of proof
% 65.49/9.79
% 65.49/9.79 Sub-proof #27 shows that the following formulas are inconsistent:
% 65.49/9.79 ----------------------------------------------------------------
% 65.49/9.79 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 65.49/9.79 e0))
% 65.49/9.79 (2) op(e1, e1) = all_14_2
% 65.49/9.79 (3) all_52_2 = all_4_2
% 65.49/9.79 (4) op(all_4_2, all_4_2) = all_4_0
% 65.49/9.79 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.49/9.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.49/9.79 (6) ~ (all_4_0 = e0)
% 65.49/9.79 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.49/9.79 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.87/9.79 (8) ~ (e3 = e1)
% 65.87/9.79 (9) op(e2, e2) = all_10_2
% 65.87/9.79 (10) ~ (all_4_0 = e1)
% 65.87/9.79 (11) all_52_1 = all_14_2
% 65.87/9.79 (12) ~ (e1 = e0)
% 65.87/9.79 (13) op(all_6_2, all_6_2) = e3
% 65.87/9.79 (14) ~ (e2 = e0)
% 65.87/9.79 (15) ~ (e2 = e1)
% 65.87/9.79 (16) all_52_3 = all_6_2
% 65.87/9.79 (17) all_52_0 = all_10_2
% 65.87/9.79 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.87/9.79 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.87/9.79
% 65.87/9.79 Begin of proof
% 65.87/9.79 |
% 65.87/9.79 | BETA: splitting (1) gives:
% 65.87/9.79 |
% 65.87/9.79 | Case 1:
% 65.87/9.79 | |
% 65.87/9.79 | | (19) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.87/9.79 | |
% 65.87/9.79 | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (14), (15), (17), (18),
% 65.87/9.79 | | (19) are inconsistent by sub-proof #111.
% 65.87/9.79 | |
% 65.87/9.79 | Case 2:
% 65.87/9.79 | |
% 65.87/9.79 | | (20) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.87/9.79 | |
% 65.87/9.79 | | ALPHA: (20) implies:
% 65.87/9.79 | | (21) all_52_3 = e2
% 65.87/9.79 | | (22) ~ (all_52_0 = e0)
% 65.87/9.79 | |
% 65.87/9.79 | | COMBINE_EQS: (16), (21) imply:
% 65.87/9.79 | | (23) all_6_2 = e2
% 65.87/9.79 | |
% 65.87/9.79 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 65.87/9.79 | | (17), (18), (21), (22), (23) are inconsistent by sub-proof #28.
% 65.87/9.79 | |
% 65.87/9.79 | End of split
% 65.87/9.79 |
% 65.87/9.79 End of proof
% 65.87/9.79
% 65.87/9.79 Sub-proof #28 shows that the following formulas are inconsistent:
% 65.87/9.79 ----------------------------------------------------------------
% 65.87/9.79 (1) op(e1, e1) = all_14_2
% 65.87/9.79 (2) all_52_2 = all_4_2
% 65.87/9.79 (3) op(all_4_2, all_4_2) = all_4_0
% 65.87/9.79 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.87/9.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.87/9.79 (5) ~ (all_4_0 = e0)
% 65.87/9.79 (6) all_6_2 = e2
% 65.87/9.79 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.87/9.79 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.87/9.79 (8) ~ (e3 = e1)
% 65.87/9.79 (9) op(e2, e2) = all_10_2
% 65.87/9.79 (10) all_52_1 = all_14_2
% 65.87/9.79 (11) ~ (e1 = e0)
% 65.87/9.79 (12) ~ (all_52_0 = e0)
% 65.87/9.79 (13) op(all_6_2, all_6_2) = e3
% 65.87/9.79 (14) all_52_3 = e2
% 65.87/9.79 (15) ~ (e2 = e1)
% 65.87/9.79 (16) all_52_0 = all_10_2
% 65.87/9.79 (17) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.87/9.79 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.87/9.79
% 65.87/9.79 Begin of proof
% 65.87/9.79 |
% 65.87/9.79 | REDUCE: (12), (16) imply:
% 65.87/9.79 | (18) ~ (all_10_2 = e0)
% 65.87/9.79 |
% 65.87/9.79 | REDUCE: (6), (13) imply:
% 65.87/9.79 | (19) op(e2, e2) = e3
% 65.87/9.79 |
% 65.87/9.79 | GROUND_INST: instantiating (4) with all_10_2, e3, e2, e2, simplifying with
% 65.87/9.79 | (9), (19) gives:
% 65.87/9.79 | (20) all_10_2 = e3
% 65.87/9.79 |
% 65.87/9.79 | COMBINE_EQS: (16), (20) imply:
% 65.87/9.79 | (21) all_52_0 = e3
% 65.87/9.79 |
% 65.87/9.79 | REDUCE: (18), (20) imply:
% 65.87/9.79 | (22) ~ (e3 = e0)
% 65.87/9.79 |
% 65.87/9.79 | BETA: splitting (7) gives:
% 65.87/9.79 |
% 65.87/9.79 | Case 1:
% 65.87/9.79 | |
% 65.87/9.79 | | (23) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.87/9.79 | |
% 65.87/9.79 | | ALPHA: (23) implies:
% 65.87/9.79 | | (24) all_52_0 = e1
% 65.87/9.79 | |
% 65.87/9.79 | | COMBINE_EQS: (21), (24) imply:
% 65.87/9.79 | | (25) e3 = e1
% 65.87/9.79 | |
% 65.87/9.79 | | REDUCE: (8), (25) imply:
% 65.87/9.79 | | (26) $false
% 65.87/9.79 | |
% 65.87/9.79 | | CLOSE: (26) is inconsistent.
% 65.87/9.79 | |
% 65.87/9.79 | Case 2:
% 65.87/9.79 | |
% 65.87/9.79 | | (27) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 65.87/9.79 | | = e0))
% 65.87/9.79 | |
% 65.87/9.79 | | BETA: splitting (27) gives:
% 65.87/9.79 | |
% 65.87/9.79 | | Case 1:
% 65.87/9.79 | | |
% 65.87/9.79 | | | (28) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.87/9.79 | | |
% 65.87/9.79 | | | ALPHA: (28) implies:
% 65.87/9.79 | | | (29) all_52_2 = e1
% 65.87/9.79 | | |
% 65.87/9.79 | | | COMBINE_EQS: (2), (29) imply:
% 65.87/9.79 | | | (30) all_4_2 = e1
% 65.87/9.79 | | |
% 65.87/9.79 | | | REDUCE: (3), (30) imply:
% 65.87/9.79 | | | (31) op(e1, e1) = all_4_0
% 65.87/9.79 | | |
% 65.87/9.79 | | | BETA: splitting (17) gives:
% 65.87/9.79 | | |
% 65.87/9.79 | | | Case 1:
% 65.87/9.79 | | | |
% 65.87/9.79 | | | | (32) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.89/9.79 | | | |
% 65.89/9.79 | | | | ALPHA: (32) implies:
% 65.89/9.79 | | | | (33) all_52_0 = e0
% 65.89/9.79 | | | |
% 65.89/9.79 | | | | REF_CLOSE: (21), (22), (33) are inconsistent by sub-proof #124.
% 65.89/9.79 | | | |
% 65.89/9.79 | | | Case 2:
% 65.89/9.79 | | | |
% 65.89/9.79 | | | | (34) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.89/9.79 | | | | (all_52_3 = e3))
% 65.89/9.79 | | | |
% 65.89/9.79 | | | | BETA: splitting (34) gives:
% 65.89/9.79 | | | |
% 65.89/9.79 | | | | Case 1:
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | (35) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | ALPHA: (35) implies:
% 65.89/9.79 | | | | | (36) all_52_1 = e0
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | COMBINE_EQS: (10), (36) imply:
% 65.89/9.79 | | | | | (37) all_14_2 = e0
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | SIMP: (37) implies:
% 65.89/9.79 | | | | | (38) all_14_2 = e0
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | REF_CLOSE: (1), (4), (5), (31), (38) are inconsistent by sub-proof
% 65.89/9.79 | | | | | #172.
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | Case 2:
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | (39) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | ALPHA: (39) implies:
% 65.89/9.79 | | | | | (40) all_52_2 = e0
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | | REF_CLOSE: (11), (29), (40) are inconsistent by sub-proof #152.
% 65.89/9.79 | | | | |
% 65.89/9.79 | | | | End of split
% 65.89/9.79 | | | |
% 65.89/9.79 | | | End of split
% 65.89/9.79 | | |
% 65.89/9.79 | | Case 2:
% 65.89/9.79 | | |
% 65.89/9.79 | | | (41) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.89/9.79 | | |
% 65.89/9.79 | | | REF_CLOSE: (14), (15), (41) are inconsistent by sub-proof #171.
% 65.89/9.79 | | |
% 65.89/9.79 | | End of split
% 65.89/9.79 | |
% 65.89/9.79 | End of split
% 65.89/9.79 |
% 65.89/9.79 End of proof
% 65.89/9.79
% 65.89/9.79 Sub-proof #29 shows that the following formulas are inconsistent:
% 65.89/9.79 ----------------------------------------------------------------
% 65.89/9.79 (1) op(all_14_2, all_14_2) = e2
% 65.89/9.79 (2) all_52_2 = all_4_2
% 65.89/9.79 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.89/9.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.89/9.79 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.89/9.79 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.89/9.79 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.89/9.79 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.89/9.79 (6) ~ (e3 = e1)
% 65.89/9.79 (7) op(e2, e2) = all_10_2
% 65.89/9.79 (8) all_52_1 = all_14_2
% 65.89/9.79 (9) ~ (e3 = e0)
% 65.89/9.79 (10) ~ (e1 = e0)
% 65.89/9.79 (11) op(e3, e3) = all_4_2
% 65.89/9.79 (12) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.89/9.79 (13) op(all_6_2, all_6_2) = e3
% 65.89/9.79 (14) all_52_3 = all_6_2
% 65.89/9.79 (15) all_52_0 = all_10_2
% 65.89/9.79 (16) ~ (e3 = e2)
% 65.89/9.79 (17) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.89/9.79 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.89/9.79
% 65.89/9.79 Begin of proof
% 65.89/9.79 |
% 65.89/9.79 | ALPHA: (12) implies:
% 65.89/9.79 | (18) all_52_1 = e2
% 65.89/9.79 | (19) ~ (all_52_0 = e1)
% 65.89/9.79 |
% 65.89/9.79 | COMBINE_EQS: (8), (18) imply:
% 65.89/9.79 | (20) all_14_2 = e2
% 65.89/9.79 |
% 65.89/9.79 | SIMP: (20) implies:
% 65.89/9.80 | (21) all_14_2 = e2
% 65.89/9.80 |
% 65.89/9.80 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 65.89/9.80 | (15), (16), (17), (18), (19), (21) are inconsistent by sub-proof
% 65.89/9.80 | #30.
% 65.89/9.80 |
% 65.89/9.80 End of proof
% 65.89/9.80
% 65.89/9.80 Sub-proof #30 shows that the following formulas are inconsistent:
% 65.89/9.80 ----------------------------------------------------------------
% 65.89/9.80 (1) ~ (all_52_0 = e1)
% 65.89/9.80 (2) op(all_14_2, all_14_2) = e2
% 65.89/9.80 (3) all_52_2 = all_4_2
% 65.89/9.80 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.89/9.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.89/9.80 (5) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.89/9.80 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.89/9.80 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.89/9.80 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.89/9.80 (7) ~ (e3 = e1)
% 65.89/9.80 (8) op(e2, e2) = all_10_2
% 65.89/9.80 (9) ~ (e3 = e0)
% 65.89/9.80 (10) ~ (e1 = e0)
% 65.89/9.80 (11) all_14_2 = e2
% 65.89/9.80 (12) op(e3, e3) = all_4_2
% 65.89/9.80 (13) op(all_6_2, all_6_2) = e3
% 65.89/9.80 (14) all_52_3 = all_6_2
% 65.89/9.80 (15) all_52_0 = all_10_2
% 65.89/9.80 (16) all_52_1 = e2
% 65.89/9.80 (17) ~ (e3 = e2)
% 65.89/9.80 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.89/9.80 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.89/9.80
% 65.89/9.80 Begin of proof
% 65.89/9.80 |
% 65.89/9.80 | REDUCE: (1), (15) imply:
% 65.89/9.80 | (19) ~ (all_10_2 = e1)
% 65.89/9.80 |
% 65.89/9.80 | REDUCE: (2), (11) imply:
% 65.89/9.80 | (20) op(e2, e2) = e2
% 65.89/9.80 |
% 65.89/9.80 | GROUND_INST: instantiating (4) with all_10_2, e2, e2, e2, simplifying with
% 65.89/9.80 | (8), (20) gives:
% 65.89/9.80 | (21) all_10_2 = e2
% 65.89/9.80 |
% 65.89/9.80 | COMBINE_EQS: (15), (21) imply:
% 65.89/9.80 | (22) all_52_0 = e2
% 65.89/9.80 |
% 65.89/9.80 | REDUCE: (19), (21) imply:
% 65.89/9.80 | (23) ~ (e2 = e1)
% 65.89/9.80 |
% 65.89/9.80 | BETA: splitting (18) gives:
% 65.89/9.80 |
% 65.89/9.80 | Case 1:
% 65.89/9.80 | |
% 65.89/9.80 | | (24) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.89/9.80 | |
% 65.89/9.80 | | ALPHA: (24) implies:
% 65.89/9.80 | | (25) all_52_0 = e0
% 65.89/9.80 | |
% 65.89/9.80 | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (16), (17),
% 65.89/9.80 | | (25) are inconsistent by sub-proof #43.
% 65.89/9.80 | |
% 65.89/9.80 | Case 2:
% 65.89/9.80 | |
% 65.89/9.80 | | (26) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.89/9.80 | | = e3))
% 65.89/9.80 | |
% 65.89/9.80 | | BETA: splitting (26) gives:
% 65.89/9.80 | |
% 65.89/9.80 | | Case 1:
% 65.89/9.80 | | |
% 65.89/9.80 | | | (27) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.89/9.80 | | |
% 65.89/9.80 | | | ALPHA: (27) implies:
% 65.89/9.80 | | | (28) all_52_1 = e0
% 65.89/9.80 | | |
% 65.89/9.80 | | | COMBINE_EQS: (16), (28) imply:
% 65.89/9.80 | | | (29) e2 = e0
% 65.89/9.80 | | |
% 65.89/9.80 | | | SIMP: (29) implies:
% 65.89/9.80 | | | (30) e2 = e0
% 65.89/9.80 | | |
% 65.89/9.80 | | | COMBINE_EQS: (22), (30) imply:
% 65.89/9.80 | | | (31) all_52_0 = e0
% 65.89/9.80 | | |
% 65.89/9.80 | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (16),
% 65.89/9.80 | | | (17), (31) are inconsistent by sub-proof #43.
% 65.89/9.80 | | |
% 65.89/9.80 | | Case 2:
% 65.89/9.80 | | |
% 65.89/9.80 | | | (32) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.89/9.80 | | |
% 65.89/9.80 | | | REF_CLOSE: (5), (6), (10), (14), (16), (17), (22), (23), (32) are
% 65.89/9.80 | | | inconsistent by sub-proof #109.
% 65.89/9.80 | | |
% 65.89/9.80 | | End of split
% 65.89/9.80 | |
% 65.89/9.80 | End of split
% 65.89/9.80 |
% 65.89/9.80 End of proof
% 65.89/9.80
% 65.89/9.80 Sub-proof #31 shows that the following formulas are inconsistent:
% 65.89/9.80 ----------------------------------------------------------------
% 65.89/9.80 (1) ~ (all_54_4 = all_6_2)
% 65.89/9.80 (2) op(e1, e1) = all_14_2
% 65.89/9.80 (3) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 65.89/9.80 (4) op(all_14_2, e1) = all_14_1
% 65.89/9.80 (5) all_44_2 = all_14_2
% 65.89/9.80 (6) all_52_2 = all_4_2
% 65.89/9.80 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.89/9.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.89/9.80 (8) ~ (all_54_4 = all_54_8)
% 65.89/9.80 (9) all_58_13 = all_54_10
% 65.89/9.80 (10) ~ (all_54_8 = all_54_12)
% 65.89/9.80 (11) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.89/9.80 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.89/9.80 (12) all_56_4 = all_54_4
% 65.89/9.80 (13) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.89/9.80 (14) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.89/9.80 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.89/9.80 (15) op(e2, e2) = all_10_2
% 65.89/9.80 (16) all_52_1 = all_14_2
% 65.89/9.80 (17) all_44_1 = all_14_1
% 65.89/9.80 (18) ~ (all_54_8 = all_6_2)
% 65.89/9.80 (19) all_58_4 = all_54_9
% 65.89/9.80 (20) ~ (e3 = e0)
% 65.89/9.80 (21) op(e2, e1) = all_54_9
% 65.89/9.80 (22) ~ (e1 = e0)
% 65.89/9.80 (23) all_58_6 = all_10_2
% 65.89/9.80 (24) op(e3, e3) = all_4_2
% 65.89/9.80 (25) all_56_12 = all_54_12
% 65.89/9.80 (26) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.89/9.80 (27) op(all_6_2, all_6_2) = e3
% 65.89/9.80 (28) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.89/9.80 (29) ~ (all_54_10 = all_4_2)
% 65.89/9.80 (30) ~ (e2 = e0)
% 65.89/9.80 (31) all_52_3 = all_6_2
% 65.89/9.80 (32) all_52_0 = all_10_2
% 65.89/9.80 (33) op(all_14_2, all_14_2) = e3
% 65.89/9.80 (34) ~ (e3 = e2)
% 65.89/9.80 (35) all_58_5 = all_54_8
% 65.92/9.80 (36) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.92/9.80 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.92/9.80 (37) ~ (all_54_4 = all_14_2)
% 65.92/9.80 (38) ~ (all_54_4 = all_54_12)
% 65.92/9.80 (39) ~ (all_54_12 = all_6_2)
% 65.92/9.80 (40) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.92/9.80
% 65.92/9.80 Begin of proof
% 65.92/9.80 |
% 65.92/9.80 | ALPHA: (26) implies:
% 65.92/9.80 | (41) all_52_1 = e2
% 65.92/9.80 | (42) ~ (all_52_0 = e1)
% 65.92/9.80 |
% 65.92/9.80 | COMBINE_EQS: (16), (41) imply:
% 65.92/9.80 | (43) all_14_2 = e2
% 65.92/9.80 |
% 65.92/9.80 | SIMP: (43) implies:
% 65.92/9.80 | (44) all_14_2 = e2
% 65.92/9.80 |
% 65.92/9.80 | COMBINE_EQS: (5), (44) imply:
% 65.92/9.80 | (45) all_44_2 = e2
% 65.92/9.80 |
% 65.92/9.80 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.92/9.80 | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 65.92/9.80 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 65.92/9.80 | (38), (39), (40), (41), (42), (44), (45) are inconsistent by
% 65.92/9.80 | sub-proof #32.
% 65.92/9.80 |
% 65.92/9.80 End of proof
% 65.92/9.80
% 65.92/9.80 Sub-proof #32 shows that the following formulas are inconsistent:
% 65.92/9.80 ----------------------------------------------------------------
% 65.92/9.80 (1) ~ (all_54_4 = all_6_2)
% 65.92/9.80 (2) ~ (all_52_0 = e1)
% 65.92/9.80 (3) op(e1, e1) = all_14_2
% 65.92/9.80 (4) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 65.92/9.80 (5) op(all_14_2, e1) = all_14_1
% 65.92/9.80 (6) all_52_2 = all_4_2
% 65.92/9.80 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.92/9.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.92/9.80 (8) ~ (all_54_4 = all_54_8)
% 65.92/9.80 (9) all_58_13 = all_54_10
% 65.92/9.80 (10) ~ (all_54_8 = all_54_12)
% 65.92/9.80 (11) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.92/9.80 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.92/9.80 (12) all_56_4 = all_54_4
% 65.92/9.80 (13) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.92/9.80 (14) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.92/9.80 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.92/9.80 (15) op(e2, e2) = all_10_2
% 65.92/9.80 (16) all_44_1 = all_14_1
% 65.92/9.80 (17) ~ (all_54_8 = all_6_2)
% 65.92/9.80 (18) all_58_4 = all_54_9
% 65.92/9.80 (19) ~ (e3 = e0)
% 65.92/9.80 (20) op(e2, e1) = all_54_9
% 65.92/9.80 (21) ~ (e1 = e0)
% 65.92/9.80 (22) all_44_2 = e2
% 65.92/9.80 (23) all_14_2 = e2
% 65.92/9.80 (24) all_58_6 = all_10_2
% 65.92/9.80 (25) op(e3, e3) = all_4_2
% 65.92/9.80 (26) all_56_12 = all_54_12
% 65.92/9.80 (27) op(all_6_2, all_6_2) = e3
% 65.92/9.80 (28) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.92/9.80 (29) ~ (all_54_10 = all_4_2)
% 65.92/9.80 (30) ~ (e2 = e0)
% 65.92/9.80 (31) all_52_3 = all_6_2
% 65.92/9.80 (32) all_52_0 = all_10_2
% 65.92/9.80 (33) op(all_14_2, all_14_2) = e3
% 65.92/9.80 (34) all_52_1 = e2
% 65.92/9.80 (35) ~ (e3 = e2)
% 65.92/9.80 (36) all_58_5 = all_54_8
% 65.92/9.80 (37) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.92/9.80 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.92/9.80 (38) ~ (all_54_4 = all_14_2)
% 65.92/9.80 (39) ~ (all_54_4 = all_54_12)
% 65.92/9.80 (40) ~ (all_54_12 = all_6_2)
% 65.92/9.80 (41) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.92/9.80
% 65.92/9.80 Begin of proof
% 65.92/9.80 |
% 65.92/9.80 | REDUCE: (23), (38) imply:
% 65.92/9.80 | (42) ~ (all_54_4 = e2)
% 65.92/9.80 |
% 65.92/9.80 | REDUCE: (2), (32) imply:
% 65.92/9.80 | (43) ~ (all_10_2 = e1)
% 65.92/9.80 |
% 65.92/9.80 | REDUCE: (23), (33) imply:
% 65.92/9.80 | (44) op(e2, e2) = e3
% 65.92/9.80 |
% 65.92/9.80 | REDUCE: (5), (23) imply:
% 65.92/9.80 | (45) op(e2, e1) = all_14_1
% 65.92/9.80 |
% 65.92/9.80 | REDUCE: (3), (23) imply:
% 65.92/9.80 | (46) op(e1, e1) = e2
% 65.92/9.80 |
% 65.94/9.81 | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 65.94/9.81 | (16), (17), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 65.94/9.81 | (28), (29), (30), (31), (32), (34), (35), (36), (37), (39), (40),
% 65.94/9.81 | (41), (42), (43), (44), (45), (46) are inconsistent by sub-proof
% 65.94/9.81 | #33.
% 65.94/9.81 |
% 65.94/9.81 End of proof
% 65.94/9.81
% 65.94/9.81 Sub-proof #33 shows that the following formulas are inconsistent:
% 65.94/9.81 ----------------------------------------------------------------
% 65.94/9.81 (1) ~ (all_54_4 = all_6_2)
% 65.94/9.81 (2) op(e1, e1) = e2
% 65.94/9.81 (3) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 65.94/9.81 (4) all_52_2 = all_4_2
% 65.94/9.81 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.81 (6) ~ (all_54_4 = e2)
% 65.94/9.81 (7) ~ (all_54_4 = all_54_8)
% 65.94/9.81 (8) all_58_13 = all_54_10
% 65.94/9.81 (9) ~ (all_54_8 = all_54_12)
% 65.94/9.81 (10) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.81 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.81 (11) all_56_4 = all_54_4
% 65.94/9.81 (12) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.94/9.81 (13) op(e2, e1) = all_14_1
% 65.94/9.81 (14) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.81 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.81 (15) op(e2, e2) = all_10_2
% 65.94/9.81 (16) all_44_1 = all_14_1
% 65.94/9.81 (17) ~ (all_54_8 = all_6_2)
% 65.94/9.81 (18) all_58_4 = all_54_9
% 65.94/9.81 (19) ~ (e3 = e0)
% 65.94/9.81 (20) op(e2, e1) = all_54_9
% 65.94/9.81 (21) ~ (e1 = e0)
% 65.94/9.81 (22) all_44_2 = e2
% 65.94/9.81 (23) all_58_6 = all_10_2
% 65.94/9.81 (24) op(e3, e3) = all_4_2
% 65.94/9.81 (25) op(e2, e2) = e3
% 65.94/9.81 (26) all_56_12 = all_54_12
% 65.94/9.81 (27) op(all_6_2, all_6_2) = e3
% 65.94/9.81 (28) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.94/9.81 (29) ~ (all_54_10 = all_4_2)
% 65.94/9.81 (30) ~ (e2 = e0)
% 65.94/9.81 (31) all_52_3 = all_6_2
% 65.94/9.81 (32) all_52_0 = all_10_2
% 65.94/9.81 (33) all_52_1 = e2
% 65.94/9.81 (34) ~ (e3 = e2)
% 65.94/9.81 (35) all_58_5 = all_54_8
% 65.94/9.81 (36) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.81 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.81 (37) ~ (all_54_4 = all_54_12)
% 65.94/9.81 (38) ~ (all_54_12 = all_6_2)
% 65.94/9.81 (39) ~ (all_10_2 = e1)
% 65.94/9.81 (40) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.94/9.81
% 65.94/9.81 Begin of proof
% 65.94/9.81 |
% 65.94/9.81 | BETA: splitting (12) gives:
% 65.94/9.81 |
% 65.94/9.81 | Case 1:
% 65.94/9.81 | |
% 65.94/9.81 | | (41) ~ (all_44_1 = e0)
% 65.94/9.81 | |
% 65.94/9.81 | | REDUCE: (16), (41) imply:
% 65.94/9.81 | | (42) ~ (all_14_1 = e0)
% 65.94/9.81 | |
% 65.94/9.81 | | GROUND_INST: instantiating (5) with all_54_9, all_14_1, e1, e2, simplifying
% 65.94/9.81 | | with (13), (20) gives:
% 65.94/9.81 | | (43) all_54_9 = all_14_1
% 65.94/9.81 | |
% 65.94/9.81 | | GROUND_INST: instantiating (5) with all_10_2, e3, e2, e2, simplifying with
% 65.94/9.81 | | (15), (25) gives:
% 65.94/9.81 | | (44) all_10_2 = e3
% 65.94/9.81 | |
% 65.94/9.81 | | COMBINE_EQS: (32), (44) imply:
% 65.94/9.81 | | (45) all_52_0 = e3
% 65.94/9.81 | |
% 65.94/9.81 | | COMBINE_EQS: (23), (44) imply:
% 65.94/9.81 | | (46) all_58_6 = e3
% 65.94/9.81 | |
% 65.94/9.81 | | COMBINE_EQS: (18), (43) imply:
% 65.94/9.81 | | (47) all_58_4 = all_14_1
% 65.94/9.81 | |
% 65.94/9.81 | | REDUCE: (39), (44) imply:
% 65.94/9.81 | | (48) ~ (e3 = e1)
% 65.94/9.81 | |
% 65.94/9.81 | | BETA: splitting (36) gives:
% 65.94/9.81 | |
% 65.94/9.81 | | Case 1:
% 65.94/9.81 | | |
% 65.94/9.81 | | | (49) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.81 | | |
% 65.94/9.81 | | | ALPHA: (49) implies:
% 65.94/9.81 | | | (50) all_52_0 = e0
% 65.94/9.81 | | |
% 65.94/9.81 | | | REF_CLOSE: (4), (5), (10), (14), (19), (21), (24), (27), (31), (33), (34),
% 65.94/9.81 | | | (48), (50) are inconsistent by sub-proof #43.
% 65.94/9.81 | | |
% 65.94/9.81 | | Case 2:
% 65.94/9.81 | | |
% 65.94/9.81 | | | (51) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 65.94/9.81 | | | (all_52_3 = e3))
% 65.94/9.81 | | |
% 65.94/9.81 | | | BETA: splitting (51) gives:
% 65.94/9.81 | | |
% 65.94/9.81 | | | Case 1:
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | (52) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | REF_CLOSE: (30), (33), (52) are inconsistent by sub-proof #179.
% 65.94/9.81 | | | |
% 65.94/9.81 | | | Case 2:
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | (53) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | ALPHA: (53) implies:
% 65.94/9.81 | | | | (54) all_52_2 = e0
% 65.94/9.81 | | | | (55) ~ (all_52_3 = e3)
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | COMBINE_EQS: (4), (54) imply:
% 65.94/9.81 | | | | (56) all_4_2 = e0
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | SIMP: (56) implies:
% 65.94/9.81 | | | | (57) all_4_2 = e0
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | REDUCE: (29), (57) imply:
% 65.94/9.81 | | | | (58) ~ (all_54_10 = e0)
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | REDUCE: (31), (55) imply:
% 65.94/9.81 | | | | (59) ~ (all_6_2 = e3)
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | BETA: splitting (14) gives:
% 65.94/9.81 | | | |
% 65.94/9.81 | | | | Case 1:
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | (60) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | ALPHA: (60) implies:
% 65.94/9.81 | | | | | (61) all_52_0 = e1
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | REF_CLOSE: (45), (48), (61) are inconsistent by sub-proof #122.
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | Case 2:
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | (62) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 65.94/9.81 | | | | | (all_52_1 = e0))
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | BETA: splitting (62) gives:
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | | Case 1:
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | (63) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | ALPHA: (63) implies:
% 65.94/9.81 | | | | | | (64) all_52_2 = e1
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REF_CLOSE: (21), (54), (64) are inconsistent by sub-proof #152.
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | Case 2:
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | (65) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | ALPHA: (65) implies:
% 65.94/9.81 | | | | | | (66) all_52_3 = e1
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | COMBINE_EQS: (31), (66) imply:
% 65.94/9.81 | | | | | | (67) all_6_2 = e1
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REDUCE: (1), (67) imply:
% 65.94/9.81 | | | | | | (68) ~ (all_54_4 = e1)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REDUCE: (17), (67) imply:
% 65.94/9.81 | | | | | | (69) ~ (all_54_8 = e1)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REDUCE: (38), (67) imply:
% 65.94/9.81 | | | | | | (70) ~ (all_54_12 = e1)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REDUCE: (59), (67) imply:
% 65.94/9.81 | | | | | | (71) ~ (e3 = e1)
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | REDUCE: (27), (67) imply:
% 65.94/9.81 | | | | | | (72) op(e1, e1) = e3
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | BETA: splitting (3) gives:
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | | Case 1:
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | (73) all_58_4 = e0
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | COMBINE_EQS: (47), (73) imply:
% 65.94/9.81 | | | | | | | (74) all_14_1 = e0
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | REDUCE: (42), (74) imply:
% 65.94/9.81 | | | | | | | (75) $false
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | CLOSE: (75) is inconsistent.
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | Case 2:
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | (76) all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | BETA: splitting (76) gives:
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | | Case 1:
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | (77) all_58_5 = e0
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | COMBINE_EQS: (35), (77) imply:
% 65.94/9.81 | | | | | | | | (78) all_54_8 = e0
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | REDUCE: (7), (78) imply:
% 65.94/9.81 | | | | | | | | (79) ~ (all_54_4 = e0)
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | REDUCE: (9), (78) imply:
% 65.94/9.81 | | | | | | | | (80) ~ (all_54_12 = e0)
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | SIMP: (80) implies:
% 65.94/9.81 | | | | | | | | (81) ~ (all_54_12 = e0)
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | REDUCE: (69), (78) imply:
% 65.94/9.81 | | | | | | | | (82) ~ (e1 = e0)
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | BETA: splitting (28) gives:
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | Case 1:
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | (83) all_56_4 = e3
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | COMBINE_EQS: (11), (83) imply:
% 65.94/9.81 | | | | | | | | | (84) all_54_4 = e3
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | REDUCE: (37), (84) imply:
% 65.94/9.81 | | | | | | | | | (85) ~ (all_54_12 = e3)
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | SIMP: (85) implies:
% 65.94/9.81 | | | | | | | | | (86) ~ (all_54_12 = e3)
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | BETA: splitting (40) gives:
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | Case 1:
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | (87) all_56_12 = e3
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | COMBINE_EQS: (26), (87) imply:
% 65.94/9.81 | | | | | | | | | | (88) all_54_12 = e3
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | SIMP: (88) implies:
% 65.94/9.81 | | | | | | | | | | (89) all_54_12 = e3
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | REDUCE: (86), (89) imply:
% 65.94/9.81 | | | | | | | | | | (90) $false
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | CLOSE: (90) is inconsistent.
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | Case 2:
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | (91) ~ (all_56_12 = e3)
% 65.94/9.81 | | | | | | | | | | (92) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | BETA: splitting (92) gives:
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | Case 1:
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | (93) all_56_12 = e2
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | COMBINE_EQS: (26), (93) imply:
% 65.94/9.81 | | | | | | | | | | | (94) all_54_12 = e2
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | REDUCE: (86), (94) imply:
% 65.94/9.81 | | | | | | | | | | | (95) ~ (e3 = e2)
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | REDUCE: (70), (94) imply:
% 65.94/9.81 | | | | | | | | | | | (96) ~ (e2 = e1)
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | GROUND_INST: instantiating (5) with e2, e3, e1, e1, simplifying
% 65.94/9.81 | | | | | | | | | | | with (2), (72) gives:
% 65.94/9.81 | | | | | | | | | | | (97) e3 = e2
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | COMBINE_EQS: (45), (97) imply:
% 65.94/9.81 | | | | | | | | | | | (98) all_52_0 = e2
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | REF_CLOSE: (10), (14), (21), (31), (33), (34), (54), (59),
% 65.94/9.81 | | | | | | | | | | | (96), (98) are inconsistent by sub-proof #140.
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | Case 2:
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | (99) all_56_12 = e1 | all_56_12 = e0
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | | REF_CLOSE: (26), (70), (81), (99) are inconsistent by
% 65.94/9.81 | | | | | | | | | | | sub-proof #68.
% 65.94/9.81 | | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | | End of split
% 65.94/9.81 | | | | | | | | | |
% 65.94/9.81 | | | | | | | | | End of split
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | Case 2:
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | (100) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | REF_CLOSE: (6), (11), (68), (79), (100) are inconsistent by
% 65.94/9.81 | | | | | | | | | sub-proof #115.
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | End of split
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | Case 2:
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | (101) all_58_6 = e0 | all_58_13 = e0
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | BETA: splitting (101) gives:
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | | Case 1:
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | (102) all_58_6 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | COMBINE_EQS: (46), (102) imply:
% 65.94/9.81 | | | | | | | | | (103) e3 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | COMBINE_EQS: (45), (103) imply:
% 65.94/9.81 | | | | | | | | | (104) all_52_0 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | REF_CLOSE: (4), (5), (10), (14), (19), (21), (24), (27), (31),
% 65.94/9.81 | | | | | | | | | (33), (34), (48), (104) are inconsistent by
% 65.94/9.81 | | | | | | | | | sub-proof #43.
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | Case 2:
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | (105) all_58_13 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | COMBINE_EQS: (8), (105) imply:
% 65.94/9.81 | | | | | | | | | (106) all_54_10 = e0
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | REDUCE: (58), (106) imply:
% 65.94/9.81 | | | | | | | | | (107) $false
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | | CLOSE: (107) is inconsistent.
% 65.94/9.81 | | | | | | | | |
% 65.94/9.81 | | | | | | | | End of split
% 65.94/9.81 | | | | | | | |
% 65.94/9.81 | | | | | | | End of split
% 65.94/9.81 | | | | | | |
% 65.94/9.81 | | | | | | End of split
% 65.94/9.81 | | | | | |
% 65.94/9.81 | | | | | End of split
% 65.94/9.81 | | | | |
% 65.94/9.81 | | | | End of split
% 65.94/9.81 | | | |
% 65.94/9.81 | | | End of split
% 65.94/9.81 | | |
% 65.94/9.81 | | End of split
% 65.94/9.81 | |
% 65.94/9.81 | Case 2:
% 65.94/9.81 | |
% 65.94/9.81 | | (108) ~ (all_44_2 = e2)
% 65.94/9.81 | |
% 65.94/9.81 | | REDUCE: (22), (108) imply:
% 65.94/9.81 | | (109) $false
% 65.94/9.81 | |
% 65.94/9.81 | | CLOSE: (109) is inconsistent.
% 65.94/9.81 | |
% 65.94/9.81 | End of split
% 65.94/9.81 |
% 65.94/9.81 End of proof
% 65.94/9.81
% 65.94/9.81 Sub-proof #34 shows that the following formulas are inconsistent:
% 65.94/9.81 ----------------------------------------------------------------
% 65.94/9.81 (1) all_52_2 = all_4_2
% 65.94/9.81 (2) op(all_4_2, all_4_2) = e1
% 65.94/9.81 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.81 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.81 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.81 (5) op(e2, e2) = all_10_2
% 65.94/9.81 (6) ~ (e3 = e0)
% 65.94/9.81 (7) ~ (e1 = e0)
% 65.94/9.81 (8) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.81 (9) op(e3, e3) = all_4_2
% 65.94/9.81 (10) op(all_6_2, all_6_2) = e3
% 65.94/9.81 (11) ~ (e2 = e0)
% 65.94/9.81 (12) all_52_3 = all_6_2
% 65.94/9.81 (13) all_52_0 = all_10_2
% 65.94/9.81 (14) ~ (e3 = e2)
% 65.94/9.82 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.82 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | ALPHA: (8) implies:
% 65.94/9.82 | (16) all_52_2 = e2
% 65.94/9.82 | (17) ~ (all_52_0 = e3)
% 65.94/9.82 |
% 65.94/9.82 | COMBINE_EQS: (1), (16) imply:
% 65.94/9.82 | (18) all_4_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 65.94/9.82 | (15), (16), (17), (18) are inconsistent by sub-proof #35.
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #35 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) op(all_4_2, all_4_2) = e1
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) ~ (all_52_0 = e3)
% 65.94/9.82 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.82 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.82 (5) op(e2, e2) = all_10_2
% 65.94/9.82 (6) ~ (e3 = e0)
% 65.94/9.82 (7) ~ (e1 = e0)
% 65.94/9.82 (8) all_4_2 = e2
% 65.94/9.82 (9) op(e3, e3) = all_4_2
% 65.94/9.82 (10) op(all_6_2, all_6_2) = e3
% 65.94/9.82 (11) ~ (e2 = e0)
% 65.94/9.82 (12) all_52_3 = all_6_2
% 65.94/9.82 (13) all_52_0 = all_10_2
% 65.94/9.82 (14) all_52_2 = e2
% 65.94/9.82 (15) ~ (e3 = e2)
% 65.94/9.82 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.82 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | REDUCE: (3), (13) imply:
% 65.94/9.82 | (17) ~ (all_10_2 = e3)
% 65.94/9.82 |
% 65.94/9.82 | REDUCE: (1), (8) imply:
% 65.94/9.82 | (18) op(e2, e2) = e1
% 65.94/9.82 |
% 65.94/9.82 | REDUCE: (8), (9) imply:
% 65.94/9.82 | (19) op(e3, e3) = e2
% 65.94/9.82 |
% 65.94/9.82 | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15), (16),
% 65.94/9.82 | (17), (18), (19) are inconsistent by sub-proof #36.
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #36 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) op(e2, e2) = e1
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.82 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.82 (4) op(e2, e2) = all_10_2
% 65.94/9.82 (5) ~ (e3 = e0)
% 65.94/9.82 (6) ~ (e1 = e0)
% 65.94/9.82 (7) op(e3, e3) = e2
% 65.94/9.82 (8) op(all_6_2, all_6_2) = e3
% 65.94/9.82 (9) ~ (e2 = e0)
% 65.94/9.82 (10) all_52_3 = all_6_2
% 65.94/9.82 (11) all_52_0 = all_10_2
% 65.94/9.82 (12) all_52_2 = e2
% 65.94/9.82 (13) ~ (e3 = e2)
% 65.94/9.82 (14) ~ (all_10_2 = e3)
% 65.94/9.82 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.82 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | GROUND_INST: instantiating (2) with all_10_2, e1, e2, e2, simplifying with
% 65.94/9.82 | (1), (4) gives:
% 65.94/9.82 | (16) all_10_2 = e1
% 65.94/9.82 |
% 65.94/9.82 | COMBINE_EQS: (11), (16) imply:
% 65.94/9.82 | (17) all_52_0 = e1
% 65.94/9.82 |
% 65.94/9.82 | REDUCE: (14), (16) imply:
% 65.94/9.82 | (18) ~ (e3 = e1)
% 65.94/9.82 |
% 65.94/9.82 | SIMP: (18) implies:
% 65.94/9.82 | (19) ~ (e3 = e1)
% 65.94/9.82 |
% 65.94/9.82 | BETA: splitting (15) gives:
% 65.94/9.82 |
% 65.94/9.82 | Case 1:
% 65.94/9.82 | |
% 65.94/9.82 | | (20) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.82 | |
% 65.94/9.82 | | ALPHA: (20) implies:
% 65.94/9.82 | | (21) all_52_0 = e0
% 65.94/9.82 | |
% 65.94/9.82 | | REF_CLOSE: (6), (17), (21) are inconsistent by sub-proof #133.
% 65.94/9.82 | |
% 65.94/9.82 | Case 2:
% 65.94/9.82 | |
% 65.94/9.82 | | (22) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.82 | | = e3))
% 65.94/9.82 | |
% 65.94/9.82 | | BETA: splitting (22) gives:
% 65.94/9.82 | |
% 65.94/9.82 | | Case 1:
% 65.94/9.82 | | |
% 65.94/9.82 | | | (23) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.82 | | |
% 65.94/9.82 | | | ALPHA: (23) implies:
% 65.94/9.82 | | | (24) all_52_1 = e0
% 65.94/9.82 | | |
% 65.94/9.82 | | | BETA: splitting (3) gives:
% 65.94/9.82 | | |
% 65.94/9.82 | | | Case 1:
% 65.94/9.82 | | | |
% 65.94/9.82 | | | | (25) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.94/9.82 | | | |
% 65.94/9.82 | | | | REF_CLOSE: (17), (19), (25) are inconsistent by sub-proof #132.
% 65.94/9.82 | | | |
% 65.94/9.82 | | | Case 2:
% 65.94/9.82 | | | |
% 65.94/9.82 | | | | (26) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 65.94/9.82 | | | | (all_52_2 = e0))
% 65.94/9.82 | | | |
% 65.94/9.82 | | | | BETA: splitting (26) gives:
% 65.94/9.82 | | | |
% 65.94/9.82 | | | | Case 1:
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | (27) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | ALPHA: (27) implies:
% 65.94/9.82 | | | | | (28) all_52_1 = e3
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | REF_CLOSE: (5), (24), (28) are inconsistent by sub-proof #102.
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | Case 2:
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | (29) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | ALPHA: (29) implies:
% 65.94/9.82 | | | | | (30) all_52_3 = e3
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | COMBINE_EQS: (10), (30) imply:
% 65.94/9.82 | | | | | (31) all_6_2 = e3
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | REDUCE: (8), (31) imply:
% 65.94/9.82 | | | | | (32) op(e3, e3) = e3
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | GROUND_INST: instantiating (2) with e2, e3, e3, e3, simplifying with
% 65.94/9.82 | | | | | (7), (32) gives:
% 65.94/9.82 | | | | | (33) e3 = e2
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | REDUCE: (13), (33) imply:
% 65.94/9.82 | | | | | (34) $false
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | | CLOSE: (34) is inconsistent.
% 65.94/9.82 | | | | |
% 65.94/9.82 | | | | End of split
% 65.94/9.82 | | | |
% 65.94/9.82 | | | End of split
% 65.94/9.82 | | |
% 65.94/9.82 | | Case 2:
% 65.94/9.82 | | |
% 65.94/9.82 | | | (35) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.82 | | |
% 65.94/9.82 | | | REF_CLOSE: (9), (12), (35) are inconsistent by sub-proof #131.
% 65.94/9.82 | | |
% 65.94/9.82 | | End of split
% 65.94/9.82 | |
% 65.94/9.82 | End of split
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #37 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) all_52_2 = all_4_2
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) ~ (all_10_0 = e1)
% 65.94/9.82 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.82 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.82 (5) ~ (e3 = e1)
% 65.94/9.82 (6) op(e2, e2) = all_10_2
% 65.94/9.82 (7) op(e3, e3) = all_4_2
% 65.94/9.82 (8) op(all_6_2, all_6_2) = e3
% 65.94/9.82 (9) ~ (e2 = e1)
% 65.94/9.82 (10) all_52_3 = all_6_2
% 65.94/9.82 (11) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.94/9.82 (12) op(all_10_2, all_10_2) = all_10_0
% 65.94/9.82 (13) all_52_0 = all_10_2
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | ALPHA: (11) implies:
% 65.94/9.82 | (14) all_52_3 = e2
% 65.94/9.82 |
% 65.94/9.82 | COMBINE_EQS: (10), (14) imply:
% 65.94/9.82 | (15) all_6_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (15)
% 65.94/9.82 | are inconsistent by sub-proof #40.
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #38 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) all_52_2 = all_4_2
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.82 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.82 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.82 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.82 (5) ~ (e3 = e1)
% 65.94/9.82 (6) op(e2, e2) = all_10_2
% 65.94/9.82 (7) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 65.94/9.82 (8) all_52_1 = all_14_2
% 65.94/9.82 (9) ~ (e3 = e0)
% 65.94/9.82 (10) ~ (e1 = e0)
% 65.94/9.82 (11) op(e3, e3) = all_4_2
% 65.94/9.82 (12) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.82 (13) op(all_14_2, all_14_2) = all_14_0
% 65.94/9.82 (14) op(all_6_2, all_6_2) = e3
% 65.94/9.82 (15) ~ (e2 = e0)
% 65.94/9.82 (16) ~ (e2 = e1)
% 65.94/9.82 (17) all_52_3 = all_6_2
% 65.94/9.82 (18) all_52_0 = all_10_2
% 65.94/9.82 (19) ~ (all_14_0 = e3)
% 65.94/9.82 (20) ~ (e3 = e2)
% 65.94/9.82 (21) all_56_10 = all_10_2
% 65.94/9.82 (22) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.82 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | ALPHA: (12) implies:
% 65.94/9.82 | (23) all_52_1 = e2
% 65.94/9.82 | (24) ~ (all_52_0 = e1)
% 65.94/9.82 |
% 65.94/9.82 | COMBINE_EQS: (8), (23) imply:
% 65.94/9.82 | (25) all_14_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | SIMP: (25) implies:
% 65.94/9.82 | (26) all_14_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 65.94/9.82 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26)
% 65.94/9.82 | are inconsistent by sub-proof #42.
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #39 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) all_52_2 = all_4_2
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) ~ (all_10_0 = e1)
% 65.94/9.82 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.82 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.82 (5) ~ (e3 = e1)
% 65.94/9.82 (6) op(e2, e2) = all_10_2
% 65.94/9.82 (7) op(e3, e3) = all_4_2
% 65.94/9.82 (8) op(all_6_2, all_6_2) = e3
% 65.94/9.82 (9) ~ (e2 = e1)
% 65.94/9.82 (10) all_52_3 = all_6_2
% 65.94/9.82 (11) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.94/9.82 (12) op(all_10_2, all_10_2) = all_10_0
% 65.94/9.82 (13) all_52_0 = all_10_2
% 65.94/9.82
% 65.94/9.82 Begin of proof
% 65.94/9.82 |
% 65.94/9.82 | ALPHA: (11) implies:
% 65.94/9.82 | (14) all_52_3 = e2
% 65.94/9.82 |
% 65.94/9.82 | COMBINE_EQS: (10), (14) imply:
% 65.94/9.82 | (15) all_6_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | SIMP: (15) implies:
% 65.94/9.82 | (16) all_6_2 = e2
% 65.94/9.82 |
% 65.94/9.82 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (16)
% 65.94/9.82 | are inconsistent by sub-proof #40.
% 65.94/9.82 |
% 65.94/9.82 End of proof
% 65.94/9.82
% 65.94/9.82 Sub-proof #40 shows that the following formulas are inconsistent:
% 65.94/9.82 ----------------------------------------------------------------
% 65.94/9.82 (1) all_52_2 = all_4_2
% 65.94/9.82 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.82 (3) ~ (all_10_0 = e1)
% 65.94/9.82 (4) all_6_2 = e2
% 65.94/9.83 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.83 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.83 (6) ~ (e3 = e1)
% 65.94/9.83 (7) op(e2, e2) = all_10_2
% 65.94/9.83 (8) op(e3, e3) = all_4_2
% 65.94/9.83 (9) op(all_6_2, all_6_2) = e3
% 65.94/9.83 (10) all_52_3 = e2
% 65.94/9.83 (11) ~ (e2 = e1)
% 65.94/9.83 (12) op(all_10_2, all_10_2) = all_10_0
% 65.94/9.83 (13) all_52_0 = all_10_2
% 65.94/9.83
% 65.94/9.83 Begin of proof
% 65.94/9.83 |
% 65.94/9.83 | REDUCE: (4), (9) imply:
% 65.94/9.83 | (14) op(e2, e2) = e3
% 65.94/9.83 |
% 65.94/9.83 | GROUND_INST: instantiating (2) with all_10_2, e3, e2, e2, simplifying with
% 65.94/9.83 | (7), (14) gives:
% 65.94/9.83 | (15) all_10_2 = e3
% 65.94/9.83 |
% 65.94/9.83 | COMBINE_EQS: (13), (15) imply:
% 65.94/9.83 | (16) all_52_0 = e3
% 65.94/9.83 |
% 65.94/9.83 | REDUCE: (12), (15) imply:
% 65.94/9.83 | (17) op(e3, e3) = all_10_0
% 65.94/9.83 |
% 65.94/9.83 | BETA: splitting (5) gives:
% 65.94/9.83 |
% 65.94/9.83 | Case 1:
% 65.94/9.83 | |
% 65.94/9.83 | | (18) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.94/9.83 | |
% 65.94/9.83 | | ALPHA: (18) implies:
% 65.94/9.83 | | (19) all_52_0 = e1
% 65.94/9.83 | |
% 65.94/9.83 | | REF_CLOSE: (6), (16), (19) are inconsistent by sub-proof #122.
% 65.94/9.83 | |
% 65.94/9.83 | Case 2:
% 65.94/9.83 | |
% 65.94/9.83 | | (20) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 65.94/9.83 | | = e0))
% 65.94/9.83 | |
% 65.94/9.83 | | BETA: splitting (20) gives:
% 65.94/9.83 | |
% 65.94/9.83 | | Case 1:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (21) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.94/9.83 | | |
% 65.94/9.83 | | | ALPHA: (21) implies:
% 65.94/9.83 | | | (22) all_52_2 = e1
% 65.94/9.83 | | |
% 65.94/9.83 | | | COMBINE_EQS: (1), (22) imply:
% 65.94/9.83 | | | (23) all_4_2 = e1
% 65.94/9.83 | | |
% 65.94/9.83 | | | SIMP: (23) implies:
% 65.94/9.83 | | | (24) all_4_2 = e1
% 65.94/9.83 | | |
% 65.94/9.83 | | | REDUCE: (8), (24) imply:
% 65.94/9.83 | | | (25) op(e3, e3) = e1
% 65.94/9.83 | | |
% 65.94/9.83 | | | GROUND_INST: instantiating (2) with e1, all_10_0, e3, e3, simplifying with
% 65.94/9.83 | | | (17), (25) gives:
% 65.94/9.83 | | | (26) all_10_0 = e1
% 65.94/9.83 | | |
% 65.94/9.83 | | | REDUCE: (3), (26) imply:
% 65.94/9.83 | | | (27) $false
% 65.94/9.83 | | |
% 65.94/9.83 | | | CLOSE: (27) is inconsistent.
% 65.94/9.83 | | |
% 65.94/9.83 | | Case 2:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (28) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.94/9.83 | | |
% 65.94/9.83 | | | REF_CLOSE: (10), (11), (28) are inconsistent by sub-proof #151.
% 65.94/9.83 | | |
% 65.94/9.83 | | End of split
% 65.94/9.83 | |
% 65.94/9.83 | End of split
% 65.94/9.83 |
% 65.94/9.83 End of proof
% 65.94/9.83
% 65.94/9.83 Sub-proof #41 shows that the following formulas are inconsistent:
% 65.94/9.83 ----------------------------------------------------------------
% 65.94/9.83 (1) all_52_2 = all_4_2
% 65.94/9.83 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.83 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.83 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.83 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.83 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.83 (5) ~ (e3 = e1)
% 65.94/9.83 (6) op(e2, e2) = all_10_2
% 65.94/9.83 (7) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 65.94/9.83 (8) all_52_1 = all_14_2
% 65.94/9.83 (9) ~ (e3 = e0)
% 65.94/9.83 (10) ~ (e1 = e0)
% 65.94/9.83 (11) op(e3, e3) = all_4_2
% 65.94/9.83 (12) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.83 (13) op(all_14_2, all_14_2) = all_14_0
% 65.94/9.83 (14) op(all_6_2, all_6_2) = e3
% 65.94/9.83 (15) ~ (e2 = e0)
% 65.94/9.83 (16) ~ (e2 = e1)
% 65.94/9.83 (17) all_52_3 = all_6_2
% 65.94/9.83 (18) all_52_0 = all_10_2
% 65.94/9.83 (19) ~ (all_14_0 = e3)
% 65.94/9.83 (20) ~ (e3 = e2)
% 65.94/9.83 (21) all_56_10 = all_10_2
% 65.94/9.83 (22) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.83 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.83
% 65.94/9.83 Begin of proof
% 65.94/9.83 |
% 65.94/9.83 | ALPHA: (12) implies:
% 65.94/9.83 | (23) all_52_1 = e2
% 65.94/9.83 | (24) ~ (all_52_0 = e1)
% 65.94/9.83 |
% 65.94/9.83 | COMBINE_EQS: (8), (23) imply:
% 65.94/9.83 | (25) all_14_2 = e2
% 65.94/9.83 |
% 65.94/9.83 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 65.94/9.83 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25)
% 65.94/9.83 | are inconsistent by sub-proof #42.
% 65.94/9.83 |
% 65.94/9.83 End of proof
% 65.94/9.83
% 65.94/9.83 Sub-proof #42 shows that the following formulas are inconsistent:
% 65.94/9.83 ----------------------------------------------------------------
% 65.94/9.83 (1) ~ (all_52_0 = e1)
% 65.94/9.83 (2) all_52_2 = all_4_2
% 65.94/9.83 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.83 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.83 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.83 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.83 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.83 (6) ~ (e3 = e1)
% 65.94/9.83 (7) op(e2, e2) = all_10_2
% 65.94/9.83 (8) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 65.94/9.83 (9) ~ (e3 = e0)
% 65.94/9.83 (10) ~ (e1 = e0)
% 65.94/9.83 (11) all_14_2 = e2
% 65.94/9.83 (12) op(e3, e3) = all_4_2
% 65.94/9.83 (13) op(all_14_2, all_14_2) = all_14_0
% 65.94/9.83 (14) op(all_6_2, all_6_2) = e3
% 65.94/9.83 (15) ~ (e2 = e0)
% 65.94/9.83 (16) ~ (e2 = e1)
% 65.94/9.83 (17) all_52_3 = all_6_2
% 65.94/9.83 (18) all_52_0 = all_10_2
% 65.94/9.83 (19) ~ (all_14_0 = e3)
% 65.94/9.83 (20) all_52_1 = e2
% 65.94/9.83 (21) ~ (e3 = e2)
% 65.94/9.83 (22) all_56_10 = all_10_2
% 65.94/9.83 (23) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.83 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.83
% 65.94/9.83 Begin of proof
% 65.94/9.83 |
% 65.94/9.83 | REDUCE: (1), (18) imply:
% 65.94/9.83 | (24) ~ (all_10_2 = e1)
% 65.94/9.83 |
% 65.94/9.83 | REDUCE: (11), (13) imply:
% 65.94/9.83 | (25) op(e2, e2) = all_14_0
% 65.94/9.83 |
% 65.94/9.83 | GROUND_INST: instantiating (3) with all_10_2, all_14_0, e2, e2, simplifying
% 65.94/9.83 | with (7), (25) gives:
% 65.94/9.83 | (26) all_14_0 = all_10_2
% 65.94/9.83 |
% 65.94/9.83 | REDUCE: (19), (26) imply:
% 65.94/9.83 | (27) ~ (all_10_2 = e3)
% 65.94/9.83 |
% 65.94/9.83 | BETA: splitting (23) gives:
% 65.94/9.83 |
% 65.94/9.83 | Case 1:
% 65.94/9.83 | |
% 65.94/9.83 | | (28) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.83 | |
% 65.94/9.83 | | ALPHA: (28) implies:
% 65.94/9.83 | | (29) all_52_0 = e0
% 65.94/9.83 | |
% 65.94/9.83 | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (14), (17), (20), (21),
% 65.94/9.83 | | (29) are inconsistent by sub-proof #43.
% 65.94/9.83 | |
% 65.94/9.83 | Case 2:
% 65.94/9.83 | |
% 65.94/9.83 | | (30) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.83 | | = e3))
% 65.94/9.83 | |
% 65.94/9.83 | | BETA: splitting (30) gives:
% 65.94/9.83 | |
% 65.94/9.83 | | Case 1:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (31) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.83 | | |
% 65.94/9.83 | | | REF_CLOSE: (15), (20), (31) are inconsistent by sub-proof #55.
% 65.94/9.83 | | |
% 65.94/9.83 | | Case 2:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (32) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.83 | | |
% 65.94/9.83 | | | ALPHA: (32) implies:
% 65.94/9.83 | | | (33) all_52_2 = e0
% 65.94/9.83 | | | (34) ~ (all_52_3 = e3)
% 65.94/9.83 | | |
% 65.94/9.83 | | | COMBINE_EQS: (2), (33) imply:
% 65.94/9.83 | | | (35) all_4_2 = e0
% 65.94/9.83 | | |
% 65.94/9.83 | | | REDUCE: (17), (34) imply:
% 65.94/9.83 | | | (36) ~ (all_6_2 = e3)
% 65.94/9.83 | | |
% 65.94/9.83 | | | BETA: splitting (8) gives:
% 65.94/9.83 | | |
% 65.94/9.83 | | | Case 1:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | (37) all_56_10 = e3
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | REF_CLOSE: (22), (27), (37) are inconsistent by sub-proof #143.
% 65.94/9.83 | | | |
% 65.94/9.83 | | | Case 2:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | (38) all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | BETA: splitting (38) gives:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | Case 1:
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | (39) all_56_10 = e2
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | REF_CLOSE: (4), (5), (10), (16), (17), (18), (20), (21), (22), (33),
% 65.94/9.83 | | | | | (36), (39) are inconsistent by sub-proof #139.
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | Case 2:
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | (40) all_56_10 = e1 | all_56_10 = e0
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | BETA: splitting (40) gives:
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | Case 1:
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | (41) all_56_10 = e1
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | REF_CLOSE: (22), (24), (41) are inconsistent by sub-proof #138.
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | Case 2:
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | (42) all_56_10 = e0
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | COMBINE_EQS: (22), (42) imply:
% 65.94/9.83 | | | | | | (43) all_10_2 = e0
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | SIMP: (43) implies:
% 65.94/9.83 | | | | | | (44) all_10_2 = e0
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | COMBINE_EQS: (18), (44) imply:
% 65.94/9.83 | | | | | | (45) all_52_0 = e0
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (14), (17),
% 65.94/9.83 | | | | | | (20), (21), (45) are inconsistent by sub-proof #43.
% 65.94/9.83 | | | | | |
% 65.94/9.83 | | | | | End of split
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | End of split
% 65.94/9.83 | | | |
% 65.94/9.83 | | | End of split
% 65.94/9.83 | | |
% 65.94/9.83 | | End of split
% 65.94/9.83 | |
% 65.94/9.83 | End of split
% 65.94/9.83 |
% 65.94/9.83 End of proof
% 65.94/9.83
% 65.94/9.83 Sub-proof #43 shows that the following formulas are inconsistent:
% 65.94/9.83 ----------------------------------------------------------------
% 65.94/9.83 (1) all_52_2 = all_4_2
% 65.94/9.83 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.83 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.83 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.83 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.83 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.83 (5) ~ (e3 = e1)
% 65.94/9.83 (6) ~ (e3 = e0)
% 65.94/9.83 (7) ~ (e1 = e0)
% 65.94/9.83 (8) op(e3, e3) = all_4_2
% 65.94/9.83 (9) all_52_0 = e0
% 65.94/9.83 (10) op(all_6_2, all_6_2) = e3
% 65.94/9.83 (11) all_52_3 = all_6_2
% 65.94/9.83 (12) all_52_1 = e2
% 65.94/9.83 (13) ~ (e3 = e2)
% 65.94/9.83
% 65.94/9.83 Begin of proof
% 65.94/9.83 |
% 65.94/9.83 | BETA: splitting (3) gives:
% 65.94/9.83 |
% 65.94/9.83 | Case 1:
% 65.94/9.83 | |
% 65.94/9.83 | | (14) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.94/9.83 | |
% 65.94/9.83 | | REF_CLOSE: (6), (9), (14) are inconsistent by sub-proof #148.
% 65.94/9.83 | |
% 65.94/9.83 | Case 2:
% 65.94/9.83 | |
% 65.94/9.83 | | (15) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 65.94/9.83 | | = e0))
% 65.94/9.83 | |
% 65.94/9.83 | | BETA: splitting (15) gives:
% 65.94/9.83 | |
% 65.94/9.83 | | Case 1:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (16) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.94/9.83 | | |
% 65.94/9.83 | | | REF_CLOSE: (12), (13), (16) are inconsistent by sub-proof #147.
% 65.94/9.83 | | |
% 65.94/9.83 | | Case 2:
% 65.94/9.83 | | |
% 65.94/9.83 | | | (17) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.94/9.83 | | |
% 65.94/9.83 | | | ALPHA: (17) implies:
% 65.94/9.83 | | | (18) all_52_3 = e3
% 65.94/9.83 | | |
% 65.94/9.83 | | | COMBINE_EQS: (11), (18) imply:
% 65.94/9.83 | | | (19) all_6_2 = e3
% 65.94/9.83 | | |
% 65.94/9.83 | | | SIMP: (19) implies:
% 65.94/9.83 | | | (20) all_6_2 = e3
% 65.94/9.83 | | |
% 65.94/9.83 | | | REDUCE: (10), (20) imply:
% 65.94/9.83 | | | (21) op(e3, e3) = e3
% 65.94/9.83 | | |
% 65.94/9.83 | | | BETA: splitting (4) gives:
% 65.94/9.83 | | |
% 65.94/9.83 | | | Case 1:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | (22) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | REF_CLOSE: (7), (9), (22) are inconsistent by sub-proof #164.
% 65.94/9.83 | | | |
% 65.94/9.83 | | | Case 2:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | (23) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 65.94/9.83 | | | | (all_52_1 = e0))
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | BETA: splitting (23) gives:
% 65.94/9.83 | | | |
% 65.94/9.83 | | | | Case 1:
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | (24) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | ALPHA: (24) implies:
% 65.94/9.83 | | | | | (25) all_52_2 = e1
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | COMBINE_EQS: (1), (25) imply:
% 65.94/9.83 | | | | | (26) all_4_2 = e1
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | SIMP: (26) implies:
% 65.94/9.83 | | | | | (27) all_4_2 = e1
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | REDUCE: (8), (27) imply:
% 65.94/9.83 | | | | | (28) op(e3, e3) = e1
% 65.94/9.83 | | | | |
% 65.94/9.83 | | | | | GROUND_INST: instantiating (2) with e1, e3, e3, e3, simplifying with
% 65.94/9.83 | | | | | (21), (28) gives:
% 65.94/9.84 | | | | | (29) e3 = e1
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | | REDUCE: (5), (29) imply:
% 65.94/9.84 | | | | | (30) $false
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | | CLOSE: (30) is inconsistent.
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | Case 2:
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | | (31) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | | REF_CLOSE: (5), (18), (31) are inconsistent by sub-proof #145.
% 65.94/9.84 | | | | |
% 65.94/9.84 | | | | End of split
% 65.94/9.84 | | | |
% 65.94/9.84 | | | End of split
% 65.94/9.84 | | |
% 65.94/9.84 | | End of split
% 65.94/9.84 | |
% 65.94/9.84 | End of split
% 65.94/9.84 |
% 65.94/9.84 End of proof
% 65.94/9.84
% 65.94/9.84 Sub-proof #44 shows that the following formulas are inconsistent:
% 65.94/9.84 ----------------------------------------------------------------
% 65.94/9.84 (1) op(e1, e1) = all_14_2
% 65.94/9.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.84 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.84 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.84 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.84 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.84 (5) all_52_1 = all_14_2
% 65.94/9.84 (6) op(all_10_2, all_10_2) = e1
% 65.94/9.84 (7) ~ (e3 = e0)
% 65.94/9.84 (8) ~ (e1 = e0)
% 65.94/9.84 (9) op(e3, e3) = e2
% 65.94/9.84 (10) ~ (e2 = e0)
% 65.94/9.84 (11) ~ (e2 = e1)
% 65.94/9.84 (12) all_52_2 = e2
% 65.94/9.84 (13) op(all_14_2, all_14_2) = e0
% 65.94/9.84 (14) ~ (all_10_2 = e3)
% 65.94/9.84 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.84 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.84 (16) all_10_2 = e1
% 65.94/9.84
% 65.94/9.84 Begin of proof
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (14), (16) imply:
% 65.94/9.84 | (17) ~ (e3 = e1)
% 65.94/9.84 |
% 65.94/9.84 | SIMP: (17) implies:
% 65.94/9.84 | (18) ~ (e3 = e1)
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (6), (16) imply:
% 65.94/9.84 | (19) op(e1, e1) = e1
% 65.94/9.84 |
% 65.94/9.84 | BETA: splitting (15) gives:
% 65.94/9.84 |
% 65.94/9.84 | Case 1:
% 65.94/9.84 | |
% 65.94/9.84 | | (20) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.84 | |
% 65.94/9.84 | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (18),
% 65.94/9.84 | | (20) are inconsistent by sub-proof #87.
% 65.94/9.84 | |
% 65.94/9.84 | Case 2:
% 65.94/9.84 | |
% 65.94/9.84 | | (21) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.84 | | = e3))
% 65.94/9.84 | |
% 65.94/9.84 | | REF_CLOSE: (1), (2), (5), (8), (10), (12), (19), (21) are inconsistent by
% 65.94/9.84 | | sub-proof #60.
% 65.94/9.84 | |
% 65.94/9.84 | End of split
% 65.94/9.84 |
% 65.94/9.84 End of proof
% 65.94/9.84
% 65.94/9.84 Sub-proof #45 shows that the following formulas are inconsistent:
% 65.94/9.84 ----------------------------------------------------------------
% 65.94/9.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.84 (2) op(e0, e0) = all_6_2
% 65.94/9.84 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.84 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.84 (4) ~ (e3 = e1)
% 65.94/9.84 (5) op(e2, e2) = all_10_2
% 65.94/9.84 (6) all_52_1 = all_14_2
% 65.94/9.84 (7) op(all_10_2, all_10_2) = e1
% 65.94/9.84 (8) ~ (e3 = e0)
% 65.94/9.84 (9) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.84 (10) all_52_3 = all_6_2
% 65.94/9.84 (11) all_52_0 = all_10_2
% 65.94/9.84 (12) ~ (e3 = e2)
% 65.94/9.84 (13) op(all_14_2, all_14_2) = e0
% 65.94/9.84 (14) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.94/9.84
% 65.94/9.84 Begin of proof
% 65.94/9.84 |
% 65.94/9.84 | ALPHA: (9) implies:
% 65.94/9.84 | (15) all_52_1 = e2
% 65.94/9.84 |
% 65.94/9.84 | COMBINE_EQS: (6), (15) imply:
% 65.94/9.84 | (16) all_14_2 = e2
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (13), (16) imply:
% 65.94/9.84 | (17) op(e2, e2) = e0
% 65.94/9.84 |
% 65.94/9.84 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14), (15),
% 65.94/9.84 | (16), (17) are inconsistent by sub-proof #46.
% 65.94/9.84 |
% 65.94/9.84 End of proof
% 65.94/9.84
% 65.94/9.84 Sub-proof #46 shows that the following formulas are inconsistent:
% 65.94/9.84 ----------------------------------------------------------------
% 65.94/9.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.84 (2) op(e0, e0) = all_6_2
% 65.94/9.84 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.84 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.84 (4) ~ (e3 = e1)
% 65.94/9.84 (5) op(e2, e2) = all_10_2
% 65.94/9.84 (6) op(all_10_2, all_10_2) = e1
% 65.94/9.84 (7) ~ (e3 = e0)
% 65.94/9.84 (8) all_14_2 = e2
% 65.94/9.84 (9) all_52_3 = all_6_2
% 65.94/9.84 (10) all_52_0 = all_10_2
% 65.94/9.84 (11) all_52_1 = e2
% 65.94/9.84 (12) ~ (e3 = e2)
% 65.94/9.84 (13) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 65.94/9.84 (14) op(e2, e2) = e0
% 65.94/9.84
% 65.94/9.84 Begin of proof
% 65.94/9.84 |
% 65.94/9.84 | BETA: splitting (13) gives:
% 65.94/9.84 |
% 65.94/9.84 | Case 1:
% 65.94/9.84 | |
% 65.94/9.84 | |
% 65.94/9.84 | | GROUND_INST: instantiating (1) with all_10_2, e0, e2, e2, simplifying with
% 65.94/9.84 | | (5), (14) gives:
% 65.94/9.84 | | (15) all_10_2 = e0
% 65.94/9.84 | |
% 65.94/9.84 | | COMBINE_EQS: (10), (15) imply:
% 65.94/9.84 | | (16) all_52_0 = e0
% 65.94/9.84 | |
% 65.94/9.84 | | REDUCE: (6), (15) imply:
% 65.94/9.84 | | (17) op(e0, e0) = e1
% 65.94/9.84 | |
% 65.94/9.84 | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (11), (12), (16), (17) are
% 65.94/9.84 | | inconsistent by sub-proof #137.
% 65.94/9.84 | |
% 65.94/9.84 | Case 2:
% 65.94/9.84 | |
% 65.94/9.84 | | (18) ~ (all_14_2 = e2)
% 65.94/9.84 | |
% 65.94/9.84 | | REDUCE: (8), (18) imply:
% 65.94/9.84 | | (19) $false
% 65.94/9.84 | |
% 65.94/9.84 | | CLOSE: (19) is inconsistent.
% 65.94/9.84 | |
% 65.94/9.84 | End of split
% 65.94/9.84 |
% 65.94/9.84 End of proof
% 65.94/9.84
% 65.94/9.84 Sub-proof #47 shows that the following formulas are inconsistent:
% 65.94/9.84 ----------------------------------------------------------------
% 65.94/9.84 (1) ~ (all_52_0 = e1)
% 65.94/9.84 (2) op(e1, e1) = all_14_2
% 65.94/9.84 (3) op(all_14_2, all_14_2) = e2
% 65.94/9.84 (4) all_52_2 = all_4_2
% 65.94/9.84 (5) op(all_4_2, all_4_2) = e1
% 65.94/9.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.84 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.84 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.84 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.84 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.84 (9) ~ (e3 = e1)
% 65.94/9.84 (10) op(e2, e2) = all_10_2
% 65.94/9.84 (11) ~ (e3 = e0)
% 65.94/9.84 (12) ~ (e1 = e0)
% 65.94/9.84 (13) all_14_2 = e2
% 65.94/9.84 (14) all_52_3 = all_6_2
% 65.94/9.84 (15) all_52_0 = all_10_2
% 65.94/9.84 (16) all_52_1 = e2
% 65.94/9.84 (17) ~ (e3 = e2)
% 65.94/9.84 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.84 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.84
% 65.94/9.84 Begin of proof
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (1), (15) imply:
% 65.94/9.84 | (19) ~ (all_10_2 = e1)
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (3), (13) imply:
% 65.94/9.84 | (20) op(e2, e2) = e2
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (2), (13) imply:
% 65.94/9.84 | (21) op(e1, e1) = e2
% 65.94/9.84 |
% 65.94/9.84 | GROUND_INST: instantiating (6) with all_10_2, e2, e2, e2, simplifying with
% 65.94/9.84 | (10), (20) gives:
% 65.94/9.84 | (22) all_10_2 = e2
% 65.94/9.84 |
% 65.94/9.84 | COMBINE_EQS: (15), (22) imply:
% 65.94/9.84 | (23) all_52_0 = e2
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (19), (22) imply:
% 65.94/9.84 | (24) ~ (e2 = e1)
% 65.94/9.84 |
% 65.94/9.84 | BETA: splitting (18) gives:
% 65.94/9.84 |
% 65.94/9.84 | Case 1:
% 65.94/9.84 | |
% 65.94/9.84 | | (25) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.84 | |
% 65.94/9.84 | | ALPHA: (25) implies:
% 65.94/9.84 | | (26) all_52_0 = e0
% 65.94/9.84 | |
% 65.94/9.84 | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (11), (12), (16), (17), (21), (24),
% 65.94/9.84 | | (26) are inconsistent by sub-proof #144.
% 65.94/9.84 | |
% 65.94/9.84 | Case 2:
% 65.94/9.84 | |
% 65.94/9.84 | | (27) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.84 | | = e3))
% 65.94/9.84 | |
% 65.94/9.84 | | BETA: splitting (27) gives:
% 65.94/9.84 | |
% 65.94/9.84 | | Case 1:
% 65.94/9.84 | | |
% 65.94/9.84 | | | (28) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.84 | | |
% 65.94/9.84 | | | ALPHA: (28) implies:
% 65.94/9.84 | | | (29) all_52_1 = e0
% 65.94/9.84 | | |
% 65.94/9.84 | | | COMBINE_EQS: (16), (29) imply:
% 65.94/9.84 | | | (30) e2 = e0
% 65.94/9.84 | | |
% 65.94/9.84 | | | SIMP: (30) implies:
% 65.94/9.84 | | | (31) e2 = e0
% 65.94/9.84 | | |
% 65.94/9.84 | | | COMBINE_EQS: (23), (31) imply:
% 65.94/9.84 | | | (32) all_52_0 = e0
% 65.94/9.84 | | |
% 65.94/9.84 | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (11), (12), (16), (17), (21),
% 65.94/9.84 | | | (24), (32) are inconsistent by sub-proof #144.
% 65.94/9.84 | | |
% 65.94/9.84 | | Case 2:
% 65.94/9.84 | | |
% 65.94/9.84 | | | (33) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.84 | | |
% 65.94/9.84 | | | ALPHA: (33) implies:
% 65.94/9.84 | | | (34) all_52_2 = e0
% 65.94/9.84 | | | (35) ~ (all_52_3 = e3)
% 65.94/9.84 | | |
% 65.94/9.84 | | | REDUCE: (14), (35) imply:
% 65.94/9.84 | | | (36) ~ (all_6_2 = e3)
% 65.94/9.84 | | |
% 65.94/9.84 | | | REF_CLOSE: (7), (8), (12), (14), (16), (17), (23), (24), (34), (36) are
% 65.94/9.84 | | | inconsistent by sub-proof #140.
% 65.94/9.84 | | |
% 65.94/9.84 | | End of split
% 65.94/9.84 | |
% 65.94/9.84 | End of split
% 65.94/9.84 |
% 65.94/9.84 End of proof
% 65.94/9.84
% 65.94/9.84 Sub-proof #48 shows that the following formulas are inconsistent:
% 65.94/9.84 ----------------------------------------------------------------
% 65.94/9.84 (1) op(e1, e1) = all_14_2
% 65.94/9.84 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.84 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.84 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.84 (4) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.94/9.84 (5) ~ (e3 = e1)
% 65.94/9.84 (6) op(e2, e2) = all_10_2
% 65.94/9.84 (7) all_16_2 = all_6_2
% 65.94/9.84 (8) all_52_1 = all_14_2
% 65.94/9.84 (9) op(all_10_2, all_10_2) = e1
% 65.94/9.84 (10) all_52_3 = all_6_2
% 65.94/9.84 (11) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.94/9.84 (12) all_52_0 = all_10_2
% 65.94/9.84 (13) op(all_6_2, all_6_2) = e1
% 65.94/9.84 (14) ~ (e3 = e2)
% 65.94/9.84
% 65.94/9.84 Begin of proof
% 65.94/9.84 |
% 65.94/9.84 | ALPHA: (11) implies:
% 65.94/9.84 | (15) all_52_3 = e2
% 65.94/9.84 |
% 65.94/9.84 | COMBINE_EQS: (10), (15) imply:
% 65.94/9.84 | (16) all_6_2 = e2
% 65.94/9.84 |
% 65.94/9.84 | COMBINE_EQS: (7), (16) imply:
% 65.94/9.84 | (17) all_16_2 = e2
% 65.94/9.84 |
% 65.94/9.84 | REDUCE: (13), (16) imply:
% 65.94/9.84 | (18) op(e2, e2) = e1
% 65.94/9.84 |
% 65.94/9.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (14), (15), (17),
% 65.94/9.84 | (18) are inconsistent by sub-proof #49.
% 65.94/9.84 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #49 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) op(e1, e1) = all_14_2
% 65.94/9.85 (2) op(e2, e2) = e1
% 65.94/9.85 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.85 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.85 (5) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.94/9.85 (6) ~ (e3 = e1)
% 65.94/9.85 (7) op(e2, e2) = all_10_2
% 65.94/9.85 (8) all_52_1 = all_14_2
% 65.94/9.85 (9) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (10) all_52_3 = e2
% 65.94/9.85 (11) all_52_0 = all_10_2
% 65.94/9.85 (12) all_16_2 = e2
% 65.94/9.85 (13) ~ (e3 = e2)
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | BETA: splitting (5) gives:
% 65.94/9.85 |
% 65.94/9.85 | Case 1:
% 65.94/9.85 | |
% 65.94/9.85 | |
% 65.94/9.85 | | GROUND_INST: instantiating (3) with all_10_2, e1, e2, e2, simplifying with
% 65.94/9.85 | | (2), (7) gives:
% 65.94/9.85 | | (14) all_10_2 = e1
% 65.94/9.85 | |
% 65.94/9.85 | | COMBINE_EQS: (11), (14) imply:
% 65.94/9.85 | | (15) all_52_0 = e1
% 65.94/9.85 | |
% 65.94/9.85 | | REDUCE: (9), (14) imply:
% 65.94/9.85 | | (16) op(e1, e1) = e1
% 65.94/9.85 | |
% 65.94/9.85 | | BETA: splitting (4) gives:
% 65.94/9.85 | |
% 65.94/9.85 | | Case 1:
% 65.94/9.85 | | |
% 65.94/9.85 | | | (17) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.94/9.85 | | |
% 65.94/9.85 | | | REF_CLOSE: (6), (15), (17) are inconsistent by sub-proof #132.
% 65.94/9.85 | | |
% 65.94/9.85 | | Case 2:
% 65.94/9.85 | | |
% 65.94/9.85 | | | (18) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 65.94/9.85 | | | (all_52_2 = e0))
% 65.94/9.85 | | |
% 65.94/9.85 | | | REF_CLOSE: (1), (3), (6), (8), (10), (13), (16), (18) are inconsistent by
% 65.94/9.85 | | | sub-proof #77.
% 65.94/9.85 | | |
% 65.94/9.85 | | End of split
% 65.94/9.85 | |
% 65.94/9.85 | Case 2:
% 65.94/9.85 | |
% 65.94/9.85 | | (19) ~ (all_16_2 = e2)
% 65.94/9.85 | |
% 65.94/9.85 | | REDUCE: (12), (19) imply:
% 65.94/9.85 | | (20) $false
% 65.94/9.85 | |
% 65.94/9.85 | | CLOSE: (20) is inconsistent.
% 65.94/9.85 | |
% 65.94/9.85 | End of split
% 65.94/9.85 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #50 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) all_44_2 = all_14_2
% 65.94/9.85 (2) all_52_2 = all_4_2
% 65.94/9.85 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (4) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.94/9.85 (5) op(e2, e2) = all_10_2
% 65.94/9.85 (6) all_52_1 = all_14_2
% 65.94/9.85 (7) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (8) ~ (e3 = e0)
% 65.94/9.85 (9) ~ (e1 = e0)
% 65.94/9.85 (10) op(e3, e3) = all_4_2
% 65.94/9.85 (11) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.85 (12) ~ (e2 = e0)
% 65.94/9.85 (13) all_52_0 = all_10_2
% 65.94/9.85 (14) op(all_14_2, all_14_2) = e3
% 65.94/9.85 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.85 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | ALPHA: (11) implies:
% 65.94/9.85 | (16) all_52_1 = e2
% 65.94/9.85 |
% 65.94/9.85 | COMBINE_EQS: (6), (16) imply:
% 65.94/9.85 | (17) all_14_2 = e2
% 65.94/9.85 |
% 65.94/9.85 | COMBINE_EQS: (1), (17) imply:
% 65.94/9.85 | (18) all_44_2 = e2
% 65.94/9.85 |
% 65.94/9.85 | REDUCE: (14), (17) imply:
% 65.94/9.85 | (19) op(e2, e2) = e3
% 65.94/9.85 |
% 65.94/9.85 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (15), (16),
% 65.94/9.85 | (18), (19) are inconsistent by sub-proof #52.
% 65.94/9.85 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #51 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) all_44_2 = all_14_2
% 65.94/9.85 (2) all_52_2 = all_4_2
% 65.94/9.85 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (4) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.94/9.85 (5) op(e2, e2) = all_10_2
% 65.94/9.85 (6) all_52_1 = all_14_2
% 65.94/9.85 (7) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (8) ~ (e3 = e0)
% 65.94/9.85 (9) ~ (e1 = e0)
% 65.94/9.85 (10) op(e3, e3) = all_4_2
% 65.94/9.85 (11) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.85 (12) ~ (e2 = e0)
% 65.94/9.85 (13) all_52_0 = all_10_2
% 65.94/9.85 (14) op(all_14_2, all_14_2) = e3
% 65.94/9.85 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.85 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | ALPHA: (11) implies:
% 65.94/9.85 | (16) all_52_1 = e2
% 65.94/9.85 |
% 65.94/9.85 | COMBINE_EQS: (6), (16) imply:
% 65.94/9.85 | (17) all_14_2 = e2
% 65.94/9.85 |
% 65.94/9.85 | SIMP: (17) implies:
% 65.94/9.85 | (18) all_14_2 = e2
% 65.94/9.85 |
% 65.94/9.85 | COMBINE_EQS: (1), (18) imply:
% 65.94/9.85 | (19) all_44_2 = e2
% 65.94/9.85 |
% 65.94/9.85 | REDUCE: (14), (18) imply:
% 65.94/9.85 | (20) op(e2, e2) = e3
% 65.94/9.85 |
% 65.94/9.85 | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (15), (16),
% 65.94/9.85 | (19), (20) are inconsistent by sub-proof #52.
% 65.94/9.85 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #52 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) all_52_2 = all_4_2
% 65.94/9.85 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (3) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 65.94/9.85 (4) op(e2, e2) = all_10_2
% 65.94/9.85 (5) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (6) ~ (e3 = e0)
% 65.94/9.85 (7) ~ (e1 = e0)
% 65.94/9.85 (8) all_44_2 = e2
% 65.94/9.85 (9) op(e3, e3) = all_4_2
% 65.94/9.85 (10) op(e2, e2) = e3
% 65.94/9.85 (11) ~ (e2 = e0)
% 65.94/9.85 (12) all_52_0 = all_10_2
% 65.94/9.85 (13) all_52_1 = e2
% 65.94/9.85 (14) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.85 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | BETA: splitting (3) gives:
% 65.94/9.85 |
% 65.94/9.85 | Case 1:
% 65.94/9.85 | |
% 65.94/9.85 | |
% 65.94/9.85 | | GROUND_INST: instantiating (2) with all_10_2, e3, e2, e2, simplifying with
% 65.94/9.85 | | (4), (10) gives:
% 65.94/9.85 | | (15) all_10_2 = e3
% 65.94/9.85 | |
% 65.94/9.85 | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (12), (13), (14), (15) are
% 65.94/9.85 | | inconsistent by sub-proof #54.
% 65.94/9.85 | |
% 65.94/9.85 | Case 2:
% 65.94/9.85 | |
% 65.94/9.85 | | (16) ~ (all_44_2 = e2)
% 65.94/9.85 | |
% 65.94/9.85 | | REDUCE: (8), (16) imply:
% 65.94/9.85 | | (17) $false
% 65.94/9.85 | |
% 65.94/9.85 | | CLOSE: (17) is inconsistent.
% 65.94/9.85 | |
% 65.94/9.85 | End of split
% 65.94/9.85 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #53 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 =
% 65.94/9.85 e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 65.94/9.85 (2) op(e1, e1) = all_14_2
% 65.94/9.85 (3) all_52_2 = all_4_2
% 65.94/9.85 (4) op(all_4_2, all_4_2) = all_4_0
% 65.94/9.85 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.85 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.85 (7) op(e2, e2) = all_10_2
% 65.94/9.85 (8) ~ (all_34_0 = e0)
% 65.94/9.85 (9) ~ (all_4_0 = e1)
% 65.94/9.85 (10) all_52_1 = all_14_2
% 65.94/9.85 (11) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (12) ~ (e3 = e0)
% 65.94/9.85 (13) ~ (e1 = e0)
% 65.94/9.85 (14) op(e3, e3) = all_4_2
% 65.94/9.85 (15) op(all_6_2, all_6_2) = all_6_0
% 65.94/9.85 (16) ~ (e2 = e0)
% 65.94/9.85 (17) ~ (e2 = e1)
% 65.94/9.85 (18) all_52_3 = all_6_2
% 65.94/9.85 (19) all_52_0 = all_10_2
% 65.94/9.85 (20) op(all_14_2, all_14_2) = e3
% 65.94/9.85 (21) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.85 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.85 (22) ~ (all_6_0 = e1)
% 65.94/9.85 (23) all_34_0 = all_4_0
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | REDUCE: (8), (23) imply:
% 65.94/9.85 | (24) ~ (all_4_0 = e0)
% 65.94/9.85 |
% 65.94/9.85 | BETA: splitting (1) gives:
% 65.94/9.85 |
% 65.94/9.85 | Case 1:
% 65.94/9.85 | |
% 65.94/9.85 | | (25) all_52_1 = e2 & ~ (all_52_0 = e1)
% 65.94/9.85 | |
% 65.94/9.85 | | ALPHA: (25) implies:
% 65.94/9.85 | | (26) all_52_1 = e2
% 65.94/9.85 | |
% 65.94/9.85 | | COMBINE_EQS: (10), (26) imply:
% 65.94/9.85 | | (27) all_14_2 = e2
% 65.94/9.85 | |
% 65.94/9.85 | | SIMP: (27) implies:
% 65.94/9.85 | | (28) all_14_2 = e2
% 65.94/9.85 | |
% 65.94/9.85 | | REDUCE: (20), (28) imply:
% 65.94/9.85 | | (29) op(e2, e2) = e3
% 65.94/9.85 | |
% 65.94/9.85 | | GROUND_INST: instantiating (5) with all_10_2, e3, e2, e2, simplifying with
% 65.94/9.85 | | (7), (29) gives:
% 65.94/9.85 | | (30) all_10_2 = e3
% 65.94/9.85 | |
% 65.94/9.85 | | REF_CLOSE: (3), (5), (11), (12), (13), (14), (16), (19), (21), (26), (30)
% 65.94/9.85 | | are inconsistent by sub-proof #54.
% 65.94/9.85 | |
% 65.94/9.85 | Case 2:
% 65.94/9.85 | |
% 65.94/9.85 | | (31) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0
% 65.94/9.85 | | = e0))
% 65.94/9.85 | |
% 65.94/9.85 | | BETA: splitting (31) gives:
% 65.94/9.85 | |
% 65.94/9.85 | | Case 1:
% 65.94/9.85 | | |
% 65.94/9.85 | | | (32) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.85 | | |
% 65.94/9.85 | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (16), (17), (19), (21),
% 65.94/9.85 | | | (24), (32) are inconsistent by sub-proof #111.
% 65.94/9.85 | | |
% 65.94/9.85 | | Case 2:
% 65.94/9.85 | | |
% 65.94/9.85 | | | (33) all_52_3 = e2 & ~ (all_52_0 = e0)
% 65.94/9.85 | | |
% 65.94/9.85 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (13), (15), (17), (18),
% 65.94/9.85 | | | (19), (21), (22), (24), (33) are inconsistent by sub-proof
% 65.94/9.85 | | | #106.
% 65.94/9.85 | | |
% 65.94/9.85 | | End of split
% 65.94/9.85 | |
% 65.94/9.85 | End of split
% 65.94/9.85 |
% 65.94/9.85 End of proof
% 65.94/9.85
% 65.94/9.85 Sub-proof #54 shows that the following formulas are inconsistent:
% 65.94/9.85 ----------------------------------------------------------------
% 65.94/9.85 (1) all_52_2 = all_4_2
% 65.94/9.85 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.85 (3) op(all_10_2, all_10_2) = e1
% 65.94/9.85 (4) ~ (e3 = e0)
% 65.94/9.85 (5) ~ (e1 = e0)
% 65.94/9.85 (6) op(e3, e3) = all_4_2
% 65.94/9.85 (7) ~ (e2 = e0)
% 65.94/9.85 (8) all_52_0 = all_10_2
% 65.94/9.85 (9) all_52_1 = e2
% 65.94/9.85 (10) all_10_2 = e3
% 65.94/9.85 (11) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.85 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.85
% 65.94/9.85 Begin of proof
% 65.94/9.85 |
% 65.94/9.85 | COMBINE_EQS: (8), (10) imply:
% 65.94/9.85 | (12) all_52_0 = e3
% 65.94/9.85 |
% 65.94/9.85 | REDUCE: (3), (10) imply:
% 65.94/9.86 | (13) op(e3, e3) = e1
% 65.94/9.86 |
% 65.94/9.86 | BETA: splitting (11) gives:
% 65.94/9.86 |
% 65.94/9.86 | Case 1:
% 65.94/9.86 | |
% 65.94/9.86 | | (14) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.86 | |
% 65.94/9.86 | | REF_CLOSE: (4), (12), (14) are inconsistent by sub-proof #56.
% 65.94/9.86 | |
% 65.94/9.86 | Case 2:
% 65.94/9.86 | |
% 65.94/9.86 | | (15) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.86 | | = e3))
% 65.94/9.86 | |
% 65.94/9.86 | | BETA: splitting (15) gives:
% 65.94/9.86 | |
% 65.94/9.86 | | Case 1:
% 65.94/9.86 | | |
% 65.94/9.86 | | | (16) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.86 | | |
% 65.94/9.86 | | | REF_CLOSE: (7), (9), (16) are inconsistent by sub-proof #55.
% 65.94/9.86 | | |
% 65.94/9.86 | | Case 2:
% 65.94/9.86 | | |
% 65.94/9.86 | | | (17) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.86 | | |
% 65.94/9.86 | | | ALPHA: (17) implies:
% 65.94/9.86 | | | (18) all_52_2 = e0
% 65.94/9.86 | | |
% 65.94/9.86 | | | COMBINE_EQS: (1), (18) imply:
% 65.94/9.86 | | | (19) all_4_2 = e0
% 65.94/9.86 | | |
% 65.94/9.86 | | | REDUCE: (6), (19) imply:
% 65.94/9.86 | | | (20) op(e3, e3) = e0
% 65.94/9.86 | | |
% 65.94/9.86 | | | GROUND_INST: instantiating (2) with e0, e1, e3, e3, simplifying with (13),
% 65.94/9.86 | | | (20) gives:
% 65.94/9.86 | | | (21) e1 = e0
% 65.94/9.86 | | |
% 65.94/9.86 | | | REDUCE: (5), (21) imply:
% 65.94/9.86 | | | (22) $false
% 65.94/9.86 | | |
% 65.94/9.86 | | | CLOSE: (22) is inconsistent.
% 65.94/9.86 | | |
% 65.94/9.86 | | End of split
% 65.94/9.86 | |
% 65.94/9.86 | End of split
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #55 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.86 (2) all_52_1 = e2
% 65.94/9.86 (3) ~ (e2 = e0)
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | ALPHA: (1) implies:
% 65.94/9.86 | (4) all_52_1 = e0
% 65.94/9.86 |
% 65.94/9.86 | COMBINE_EQS: (2), (4) imply:
% 65.94/9.86 | (5) e2 = e0
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (3), (5) imply:
% 65.94/9.86 | (6) $false
% 65.94/9.86 |
% 65.94/9.86 | CLOSE: (6) is inconsistent.
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #56 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.86 (2) all_52_0 = e3
% 65.94/9.86 (3) ~ (e3 = e0)
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | ALPHA: (1) implies:
% 65.94/9.86 | (4) all_52_0 = e0
% 65.94/9.86 |
% 65.94/9.86 | COMBINE_EQS: (2), (4) imply:
% 65.94/9.86 | (5) e3 = e0
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (3), (5) imply:
% 65.94/9.86 | (6) $false
% 65.94/9.86 |
% 65.94/9.86 | CLOSE: (6) is inconsistent.
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #57 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) op(e1, e1) = all_14_2
% 65.94/9.86 (2) all_52_2 = all_4_2
% 65.94/9.86 (3) op(all_4_2, all_4_2) = e1
% 65.94/9.86 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (5) op(e2, e2) = all_10_2
% 65.94/9.86 (6) all_52_1 = all_14_2
% 65.94/9.86 (7) op(all_10_2, all_10_2) = e1
% 65.94/9.86 (8) ~ (e1 = e0)
% 65.94/9.86 (9) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.86 (10) ~ (e2 = e0)
% 65.94/9.86 (11) all_52_0 = all_10_2
% 65.94/9.86 (12) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.86 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | ALPHA: (9) implies:
% 65.94/9.86 | (13) all_52_2 = e2
% 65.94/9.86 |
% 65.94/9.86 | COMBINE_EQS: (2), (13) imply:
% 65.94/9.86 | (14) all_4_2 = e2
% 65.94/9.86 |
% 65.94/9.86 | SIMP: (14) implies:
% 65.94/9.86 | (15) all_4_2 = e2
% 65.94/9.86 |
% 65.94/9.86 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (15) are
% 65.94/9.86 | inconsistent by sub-proof #59.
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #58 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) op(e1, e1) = all_14_2
% 65.94/9.86 (2) all_52_2 = all_4_2
% 65.94/9.86 (3) op(all_4_2, all_4_2) = e1
% 65.94/9.86 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (5) op(e2, e2) = all_10_2
% 65.94/9.86 (6) all_52_1 = all_14_2
% 65.94/9.86 (7) op(all_10_2, all_10_2) = e1
% 65.94/9.86 (8) ~ (e1 = e0)
% 65.94/9.86 (9) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.86 (10) ~ (e2 = e0)
% 65.94/9.86 (11) all_52_0 = all_10_2
% 65.94/9.86 (12) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.86 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | ALPHA: (9) implies:
% 65.94/9.86 | (13) all_52_2 = e2
% 65.94/9.86 |
% 65.94/9.86 | COMBINE_EQS: (2), (13) imply:
% 65.94/9.86 | (14) all_4_2 = e2
% 65.94/9.86 |
% 65.94/9.86 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14) are
% 65.94/9.86 | inconsistent by sub-proof #59.
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #59 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) op(e1, e1) = all_14_2
% 65.94/9.86 (2) op(all_4_2, all_4_2) = e1
% 65.94/9.86 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (4) op(e2, e2) = all_10_2
% 65.94/9.86 (5) all_52_1 = all_14_2
% 65.94/9.86 (6) op(all_10_2, all_10_2) = e1
% 65.94/9.86 (7) ~ (e1 = e0)
% 65.94/9.86 (8) all_4_2 = e2
% 65.94/9.86 (9) ~ (e2 = e0)
% 65.94/9.86 (10) all_52_0 = all_10_2
% 65.94/9.86 (11) all_52_2 = e2
% 65.94/9.86 (12) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.86 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (2), (8) imply:
% 65.94/9.86 | (13) op(e2, e2) = e1
% 65.94/9.86 |
% 65.94/9.86 | GROUND_INST: instantiating (3) with all_10_2, e1, e2, e2, simplifying with
% 65.94/9.86 | (4), (13) gives:
% 65.94/9.86 | (14) all_10_2 = e1
% 65.94/9.86 |
% 65.94/9.86 | COMBINE_EQS: (10), (14) imply:
% 65.94/9.86 | (15) all_52_0 = e1
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (6), (14) imply:
% 65.94/9.86 | (16) op(e1, e1) = e1
% 65.94/9.86 |
% 65.94/9.86 | BETA: splitting (12) gives:
% 65.94/9.86 |
% 65.94/9.86 | Case 1:
% 65.94/9.86 | |
% 65.94/9.86 | | (17) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.86 | |
% 65.94/9.86 | | ALPHA: (17) implies:
% 65.94/9.86 | | (18) all_52_0 = e0
% 65.94/9.86 | |
% 65.94/9.86 | | REF_CLOSE: (7), (15), (18) are inconsistent by sub-proof #133.
% 65.94/9.86 | |
% 65.94/9.86 | Case 2:
% 65.94/9.86 | |
% 65.94/9.86 | | (19) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 65.94/9.86 | | = e3))
% 65.94/9.86 | |
% 65.94/9.86 | | REF_CLOSE: (1), (3), (5), (7), (9), (11), (16), (19) are inconsistent by
% 65.94/9.86 | | sub-proof #60.
% 65.94/9.86 | |
% 65.94/9.86 | End of split
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #60 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) op(e1, e1) = all_14_2
% 65.94/9.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (3) op(e1, e1) = e1
% 65.94/9.86 (4) all_52_1 = all_14_2
% 65.94/9.86 (5) ~ (e1 = e0)
% 65.94/9.86 (6) ~ (e2 = e0)
% 65.94/9.86 (7) all_52_2 = e2
% 65.94/9.86 (8) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3 =
% 65.94/9.86 e3))
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | BETA: splitting (8) gives:
% 65.94/9.86 |
% 65.94/9.86 | Case 1:
% 65.94/9.86 | |
% 65.94/9.86 | | (9) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.86 | |
% 65.94/9.86 | | ALPHA: (9) implies:
% 65.94/9.86 | | (10) all_52_1 = e0
% 65.94/9.86 | |
% 65.94/9.86 | | COMBINE_EQS: (4), (10) imply:
% 65.94/9.86 | | (11) all_14_2 = e0
% 65.94/9.86 | |
% 65.94/9.86 | | SIMP: (11) implies:
% 65.94/9.86 | | (12) all_14_2 = e0
% 65.94/9.86 | |
% 65.94/9.86 | | REF_CLOSE: (1), (2), (3), (5), (12) are inconsistent by sub-proof #61.
% 65.94/9.86 | |
% 65.94/9.86 | Case 2:
% 65.94/9.86 | |
% 65.94/9.86 | | (13) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.86 | |
% 65.94/9.86 | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #131.
% 65.94/9.86 | |
% 65.94/9.86 | End of split
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #61 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) op(e1, e1) = all_14_2
% 65.94/9.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (3) all_14_2 = e0
% 65.94/9.86 (4) op(e1, e1) = e1
% 65.94/9.86 (5) ~ (e1 = e0)
% 65.94/9.86
% 65.94/9.86 Begin of proof
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (1), (3) imply:
% 65.94/9.86 | (6) op(e1, e1) = e0
% 65.94/9.86 |
% 65.94/9.86 | GROUND_INST: instantiating (2) with e0, e1, e1, e1, simplifying with (4), (6)
% 65.94/9.86 | gives:
% 65.94/9.86 | (7) e1 = e0
% 65.94/9.86 |
% 65.94/9.86 | REDUCE: (5), (7) imply:
% 65.94/9.86 | (8) $false
% 65.94/9.86 |
% 65.94/9.86 | CLOSE: (8) is inconsistent.
% 65.94/9.86 |
% 65.94/9.86 End of proof
% 65.94/9.86
% 65.94/9.86 Sub-proof #62 shows that the following formulas are inconsistent:
% 65.94/9.86 ----------------------------------------------------------------
% 65.94/9.86 (1) ~ (all_54_2 = all_6_2)
% 65.94/9.86 (2) ~ (all_54_2 = all_54_10)
% 65.94/9.86 (3) all_52_2 = all_4_2
% 65.94/9.86 (4) all_30_2 = all_10_2
% 65.94/9.86 (5) ~ (all_54_1 = all_14_2)
% 65.94/9.86 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.86 (7) ~ (all_54_1 = all_54_3)
% 65.94/9.86 (8) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.86 (9) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.94/9.86 (10) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.86 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.86 (11) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.86 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.86 (12) op(e2, e2) = all_10_2
% 65.94/9.86 (13) all_56_1 = all_54_1
% 65.94/9.86 (14) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.94/9.86 (15) op(e0, e2) = all_54_3
% 65.94/9.86 (16) all_56_2 = all_54_3
% 65.94/9.86 (17) all_52_1 = all_14_2
% 65.94/9.86 (18) ~ (e1 = e0)
% 65.94/9.86 (19) ~ (all_54_2 = all_4_2)
% 65.94/9.86 (20) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.94/9.86 (21) op(e2, e3) = all_54_10
% 65.94/9.86 (22) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.86 (23) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.86 (24) ~ (all_54_1 = all_54_2)
% 65.94/9.86 (25) all_50_1 = all_4_1
% 65.94/9.86 (26) all_50_2 = all_4_2
% 65.94/9.86 (27) all_30_1 = all_10_1
% 65.94/9.86 (28) ~ (all_54_10 = all_4_2)
% 65.94/9.86 (29) op(all_4_2, e3) = all_4_1
% 65.94/9.86 (30) ~ (e2 = e1)
% 65.94/9.86 (31) op(all_4_2, all_4_2) = e0
% 65.94/9.86 (32) all_56_3 = all_54_2
% 65.94/9.86 (33) ~ (all_54_1 = all_6_2)
% 65.94/9.86 (34) ~ (all_54_2 = all_54_3)
% 65.94/9.86 (35) all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 65.94/9.86 (36) all_52_3 = all_6_2
% 65.94/9.87 (37) op(all_10_2, e2) = all_10_1
% 65.94/9.87 (38) all_52_0 = all_10_2
% 65.94/9.87 (39) ~ (all_54_10 = all_10_2)
% 65.94/9.87 (40) all_56_11 = all_54_10
% 65.94/9.87 (41) ~ (all_54_3 = all_6_2)
% 65.94/9.87
% 65.94/9.87 Begin of proof
% 65.94/9.87 |
% 65.94/9.87 | ALPHA: (23) implies:
% 65.94/9.87 | (42) all_52_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | COMBINE_EQS: (3), (42) imply:
% 65.94/9.87 | (43) all_4_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | SIMP: (43) implies:
% 65.94/9.87 | (44) all_4_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | COMBINE_EQS: (26), (44) imply:
% 65.94/9.87 | (45) all_50_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.94/9.87 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 65.94/9.87 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 65.94/9.87 | (38), (39), (40), (41), (42), (44), (45) are inconsistent by
% 65.94/9.87 | sub-proof #64.
% 65.94/9.87 |
% 65.94/9.87 End of proof
% 65.94/9.87
% 65.94/9.87 Sub-proof #63 shows that the following formulas are inconsistent:
% 65.94/9.87 ----------------------------------------------------------------
% 65.94/9.87 (1) ~ (all_54_2 = all_6_2)
% 65.94/9.87 (2) ~ (all_54_2 = all_54_10)
% 65.94/9.87 (3) all_52_2 = all_4_2
% 65.94/9.87 (4) all_30_2 = all_10_2
% 65.94/9.87 (5) ~ (all_54_1 = all_14_2)
% 65.94/9.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.87 (7) ~ (all_54_1 = all_54_3)
% 65.94/9.87 (8) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.87 (9) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.94/9.87 (10) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.87 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.87 (11) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.87 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.87 (12) op(e2, e2) = all_10_2
% 65.94/9.87 (13) all_56_1 = all_54_1
% 65.94/9.87 (14) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.94/9.87 (15) op(e0, e2) = all_54_3
% 65.94/9.87 (16) all_56_2 = all_54_3
% 65.94/9.87 (17) all_52_1 = all_14_2
% 65.94/9.87 (18) ~ (e1 = e0)
% 65.94/9.87 (19) ~ (all_54_2 = all_4_2)
% 65.94/9.87 (20) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.94/9.87 (21) op(e2, e3) = all_54_10
% 65.94/9.87 (22) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.87 (23) all_52_2 = e2 & ~ (all_52_0 = e3)
% 65.94/9.87 (24) ~ (all_54_1 = all_54_2)
% 65.94/9.87 (25) all_50_1 = all_4_1
% 65.94/9.87 (26) all_50_2 = all_4_2
% 65.94/9.87 (27) all_30_1 = all_10_1
% 65.94/9.87 (28) ~ (all_54_10 = all_4_2)
% 65.94/9.87 (29) op(all_4_2, e3) = all_4_1
% 65.94/9.87 (30) ~ (e2 = e1)
% 65.94/9.87 (31) op(all_4_2, all_4_2) = e0
% 65.94/9.87 (32) all_56_3 = all_54_2
% 65.94/9.87 (33) ~ (all_54_1 = all_6_2)
% 65.94/9.87 (34) ~ (all_54_2 = all_54_3)
% 65.94/9.87 (35) all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 65.94/9.87 (36) all_52_3 = all_6_2
% 65.94/9.87 (37) op(all_10_2, e2) = all_10_1
% 65.94/9.87 (38) all_52_0 = all_10_2
% 65.94/9.87 (39) ~ (all_54_10 = all_10_2)
% 65.94/9.87 (40) all_56_11 = all_54_10
% 65.94/9.87 (41) ~ (all_54_3 = all_6_2)
% 65.94/9.87
% 65.94/9.87 Begin of proof
% 65.94/9.87 |
% 65.94/9.87 | ALPHA: (23) implies:
% 65.94/9.87 | (42) all_52_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | COMBINE_EQS: (3), (42) imply:
% 65.94/9.87 | (43) all_4_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | COMBINE_EQS: (26), (43) imply:
% 65.94/9.87 | (44) all_50_2 = e2
% 65.94/9.87 |
% 65.94/9.87 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 65.94/9.87 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 65.94/9.87 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 65.94/9.87 | (38), (39), (40), (41), (42), (43), (44) are inconsistent by
% 65.94/9.87 | sub-proof #64.
% 65.94/9.87 |
% 65.94/9.87 End of proof
% 65.94/9.87
% 65.94/9.87 Sub-proof #64 shows that the following formulas are inconsistent:
% 65.94/9.87 ----------------------------------------------------------------
% 65.94/9.87 (1) all_50_2 = e2
% 65.94/9.87 (2) ~ (all_54_2 = all_6_2)
% 65.94/9.87 (3) ~ (all_54_2 = all_54_10)
% 65.94/9.87 (4) all_30_2 = all_10_2
% 65.94/9.87 (5) ~ (all_54_1 = all_14_2)
% 65.94/9.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.87 (7) ~ (all_54_1 = all_54_3)
% 65.94/9.87 (8) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.87 (9) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.94/9.87 (10) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.87 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.87 (11) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.87 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.87 (12) op(e2, e2) = all_10_2
% 65.94/9.87 (13) all_56_1 = all_54_1
% 65.94/9.87 (14) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.94/9.87 (15) op(e0, e2) = all_54_3
% 65.94/9.87 (16) all_56_2 = all_54_3
% 65.94/9.87 (17) all_52_1 = all_14_2
% 65.94/9.87 (18) ~ (e1 = e0)
% 65.94/9.87 (19) ~ (all_54_2 = all_4_2)
% 65.94/9.87 (20) all_4_2 = e2
% 65.94/9.87 (21) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.94/9.87 (22) op(e2, e3) = all_54_10
% 65.94/9.87 (23) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.87 (24) ~ (all_54_1 = all_54_2)
% 65.94/9.87 (25) all_50_1 = all_4_1
% 65.94/9.87 (26) all_30_1 = all_10_1
% 65.94/9.87 (27) ~ (all_54_10 = all_4_2)
% 65.94/9.87 (28) op(all_4_2, e3) = all_4_1
% 65.94/9.87 (29) ~ (e2 = e1)
% 65.94/9.87 (30) op(all_4_2, all_4_2) = e0
% 65.94/9.87 (31) all_56_3 = all_54_2
% 65.94/9.87 (32) ~ (all_54_1 = all_6_2)
% 65.94/9.87 (33) ~ (all_54_2 = all_54_3)
% 65.94/9.87 (34) all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 65.94/9.87 (35) all_52_3 = all_6_2
% 65.94/9.87 (36) op(all_10_2, e2) = all_10_1
% 65.94/9.87 (37) all_52_0 = all_10_2
% 65.94/9.87 (38) ~ (all_54_10 = all_10_2)
% 65.94/9.87 (39) all_52_2 = e2
% 65.94/9.87 (40) all_56_11 = all_54_10
% 65.94/9.87 (41) ~ (all_54_3 = all_6_2)
% 65.94/9.87
% 65.94/9.87 Begin of proof
% 65.94/9.87 |
% 65.94/9.87 | REDUCE: (19), (20) imply:
% 65.94/9.87 | (42) ~ (all_54_2 = e2)
% 65.94/9.87 |
% 65.94/9.87 | REDUCE: (20), (27) imply:
% 65.94/9.87 | (43) ~ (all_54_10 = e2)
% 65.94/9.87 |
% 65.94/9.87 | REDUCE: (20), (30) imply:
% 65.94/9.87 | (44) op(e2, e2) = e0
% 65.94/9.87 |
% 65.94/9.87 | REDUCE: (20), (28) imply:
% 65.94/9.87 | (45) op(e2, e3) = all_4_1
% 65.94/9.87 |
% 65.94/9.87 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 65.94/9.87 | (13), (14), (15), (16), (17), (18), (21), (22), (23), (24), (25),
% 65.94/9.87 | (26), (29), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 65.94/9.87 | (40), (41), (42), (43), (44), (45) are inconsistent by sub-proof
% 65.94/9.87 | #65.
% 65.94/9.87 |
% 65.94/9.87 End of proof
% 65.94/9.87
% 65.94/9.87 Sub-proof #65 shows that the following formulas are inconsistent:
% 65.94/9.87 ----------------------------------------------------------------
% 65.94/9.87 (1) all_50_2 = e2
% 65.94/9.87 (2) ~ (all_54_2 = all_6_2)
% 65.94/9.87 (3) ~ (all_54_2 = all_54_10)
% 65.94/9.87 (4) all_30_2 = all_10_2
% 65.94/9.87 (5) ~ (all_54_1 = all_14_2)
% 65.94/9.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.87 (7) ~ (all_54_1 = all_54_3)
% 65.94/9.87 (8) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.87 (9) ~ (all_50_1 = e1) | ~ (all_50_2 = e2)
% 65.94/9.87 (10) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.87 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.87 (11) ~ (all_54_2 = e2)
% 65.94/9.87 (12) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.87 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.87 (13) op(e2, e2) = all_10_2
% 65.94/9.87 (14) all_56_1 = all_54_1
% 65.94/9.87 (15) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.94/9.87 (16) op(e0, e2) = all_54_3
% 65.94/9.87 (17) all_56_2 = all_54_3
% 65.94/9.87 (18) all_52_1 = all_14_2
% 65.94/9.87 (19) ~ (e1 = e0)
% 65.94/9.87 (20) ~ (all_30_1 = e3) | ~ (all_30_2 = e0)
% 65.94/9.87 (21) op(e2, e3) = all_54_10
% 65.94/9.87 (22) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.87 (23) ~ (all_54_1 = all_54_2)
% 65.94/9.87 (24) all_50_1 = all_4_1
% 65.94/9.87 (25) all_30_1 = all_10_1
% 65.94/9.87 (26) ~ (e2 = e1)
% 65.94/9.87 (27) all_56_3 = all_54_2
% 65.94/9.87 (28) ~ (all_54_1 = all_6_2)
% 65.94/9.87 (29) ~ (all_54_2 = all_54_3)
% 65.94/9.87 (30) all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 65.94/9.87 (31) all_52_3 = all_6_2
% 65.94/9.87 (32) op(all_10_2, e2) = all_10_1
% 65.94/9.87 (33) ~ (all_54_10 = e2)
% 65.94/9.87 (34) all_52_0 = all_10_2
% 65.94/9.87 (35) ~ (all_54_10 = all_10_2)
% 65.94/9.87 (36) all_52_2 = e2
% 65.94/9.87 (37) all_56_11 = all_54_10
% 65.94/9.87 (38) op(e2, e3) = all_4_1
% 65.94/9.87 (39) ~ (all_54_3 = all_6_2)
% 65.94/9.87 (40) op(e2, e2) = e0
% 65.94/9.87
% 65.94/9.87 Begin of proof
% 65.94/9.87 |
% 65.94/9.87 | BETA: splitting (9) gives:
% 65.94/9.87 |
% 65.94/9.87 | Case 1:
% 65.94/9.87 | |
% 65.94/9.87 | | (41) ~ (all_50_1 = e1)
% 65.94/9.87 | |
% 65.94/9.87 | | REDUCE: (24), (41) imply:
% 65.94/9.87 | | (42) ~ (all_4_1 = e1)
% 65.94/9.87 | |
% 65.94/9.87 | | GROUND_INST: instantiating (6) with all_10_2, e0, e2, e2, simplifying with
% 65.94/9.87 | | (13), (40) gives:
% 65.94/9.87 | | (43) all_10_2 = e0
% 65.94/9.87 | |
% 65.94/9.87 | | GROUND_INST: instantiating (6) with all_54_10, all_4_1, e3, e2, simplifying
% 65.94/9.87 | | with (21), (38) gives:
% 65.94/9.87 | | (44) all_54_10 = all_4_1
% 65.94/9.87 | |
% 65.94/9.87 | | COMBINE_EQS: (4), (43) imply:
% 65.94/9.87 | | (45) all_30_2 = e0
% 65.94/9.87 | |
% 65.94/9.87 | | COMBINE_EQS: (34), (43) imply:
% 65.94/9.87 | | (46) all_52_0 = e0
% 65.94/9.87 | |
% 65.94/9.87 | | COMBINE_EQS: (37), (44) imply:
% 65.94/9.87 | | (47) all_56_11 = all_4_1
% 65.94/9.87 | |
% 65.94/9.87 | | REDUCE: (3), (44) imply:
% 65.94/9.87 | | (48) ~ (all_54_2 = all_4_1)
% 65.94/9.87 | |
% 65.94/9.87 | | REDUCE: (35), (43), (44) imply:
% 65.94/9.87 | | (49) ~ (all_4_1 = e0)
% 65.94/9.87 | |
% 65.94/9.87 | | REDUCE: (33), (44) imply:
% 65.94/9.88 | | (50) ~ (all_4_1 = e2)
% 65.94/9.88 | |
% 65.94/9.88 | | REDUCE: (32), (43) imply:
% 65.94/9.88 | | (51) op(e0, e2) = all_10_1
% 65.94/9.88 | |
% 65.94/9.88 | | BETA: splitting (15) gives:
% 65.94/9.88 | |
% 65.94/9.88 | | Case 1:
% 65.94/9.88 | | |
% 65.94/9.88 | | | (52) all_56_11 = e3
% 65.94/9.88 | | |
% 65.94/9.88 | | | COMBINE_EQS: (47), (52) imply:
% 65.94/9.88 | | | (53) all_4_1 = e3
% 65.94/9.88 | | |
% 65.94/9.88 | | | SIMP: (53) implies:
% 65.94/9.88 | | | (54) all_4_1 = e3
% 65.94/9.88 | | |
% 65.94/9.88 | | | REDUCE: (48), (54) imply:
% 65.94/9.88 | | | (55) ~ (all_54_2 = e3)
% 65.94/9.88 | | |
% 65.94/9.88 | | | REDUCE: (42), (54) imply:
% 65.94/9.88 | | | (56) ~ (e3 = e1)
% 65.94/9.88 | | |
% 65.94/9.88 | | | REDUCE: (49), (54) imply:
% 65.94/9.88 | | | (57) ~ (e3 = e0)
% 65.94/9.88 | | |
% 65.94/9.88 | | | BETA: splitting (12) gives:
% 65.94/9.88 | | |
% 65.94/9.88 | | | Case 1:
% 65.94/9.88 | | | |
% 65.94/9.88 | | | | (58) all_52_0 = e1 & ~ (all_52_1 = e2)
% 65.94/9.88 | | | |
% 65.94/9.88 | | | | REF_CLOSE: (19), (46), (58) are inconsistent by sub-proof #164.
% 65.94/9.88 | | | |
% 65.94/9.88 | | | Case 2:
% 65.94/9.88 | | | |
% 65.94/9.88 | | | | (59) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 65.94/9.88 | | | | (all_52_1 = e0))
% 65.94/9.88 | | | |
% 65.94/9.88 | | | | BETA: splitting (59) gives:
% 65.94/9.88 | | | |
% 65.94/9.88 | | | | Case 1:
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | (60) all_52_2 = e1 & ~ (all_52_1 = e3)
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | REF_CLOSE: (26), (36), (60) are inconsistent by sub-proof #175.
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | Case 2:
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | (61) all_52_3 = e1 & ~ (all_52_1 = e0)
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | ALPHA: (61) implies:
% 65.94/9.88 | | | | | (62) all_52_3 = e1
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | COMBINE_EQS: (31), (62) imply:
% 65.94/9.88 | | | | | (63) all_6_2 = e1
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | SIMP: (63) implies:
% 65.94/9.88 | | | | | (64) all_6_2 = e1
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | REDUCE: (28), (64) imply:
% 65.94/9.88 | | | | | (65) ~ (all_54_1 = e1)
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | REDUCE: (2), (64) imply:
% 65.94/9.88 | | | | | (66) ~ (all_54_2 = e1)
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | REDUCE: (39), (64) imply:
% 65.94/9.88 | | | | | (67) ~ (all_54_3 = e1)
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | BETA: splitting (20) gives:
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | | Case 1:
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | (68) ~ (all_30_1 = e3)
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | REDUCE: (25), (68) imply:
% 65.94/9.88 | | | | | | (69) ~ (all_10_1 = e3)
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | BETA: splitting (10) gives:
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | Case 1:
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | | (70) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | | REF_CLOSE: (46), (57), (70) are inconsistent by sub-proof #148.
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | Case 2:
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | | (71) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 65.94/9.88 | | | | | | | (all_52_2 = e0))
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | | BETA: splitting (71) gives:
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | (72) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | ALPHA: (72) implies:
% 65.94/9.88 | | | | | | | | (73) all_52_1 = e3
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | COMBINE_EQS: (18), (73) imply:
% 65.94/9.88 | | | | | | | | (74) all_14_2 = e3
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | SIMP: (74) implies:
% 65.94/9.88 | | | | | | | | (75) all_14_2 = e3
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | REDUCE: (5), (75) imply:
% 65.94/9.88 | | | | | | | | (76) ~ (all_54_1 = e3)
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | BETA: splitting (22) gives:
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | (77) all_56_3 = e3
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | COMBINE_EQS: (27), (77) imply:
% 65.94/9.88 | | | | | | | | | (78) all_54_2 = e3
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | REDUCE: (55), (78) imply:
% 65.94/9.88 | | | | | | | | | (79) $false
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | CLOSE: (79) is inconsistent.
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | (80) all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | BETA: splitting (80) gives:
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | (81) all_56_3 = e2
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | COMBINE_EQS: (27), (81) imply:
% 65.94/9.88 | | | | | | | | | | (82) all_54_2 = e2
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | REDUCE: (11), (82) imply:
% 65.94/9.88 | | | | | | | | | | (83) $false
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | CLOSE: (83) is inconsistent.
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | (84) all_56_3 = e1 | all_56_3 = e0
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | BETA: splitting (84) gives:
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | (85) all_56_3 = e1
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | COMBINE_EQS: (27), (85) imply:
% 65.94/9.88 | | | | | | | | | | | (86) all_54_2 = e1
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | REDUCE: (66), (86) imply:
% 65.94/9.88 | | | | | | | | | | | (87) $false
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | CLOSE: (87) is inconsistent.
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | (88) all_56_3 = e0
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | COMBINE_EQS: (27), (88) imply:
% 65.94/9.88 | | | | | | | | | | | (89) all_54_2 = e0
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | REDUCE: (23), (89) imply:
% 65.94/9.88 | | | | | | | | | | | (90) ~ (all_54_1 = e0)
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | REDUCE: (29), (89) imply:
% 65.94/9.88 | | | | | | | | | | | (91) ~ (all_54_3 = e0)
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | SIMP: (91) implies:
% 65.94/9.88 | | | | | | | | | | | (92) ~ (all_54_3 = e0)
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | BETA: splitting (8) gives:
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | (93) all_56_1 = e3
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | COMBINE_EQS: (14), (93) imply:
% 65.94/9.88 | | | | | | | | | | | | (94) all_54_1 = e3
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | REDUCE: (76), (94) imply:
% 65.94/9.88 | | | | | | | | | | | | (95) $false
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | CLOSE: (95) is inconsistent.
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | (96) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | BETA: splitting (96) gives:
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | (97) all_56_1 = e2
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | COMBINE_EQS: (14), (97) imply:
% 65.94/9.88 | | | | | | | | | | | | | (98) all_54_1 = e2
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | REDUCE: (7), (98) imply:
% 65.94/9.88 | | | | | | | | | | | | | (99) ~ (all_54_3 = e2)
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | SIMP: (99) implies:
% 65.94/9.88 | | | | | | | | | | | | | (100) ~ (all_54_3 = e2)
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | BETA: splitting (30) gives:
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | (101) all_56_2 = e3
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | COMBINE_EQS: (17), (101) imply:
% 65.94/9.88 | | | | | | | | | | | | | | (102) all_54_3 = e3
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | REDUCE: (16), (102) imply:
% 65.94/9.88 | | | | | | | | | | | | | | (103) op(e0, e2) = e3
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_10_1, e2, e0,
% 65.94/9.88 | | | | | | | | | | | | | | simplifying with (51), (103) gives:
% 65.94/9.88 | | | | | | | | | | | | | | (104) all_10_1 = e3
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | REDUCE: (69), (104) imply:
% 65.94/9.88 | | | | | | | | | | | | | | (105) $false
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | CLOSE: (105) is inconsistent.
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | (106) all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | (107) all_56_2 = e2
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | COMBINE_EQS: (17), (107) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | (108) all_54_3 = e2
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | REDUCE: (100), (108) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | (109) $false
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | (110) all_56_2 = e1 | all_56_2 = e0
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | Case 1:
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | (111) all_56_2 = e1
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (111) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | | (112) all_54_3 = e1
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | REDUCE: (67), (112) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | | (113) $false
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | CLOSE: (113) is inconsistent.
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | (114) all_56_2 = e0
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (114) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | | (115) all_54_3 = e0
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | REDUCE: (92), (115) imply:
% 65.94/9.88 | | | | | | | | | | | | | | | | (116) $false
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 65.94/9.88 | | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | (117) all_56_1 = e1 | all_56_1 = e0
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | | REF_CLOSE: (14), (65), (90), (117) are inconsistent by
% 65.94/9.88 | | | | | | | | | | | | | sub-proof #118.
% 65.94/9.88 | | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | | |
% 65.94/9.88 | | | | | | | | | End of split
% 65.94/9.88 | | | | | | | | |
% 65.94/9.88 | | | | | | | | End of split
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | Case 2:
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | (118) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | | REF_CLOSE: (56), (62), (118) are inconsistent by sub-proof #141.
% 65.94/9.88 | | | | | | | |
% 65.94/9.88 | | | | | | | End of split
% 65.94/9.88 | | | | | | |
% 65.94/9.88 | | | | | | End of split
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | Case 2:
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | (119) ~ (all_30_2 = e0)
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | REDUCE: (45), (119) imply:
% 65.94/9.88 | | | | | | (120) $false
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | | CLOSE: (120) is inconsistent.
% 65.94/9.88 | | | | | |
% 65.94/9.88 | | | | | End of split
% 65.94/9.88 | | | | |
% 65.94/9.88 | | | | End of split
% 65.94/9.88 | | | |
% 65.94/9.88 | | | End of split
% 65.94/9.88 | | |
% 65.94/9.88 | | Case 2:
% 65.94/9.88 | | |
% 65.94/9.88 | | | (121) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 65.94/9.88 | | |
% 65.94/9.88 | | | REF_CLOSE: (42), (47), (49), (50), (121) are inconsistent by sub-proof
% 65.94/9.88 | | | #127.
% 65.94/9.88 | | |
% 65.94/9.88 | | End of split
% 65.94/9.88 | |
% 65.94/9.88 | Case 2:
% 65.94/9.88 | |
% 65.94/9.88 | | (122) ~ (all_50_2 = e2)
% 65.94/9.88 | |
% 65.94/9.88 | | REDUCE: (1), (122) imply:
% 65.94/9.88 | | (123) $false
% 65.94/9.88 | |
% 65.94/9.88 | | CLOSE: (123) is inconsistent.
% 65.94/9.88 | |
% 65.94/9.88 | End of split
% 65.94/9.88 |
% 65.94/9.88 End of proof
% 65.94/9.88
% 65.94/9.88 Sub-proof #66 shows that the following formulas are inconsistent:
% 65.94/9.88 ----------------------------------------------------------------
% 65.94/9.88 (1) all_58_1 = e1 | all_58_2 = e1 | all_58_7 = e1 | all_58_14 = e1
% 65.94/9.88 (2) ~ (all_10_2 = e0)
% 65.94/9.88 (3) all_58_2 = e0 | all_58_3 = e0 | all_58_4 = e0 | all_58_10 = e0
% 65.94/9.88 (4) ~ (all_54_2 = all_54_10)
% 65.94/9.88 (5) ~ (all_54_4 = all_54_6)
% 65.94/9.88 (6) all_52_2 = all_4_2
% 65.94/9.88 (7) op(e2, e2) = e1
% 65.94/9.88 (8) all_58_9 = all_54_15
% 65.94/9.88 (9) all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 65.94/9.88 (10) op(all_4_2, all_4_2) = e1
% 65.94/9.88 (11) ~ (all_54_1 = all_14_2)
% 65.94/9.88 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 65.94/9.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 65.94/9.88 (13) ~ (all_54_4 = e2)
% 65.94/9.88 (14) ~ (all_54_8 = all_54_10)
% 65.94/9.88 (15) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.88 (16) ~ (all_54_4 = all_54_8)
% 65.94/9.88 (17) op(e2, e0) = all_6_1
% 65.94/9.88 (18) all_58_13 = all_54_10
% 65.94/9.88 (19) op(e2, e0) = all_54_8
% 65.94/9.88 (20) ~ (all_54_8 = all_54_12)
% 65.94/9.88 (21) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 65.94/9.88 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 65.94/9.88 (22) all_56_4 = all_54_4
% 65.94/9.88 (23) ~ (all_16_1 = e3) | ~ (all_16_2 = e2)
% 65.94/9.88 (24) ~ (all_54_2 = e2)
% 65.94/9.88 (25) ~ (all_54_6 = all_54_10)
% 65.94/9.88 (26) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 65.94/9.88 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 65.94/9.88 (27) ~ (e3 = e1)
% 65.94/9.88 (28) ~ (all_54_8 = e2)
% 65.94/9.88 (29) op(e2, e2) = all_10_2
% 65.94/9.88 (30) all_56_7 = all_54_6
% 65.94/9.88 (31) all_56_1 = all_54_1
% 65.94/9.88 (32) all_56_8 = all_54_8
% 65.94/9.88 (33) all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2
% 65.94/9.88 (34) all_58_4 = e3 | all_58_5 = e3 | all_58_6 = e3 | all_58_13 = e3
% 65.94/9.88 (35) all_58_8 = all_54_3
% 65.94/9.88 (36) all_52_1 = all_14_2
% 65.94/9.88 (37) all_58_4 = all_54_9
% 65.94/9.88 (38) ~ (e3 = e0)
% 65.94/9.88 (39) ~ (all_54_2 = all_54_6)
% 65.94/9.88 (40) ~ (all_54_12 = e2)
% 65.94/9.88 (41) ~ (all_54_8 = all_10_2)
% 65.94/9.88 (42) all_58_7 = all_54_7
% 65.94/9.88 (43) ~ (all_54_2 = all_4_2)
% 65.94/9.88 (44) all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.88 (45) all_58_6 = all_10_2
% 65.94/9.88 (46) ~ (all_54_4 = all_54_7)
% 65.94/9.88 (47) ~ (all_54_1 = all_54_2)
% 65.94/9.88 (48) ~ (all_54_9 = all_14_2)
% 65.94/9.88 (49) all_56_12 = all_54_12
% 65.94/9.88 (50) all_58_2 = all_14_2
% 65.94/9.88 (51) ~ (all_54_6 = all_4_2)
% 65.94/9.88 (52) all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.94/9.88 (53) op(e0, e0) = e2
% 65.94/9.88 (54) ~ (all_54_1 = e2)
% 65.94/9.88 (55) all_56_6 = all_54_7
% 65.94/9.88 (56) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.94/9.88 (57) all_52_3 = e2
% 65.94/9.88 (58) ~ (all_54_15 = all_4_2)
% 65.94/9.88 (59) ~ (e2 = e0)
% 65.94/9.88 (60) ~ (e2 = e1)
% 65.94/9.88 (61) all_58_1 = all_54_4
% 65.94/9.88 (62) all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_12 = e2
% 65.94/9.88 (63) all_56_3 = all_54_2
% 65.94/9.88 (64) all_52_0 = all_10_2
% 65.94/9.88 (65) all_16_2 = e2
% 65.94/9.88 (66) all_58_3 = all_54_1
% 65.94/9.88 (67) all_16_1 = all_6_1
% 65.94/9.88 (68) ~ (e3 = e2)
% 65.94/9.88 (69) op(all_14_2, all_14_2) = e0
% 65.94/9.88 (70) all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.94/9.88 (71) all_58_5 = all_54_8
% 65.94/9.89 (72) ~ (all_54_3 = all_54_15)
% 65.94/9.89 (73) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 65.94/9.89 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 65.94/9.89 (74) ~ (all_54_15 = all_10_2)
% 65.94/9.89 (75) ~ (all_54_4 = all_14_2)
% 65.94/9.89 (76) ~ (all_54_6 = all_54_7)
% 65.94/9.89 (77) ~ (all_54_7 = all_14_2)
% 65.94/9.89 (78) ~ (all_54_4 = all_54_12)
% 65.94/9.89 (79) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.94/9.89 (80) ~ (all_54_12 = all_54_15)
% 65.94/9.89 (81) all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.94/9.89 (82) all_56_14 = all_54_15
% 65.94/9.89
% 65.94/9.89 Begin of proof
% 65.94/9.89 |
% 65.94/9.89 | BETA: splitting (23) gives:
% 65.94/9.89 |
% 65.94/9.89 | Case 1:
% 65.94/9.89 | |
% 65.94/9.89 | | (83) ~ (all_16_1 = e3)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (67), (83) imply:
% 65.94/9.89 | | (84) ~ (all_6_1 = e3)
% 65.94/9.89 | |
% 65.94/9.89 | | GROUND_INST: instantiating (12) with all_54_8, all_6_1, e0, e2, simplifying
% 65.94/9.89 | | with (17), (19) gives:
% 65.94/9.89 | | (85) all_54_8 = all_6_1
% 65.94/9.89 | |
% 65.94/9.89 | | GROUND_INST: instantiating (12) with all_10_2, e1, e2, e2, simplifying with
% 65.94/9.89 | | (7), (29) gives:
% 65.94/9.89 | | (86) all_10_2 = e1
% 65.94/9.89 | |
% 65.94/9.89 | | COMBINE_EQS: (64), (86) imply:
% 65.94/9.89 | | (87) all_52_0 = e1
% 65.94/9.89 | |
% 65.94/9.89 | | COMBINE_EQS: (32), (85) imply:
% 65.94/9.89 | | (88) all_56_8 = all_6_1
% 65.94/9.89 | |
% 65.94/9.89 | | COMBINE_EQS: (45), (86) imply:
% 65.94/9.89 | | (89) all_58_6 = e1
% 65.94/9.89 | |
% 65.94/9.89 | | COMBINE_EQS: (71), (85) imply:
% 65.94/9.89 | | (90) all_58_5 = all_6_1
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (16), (85) imply:
% 65.94/9.89 | | (91) ~ (all_54_4 = all_6_1)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (14), (85) imply:
% 65.94/9.89 | | (92) ~ (all_54_10 = all_6_1)
% 65.94/9.89 | |
% 65.94/9.89 | | SIMP: (92) implies:
% 65.94/9.89 | | (93) ~ (all_54_10 = all_6_1)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (20), (85) imply:
% 65.94/9.89 | | (94) ~ (all_54_12 = all_6_1)
% 65.94/9.89 | |
% 65.94/9.89 | | SIMP: (94) implies:
% 65.94/9.89 | | (95) ~ (all_54_12 = all_6_1)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (41), (85), (86) imply:
% 65.94/9.89 | | (96) ~ (all_6_1 = e1)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (28), (85) imply:
% 65.94/9.89 | | (97) ~ (all_6_1 = e2)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (74), (86) imply:
% 65.94/9.89 | | (98) ~ (all_54_15 = e1)
% 65.94/9.89 | |
% 65.94/9.89 | | REDUCE: (2), (86) imply:
% 65.94/9.89 | | (99) ~ (e1 = e0)
% 65.94/9.89 | |
% 65.94/9.89 | | BETA: splitting (21) gives:
% 65.94/9.89 | |
% 65.94/9.89 | | Case 1:
% 65.94/9.89 | | |
% 65.94/9.89 | | | (100) all_52_0 = e3 & ~ (all_52_2 = e2)
% 65.94/9.89 | | |
% 65.94/9.89 | | | ALPHA: (100) implies:
% 65.94/9.89 | | | (101) all_52_0 = e3
% 65.94/9.89 | | |
% 65.94/9.89 | | | REF_CLOSE: (12), (26), (27), (36), (38), (53), (57), (59), (60), (69),
% 65.94/9.89 | | | (73), (99), (101) are inconsistent by sub-proof #80.
% 65.94/9.89 | | |
% 65.94/9.89 | | Case 2:
% 65.94/9.89 | | |
% 65.94/9.89 | | | (102) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 65.94/9.89 | | | (all_52_2 = e0))
% 65.94/9.89 | | |
% 65.94/9.89 | | | BETA: splitting (102) gives:
% 65.94/9.89 | | |
% 65.94/9.89 | | | Case 1:
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | (103) all_52_1 = e3 & ~ (all_52_2 = e1)
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | ALPHA: (103) implies:
% 65.94/9.89 | | | | (104) all_52_1 = e3
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | COMBINE_EQS: (36), (104) imply:
% 65.94/9.89 | | | | (105) all_14_2 = e3
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | SIMP: (105) implies:
% 65.94/9.89 | | | | (106) all_14_2 = e3
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | COMBINE_EQS: (50), (106) imply:
% 65.94/9.89 | | | | (107) all_58_2 = e3
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | REDUCE: (11), (106) imply:
% 65.94/9.89 | | | | (108) ~ (all_54_1 = e3)
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | REDUCE: (75), (106) imply:
% 65.94/9.89 | | | | (109) ~ (all_54_4 = e3)
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | REDUCE: (77), (106) imply:
% 65.94/9.89 | | | | (110) ~ (all_54_7 = e3)
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | REDUCE: (48), (106) imply:
% 65.94/9.89 | | | | (111) ~ (all_54_9 = e3)
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | BETA: splitting (34) gives:
% 65.94/9.89 | | | |
% 65.94/9.89 | | | | Case 1:
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | (112) all_58_4 = e3
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | COMBINE_EQS: (37), (112) imply:
% 65.94/9.89 | | | | | (113) all_54_9 = e3
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | REDUCE: (111), (113) imply:
% 65.94/9.89 | | | | | (114) $false
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | CLOSE: (114) is inconsistent.
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | Case 2:
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | (115) all_58_5 = e3 | all_58_6 = e3 | all_58_13 = e3
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | BETA: splitting (115) gives:
% 65.94/9.89 | | | | |
% 65.94/9.89 | | | | | Case 1:
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | (116) all_58_5 = e3
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | COMBINE_EQS: (90), (116) imply:
% 65.94/9.89 | | | | | | (117) all_6_1 = e3
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | REDUCE: (84), (117) imply:
% 65.94/9.89 | | | | | | (118) $false
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | CLOSE: (118) is inconsistent.
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | Case 2:
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | (119) all_58_6 = e3 | all_58_13 = e3
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | BETA: splitting (73) gives:
% 65.94/9.89 | | | | | |
% 65.94/9.89 | | | | | | Case 1:
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | (120) all_52_0 = e0 & ~ (all_52_3 = e2)
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | ALPHA: (120) implies:
% 65.94/9.89 | | | | | | | (121) all_52_0 = e0
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | REF_CLOSE: (87), (99), (121) are inconsistent by sub-proof #133.
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | Case 2:
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | (122) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 &
% 65.94/9.89 | | | | | | | ~ (all_52_3 = e3))
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | BETA: splitting (122) gives:
% 65.94/9.89 | | | | | | |
% 65.94/9.89 | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | (123) all_52_1 = e0 & ~ (all_52_3 = e1)
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | ALPHA: (123) implies:
% 65.94/9.89 | | | | | | | | (124) all_52_1 = e0
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | REF_CLOSE: (38), (104), (124) are inconsistent by sub-proof
% 65.94/9.89 | | | | | | | | #102.
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | (125) all_52_2 = e0 & ~ (all_52_3 = e3)
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | ALPHA: (125) implies:
% 65.94/9.89 | | | | | | | | (126) all_52_2 = e0
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | COMBINE_EQS: (6), (126) imply:
% 65.94/9.89 | | | | | | | | (127) all_4_2 = e0
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | SIMP: (127) implies:
% 65.94/9.89 | | | | | | | | (128) all_4_2 = e0
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | REDUCE: (43), (128) imply:
% 65.94/9.89 | | | | | | | | (129) ~ (all_54_2 = e0)
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | REDUCE: (51), (128) imply:
% 65.94/9.89 | | | | | | | | (130) ~ (all_54_6 = e0)
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | REDUCE: (58), (128) imply:
% 65.94/9.89 | | | | | | | | (131) ~ (all_54_15 = e0)
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | REDUCE: (10), (128) imply:
% 65.94/9.89 | | | | | | | | (132) op(e0, e0) = e1
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | BETA: splitting (119) gives:
% 65.94/9.89 | | | | | | | |
% 65.94/9.89 | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | (133) all_58_6 = e3
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | COMBINE_EQS: (89), (133) imply:
% 65.94/9.89 | | | | | | | | | (134) e3 = e1
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | REDUCE: (27), (134) imply:
% 65.94/9.89 | | | | | | | | | (135) $false
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | CLOSE: (135) is inconsistent.
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | (136) all_58_13 = e3
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | COMBINE_EQS: (18), (136) imply:
% 65.94/9.89 | | | | | | | | | (137) all_54_10 = e3
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | SIMP: (137) implies:
% 65.94/9.89 | | | | | | | | | (138) all_54_10 = e3
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | REDUCE: (4), (138) imply:
% 65.94/9.89 | | | | | | | | | (139) ~ (all_54_2 = e3)
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | REDUCE: (25), (138) imply:
% 65.94/9.89 | | | | | | | | | (140) ~ (all_54_6 = e3)
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | REDUCE: (93), (138) imply:
% 65.94/9.89 | | | | | | | | | (141) ~ (all_6_1 = e3)
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | BETA: splitting (70) gives:
% 65.94/9.89 | | | | | | | | |
% 65.94/9.89 | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | (142) all_56_8 = e3
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | COMBINE_EQS: (88), (142) imply:
% 65.94/9.89 | | | | | | | | | | (143) all_6_1 = e3
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | REDUCE: (84), (143) imply:
% 65.94/9.89 | | | | | | | | | | (144) $false
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | CLOSE: (144) is inconsistent.
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | (145) ~ (all_56_8 = e3)
% 65.94/9.89 | | | | | | | | | | (146) all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | BETA: splitting (146) gives:
% 65.94/9.89 | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | (147) all_56_8 = e2
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | COMBINE_EQS: (88), (147) imply:
% 65.94/9.89 | | | | | | | | | | | (148) all_6_1 = e2
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | REDUCE: (97), (148) imply:
% 65.94/9.89 | | | | | | | | | | | (149) $false
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | (150) all_56_8 = e1 | all_56_8 = e0
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | BETA: splitting (150) gives:
% 65.94/9.89 | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | (151) all_56_8 = e1
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | COMBINE_EQS: (88), (151) imply:
% 65.94/9.89 | | | | | | | | | | | | (152) all_6_1 = e1
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | REDUCE: (96), (152) imply:
% 65.94/9.89 | | | | | | | | | | | | (153) $false
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | (154) all_56_8 = e0
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | COMBINE_EQS: (88), (154) imply:
% 65.94/9.89 | | | | | | | | | | | | (155) all_6_1 = e0
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | REDUCE: (91), (155) imply:
% 65.94/9.89 | | | | | | | | | | | | (156) ~ (all_54_4 = e0)
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | REDUCE: (95), (155) imply:
% 65.94/9.89 | | | | | | | | | | | | (157) ~ (all_54_12 = e0)
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | REDUCE: (84), (155) imply:
% 65.94/9.89 | | | | | | | | | | | | (158) ~ (e3 = e0)
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | BETA: splitting (56) gives:
% 65.94/9.89 | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | (159) all_56_4 = e3
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | COMBINE_EQS: (22), (159) imply:
% 65.94/9.89 | | | | | | | | | | | | | (160) all_54_4 = e3
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | REDUCE: (109), (160) imply:
% 65.94/9.89 | | | | | | | | | | | | | (161) $false
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | (162) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | BETA: splitting (162) gives:
% 65.94/9.89 | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | (163) all_56_4 = e2
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | COMBINE_EQS: (22), (163) imply:
% 65.94/9.89 | | | | | | | | | | | | | | (164) all_54_4 = e2
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | REDUCE: (13), (164) imply:
% 65.94/9.89 | | | | | | | | | | | | | | (165) $false
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | (166) all_56_4 = e1 | all_56_4 = e0
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 65.94/9.89 | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | (167) all_56_3 = e3
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | COMBINE_EQS: (63), (167) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | (168) all_54_2 = e3
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | REDUCE: (139), (168) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | (169) $false
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | (170) all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 65.94/9.89 | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | (171) all_56_3 = e2
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (171) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | (172) all_54_2 = e2
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | REDUCE: (24), (172) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | (173) $false
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | (174) all_56_3 = e1 | all_56_3 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | (175) all_56_3 = e1
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (175) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | (176) all_54_2 = e1
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | REDUCE: (47), (176) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | (177) ~ (all_54_1 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | REDUCE: (39), (176) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | (178) ~ (all_54_6 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 65.94/9.89 | | | | | | | | | | | | | | | | | (179) ~ (all_54_6 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | (180) all_56_7 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (180) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | (181) all_54_6 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | REDUCE: (140), (181) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | (182) $false
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | (183) all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | (184) all_56_7 = e2
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (184) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | (185) all_54_6 = e2
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | REDUCE: (76), (185) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | (186) ~ (all_54_7 = e2)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | SIMP: (186) implies:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | (187) ~ (all_54_7 = e2)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | (188) all_56_6 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (188) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | (189) all_54_7 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (189) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | (190) $false
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | (191) all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | (192) all_58_2 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (192) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | (193) e3 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (193) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | (194) $false
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | (195) all_58_3 = e0 | all_58_4 = e0 | all_58_10 = e0
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (196) all_58_1 = e1
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (196) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (197) all_54_4 = e1
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (197) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_54_7 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_54_7 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (197) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (200) ~ (all_54_12 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (201) ~ (all_54_12 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (197) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | (202) ~ (e2 = e1)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | (203) all_56_12 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (203) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | (204) all_54_12 = e3
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (204) imply:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | (205) ~ (all_54_15 = e3)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_54_15 = e3)
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.89 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | (207) all_56_14 = e3
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (206), (207) are inconsistent by sub-proof
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | #71.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | (208) all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_58_6 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (209) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | (210) e2 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | (211) e2 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (211) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | (212) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_7 = e2 | all_58_8 = e2 | all_58_9 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_56_6 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (214) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_54_7 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (215) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (216) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (216) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_56_6 = e1 | all_56_6 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_9 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (218) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_54_15 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (219) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) ~ (all_54_3 = e2)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_56_1 = e3
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (221) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_54_1 = e3
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_54_1 = e3
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (223) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_56_6 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (226) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_54_7 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (227) implies:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_54_7 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (228) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_56_6 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (230) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_54_7 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_54_7 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (232) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_58_7 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_58_3 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (234) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_1 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (235) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (e2 = e0)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e2, e1, e0, e0,
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (53), (132) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) e2 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (237) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_58_9 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_58_7 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (239) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) e2 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (240) implies:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) e2 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (241) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_58_8 = e2 | all_58_9 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_8 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (244) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_54_3 = e2
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (245) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (238) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) e2 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (237) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_58_3 = e0)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (249) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_54_1 = e0)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (54), (177), (225), (250) are inconsistent
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #117.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_58_9 = e2)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (251) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) ~ (all_54_15 = e2)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (98), (131), (208), (252) are inconsistent
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #69.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | (253) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (49), (157), (201), (253) are inconsistent
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #67.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_58_1 = e1)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (254) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | (255) ~ (all_54_4 = e1)
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (156), (166), (255) are inconsistent by
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | (256) all_56_7 = e1 | all_56_7 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (257) all_56_7 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (257) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (258) all_54_6 = e1
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (258) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (259) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (260) all_56_7 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (260) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (261) all_54_6 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (261) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | (262) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | Case 2:
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | (263) all_56_3 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (263) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | (264) all_54_2 = e0
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | REDUCE: (129), (264) imply:
% 65.94/9.90 | | | | | | | | | | | | | | | | | (265) $false
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 65.94/9.90 | | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | | |
% 65.94/9.90 | | | | | | | | | End of split
% 65.94/9.90 | | | | | | | | |
% 65.94/9.90 | | | | | | | | End of split
% 65.94/9.90 | | | | | | | |
% 65.94/9.90 | | | | | | | End of split
% 65.94/9.90 | | | | | | |
% 65.94/9.90 | | | | | | End of split
% 65.94/9.90 | | | | | |
% 65.94/9.90 | | | | | End of split
% 65.94/9.90 | | | | |
% 65.94/9.90 | | | | End of split
% 65.94/9.90 | | | |
% 65.94/9.90 | | | Case 2:
% 65.94/9.90 | | | |
% 65.94/9.90 | | | | (266) all_52_3 = e3 & ~ (all_52_2 = e0)
% 65.94/9.90 | | | |
% 65.94/9.90 | | | | REF_CLOSE: (57), (68), (266) are inconsistent by sub-proof #153.
% 65.94/9.90 | | | |
% 65.94/9.90 | | | End of split
% 65.94/9.90 | | |
% 65.94/9.90 | | End of split
% 65.94/9.90 | |
% 65.94/9.90 | Case 2:
% 65.94/9.90 | |
% 65.94/9.90 | | (267) ~ (all_16_2 = e2)
% 65.94/9.90 | |
% 65.94/9.90 | | REDUCE: (65), (267) imply:
% 65.94/9.90 | | (268) $false
% 65.94/9.90 | |
% 65.94/9.90 | | CLOSE: (268) is inconsistent.
% 65.94/9.90 | |
% 65.94/9.90 | End of split
% 65.94/9.90 |
% 65.94/9.90 End of proof
% 65.94/9.90
% 65.94/9.90 Sub-proof #67 shows that the following formulas are inconsistent:
% 65.94/9.90 ----------------------------------------------------------------
% 65.94/9.90 (1) ~ (all_54_12 = e1)
% 65.94/9.90 (2) ~ (all_54_12 = e0)
% 65.94/9.90 (3) ~ (all_54_12 = e2)
% 65.94/9.90 (4) all_56_12 = all_54_12
% 65.94/9.90 (5) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 65.94/9.90
% 65.94/9.90 Begin of proof
% 65.94/9.90 |
% 65.94/9.90 | BETA: splitting (5) gives:
% 65.94/9.90 |
% 65.94/9.90 | Case 1:
% 65.94/9.90 | |
% 65.94/9.90 | | (6) all_56_12 = e2
% 65.94/9.90 | |
% 65.94/9.90 | | COMBINE_EQS: (4), (6) imply:
% 65.94/9.90 | | (7) all_54_12 = e2
% 65.94/9.90 | |
% 65.94/9.90 | | REDUCE: (3), (7) imply:
% 65.94/9.90 | | (8) $false
% 65.94/9.90 | |
% 65.94/9.90 | | CLOSE: (8) is inconsistent.
% 65.94/9.90 | |
% 65.94/9.90 | Case 2:
% 65.94/9.90 | |
% 65.94/9.90 | | (9) all_56_12 = e1 | all_56_12 = e0
% 65.94/9.90 | |
% 65.94/9.90 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #68.
% 65.94/9.90 | |
% 65.94/9.90 | End of split
% 65.94/9.90 |
% 65.94/9.90 End of proof
% 65.94/9.90
% 65.94/9.90 Sub-proof #68 shows that the following formulas are inconsistent:
% 65.94/9.90 ----------------------------------------------------------------
% 65.94/9.90 (1) all_56_12 = e1 | all_56_12 = e0
% 65.94/9.90 (2) all_56_12 = all_54_12
% 65.94/9.90 (3) ~ (all_54_12 = e1)
% 65.94/9.90 (4) ~ (all_54_12 = e0)
% 65.94/9.90
% 65.94/9.90 Begin of proof
% 65.94/9.90 |
% 65.94/9.90 | BETA: splitting (1) gives:
% 65.94/9.90 |
% 66.36/9.90 | Case 1:
% 66.36/9.90 | |
% 66.36/9.90 | | (5) all_56_12 = e1
% 66.36/9.90 | |
% 66.36/9.90 | | COMBINE_EQS: (2), (5) imply:
% 66.36/9.90 | | (6) all_54_12 = e1
% 66.36/9.90 | |
% 66.36/9.90 | | REDUCE: (3), (6) imply:
% 66.36/9.90 | | (7) $false
% 66.36/9.90 | |
% 66.36/9.90 | | CLOSE: (7) is inconsistent.
% 66.36/9.90 | |
% 66.36/9.90 | Case 2:
% 66.36/9.90 | |
% 66.36/9.90 | | (8) all_56_12 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | COMBINE_EQS: (2), (8) imply:
% 66.36/9.90 | | (9) all_54_12 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | REDUCE: (4), (9) imply:
% 66.36/9.90 | | (10) $false
% 66.36/9.90 | |
% 66.36/9.90 | | CLOSE: (10) is inconsistent.
% 66.36/9.90 | |
% 66.36/9.90 | End of split
% 66.36/9.90 |
% 66.36/9.90 End of proof
% 66.36/9.90
% 66.36/9.90 Sub-proof #69 shows that the following formulas are inconsistent:
% 66.36/9.90 ----------------------------------------------------------------
% 66.36/9.90 (1) ~ (all_54_15 = e1)
% 66.36/9.90 (2) ~ (all_54_15 = e0)
% 66.36/9.90 (3) all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 66.36/9.90 (4) ~ (all_54_15 = e2)
% 66.36/9.90 (5) all_56_14 = all_54_15
% 66.36/9.90
% 66.36/9.90 Begin of proof
% 66.36/9.90 |
% 66.36/9.90 | BETA: splitting (3) gives:
% 66.36/9.90 |
% 66.36/9.90 | Case 1:
% 66.36/9.90 | |
% 66.36/9.90 | | (6) all_56_14 = e2
% 66.36/9.90 | |
% 66.36/9.90 | | COMBINE_EQS: (5), (6) imply:
% 66.36/9.90 | | (7) all_54_15 = e2
% 66.36/9.90 | |
% 66.36/9.90 | | SIMP: (7) implies:
% 66.36/9.90 | | (8) all_54_15 = e2
% 66.36/9.90 | |
% 66.36/9.90 | | REDUCE: (4), (8) imply:
% 66.36/9.90 | | (9) $false
% 66.36/9.90 | |
% 66.36/9.90 | | CLOSE: (9) is inconsistent.
% 66.36/9.90 | |
% 66.36/9.90 | Case 2:
% 66.36/9.90 | |
% 66.36/9.90 | | (10) all_56_14 = e1 | all_56_14 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #70.
% 66.36/9.90 | |
% 66.36/9.90 | End of split
% 66.36/9.90 |
% 66.36/9.90 End of proof
% 66.36/9.90
% 66.36/9.90 Sub-proof #70 shows that the following formulas are inconsistent:
% 66.36/9.90 ----------------------------------------------------------------
% 66.36/9.90 (1) all_56_14 = e1 | all_56_14 = e0
% 66.36/9.90 (2) all_56_14 = all_54_15
% 66.36/9.90 (3) ~ (all_54_15 = e1)
% 66.36/9.90 (4) ~ (all_54_15 = e0)
% 66.36/9.90
% 66.36/9.90 Begin of proof
% 66.36/9.90 |
% 66.36/9.90 | BETA: splitting (1) gives:
% 66.36/9.90 |
% 66.36/9.90 | Case 1:
% 66.36/9.90 | |
% 66.36/9.90 | | (5) all_56_14 = e1
% 66.36/9.90 | |
% 66.36/9.90 | | COMBINE_EQS: (2), (5) imply:
% 66.36/9.90 | | (6) all_54_15 = e1
% 66.36/9.90 | |
% 66.36/9.90 | | SIMP: (6) implies:
% 66.36/9.90 | | (7) all_54_15 = e1
% 66.36/9.90 | |
% 66.36/9.90 | | REDUCE: (3), (7) imply:
% 66.36/9.90 | | (8) $false
% 66.36/9.90 | |
% 66.36/9.90 | | CLOSE: (8) is inconsistent.
% 66.36/9.90 | |
% 66.36/9.90 | Case 2:
% 66.36/9.90 | |
% 66.36/9.90 | | (9) all_56_14 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | COMBINE_EQS: (2), (9) imply:
% 66.36/9.90 | | (10) all_54_15 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | SIMP: (10) implies:
% 66.36/9.90 | | (11) all_54_15 = e0
% 66.36/9.90 | |
% 66.36/9.90 | | REDUCE: (4), (11) imply:
% 66.36/9.90 | | (12) $false
% 66.36/9.90 | |
% 66.36/9.90 | | CLOSE: (12) is inconsistent.
% 66.36/9.90 | |
% 66.36/9.90 | End of split
% 66.36/9.90 |
% 66.36/9.90 End of proof
% 66.36/9.90
% 66.36/9.90 Sub-proof #71 shows that the following formulas are inconsistent:
% 66.36/9.90 ----------------------------------------------------------------
% 66.36/9.90 (1) all_56_14 = all_54_15
% 66.36/9.90 (2) all_56_14 = e3
% 66.36/9.90 (3) ~ (all_54_15 = e3)
% 66.36/9.90
% 66.36/9.90 Begin of proof
% 66.36/9.90 |
% 66.36/9.90 | COMBINE_EQS: (1), (2) imply:
% 66.36/9.90 | (4) all_54_15 = e3
% 66.36/9.90 |
% 66.36/9.90 | SIMP: (4) implies:
% 66.36/9.90 | (5) all_54_15 = e3
% 66.36/9.90 |
% 66.36/9.90 | REDUCE: (3), (5) imply:
% 66.36/9.90 | (6) $false
% 66.36/9.90 |
% 66.36/9.90 | CLOSE: (6) is inconsistent.
% 66.36/9.90 |
% 66.36/9.90 End of proof
% 66.36/9.90
% 66.36/9.90 Sub-proof #72 shows that the following formulas are inconsistent:
% 66.36/9.90 ----------------------------------------------------------------
% 66.36/9.90 (1) op(e1, e1) = all_14_2
% 66.36/9.90 (2) all_52_2 = all_4_2
% 66.36/9.90 (3) op(all_4_2, all_4_2) = e1
% 66.36/9.90 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.90 (5) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.90 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.90 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.90 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.90 (7) ~ (e3 = e1)
% 66.36/9.90 (8) op(e2, e2) = all_10_2
% 66.36/9.90 (9) all_52_1 = all_14_2
% 66.36/9.90 (10) ~ (e3 = e0)
% 66.36/9.90 (11) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.36/9.90 (12) ~ (e2 = e1)
% 66.36/9.90 (13) all_52_0 = all_10_2
% 66.36/9.90 (14) ~ (e3 = e2)
% 66.36/9.90 (15) op(all_14_2, all_14_2) = e0
% 66.36/9.90 (16) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 66.36/9.90
% 66.36/9.90 Begin of proof
% 66.36/9.90 |
% 66.36/9.90 | ALPHA: (11) implies:
% 66.36/9.90 | (17) all_52_1 = e2
% 66.36/9.90 | (18) ~ (all_52_0 = e1)
% 66.36/9.90 |
% 66.36/9.90 | COMBINE_EQS: (9), (17) imply:
% 66.36/9.90 | (19) all_14_2 = e2
% 66.36/9.90 |
% 66.36/9.90 | SIMP: (19) implies:
% 66.36/9.90 | (20) all_14_2 = e2
% 66.36/9.90 |
% 66.36/9.90 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 66.36/9.90 | (15), (16), (17), (18), (20) are inconsistent by sub-proof #73.
% 66.36/9.90 |
% 66.36/9.90 End of proof
% 66.36/9.90
% 66.36/9.90 Sub-proof #73 shows that the following formulas are inconsistent:
% 66.36/9.90 ----------------------------------------------------------------
% 66.36/9.91 (1) ~ (all_52_0 = e1)
% 66.36/9.91 (2) op(e1, e1) = all_14_2
% 66.36/9.91 (3) all_52_2 = all_4_2
% 66.36/9.91 (4) op(all_4_2, all_4_2) = e1
% 66.36/9.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.91 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.91 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.91 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.91 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.91 (8) ~ (e3 = e1)
% 66.36/9.91 (9) op(e2, e2) = all_10_2
% 66.36/9.91 (10) ~ (e3 = e0)
% 66.36/9.91 (11) all_14_2 = e2
% 66.36/9.91 (12) ~ (e2 = e1)
% 66.36/9.91 (13) all_52_0 = all_10_2
% 66.36/9.91 (14) all_52_1 = e2
% 66.36/9.91 (15) ~ (e3 = e2)
% 66.36/9.91 (16) op(all_14_2, all_14_2) = e0
% 66.36/9.91 (17) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 66.36/9.91
% 66.36/9.91 Begin of proof
% 66.36/9.91 |
% 66.36/9.91 | REDUCE: (1), (13) imply:
% 66.36/9.91 | (18) ~ (all_10_2 = e1)
% 66.36/9.91 |
% 66.36/9.91 | REDUCE: (11), (16) imply:
% 66.36/9.91 | (19) op(e2, e2) = e0
% 66.36/9.91 |
% 66.36/9.91 | REDUCE: (2), (11) imply:
% 66.36/9.91 | (20) op(e1, e1) = e2
% 66.36/9.91 |
% 66.36/9.91 | BETA: splitting (17) gives:
% 66.36/9.91 |
% 66.36/9.91 | Case 1:
% 66.36/9.91 | |
% 66.36/9.91 | |
% 66.36/9.91 | | GROUND_INST: instantiating (5) with all_10_2, e0, e2, e2, simplifying with
% 66.36/9.91 | | (9), (19) gives:
% 66.36/9.91 | | (21) all_10_2 = e0
% 66.36/9.91 | |
% 66.36/9.91 | | COMBINE_EQS: (13), (21) imply:
% 66.36/9.91 | | (22) all_52_0 = e0
% 66.36/9.91 | |
% 66.36/9.91 | | REDUCE: (18), (21) imply:
% 66.36/9.91 | | (23) ~ (e1 = e0)
% 66.36/9.91 | |
% 66.36/9.91 | | SIMP: (23) implies:
% 66.36/9.91 | | (24) ~ (e1 = e0)
% 66.36/9.91 | |
% 66.36/9.91 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (12), (14), (15), (20), (22),
% 66.36/9.91 | | (24) are inconsistent by sub-proof #144.
% 66.36/9.91 | |
% 66.36/9.91 | Case 2:
% 66.36/9.91 | |
% 66.36/9.91 | | (25) ~ (all_14_2 = e2)
% 66.36/9.91 | |
% 66.36/9.91 | | REDUCE: (11), (25) imply:
% 66.36/9.91 | | (26) $false
% 66.36/9.91 | |
% 66.36/9.91 | | CLOSE: (26) is inconsistent.
% 66.36/9.91 | |
% 66.36/9.91 | End of split
% 66.36/9.91 |
% 66.36/9.91 End of proof
% 66.36/9.91
% 66.36/9.91 Sub-proof #74 shows that the following formulas are inconsistent:
% 66.36/9.91 ----------------------------------------------------------------
% 66.36/9.91 (1) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.91 (2) all_52_3 = e2
% 66.36/9.91 (3) ~ (e3 = e2)
% 66.36/9.91
% 66.36/9.91 Begin of proof
% 66.36/9.91 |
% 66.36/9.91 | ALPHA: (1) implies:
% 66.36/9.91 | (4) all_52_3 = e3
% 66.36/9.91 |
% 66.36/9.91 | COMBINE_EQS: (2), (4) imply:
% 66.36/9.91 | (5) e3 = e2
% 66.36/9.91 |
% 66.36/9.91 | SIMP: (5) implies:
% 66.36/9.91 | (6) e3 = e2
% 66.36/9.91 |
% 66.36/9.91 | REDUCE: (3), (6) imply:
% 66.36/9.91 | (7) $false
% 66.36/9.91 |
% 66.36/9.91 | CLOSE: (7) is inconsistent.
% 66.36/9.91 |
% 66.36/9.91 End of proof
% 66.36/9.91
% 66.36/9.91 Sub-proof #75 shows that the following formulas are inconsistent:
% 66.36/9.91 ----------------------------------------------------------------
% 66.36/9.91 (1) op(e1, e1) = all_14_2
% 66.36/9.91 (2) all_52_2 = all_4_2
% 66.36/9.91 (3) op(all_4_2, all_4_2) = e1
% 66.36/9.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.91 (5) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.91 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.91 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.91 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.91 (7) ~ (e3 = e1)
% 66.36/9.91 (8) op(e2, e2) = all_10_2
% 66.36/9.91 (9) all_52_1 = all_14_2
% 66.36/9.91 (10) op(e2, e2) = all_6_0
% 66.36/9.91 (11) ~ (e3 = e0)
% 66.36/9.91 (12) ~ (e1 = e0)
% 66.36/9.91 (13) op(e0, e0) = e2
% 66.36/9.91 (14) all_52_3 = e2
% 66.36/9.91 (15) ~ (e2 = e0)
% 66.36/9.91 (16) ~ (e2 = e1)
% 66.36/9.91 (17) all_52_0 = all_10_2
% 66.36/9.91 (18) ~ (e3 = e2)
% 66.36/9.91 (19) op(all_14_2, all_14_2) = e0
% 66.36/9.91 (20) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.91 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.91 (21) ~ (all_6_0 = e1)
% 66.36/9.91
% 66.36/9.91 Begin of proof
% 66.36/9.91 |
% 66.36/9.91 | GROUND_INST: instantiating (4) with all_10_2, all_6_0, e2, e2, simplifying
% 66.36/9.91 | with (8), (10) gives:
% 66.36/9.91 | (22) all_10_2 = all_6_0
% 66.36/9.91 |
% 66.36/9.91 | COMBINE_EQS: (17), (22) imply:
% 66.36/9.91 | (23) all_52_0 = all_6_0
% 66.36/9.91 |
% 66.36/9.91 | BETA: splitting (6) gives:
% 66.36/9.91 |
% 66.36/9.91 | Case 1:
% 66.36/9.91 | |
% 66.36/9.91 | | (24) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.91 | |
% 66.36/9.91 | | ALPHA: (24) implies:
% 66.36/9.91 | | (25) all_52_0 = e1
% 66.36/9.91 | |
% 66.36/9.91 | | COMBINE_EQS: (23), (25) imply:
% 66.36/9.91 | | (26) all_6_0 = e1
% 66.36/9.91 | |
% 66.36/9.91 | | SIMP: (26) implies:
% 66.36/9.91 | | (27) all_6_0 = e1
% 66.36/9.91 | |
% 66.36/9.91 | | REDUCE: (21), (27) imply:
% 66.36/9.91 | | (28) $false
% 66.36/9.91 | |
% 66.36/9.91 | | CLOSE: (28) is inconsistent.
% 66.36/9.91 | |
% 66.36/9.91 | Case 2:
% 66.36/9.91 | |
% 66.36/9.91 | | (29) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.91 | | = e0))
% 66.36/9.91 | |
% 66.36/9.91 | | BETA: splitting (29) gives:
% 66.36/9.91 | |
% 66.36/9.91 | | Case 1:
% 66.36/9.91 | | |
% 66.36/9.91 | | | (30) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.91 | | |
% 66.36/9.91 | | | ALPHA: (30) implies:
% 66.36/9.91 | | | (31) all_52_2 = e1
% 66.36/9.91 | | |
% 66.36/9.91 | | | COMBINE_EQS: (2), (31) imply:
% 66.36/9.91 | | | (32) all_4_2 = e1
% 66.36/9.91 | | |
% 66.36/9.91 | | | SIMP: (32) implies:
% 66.36/9.91 | | | (33) all_4_2 = e1
% 66.36/9.91 | | |
% 66.36/9.91 | | | REDUCE: (3), (33) imply:
% 66.36/9.91 | | | (34) op(e1, e1) = e1
% 66.36/9.91 | | |
% 66.36/9.91 | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 66.36/9.91 | | | (16), (18), (19), (20), (34) are inconsistent by sub-proof #76.
% 66.36/9.91 | | |
% 66.36/9.91 | | Case 2:
% 66.36/9.91 | | |
% 66.36/9.91 | | | (35) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.91 | | |
% 66.36/9.91 | | | REF_CLOSE: (14), (16), (35) are inconsistent by sub-proof #151.
% 66.36/9.91 | | |
% 66.36/9.91 | | End of split
% 66.36/9.91 | |
% 66.36/9.91 | End of split
% 66.36/9.91 |
% 66.36/9.91 End of proof
% 66.36/9.91
% 66.36/9.91 Sub-proof #76 shows that the following formulas are inconsistent:
% 66.36/9.91 ----------------------------------------------------------------
% 66.36/9.91 (1) op(e1, e1) = all_14_2
% 66.36/9.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.91 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.91 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.91 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.91 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.91 (5) ~ (e3 = e1)
% 66.36/9.91 (6) op(e1, e1) = e1
% 66.36/9.91 (7) all_52_1 = all_14_2
% 66.36/9.91 (8) ~ (e3 = e0)
% 66.36/9.91 (9) ~ (e1 = e0)
% 66.36/9.91 (10) op(e0, e0) = e2
% 66.36/9.91 (11) all_52_3 = e2
% 66.36/9.91 (12) ~ (e2 = e0)
% 66.36/9.91 (13) ~ (e2 = e1)
% 66.36/9.91 (14) ~ (e3 = e2)
% 66.36/9.91 (15) op(all_14_2, all_14_2) = e0
% 66.36/9.91 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.91 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.91
% 66.36/9.91 Begin of proof
% 66.36/9.91 |
% 66.36/9.91 | BETA: splitting (3) gives:
% 66.36/9.91 |
% 66.36/9.91 | Case 1:
% 66.36/9.91 | |
% 66.36/9.91 | | (17) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.91 | |
% 66.36/9.91 | | ALPHA: (17) implies:
% 66.36/9.91 | | (18) all_52_0 = e3
% 66.36/9.91 | |
% 66.36/9.91 | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15), (16),
% 66.36/9.91 | | (18) are inconsistent by sub-proof #80.
% 66.36/9.91 | |
% 66.36/9.91 | Case 2:
% 66.36/9.91 | |
% 66.36/9.91 | | (19) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.36/9.91 | | = e0))
% 66.36/9.91 | |
% 66.36/9.91 | | REF_CLOSE: (1), (2), (5), (6), (7), (11), (14), (19) are inconsistent by
% 66.36/9.91 | | sub-proof #77.
% 66.36/9.91 | |
% 66.36/9.91 | End of split
% 66.36/9.91 |
% 66.36/9.91 End of proof
% 66.36/9.91
% 66.36/9.91 Sub-proof #77 shows that the following formulas are inconsistent:
% 66.36/9.91 ----------------------------------------------------------------
% 66.36/9.91 (1) op(e1, e1) = all_14_2
% 66.36/9.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.91 (3) ~ (e3 = e1)
% 66.36/9.91 (4) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2 =
% 66.36/9.91 e0))
% 66.36/9.91 (5) op(e1, e1) = e1
% 66.36/9.91 (6) all_52_1 = all_14_2
% 66.36/9.91 (7) all_52_3 = e2
% 66.36/9.91 (8) ~ (e3 = e2)
% 66.36/9.91
% 66.36/9.91 Begin of proof
% 66.36/9.91 |
% 66.36/9.91 | BETA: splitting (4) gives:
% 66.36/9.91 |
% 66.36/9.91 | Case 1:
% 66.36/9.91 | |
% 66.36/9.91 | | (9) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.91 | |
% 66.36/9.91 | | ALPHA: (9) implies:
% 66.36/9.91 | | (10) all_52_1 = e3
% 66.36/9.91 | |
% 66.36/9.91 | | COMBINE_EQS: (6), (10) imply:
% 66.36/9.91 | | (11) all_14_2 = e3
% 66.36/9.91 | |
% 66.36/9.91 | | SIMP: (11) implies:
% 66.36/9.91 | | (12) all_14_2 = e3
% 66.36/9.91 | |
% 66.36/9.91 | | REDUCE: (1), (12) imply:
% 66.36/9.91 | | (13) op(e1, e1) = e3
% 66.36/9.91 | |
% 66.36/9.91 | | GROUND_INST: instantiating (2) with e1, e3, e1, e1, simplifying with (5),
% 66.36/9.91 | | (13) gives:
% 66.36/9.91 | | (14) e3 = e1
% 66.36/9.91 | |
% 66.36/9.91 | | REDUCE: (3), (14) imply:
% 66.36/9.91 | | (15) $false
% 66.36/9.91 | |
% 66.36/9.91 | | CLOSE: (15) is inconsistent.
% 66.36/9.91 | |
% 66.36/9.91 | Case 2:
% 66.36/9.91 | |
% 66.36/9.91 | | (16) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.91 | |
% 66.36/9.91 | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #153.
% 66.36/9.91 | |
% 66.36/9.91 | End of split
% 66.36/9.91 |
% 66.36/9.91 End of proof
% 66.36/9.91
% 66.36/9.91 Sub-proof #78 shows that the following formulas are inconsistent:
% 66.36/9.91 ----------------------------------------------------------------
% 66.36/9.91 (1) all_52_0 = e1
% 66.36/9.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.91 (3) op(e0, e0) = all_6_2
% 66.36/9.91 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.91 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.91 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.91 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.91 (6) ~ (e3 = e1)
% 66.36/9.91 (7) all_52_1 = all_14_2
% 66.36/9.92 (8) ~ (e3 = e0)
% 66.36/9.92 (9) ~ (e1 = e0)
% 66.36/9.92 (10) op(e3, e3) = e2
% 66.36/9.92 (11) ~ (e2 = e0)
% 66.36/9.92 (12) ~ (e2 = e1)
% 66.36/9.92 (13) all_52_3 = all_6_2
% 66.36/9.92 (14) all_52_2 = e2
% 66.36/9.92 (15) op(all_14_2, all_14_2) = e0
% 66.36/9.92 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.92 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.92
% 66.36/9.92 Begin of proof
% 66.36/9.92 |
% 66.36/9.92 | BETA: splitting (16) gives:
% 66.36/9.92 |
% 66.36/9.92 | Case 1:
% 66.36/9.92 | |
% 66.36/9.92 | | (17) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.92 | |
% 66.36/9.92 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 66.36/9.92 | | (17) are inconsistent by sub-proof #87.
% 66.36/9.92 | |
% 66.36/9.92 | Case 2:
% 66.36/9.92 | |
% 66.36/9.92 | | (18) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.92 | | = e3))
% 66.36/9.92 | |
% 66.36/9.92 | | BETA: splitting (18) gives:
% 66.36/9.92 | |
% 66.36/9.92 | | Case 1:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (19) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.92 | | |
% 66.36/9.92 | | | ALPHA: (19) implies:
% 66.36/9.92 | | | (20) all_52_1 = e0
% 66.36/9.92 | | |
% 66.36/9.92 | | | COMBINE_EQS: (7), (20) imply:
% 66.36/9.92 | | | (21) all_14_2 = e0
% 66.36/9.92 | | |
% 66.36/9.92 | | | SIMP: (21) implies:
% 66.36/9.92 | | | (22) all_14_2 = e0
% 66.36/9.92 | | |
% 66.36/9.92 | | | REDUCE: (15), (22) imply:
% 66.36/9.92 | | | (23) op(e0, e0) = e0
% 66.36/9.92 | | |
% 66.36/9.92 | | | BETA: splitting (4) gives:
% 66.36/9.92 | | |
% 66.36/9.92 | | | Case 1:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (24) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | REF_CLOSE: (1), (6), (24) are inconsistent by sub-proof #132.
% 66.36/9.92 | | | |
% 66.36/9.92 | | | Case 2:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (25) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.36/9.92 | | | | (all_52_2 = e0))
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | BETA: splitting (25) gives:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | Case 1:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (26) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REF_CLOSE: (8), (20), (26) are inconsistent by sub-proof #154.
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | Case 2:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (27) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | ALPHA: (27) implies:
% 66.36/9.92 | | | | | (28) all_52_3 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | COMBINE_EQS: (13), (28) imply:
% 66.36/9.92 | | | | | (29) all_6_2 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | SIMP: (29) implies:
% 66.36/9.92 | | | | | (30) all_6_2 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REDUCE: (3), (30) imply:
% 66.36/9.92 | | | | | (31) op(e0, e0) = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | GROUND_INST: instantiating (2) with e0, e3, e0, e0, simplifying with
% 66.36/9.92 | | | | | (23), (31) gives:
% 66.36/9.92 | | | | | (32) e3 = e0
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REDUCE: (8), (32) imply:
% 66.36/9.92 | | | | | (33) $false
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | CLOSE: (33) is inconsistent.
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | End of split
% 66.36/9.92 | | | |
% 66.36/9.92 | | | End of split
% 66.36/9.92 | | |
% 66.36/9.92 | | Case 2:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (34) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.92 | | |
% 66.36/9.92 | | | REF_CLOSE: (11), (14), (34) are inconsistent by sub-proof #131.
% 66.36/9.92 | | |
% 66.36/9.92 | | End of split
% 66.36/9.92 | |
% 66.36/9.92 | End of split
% 66.36/9.92 |
% 66.36/9.92 End of proof
% 66.36/9.92
% 66.36/9.92 Sub-proof #79 shows that the following formulas are inconsistent:
% 66.36/9.92 ----------------------------------------------------------------
% 66.36/9.92 (1) all_52_2 = all_4_2
% 66.36/9.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.92 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.92 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.92 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.92 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.92 (5) ~ (e3 = e1)
% 66.36/9.92 (6) all_52_1 = all_14_2
% 66.36/9.92 (7) ~ (e3 = e0)
% 66.36/9.92 (8) ~ (e1 = e0)
% 66.36/9.92 (9) op(e0, e0) = e2
% 66.36/9.92 (10) all_52_3 = e2
% 66.36/9.92 (11) ~ (e2 = e0)
% 66.36/9.92 (12) ~ (e2 = e1)
% 66.36/9.92 (13) op(all_4_2, all_4_2) = e0
% 66.36/9.92 (14) ~ (e3 = e2)
% 66.36/9.92 (15) op(all_14_2, all_14_2) = e0
% 66.36/9.92 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.92 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.92
% 66.36/9.92 Begin of proof
% 66.36/9.92 |
% 66.36/9.92 | BETA: splitting (4) gives:
% 66.36/9.92 |
% 66.36/9.92 | Case 1:
% 66.36/9.92 | |
% 66.36/9.92 | | (17) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.92 | |
% 66.36/9.92 | | ALPHA: (17) implies:
% 66.36/9.92 | | (18) all_52_0 = e1
% 66.36/9.92 | |
% 66.36/9.92 | | BETA: splitting (3) gives:
% 66.36/9.92 | |
% 66.36/9.92 | | Case 1:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (19) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.92 | | |
% 66.36/9.92 | | | ALPHA: (19) implies:
% 66.36/9.92 | | | (20) all_52_0 = e3
% 66.36/9.92 | | |
% 66.36/9.92 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 66.36/9.92 | | | (16), (20) are inconsistent by sub-proof #80.
% 66.36/9.92 | | |
% 66.36/9.92 | | Case 2:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (21) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.36/9.92 | | | (all_52_2 = e0))
% 66.36/9.92 | | |
% 66.36/9.92 | | | BETA: splitting (21) gives:
% 66.36/9.92 | | |
% 66.36/9.92 | | | Case 1:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (22) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | ALPHA: (22) implies:
% 66.36/9.92 | | | | (23) all_52_1 = e3
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | BETA: splitting (16) gives:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | Case 1:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (24) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | ALPHA: (24) implies:
% 66.36/9.92 | | | | | (25) all_52_0 = e0
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REF_CLOSE: (8), (18), (25) are inconsistent by sub-proof #133.
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | Case 2:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (26) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.36/9.92 | | | | | (all_52_3 = e3))
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | BETA: splitting (26) gives:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | Case 1:
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | (27) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | ALPHA: (27) implies:
% 66.36/9.92 | | | | | | (28) all_52_1 = e0
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | REF_CLOSE: (7), (23), (28) are inconsistent by sub-proof #102.
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | Case 2:
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | (29) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | ALPHA: (29) implies:
% 66.36/9.92 | | | | | | (30) all_52_2 = e0
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | COMBINE_EQS: (1), (30) imply:
% 66.36/9.92 | | | | | | (31) all_4_2 = e0
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | SIMP: (31) implies:
% 66.36/9.92 | | | | | | (32) all_4_2 = e0
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | REDUCE: (13), (32) imply:
% 66.36/9.92 | | | | | | (33) op(e0, e0) = e0
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | | REF_CLOSE: (2), (9), (11), (33) are inconsistent by sub-proof #82.
% 66.36/9.92 | | | | | |
% 66.36/9.92 | | | | | End of split
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | End of split
% 66.36/9.92 | | | |
% 66.36/9.92 | | | Case 2:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (34) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | REF_CLOSE: (10), (14), (34) are inconsistent by sub-proof #153.
% 66.36/9.92 | | | |
% 66.36/9.92 | | | End of split
% 66.36/9.92 | | |
% 66.36/9.92 | | End of split
% 66.36/9.92 | |
% 66.36/9.92 | Case 2:
% 66.36/9.92 | |
% 66.36/9.92 | | (35) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.92 | | = e0))
% 66.36/9.92 | |
% 66.36/9.92 | | BETA: splitting (35) gives:
% 66.36/9.92 | |
% 66.36/9.92 | | Case 1:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (36) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.92 | | |
% 66.36/9.92 | | | ALPHA: (36) implies:
% 66.36/9.92 | | | (37) all_52_2 = e1
% 66.36/9.92 | | | (38) ~ (all_52_1 = e3)
% 66.36/9.92 | | |
% 66.36/9.92 | | | REDUCE: (6), (38) imply:
% 66.36/9.92 | | | (39) ~ (all_14_2 = e3)
% 66.36/9.92 | | |
% 66.36/9.92 | | | BETA: splitting (3) gives:
% 66.36/9.92 | | |
% 66.36/9.92 | | | Case 1:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (40) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | ALPHA: (40) implies:
% 66.36/9.92 | | | | (41) all_52_0 = e3
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (15), (16), (37), (41) are
% 66.36/9.92 | | | | inconsistent by sub-proof #81.
% 66.36/9.92 | | | |
% 66.36/9.92 | | | Case 2:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | (42) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.36/9.92 | | | | (all_52_2 = e0))
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | BETA: splitting (42) gives:
% 66.36/9.92 | | | |
% 66.36/9.92 | | | | Case 1:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (43) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | ALPHA: (43) implies:
% 66.36/9.92 | | | | | (44) all_52_1 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | COMBINE_EQS: (6), (44) imply:
% 66.36/9.92 | | | | | (45) all_14_2 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | SIMP: (45) implies:
% 66.36/9.92 | | | | | (46) all_14_2 = e3
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REDUCE: (39), (46) imply:
% 66.36/9.92 | | | | | (47) $false
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | CLOSE: (47) is inconsistent.
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | Case 2:
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | (48) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | | REF_CLOSE: (10), (14), (48) are inconsistent by sub-proof #153.
% 66.36/9.92 | | | | |
% 66.36/9.92 | | | | End of split
% 66.36/9.92 | | | |
% 66.36/9.92 | | | End of split
% 66.36/9.92 | | |
% 66.36/9.92 | | Case 2:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (49) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.92 | | |
% 66.36/9.92 | | | REF_CLOSE: (10), (12), (49) are inconsistent by sub-proof #151.
% 66.36/9.92 | | |
% 66.36/9.92 | | End of split
% 66.36/9.92 | |
% 66.36/9.92 | End of split
% 66.36/9.92 |
% 66.36/9.92 End of proof
% 66.36/9.92
% 66.36/9.92 Sub-proof #80 shows that the following formulas are inconsistent:
% 66.36/9.92 ----------------------------------------------------------------
% 66.36/9.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.92 (2) all_52_0 = e3
% 66.36/9.92 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.92 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.92 (4) ~ (e3 = e1)
% 66.36/9.92 (5) all_52_1 = all_14_2
% 66.36/9.92 (6) ~ (e3 = e0)
% 66.36/9.92 (7) ~ (e1 = e0)
% 66.36/9.92 (8) op(e0, e0) = e2
% 66.36/9.92 (9) all_52_3 = e2
% 66.36/9.92 (10) ~ (e2 = e0)
% 66.36/9.92 (11) ~ (e2 = e1)
% 66.36/9.92 (12) op(all_14_2, all_14_2) = e0
% 66.36/9.92 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.92 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.92
% 66.36/9.92 Begin of proof
% 66.36/9.92 |
% 66.36/9.92 | BETA: splitting (3) gives:
% 66.36/9.92 |
% 66.36/9.92 | Case 1:
% 66.36/9.92 | |
% 66.36/9.92 | | (14) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.92 | |
% 66.36/9.92 | | ALPHA: (14) implies:
% 66.36/9.92 | | (15) all_52_0 = e1
% 66.36/9.92 | |
% 66.36/9.92 | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #122.
% 66.36/9.92 | |
% 66.36/9.92 | Case 2:
% 66.36/9.92 | |
% 66.36/9.92 | | (16) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.92 | | = e0))
% 66.36/9.92 | |
% 66.36/9.92 | | BETA: splitting (16) gives:
% 66.36/9.92 | |
% 66.36/9.92 | | Case 1:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (17) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.92 | | |
% 66.36/9.92 | | | ALPHA: (17) implies:
% 66.36/9.92 | | | (18) all_52_2 = e1
% 66.36/9.92 | | |
% 66.36/9.92 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (12), (13), (18) are
% 66.36/9.92 | | | inconsistent by sub-proof #81.
% 66.36/9.92 | | |
% 66.36/9.92 | | Case 2:
% 66.36/9.92 | | |
% 66.36/9.92 | | | (19) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.92 | | |
% 66.36/9.92 | | | REF_CLOSE: (9), (11), (19) are inconsistent by sub-proof #151.
% 66.36/9.92 | | |
% 66.36/9.92 | | End of split
% 66.36/9.92 | |
% 66.36/9.92 | End of split
% 66.36/9.92 |
% 66.36/9.92 End of proof
% 66.36/9.92
% 66.36/9.92 Sub-proof #81 shows that the following formulas are inconsistent:
% 66.36/9.92 ----------------------------------------------------------------
% 66.36/9.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.92 (2) all_52_2 = e1
% 66.36/9.92 (3) all_52_0 = e3
% 66.36/9.92 (4) all_52_1 = all_14_2
% 66.36/9.92 (5) ~ (e3 = e0)
% 66.36/9.92 (6) ~ (e1 = e0)
% 66.36/9.92 (7) op(e0, e0) = e2
% 66.36/9.92 (8) ~ (e2 = e0)
% 66.36/9.92 (9) op(all_14_2, all_14_2) = e0
% 66.36/9.92 (10) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.92 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.92
% 66.36/9.92 Begin of proof
% 66.36/9.92 |
% 66.36/9.92 | BETA: splitting (10) gives:
% 66.36/9.92 |
% 66.36/9.92 | Case 1:
% 66.36/9.92 | |
% 66.36/9.92 | | (11) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.92 | |
% 66.36/9.92 | | ALPHA: (11) implies:
% 66.36/9.92 | | (12) all_52_0 = e0
% 66.36/9.92 | |
% 66.36/9.92 | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #124.
% 66.36/9.92 | |
% 66.36/9.92 | Case 2:
% 66.36/9.92 | |
% 66.36/9.93 | | (13) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.93 | | = e3))
% 66.36/9.93 | |
% 66.36/9.93 | | BETA: splitting (13) gives:
% 66.36/9.93 | |
% 66.36/9.93 | | Case 1:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (14) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.93 | | |
% 66.36/9.93 | | | ALPHA: (14) implies:
% 66.36/9.93 | | | (15) all_52_1 = e0
% 66.36/9.93 | | |
% 66.36/9.93 | | | COMBINE_EQS: (4), (15) imply:
% 66.36/9.93 | | | (16) all_14_2 = e0
% 66.36/9.93 | | |
% 66.36/9.93 | | | SIMP: (16) implies:
% 66.36/9.93 | | | (17) all_14_2 = e0
% 66.36/9.93 | | |
% 66.36/9.93 | | | REDUCE: (9), (17) imply:
% 66.36/9.93 | | | (18) op(e0, e0) = e0
% 66.36/9.93 | | |
% 66.36/9.93 | | | REF_CLOSE: (1), (7), (8), (18) are inconsistent by sub-proof #82.
% 66.36/9.93 | | |
% 66.36/9.93 | | Case 2:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (19) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.93 | | |
% 66.36/9.93 | | | ALPHA: (19) implies:
% 66.36/9.93 | | | (20) all_52_2 = e0
% 66.36/9.93 | | |
% 66.36/9.93 | | | REF_CLOSE: (2), (6), (20) are inconsistent by sub-proof #152.
% 66.36/9.93 | | |
% 66.36/9.93 | | End of split
% 66.36/9.93 | |
% 66.36/9.93 | End of split
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #82 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (2) op(e0, e0) = e2
% 66.36/9.93 (3) op(e0, e0) = e0
% 66.36/9.93 (4) ~ (e2 = e0)
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | GROUND_INST: instantiating (1) with e2, e0, e0, e0, simplifying with (2), (3)
% 66.36/9.93 | gives:
% 66.36/9.93 | (5) e2 = e0
% 66.36/9.93 |
% 66.36/9.93 | REDUCE: (4), (5) imply:
% 66.36/9.93 | (6) $false
% 66.36/9.93 |
% 66.36/9.93 | CLOSE: (6) is inconsistent.
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #83 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) all_52_2 = all_4_2
% 66.36/9.93 (2) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.93 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.93 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.93 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.93 (6) ~ (e3 = e1)
% 66.36/9.93 (7) op(e2, e2) = all_10_2
% 66.36/9.93 (8) ~ (all_4_0 = e1)
% 66.36/9.93 (9) all_52_1 = all_14_2
% 66.36/9.93 (10) ~ (e3 = e0)
% 66.36/9.93 (11) ~ (e1 = e0)
% 66.36/9.93 (12) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.36/9.93 (13) op(e3, e3) = all_4_2
% 66.36/9.93 (14) ~ (e2 = e0)
% 66.36/9.93 (15) ~ (e2 = e1)
% 66.36/9.93 (16) all_52_0 = all_10_2
% 66.36/9.93 (17) op(all_14_2, all_14_2) = e0
% 66.36/9.93 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.93 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | ALPHA: (12) implies:
% 66.36/9.93 | (19) all_52_2 = e2
% 66.36/9.93 |
% 66.36/9.93 | COMBINE_EQS: (1), (19) imply:
% 66.36/9.93 | (20) all_4_2 = e2
% 66.36/9.93 |
% 66.36/9.93 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 66.36/9.93 | (15), (16), (17), (18), (19), (20) are inconsistent by sub-proof
% 66.36/9.93 | #84.
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #84 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.93 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.93 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.93 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.93 (5) ~ (e3 = e1)
% 66.36/9.93 (6) op(e2, e2) = all_10_2
% 66.36/9.93 (7) ~ (all_4_0 = e1)
% 66.36/9.93 (8) all_52_1 = all_14_2
% 66.36/9.93 (9) ~ (e3 = e0)
% 66.36/9.93 (10) ~ (e1 = e0)
% 66.36/9.93 (11) all_4_2 = e2
% 66.36/9.93 (12) op(e3, e3) = all_4_2
% 66.36/9.93 (13) ~ (e2 = e0)
% 66.36/9.93 (14) ~ (e2 = e1)
% 66.36/9.93 (15) all_52_0 = all_10_2
% 66.36/9.93 (16) all_52_2 = e2
% 66.36/9.93 (17) op(all_14_2, all_14_2) = e0
% 66.36/9.93 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.93 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | REDUCE: (1), (11) imply:
% 66.36/9.93 | (19) op(e2, e2) = all_4_0
% 66.36/9.93 |
% 66.36/9.93 | REDUCE: (11), (12) imply:
% 66.36/9.93 | (20) op(e3, e3) = e2
% 66.36/9.93 |
% 66.36/9.93 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 66.36/9.93 | (16), (17), (18), (19), (20) are inconsistent by sub-proof #85.
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #85 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.93 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.93 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.93 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.93 (4) ~ (e3 = e1)
% 66.36/9.93 (5) op(e2, e2) = all_10_2
% 66.36/9.93 (6) ~ (all_4_0 = e1)
% 66.36/9.93 (7) all_52_1 = all_14_2
% 66.36/9.93 (8) ~ (e3 = e0)
% 66.36/9.93 (9) ~ (e1 = e0)
% 66.36/9.93 (10) op(e3, e3) = e2
% 66.36/9.93 (11) ~ (e2 = e0)
% 66.36/9.93 (12) ~ (e2 = e1)
% 66.36/9.93 (13) op(e2, e2) = all_4_0
% 66.36/9.93 (14) all_52_0 = all_10_2
% 66.36/9.93 (15) all_52_2 = e2
% 66.36/9.93 (16) op(all_14_2, all_14_2) = e0
% 66.36/9.93 (17) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.93 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | GROUND_INST: instantiating (1) with all_10_2, all_4_0, e2, e2, simplifying
% 66.36/9.93 | with (5), (13) gives:
% 66.36/9.93 | (18) all_10_2 = all_4_0
% 66.36/9.93 |
% 66.36/9.93 | COMBINE_EQS: (14), (18) imply:
% 66.36/9.93 | (19) all_52_0 = all_4_0
% 66.36/9.93 |
% 66.36/9.93 | BETA: splitting (3) gives:
% 66.36/9.93 |
% 66.36/9.93 | Case 1:
% 66.36/9.93 | |
% 66.36/9.93 | | (20) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.93 | |
% 66.36/9.93 | | REF_CLOSE: (6), (19), (20) are inconsistent by sub-proof #176.
% 66.36/9.93 | |
% 66.36/9.93 | Case 2:
% 66.36/9.93 | |
% 66.36/9.93 | | (21) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.93 | | = e0))
% 66.36/9.93 | |
% 66.36/9.93 | | BETA: splitting (21) gives:
% 66.36/9.93 | |
% 66.36/9.93 | | Case 1:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (22) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.93 | | |
% 66.36/9.93 | | | REF_CLOSE: (12), (15), (22) are inconsistent by sub-proof #175.
% 66.36/9.93 | | |
% 66.36/9.93 | | Case 2:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (23) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.93 | | |
% 66.36/9.93 | | | ALPHA: (23) implies:
% 66.36/9.93 | | | (24) ~ (all_52_1 = e0)
% 66.36/9.93 | | |
% 66.36/9.93 | | | REDUCE: (7), (24) imply:
% 66.36/9.93 | | | (25) ~ (all_14_2 = e0)
% 66.36/9.93 | | |
% 66.36/9.93 | | | BETA: splitting (17) gives:
% 66.36/9.93 | | |
% 66.36/9.93 | | | Case 1:
% 66.36/9.93 | | | |
% 66.36/9.93 | | | | (26) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.93 | | | |
% 66.36/9.93 | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (15),
% 66.36/9.93 | | | | (16), (26) are inconsistent by sub-proof #87.
% 66.36/9.93 | | | |
% 66.36/9.93 | | | Case 2:
% 66.36/9.93 | | | |
% 66.36/9.93 | | | | (27) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.36/9.93 | | | | (all_52_3 = e3))
% 66.36/9.93 | | | |
% 66.36/9.93 | | | | REF_CLOSE: (7), (11), (15), (25), (27) are inconsistent by sub-proof
% 66.36/9.93 | | | | #86.
% 66.36/9.93 | | | |
% 66.36/9.93 | | | End of split
% 66.36/9.93 | | |
% 66.36/9.93 | | End of split
% 66.36/9.93 | |
% 66.36/9.93 | End of split
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #86 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) ~ (all_14_2 = e0)
% 66.36/9.93 (2) all_52_1 = all_14_2
% 66.36/9.93 (3) ~ (e2 = e0)
% 66.36/9.93 (4) all_52_2 = e2
% 66.36/9.93 (5) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3 =
% 66.36/9.93 e3))
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | BETA: splitting (5) gives:
% 66.36/9.93 |
% 66.36/9.93 | Case 1:
% 66.36/9.93 | |
% 66.36/9.93 | | (6) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.93 | |
% 66.36/9.93 | | ALPHA: (6) implies:
% 66.36/9.93 | | (7) all_52_1 = e0
% 66.36/9.93 | |
% 66.36/9.93 | | COMBINE_EQS: (2), (7) imply:
% 66.36/9.93 | | (8) all_14_2 = e0
% 66.36/9.93 | |
% 66.36/9.93 | | SIMP: (8) implies:
% 66.36/9.93 | | (9) all_14_2 = e0
% 66.36/9.93 | |
% 66.36/9.93 | | REDUCE: (1), (9) imply:
% 66.36/9.93 | | (10) $false
% 66.36/9.93 | |
% 66.36/9.93 | | CLOSE: (10) is inconsistent.
% 66.36/9.93 | |
% 66.36/9.93 | Case 2:
% 66.36/9.93 | |
% 66.36/9.93 | | (11) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.93 | |
% 66.36/9.93 | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #131.
% 66.36/9.93 | |
% 66.36/9.93 | End of split
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #87 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (2) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.93 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.93 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.93 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.93 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.93 (5) ~ (e3 = e1)
% 66.36/9.93 (6) all_52_1 = all_14_2
% 66.36/9.93 (7) ~ (e3 = e0)
% 66.36/9.93 (8) ~ (e1 = e0)
% 66.36/9.93 (9) op(e3, e3) = e2
% 66.36/9.93 (10) ~ (e2 = e0)
% 66.36/9.93 (11) ~ (e2 = e1)
% 66.36/9.93 (12) all_52_2 = e2
% 66.36/9.93 (13) op(all_14_2, all_14_2) = e0
% 66.36/9.93
% 66.36/9.93 Begin of proof
% 66.36/9.93 |
% 66.36/9.93 | ALPHA: (2) implies:
% 66.36/9.93 | (14) all_52_0 = e0
% 66.36/9.93 |
% 66.36/9.93 | BETA: splitting (4) gives:
% 66.36/9.93 |
% 66.36/9.93 | Case 1:
% 66.36/9.93 | |
% 66.36/9.93 | | (15) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.93 | |
% 66.36/9.93 | | REF_CLOSE: (8), (14), (15) are inconsistent by sub-proof #164.
% 66.36/9.93 | |
% 66.36/9.93 | Case 2:
% 66.36/9.93 | |
% 66.36/9.93 | | (16) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.93 | | = e0))
% 66.36/9.93 | |
% 66.36/9.93 | | BETA: splitting (16) gives:
% 66.36/9.93 | |
% 66.36/9.93 | | Case 1:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (17) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.93 | | |
% 66.36/9.93 | | | REF_CLOSE: (11), (12), (17) are inconsistent by sub-proof #175.
% 66.36/9.93 | | |
% 66.36/9.93 | | Case 2:
% 66.36/9.93 | | |
% 66.36/9.93 | | | (18) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.93 | | |
% 66.36/9.93 | | | ALPHA: (18) implies:
% 66.36/9.93 | | | (19) all_52_3 = e1
% 66.36/9.93 | | |
% 66.36/9.93 | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (13), (14), (19) are
% 66.36/9.93 | | | inconsistent by sub-proof #88.
% 66.36/9.93 | | |
% 66.36/9.93 | | End of split
% 66.36/9.93 | |
% 66.36/9.93 | End of split
% 66.36/9.93 |
% 66.36/9.93 End of proof
% 66.36/9.93
% 66.36/9.93 Sub-proof #88 shows that the following formulas are inconsistent:
% 66.36/9.93 ----------------------------------------------------------------
% 66.36/9.93 (1) all_52_3 = e1
% 66.36/9.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.93 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.93 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.93 (4) ~ (e3 = e1)
% 66.36/9.93 (5) all_52_1 = all_14_2
% 66.36/9.93 (6) ~ (e3 = e0)
% 66.36/9.93 (7) op(e3, e3) = e2
% 66.36/9.94 (8) all_52_0 = e0
% 66.36/9.94 (9) ~ (e2 = e0)
% 66.36/9.94 (10) op(all_14_2, all_14_2) = e0
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | BETA: splitting (3) gives:
% 66.36/9.94 |
% 66.36/9.94 | Case 1:
% 66.36/9.94 | |
% 66.36/9.94 | | (11) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.94 | |
% 66.36/9.94 | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #148.
% 66.36/9.94 | |
% 66.36/9.94 | Case 2:
% 66.36/9.94 | |
% 66.36/9.94 | | (12) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.36/9.94 | | = e0))
% 66.36/9.94 | |
% 66.36/9.94 | | BETA: splitting (12) gives:
% 66.36/9.94 | |
% 66.36/9.94 | | Case 1:
% 66.36/9.94 | | |
% 66.36/9.94 | | | (13) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.94 | | |
% 66.36/9.94 | | | ALPHA: (13) implies:
% 66.36/9.94 | | | (14) all_52_1 = e3
% 66.36/9.94 | | |
% 66.36/9.94 | | | COMBINE_EQS: (5), (14) imply:
% 66.36/9.94 | | | (15) all_14_2 = e3
% 66.36/9.94 | | |
% 66.36/9.94 | | | SIMP: (15) implies:
% 66.36/9.94 | | | (16) all_14_2 = e3
% 66.36/9.94 | | |
% 66.36/9.94 | | | REDUCE: (10), (16) imply:
% 66.36/9.94 | | | (17) op(e3, e3) = e0
% 66.36/9.94 | | |
% 66.36/9.94 | | | REF_CLOSE: (2), (7), (9), (17) are inconsistent by sub-proof #89.
% 66.36/9.94 | | |
% 66.36/9.94 | | Case 2:
% 66.36/9.94 | | |
% 66.36/9.94 | | | (18) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.94 | | |
% 66.36/9.94 | | | REF_CLOSE: (1), (4), (18) are inconsistent by sub-proof #141.
% 66.36/9.94 | | |
% 66.36/9.94 | | End of split
% 66.36/9.94 | |
% 66.36/9.94 | End of split
% 66.36/9.94 |
% 66.36/9.94 End of proof
% 66.36/9.94
% 66.36/9.94 Sub-proof #89 shows that the following formulas are inconsistent:
% 66.36/9.94 ----------------------------------------------------------------
% 66.36/9.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.94 (2) op(e3, e3) = e2
% 66.36/9.94 (3) op(e3, e3) = e0
% 66.36/9.94 (4) ~ (e2 = e0)
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | GROUND_INST: instantiating (1) with e2, e0, e3, e3, simplifying with (2), (3)
% 66.36/9.94 | gives:
% 66.36/9.94 | (5) e2 = e0
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (4), (5) imply:
% 66.36/9.94 | (6) $false
% 66.36/9.94 |
% 66.36/9.94 | CLOSE: (6) is inconsistent.
% 66.36/9.94 |
% 66.36/9.94 End of proof
% 66.36/9.94
% 66.36/9.94 Sub-proof #90 shows that the following formulas are inconsistent:
% 66.36/9.94 ----------------------------------------------------------------
% 66.36/9.94 (1) ~ (all_52_0 = e1)
% 66.36/9.94 (2) ~ (all_4_0 = e2)
% 66.36/9.94 (3) op(e1, e1) = all_14_2
% 66.36/9.94 (4) all_52_2 = all_4_2
% 66.36/9.94 (5) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.94 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.94 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.94 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.94 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.94 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.94 (9) ~ (e3 = e1)
% 66.36/9.94 (10) op(e2, e2) = all_10_2
% 66.36/9.94 (11) ~ (e3 = e0)
% 66.36/9.94 (12) all_14_2 = e2
% 66.36/9.94 (13) all_52_3 = all_6_2
% 66.36/9.94 (14) all_52_0 = all_10_2
% 66.36/9.94 (15) all_52_1 = e2
% 66.36/9.94 (16) ~ (e3 = e2)
% 66.36/9.94 (17) op(all_14_2, all_14_2) = e0
% 66.36/9.94 (18) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (1), (14) imply:
% 66.36/9.94 | (19) ~ (all_10_2 = e1)
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (12), (17) imply:
% 66.36/9.94 | (20) op(e2, e2) = e0
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (3), (12) imply:
% 66.36/9.94 | (21) op(e1, e1) = e2
% 66.36/9.94 |
% 66.36/9.94 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 66.36/9.94 | (15), (16), (18), (19), (20), (21) are inconsistent by sub-proof
% 66.36/9.94 | #91.
% 66.36/9.94 |
% 66.36/9.94 End of proof
% 66.36/9.94
% 66.36/9.94 Sub-proof #91 shows that the following formulas are inconsistent:
% 66.36/9.94 ----------------------------------------------------------------
% 66.36/9.94 (1) ~ (all_4_0 = e2)
% 66.36/9.94 (2) op(e1, e1) = e2
% 66.36/9.94 (3) all_52_2 = all_4_2
% 66.36/9.94 (4) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.94 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.94 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.94 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.94 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.94 (8) ~ (e3 = e1)
% 66.36/9.94 (9) op(e2, e2) = all_10_2
% 66.36/9.94 (10) ~ (e3 = e0)
% 66.36/9.94 (11) all_14_2 = e2
% 66.36/9.94 (12) all_52_3 = all_6_2
% 66.36/9.94 (13) all_52_0 = all_10_2
% 66.36/9.94 (14) all_52_1 = e2
% 66.36/9.94 (15) ~ (e3 = e2)
% 66.36/9.94 (16) ~ (all_14_1 = e3) | ~ (all_14_2 = e2)
% 66.36/9.94 (17) ~ (all_10_2 = e1)
% 66.36/9.94 (18) op(e2, e2) = e0
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | BETA: splitting (16) gives:
% 66.36/9.94 |
% 66.36/9.94 | Case 1:
% 66.36/9.94 | |
% 66.36/9.94 | |
% 66.36/9.94 | | GROUND_INST: instantiating (5) with all_10_2, e0, e2, e2, simplifying with
% 66.36/9.94 | | (9), (18) gives:
% 66.36/9.94 | | (19) all_10_2 = e0
% 66.36/9.94 | |
% 66.36/9.94 | | COMBINE_EQS: (13), (19) imply:
% 66.36/9.94 | | (20) all_52_0 = e0
% 66.36/9.94 | |
% 66.36/9.94 | | REDUCE: (17), (19) imply:
% 66.36/9.94 | | (21) ~ (e1 = e0)
% 66.36/9.94 | |
% 66.36/9.94 | | SIMP: (21) implies:
% 66.36/9.94 | | (22) ~ (e1 = e0)
% 66.36/9.94 | |
% 66.36/9.94 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15),
% 66.36/9.94 | | (20), (22) are inconsistent by sub-proof #123.
% 66.36/9.94 | |
% 66.36/9.94 | Case 2:
% 66.36/9.94 | |
% 66.36/9.94 | | (23) ~ (all_14_2 = e2)
% 66.36/9.94 | |
% 66.36/9.94 | | REDUCE: (11), (23) imply:
% 66.36/9.94 | | (24) $false
% 66.36/9.94 | |
% 66.36/9.94 | | CLOSE: (24) is inconsistent.
% 66.36/9.94 | |
% 66.36/9.94 | End of split
% 66.36/9.94 |
% 66.36/9.94 End of proof
% 66.36/9.94
% 66.36/9.94 Sub-proof #92 shows that the following formulas are inconsistent:
% 66.36/9.94 ----------------------------------------------------------------
% 66.36/9.94 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 66.36/9.94 e0))
% 66.36/9.94 (2) ~ (all_4_0 = e2)
% 66.36/9.94 (3) all_52_2 = all_4_2
% 66.36/9.94 (4) op(all_4_2, all_4_2) = e1
% 66.36/9.94 (5) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.94 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.94 (7) op(e0, e0) = all_6_2
% 66.36/9.94 (8) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.94 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.94 (9) ~ (e3 = e1)
% 66.36/9.94 (10) op(e2, e2) = all_10_2
% 66.36/9.94 (11) ~ (e3 = e0)
% 66.36/9.94 (12) ~ (e1 = e0)
% 66.36/9.94 (13) op(e3, e3) = all_4_2
% 66.36/9.94 (14) ~ (e2 = e0)
% 66.36/9.94 (15) ~ (e2 = e1)
% 66.36/9.94 (16) all_52_3 = all_6_2
% 66.36/9.94 (17) all_52_0 = all_10_2
% 66.36/9.94 (18) op(all_6_2, all_6_2) = e1
% 66.36/9.94 (19) ~ (e3 = e2)
% 66.36/9.94 (20) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.94 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | BETA: splitting (1) gives:
% 66.36/9.94 |
% 66.36/9.94 | Case 1:
% 66.36/9.94 | |
% 66.36/9.94 | | (21) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.36/9.94 | |
% 66.36/9.94 | | ALPHA: (21) implies:
% 66.36/9.94 | | (22) all_52_2 = e2
% 66.36/9.94 | | (23) ~ (all_52_0 = e3)
% 66.36/9.94 | |
% 66.36/9.94 | | COMBINE_EQS: (3), (22) imply:
% 66.36/9.94 | | (24) all_4_2 = e2
% 66.36/9.94 | |
% 66.36/9.94 | | SIMP: (24) implies:
% 66.36/9.94 | | (25) all_4_2 = e2
% 66.36/9.94 | |
% 66.36/9.94 | | REF_CLOSE: (4), (6), (8), (10), (11), (12), (13), (14), (15), (16), (17),
% 66.36/9.94 | | (18), (20), (22), (23), (25) are inconsistent by sub-proof #95.
% 66.36/9.94 | |
% 66.36/9.94 | Case 2:
% 66.36/9.94 | |
% 66.36/9.94 | | (26) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.94 | |
% 66.36/9.94 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (16), (17), (18),
% 66.36/9.94 | | (19), (20), (26) are inconsistent by sub-proof #99.
% 66.36/9.94 | |
% 66.36/9.94 | End of split
% 66.36/9.94 |
% 66.36/9.94 End of proof
% 66.36/9.94
% 66.36/9.94 Sub-proof #93 shows that the following formulas are inconsistent:
% 66.36/9.94 ----------------------------------------------------------------
% 66.36/9.94 (1) ~ (all_4_0 = e2)
% 66.36/9.94 (2) op(e1, e1) = all_14_2
% 66.36/9.94 (3) all_52_2 = all_4_2
% 66.36/9.94 (4) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.94 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.94 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.94 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.94 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.94 (8) op(e2, e2) = all_10_2
% 66.36/9.94 (9) all_52_1 = all_14_2
% 66.36/9.94 (10) ~ (e3 = e0)
% 66.36/9.94 (11) ~ (e1 = e0)
% 66.36/9.94 (12) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.36/9.94 (13) ~ (e2 = e0)
% 66.36/9.94 (14) ~ (e2 = e1)
% 66.36/9.94 (15) all_52_3 = all_6_2
% 66.36/9.94 (16) all_52_0 = all_10_2
% 66.36/9.94 (17) op(all_14_2, all_14_2) = e3
% 66.36/9.94 (18) op(all_6_2, all_6_2) = e1
% 66.36/9.94 (19) ~ (e3 = e2)
% 66.36/9.94 (20) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.94 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.94
% 66.36/9.94 Begin of proof
% 66.36/9.94 |
% 66.36/9.94 | ALPHA: (12) implies:
% 66.36/9.94 | (21) all_52_1 = e2
% 66.36/9.94 | (22) ~ (all_52_0 = e1)
% 66.36/9.94 |
% 66.36/9.94 | COMBINE_EQS: (9), (21) imply:
% 66.36/9.94 | (23) all_14_2 = e2
% 66.36/9.94 |
% 66.36/9.94 | SIMP: (23) implies:
% 66.36/9.94 | (24) all_14_2 = e2
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (16), (22) imply:
% 66.36/9.94 | (25) ~ (all_10_2 = e1)
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (17), (24) imply:
% 66.36/9.94 | (26) op(e2, e2) = e3
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (2), (24) imply:
% 66.36/9.94 | (27) op(e1, e1) = e2
% 66.36/9.94 |
% 66.36/9.94 | GROUND_INST: instantiating (5) with all_10_2, e3, e2, e2, simplifying with
% 66.36/9.94 | (8), (26) gives:
% 66.36/9.94 | (28) all_10_2 = e3
% 66.36/9.94 |
% 66.36/9.94 | COMBINE_EQS: (16), (28) imply:
% 66.36/9.94 | (29) all_52_0 = e3
% 66.36/9.94 |
% 66.36/9.94 | REDUCE: (25), (28) imply:
% 66.36/9.94 | (30) ~ (e3 = e1)
% 66.36/9.94 |
% 66.36/9.94 | BETA: splitting (20) gives:
% 66.36/9.94 |
% 66.36/9.94 | Case 1:
% 66.36/9.94 | |
% 66.36/9.94 | | (31) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.94 | |
% 66.36/9.94 | | ALPHA: (31) implies:
% 66.36/9.94 | | (32) all_52_0 = e0
% 66.36/9.94 | |
% 66.36/9.94 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (15), (19), (21), (27),
% 66.36/9.94 | | (30), (32) are inconsistent by sub-proof #123.
% 66.36/9.94 | |
% 66.36/9.94 | Case 2:
% 66.36/9.94 | |
% 66.36/9.95 | | (33) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.95 | | = e3))
% 66.36/9.95 | |
% 66.36/9.95 | | REF_CLOSE: (5), (7), (11), (13), (14), (15), (18), (21), (27), (29), (30),
% 66.36/9.95 | | (33) are inconsistent by sub-proof #94.
% 66.36/9.95 | |
% 66.36/9.95 | End of split
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #94 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) op(e1, e1) = e2
% 66.36/9.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (3) all_52_0 = e3
% 66.36/9.95 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.95 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.95 (5) ~ (e3 = e1)
% 66.36/9.95 (6) ~ (e1 = e0)
% 66.36/9.95 (7) ~ (e2 = e0)
% 66.36/9.95 (8) ~ (e2 = e1)
% 66.36/9.95 (9) all_52_3 = all_6_2
% 66.36/9.95 (10) all_52_1 = e2
% 66.36/9.95 (11) op(all_6_2, all_6_2) = e1
% 66.36/9.95 (12) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3 =
% 66.36/9.95 e3))
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | BETA: splitting (12) gives:
% 66.36/9.95 |
% 66.36/9.95 | Case 1:
% 66.36/9.95 | |
% 66.36/9.95 | | (13) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.95 | |
% 66.36/9.95 | | REF_CLOSE: (7), (10), (13) are inconsistent by sub-proof #179.
% 66.36/9.95 | |
% 66.36/9.95 | Case 2:
% 66.36/9.95 | |
% 66.36/9.95 | | (14) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.95 | |
% 66.36/9.95 | | ALPHA: (14) implies:
% 66.36/9.95 | | (15) all_52_2 = e0
% 66.36/9.95 | |
% 66.36/9.95 | | BETA: splitting (4) gives:
% 66.36/9.95 | |
% 66.36/9.95 | | Case 1:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (16) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.95 | | |
% 66.36/9.95 | | | ALPHA: (16) implies:
% 66.36/9.95 | | | (17) all_52_0 = e1
% 66.36/9.95 | | |
% 66.36/9.95 | | | REF_CLOSE: (3), (5), (17) are inconsistent by sub-proof #122.
% 66.36/9.95 | | |
% 66.36/9.95 | | Case 2:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (18) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 66.36/9.95 | | | (all_52_1 = e0))
% 66.36/9.95 | | |
% 66.36/9.95 | | | BETA: splitting (18) gives:
% 66.36/9.95 | | |
% 66.36/9.95 | | | Case 1:
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | (19) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | REF_CLOSE: (6), (15), (19) are inconsistent by sub-proof #142.
% 66.36/9.95 | | | |
% 66.36/9.95 | | | Case 2:
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | (20) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | ALPHA: (20) implies:
% 66.36/9.95 | | | | (21) all_52_3 = e1
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | COMBINE_EQS: (9), (21) imply:
% 66.36/9.95 | | | | (22) all_6_2 = e1
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | SIMP: (22) implies:
% 66.36/9.95 | | | | (23) all_6_2 = e1
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | REDUCE: (11), (23) imply:
% 66.36/9.95 | | | | (24) op(e1, e1) = e1
% 66.36/9.95 | | | |
% 66.36/9.95 | | | | REF_CLOSE: (1), (2), (8), (24) are inconsistent by sub-proof #146.
% 66.36/9.95 | | | |
% 66.36/9.95 | | | End of split
% 66.36/9.95 | | |
% 66.36/9.95 | | End of split
% 66.36/9.95 | |
% 66.36/9.95 | End of split
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #95 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) op(all_4_2, all_4_2) = e1
% 66.36/9.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (3) ~ (all_52_0 = e3)
% 66.36/9.95 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.95 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.95 (5) op(e2, e2) = all_10_2
% 66.36/9.95 (6) ~ (e3 = e0)
% 66.36/9.95 (7) ~ (e1 = e0)
% 66.36/9.95 (8) all_4_2 = e2
% 66.36/9.95 (9) op(e3, e3) = all_4_2
% 66.36/9.95 (10) ~ (e2 = e0)
% 66.36/9.95 (11) ~ (e2 = e1)
% 66.36/9.95 (12) all_52_3 = all_6_2
% 66.36/9.95 (13) all_52_0 = all_10_2
% 66.36/9.95 (14) all_52_2 = e2
% 66.36/9.95 (15) op(all_6_2, all_6_2) = e1
% 66.36/9.95 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.95 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | REDUCE: (3), (13) imply:
% 66.36/9.95 | (17) ~ (all_10_2 = e3)
% 66.36/9.95 |
% 66.36/9.95 | REDUCE: (1), (8) imply:
% 66.36/9.95 | (18) op(e2, e2) = e1
% 66.36/9.95 |
% 66.36/9.95 | REDUCE: (8), (9) imply:
% 66.36/9.95 | (19) op(e3, e3) = e2
% 66.36/9.95 |
% 66.36/9.95 | GROUND_INST: instantiating (2) with all_10_2, e1, e2, e2, simplifying with
% 66.36/9.95 | (5), (18) gives:
% 66.36/9.95 | (20) all_10_2 = e1
% 66.36/9.95 |
% 66.36/9.95 | COMBINE_EQS: (13), (20) imply:
% 66.36/9.95 | (21) all_52_0 = e1
% 66.36/9.95 |
% 66.36/9.95 | REDUCE: (17), (20) imply:
% 66.36/9.95 | (22) ~ (e3 = e1)
% 66.36/9.95 |
% 66.36/9.95 | SIMP: (22) implies:
% 66.36/9.95 | (23) ~ (e3 = e1)
% 66.36/9.95 |
% 66.36/9.95 | BETA: splitting (16) gives:
% 66.36/9.95 |
% 66.36/9.95 | Case 1:
% 66.36/9.95 | |
% 66.36/9.95 | | (24) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.95 | |
% 66.36/9.95 | | ALPHA: (24) implies:
% 66.36/9.95 | | (25) all_52_0 = e0
% 66.36/9.95 | |
% 66.36/9.95 | | REF_CLOSE: (7), (21), (25) are inconsistent by sub-proof #133.
% 66.36/9.95 | |
% 66.36/9.95 | Case 2:
% 66.36/9.95 | |
% 66.36/9.95 | | (26) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.95 | | = e3))
% 66.36/9.95 | |
% 66.36/9.95 | | BETA: splitting (26) gives:
% 66.36/9.95 | |
% 66.36/9.95 | | Case 1:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (27) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.95 | | |
% 66.36/9.95 | | | REF_CLOSE: (2), (4), (6), (11), (12), (15), (19), (21), (23), (27) are
% 66.36/9.95 | | | inconsistent by sub-proof #96.
% 66.36/9.95 | | |
% 66.36/9.95 | | Case 2:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (28) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.95 | | |
% 66.36/9.95 | | | REF_CLOSE: (10), (14), (28) are inconsistent by sub-proof #131.
% 66.36/9.95 | | |
% 66.36/9.95 | | End of split
% 66.36/9.95 | |
% 66.36/9.95 | End of split
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #96 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) all_52_0 = e1
% 66.36/9.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.95 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.95 (4) ~ (e3 = e1)
% 66.36/9.95 (5) ~ (e3 = e0)
% 66.36/9.95 (6) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.95 (7) op(e3, e3) = e2
% 66.36/9.95 (8) ~ (e2 = e1)
% 66.36/9.95 (9) all_52_3 = all_6_2
% 66.36/9.95 (10) op(all_6_2, all_6_2) = e1
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | ALPHA: (6) implies:
% 66.36/9.95 | (11) all_52_1 = e0
% 66.36/9.95 |
% 66.36/9.95 | BETA: splitting (3) gives:
% 66.36/9.95 |
% 66.36/9.95 | Case 1:
% 66.36/9.95 | |
% 66.36/9.95 | | (12) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.95 | |
% 66.36/9.95 | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #132.
% 66.36/9.95 | |
% 66.36/9.95 | Case 2:
% 66.36/9.95 | |
% 66.36/9.95 | | (13) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.36/9.95 | | = e0))
% 66.36/9.95 | |
% 66.36/9.95 | | BETA: splitting (13) gives:
% 66.36/9.95 | |
% 66.36/9.95 | | Case 1:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (14) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.95 | | |
% 66.36/9.95 | | | REF_CLOSE: (5), (11), (14) are inconsistent by sub-proof #154.
% 66.36/9.95 | | |
% 66.36/9.95 | | Case 2:
% 66.36/9.95 | | |
% 66.36/9.95 | | | (15) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.95 | | |
% 66.36/9.95 | | | ALPHA: (15) implies:
% 66.36/9.95 | | | (16) all_52_3 = e3
% 66.36/9.95 | | |
% 66.36/9.95 | | | COMBINE_EQS: (9), (16) imply:
% 66.36/9.95 | | | (17) all_6_2 = e3
% 66.36/9.95 | | |
% 66.36/9.95 | | | SIMP: (17) implies:
% 66.36/9.95 | | | (18) all_6_2 = e3
% 66.36/9.95 | | |
% 66.36/9.95 | | | REDUCE: (10), (18) imply:
% 66.36/9.95 | | | (19) op(e3, e3) = e1
% 66.36/9.95 | | |
% 66.36/9.95 | | | REF_CLOSE: (2), (7), (8), (19) are inconsistent by sub-proof #97.
% 66.36/9.95 | | |
% 66.36/9.95 | | End of split
% 66.36/9.95 | |
% 66.36/9.95 | End of split
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #97 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (2) op(e3, e3) = e2
% 66.36/9.95 (3) op(e3, e3) = e1
% 66.36/9.95 (4) ~ (e2 = e1)
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | GROUND_INST: instantiating (1) with e2, e1, e3, e3, simplifying with (2), (3)
% 66.36/9.95 | gives:
% 66.36/9.95 | (5) e2 = e1
% 66.36/9.95 |
% 66.36/9.95 | REDUCE: (4), (5) imply:
% 66.36/9.95 | (6) $false
% 66.36/9.95 |
% 66.36/9.95 | CLOSE: (6) is inconsistent.
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #98 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) ~ (all_4_0 = e2)
% 66.36/9.95 (2) all_52_2 = all_4_2
% 66.36/9.95 (3) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (5) op(e0, e0) = all_6_2
% 66.36/9.95 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.95 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.95 (7) ~ (e3 = e1)
% 66.36/9.95 (8) op(e2, e2) = all_10_2
% 66.36/9.95 (9) ~ (e3 = e0)
% 66.36/9.95 (10) all_52_3 = all_6_2
% 66.36/9.95 (11) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.95 (12) all_52_0 = all_10_2
% 66.36/9.95 (13) op(all_6_2, all_6_2) = e1
% 66.36/9.95 (14) ~ (e3 = e2)
% 66.36/9.95 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.95 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | ALPHA: (11) implies:
% 66.36/9.95 | (16) all_52_3 = e2
% 66.36/9.95 | (17) ~ (all_52_0 = e0)
% 66.36/9.95 |
% 66.36/9.95 | COMBINE_EQS: (10), (16) imply:
% 66.36/9.95 | (18) all_6_2 = e2
% 66.36/9.95 |
% 66.36/9.95 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 66.36/9.95 | (15), (16), (17), (18) are inconsistent by sub-proof #100.
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #99 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) ~ (all_4_0 = e2)
% 66.36/9.95 (2) all_52_2 = all_4_2
% 66.36/9.95 (3) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.95 (5) op(e0, e0) = all_6_2
% 66.36/9.95 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.95 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.95 (7) ~ (e3 = e1)
% 66.36/9.95 (8) op(e2, e2) = all_10_2
% 66.36/9.95 (9) ~ (e3 = e0)
% 66.36/9.95 (10) all_52_3 = all_6_2
% 66.36/9.95 (11) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.95 (12) all_52_0 = all_10_2
% 66.36/9.95 (13) op(all_6_2, all_6_2) = e1
% 66.36/9.95 (14) ~ (e3 = e2)
% 66.36/9.95 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.95 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.95
% 66.36/9.95 Begin of proof
% 66.36/9.95 |
% 66.36/9.95 | ALPHA: (11) implies:
% 66.36/9.95 | (16) all_52_3 = e2
% 66.36/9.95 | (17) ~ (all_52_0 = e0)
% 66.36/9.95 |
% 66.36/9.95 | COMBINE_EQS: (10), (16) imply:
% 66.36/9.95 | (18) all_6_2 = e2
% 66.36/9.95 |
% 66.36/9.95 | SIMP: (18) implies:
% 66.36/9.95 | (19) all_6_2 = e2
% 66.36/9.95 |
% 66.36/9.95 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 66.36/9.95 | (15), (16), (17), (19) are inconsistent by sub-proof #100.
% 66.36/9.95 |
% 66.36/9.95 End of proof
% 66.36/9.95
% 66.36/9.95 Sub-proof #100 shows that the following formulas are inconsistent:
% 66.36/9.95 ----------------------------------------------------------------
% 66.36/9.95 (1) ~ (all_4_0 = e2)
% 66.36/9.95 (2) all_52_2 = all_4_2
% 66.36/9.95 (3) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.96 (5) op(e0, e0) = all_6_2
% 66.36/9.96 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.96 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.96 (7) all_6_2 = e2
% 66.36/9.96 (8) ~ (e3 = e1)
% 66.36/9.96 (9) op(e2, e2) = all_10_2
% 66.36/9.96 (10) ~ (e3 = e0)
% 66.36/9.96 (11) ~ (all_52_0 = e0)
% 66.36/9.96 (12) all_52_3 = e2
% 66.36/9.96 (13) all_52_0 = all_10_2
% 66.36/9.96 (14) op(all_6_2, all_6_2) = e1
% 66.36/9.96 (15) ~ (e3 = e2)
% 66.36/9.96 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.96 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (11), (13) imply:
% 66.36/9.96 | (17) ~ (all_10_2 = e0)
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (7), (14) imply:
% 66.36/9.96 | (18) op(e2, e2) = e1
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (5), (7) imply:
% 66.36/9.96 | (19) op(e0, e0) = e2
% 66.36/9.96 |
% 66.36/9.96 | GROUND_INST: instantiating (4) with all_10_2, e1, e2, e2, simplifying with
% 66.36/9.96 | (9), (18) gives:
% 66.36/9.96 | (20) all_10_2 = e1
% 66.36/9.96 |
% 66.36/9.96 | COMBINE_EQS: (13), (20) imply:
% 66.36/9.96 | (21) all_52_0 = e1
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (17), (20) imply:
% 66.36/9.96 | (22) ~ (e1 = e0)
% 66.36/9.96 |
% 66.36/9.96 | BETA: splitting (6) gives:
% 66.36/9.96 |
% 66.36/9.96 | Case 1:
% 66.36/9.96 | |
% 66.36/9.96 | | (23) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/9.96 | |
% 66.36/9.96 | | REF_CLOSE: (8), (21), (23) are inconsistent by sub-proof #132.
% 66.36/9.96 | |
% 66.36/9.96 | Case 2:
% 66.36/9.96 | |
% 66.36/9.96 | | (24) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.36/9.96 | | = e0))
% 66.36/9.96 | |
% 66.36/9.96 | | BETA: splitting (24) gives:
% 66.36/9.96 | |
% 66.36/9.96 | | Case 1:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (25) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/9.96 | | |
% 66.36/9.96 | | | ALPHA: (25) implies:
% 66.36/9.96 | | | (26) all_52_1 = e3
% 66.36/9.96 | | |
% 66.36/9.96 | | | REF_CLOSE: (1), (2), (3), (4), (10), (16), (19), (21), (22), (26) are
% 66.36/9.96 | | | inconsistent by sub-proof #101.
% 66.36/9.96 | | |
% 66.36/9.96 | | Case 2:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (27) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/9.96 | | |
% 66.36/9.96 | | | REF_CLOSE: (12), (15), (27) are inconsistent by sub-proof #153.
% 66.36/9.96 | | |
% 66.36/9.96 | | End of split
% 66.36/9.96 | |
% 66.36/9.96 | End of split
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #101 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) all_52_0 = e1
% 66.36/9.96 (2) ~ (all_4_0 = e2)
% 66.36/9.96 (3) all_52_2 = all_4_2
% 66.36/9.96 (4) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.96 (6) all_52_1 = e3
% 66.36/9.96 (7) ~ (e3 = e0)
% 66.36/9.96 (8) ~ (e1 = e0)
% 66.36/9.96 (9) op(e0, e0) = e2
% 66.36/9.96 (10) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.96 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | BETA: splitting (10) gives:
% 66.36/9.96 |
% 66.36/9.96 | Case 1:
% 66.36/9.96 | |
% 66.36/9.96 | | (11) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.96 | |
% 66.36/9.96 | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #103.
% 66.36/9.96 | |
% 66.36/9.96 | Case 2:
% 66.36/9.96 | |
% 66.36/9.96 | | (12) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.96 | | = e3))
% 66.36/9.96 | |
% 66.36/9.96 | | BETA: splitting (12) gives:
% 66.36/9.96 | |
% 66.36/9.96 | | Case 1:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (13) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.96 | | |
% 66.36/9.96 | | | ALPHA: (13) implies:
% 66.36/9.96 | | | (14) all_52_1 = e0
% 66.36/9.96 | | |
% 66.36/9.96 | | | REF_CLOSE: (6), (7), (14) are inconsistent by sub-proof #102.
% 66.36/9.96 | | |
% 66.36/9.96 | | Case 2:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (15) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.96 | | |
% 66.36/9.96 | | | ALPHA: (15) implies:
% 66.36/9.96 | | | (16) all_52_2 = e0
% 66.36/9.96 | | |
% 66.36/9.96 | | | COMBINE_EQS: (3), (16) imply:
% 66.36/9.96 | | | (17) all_4_2 = e0
% 66.36/9.96 | | |
% 66.36/9.96 | | | REDUCE: (4), (17) imply:
% 66.36/9.96 | | | (18) op(e0, e0) = all_4_0
% 66.36/9.96 | | |
% 66.36/9.96 | | | GROUND_INST: instantiating (5) with e2, all_4_0, e0, e0, simplifying with
% 66.36/9.96 | | | (9), (18) gives:
% 66.36/9.96 | | | (19) all_4_0 = e2
% 66.36/9.96 | | |
% 66.36/9.96 | | | REDUCE: (2), (19) imply:
% 66.36/9.96 | | | (20) $false
% 66.36/9.96 | | |
% 66.36/9.96 | | | CLOSE: (20) is inconsistent.
% 66.36/9.96 | | |
% 66.36/9.96 | | End of split
% 66.36/9.96 | |
% 66.36/9.96 | End of split
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #102 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) all_52_1 = e3
% 66.36/9.96 (2) all_52_1 = e0
% 66.36/9.96 (3) ~ (e3 = e0)
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | COMBINE_EQS: (1), (2) imply:
% 66.36/9.96 | (4) e3 = e0
% 66.36/9.96 |
% 66.36/9.96 | SIMP: (4) implies:
% 66.36/9.96 | (5) e3 = e0
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (3), (5) imply:
% 66.36/9.96 | (6) $false
% 66.36/9.96 |
% 66.36/9.96 | CLOSE: (6) is inconsistent.
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #103 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.96 (2) all_52_0 = e1
% 66.36/9.96 (3) ~ (e1 = e0)
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | ALPHA: (1) implies:
% 66.36/9.96 | (4) all_52_0 = e0
% 66.36/9.96 |
% 66.36/9.96 | COMBINE_EQS: (2), (4) imply:
% 66.36/9.96 | (5) e1 = e0
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (3), (5) imply:
% 66.36/9.96 | (6) $false
% 66.36/9.96 |
% 66.36/9.96 | CLOSE: (6) is inconsistent.
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #104 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) op(all_14_2, all_14_2) = e2
% 66.36/9.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.96 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.96 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.96 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.96 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.96 (5) op(e2, e2) = all_10_2
% 66.36/9.96 (6) all_52_1 = all_14_2
% 66.36/9.96 (7) ~ (e1 = e0)
% 66.36/9.96 (8) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.36/9.96 (9) ~ (e2 = e0)
% 66.36/9.96 (10) all_52_3 = all_6_2
% 66.36/9.96 (11) all_52_0 = all_10_2
% 66.36/9.96 (12) ~ (e3 = e2)
% 66.36/9.96 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.96 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | ALPHA: (8) implies:
% 66.36/9.96 | (14) all_52_1 = e2
% 66.36/9.96 | (15) ~ (all_52_0 = e1)
% 66.36/9.96 |
% 66.36/9.96 | COMBINE_EQS: (6), (14) imply:
% 66.36/9.96 | (16) all_14_2 = e2
% 66.36/9.96 |
% 66.36/9.96 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 66.36/9.96 | (15), (16) are inconsistent by sub-proof #108.
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #105 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 =
% 66.36/9.96 e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 66.36/9.96 (2) op(e1, e1) = all_14_2
% 66.36/9.96 (3) op(all_14_2, all_14_2) = e2
% 66.36/9.96 (4) all_52_2 = all_4_2
% 66.36/9.96 (5) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.96 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.96 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.96 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.96 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.96 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.96 (9) op(e2, e2) = all_10_2
% 66.36/9.96 (10) ~ (all_34_0 = e0)
% 66.36/9.96 (11) ~ (all_4_0 = e1)
% 66.36/9.96 (12) all_52_1 = all_14_2
% 66.36/9.96 (13) ~ (e1 = e0)
% 66.36/9.96 (14) op(all_6_2, all_6_2) = all_6_0
% 66.36/9.96 (15) ~ (e2 = e0)
% 66.36/9.96 (16) ~ (e2 = e1)
% 66.36/9.96 (17) all_52_3 = all_6_2
% 66.36/9.96 (18) all_52_0 = all_10_2
% 66.36/9.96 (19) ~ (e3 = e2)
% 66.36/9.96 (20) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.96 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.96 (21) ~ (all_6_0 = e1)
% 66.36/9.96 (22) all_34_0 = all_4_0
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | REDUCE: (10), (22) imply:
% 66.36/9.96 | (23) ~ (all_4_0 = e0)
% 66.36/9.96 |
% 66.36/9.96 | BETA: splitting (1) gives:
% 66.36/9.96 |
% 66.36/9.96 | Case 1:
% 66.36/9.96 | |
% 66.36/9.96 | | (24) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.36/9.96 | |
% 66.36/9.96 | | REF_CLOSE: (3), (6), (7), (8), (9), (12), (13), (15), (17), (18), (19),
% 66.36/9.96 | | (20), (24) are inconsistent by sub-proof #107.
% 66.36/9.96 | |
% 66.36/9.96 | Case 2:
% 66.36/9.96 | |
% 66.36/9.96 | | (25) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0
% 66.36/9.96 | | = e0))
% 66.36/9.96 | |
% 66.36/9.96 | | BETA: splitting (25) gives:
% 66.36/9.96 | |
% 66.36/9.96 | | Case 1:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (26) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.36/9.96 | | |
% 66.36/9.96 | | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (12), (15), (16), (18), (20),
% 66.36/9.96 | | | (23), (26) are inconsistent by sub-proof #111.
% 66.36/9.96 | | |
% 66.36/9.96 | | Case 2:
% 66.36/9.96 | | |
% 66.36/9.96 | | | (27) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.96 | | |
% 66.36/9.96 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (12), (13), (14), (16), (17),
% 66.36/9.96 | | | (18), (20), (21), (23), (27) are inconsistent by sub-proof
% 66.36/9.96 | | | #106.
% 66.36/9.96 | | |
% 66.36/9.96 | | End of split
% 66.36/9.96 | |
% 66.36/9.96 | End of split
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #106 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) op(e1, e1) = all_14_2
% 66.36/9.96 (2) all_52_2 = all_4_2
% 66.36/9.96 (3) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.96 (5) ~ (all_4_0 = e0)
% 66.36/9.96 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.96 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.96 (7) op(e2, e2) = all_10_2
% 66.36/9.96 (8) all_52_1 = all_14_2
% 66.36/9.96 (9) ~ (e1 = e0)
% 66.36/9.96 (10) op(all_6_2, all_6_2) = all_6_0
% 66.36/9.96 (11) ~ (e2 = e1)
% 66.36/9.96 (12) all_52_3 = all_6_2
% 66.36/9.96 (13) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.96 (14) all_52_0 = all_10_2
% 66.36/9.96 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.96 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.96 (16) ~ (all_6_0 = e1)
% 66.36/9.96
% 66.36/9.96 Begin of proof
% 66.36/9.96 |
% 66.36/9.96 | ALPHA: (13) implies:
% 66.36/9.96 | (17) all_52_3 = e2
% 66.36/9.96 | (18) ~ (all_52_0 = e0)
% 66.36/9.96 |
% 66.36/9.96 | COMBINE_EQS: (12), (17) imply:
% 66.36/9.96 | (19) all_6_2 = e2
% 66.36/9.96 |
% 66.36/9.96 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14),
% 66.36/9.96 | (15), (16), (17), (18), (19) are inconsistent by sub-proof #169.
% 66.36/9.96 |
% 66.36/9.96 End of proof
% 66.36/9.96
% 66.36/9.96 Sub-proof #107 shows that the following formulas are inconsistent:
% 66.36/9.96 ----------------------------------------------------------------
% 66.36/9.96 (1) op(all_14_2, all_14_2) = e2
% 66.36/9.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.97 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.97 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.97 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (5) op(e2, e2) = all_10_2
% 66.36/9.97 (6) all_52_1 = all_14_2
% 66.36/9.97 (7) ~ (e1 = e0)
% 66.36/9.97 (8) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.36/9.97 (9) ~ (e2 = e0)
% 66.36/9.97 (10) all_52_3 = all_6_2
% 66.36/9.97 (11) all_52_0 = all_10_2
% 66.36/9.97 (12) ~ (e3 = e2)
% 66.36/9.97 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.97 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | ALPHA: (8) implies:
% 66.36/9.97 | (14) all_52_1 = e2
% 66.36/9.97 | (15) ~ (all_52_0 = e1)
% 66.36/9.97 |
% 66.36/9.97 | COMBINE_EQS: (6), (14) imply:
% 66.36/9.97 | (16) all_14_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | SIMP: (16) implies:
% 66.36/9.97 | (17) all_14_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 66.36/9.97 | (15), (17) are inconsistent by sub-proof #108.
% 66.36/9.97 |
% 66.36/9.97 End of proof
% 66.36/9.97
% 66.36/9.97 Sub-proof #108 shows that the following formulas are inconsistent:
% 66.36/9.97 ----------------------------------------------------------------
% 66.36/9.97 (1) ~ (all_52_0 = e1)
% 66.36/9.97 (2) op(all_14_2, all_14_2) = e2
% 66.36/9.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.97 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.97 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.97 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (6) op(e2, e2) = all_10_2
% 66.36/9.97 (7) ~ (e1 = e0)
% 66.36/9.97 (8) all_14_2 = e2
% 66.36/9.97 (9) ~ (e2 = e0)
% 66.36/9.97 (10) all_52_3 = all_6_2
% 66.36/9.97 (11) all_52_0 = all_10_2
% 66.36/9.97 (12) all_52_1 = e2
% 66.36/9.97 (13) ~ (e3 = e2)
% 66.36/9.97 (14) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.97 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | REDUCE: (1), (11) imply:
% 66.36/9.97 | (15) ~ (all_10_2 = e1)
% 66.36/9.97 |
% 66.36/9.97 | REDUCE: (2), (8) imply:
% 66.36/9.97 | (16) op(e2, e2) = e2
% 66.36/9.97 |
% 66.36/9.97 | GROUND_INST: instantiating (3) with all_10_2, e2, e2, e2, simplifying with
% 66.36/9.97 | (6), (16) gives:
% 66.36/9.97 | (17) all_10_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | COMBINE_EQS: (11), (17) imply:
% 66.36/9.97 | (18) all_52_0 = e2
% 66.36/9.97 |
% 66.36/9.97 | REDUCE: (15), (17) imply:
% 66.36/9.97 | (19) ~ (e2 = e1)
% 66.36/9.97 |
% 66.36/9.97 | BETA: splitting (14) gives:
% 66.36/9.97 |
% 66.36/9.97 | Case 1:
% 66.36/9.97 | |
% 66.36/9.97 | | (20) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.97 | |
% 66.36/9.97 | | REF_CLOSE: (9), (18), (20) are inconsistent by sub-proof #156.
% 66.36/9.97 | |
% 66.36/9.97 | Case 2:
% 66.36/9.97 | |
% 66.36/9.97 | | (21) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/9.97 | | = e3))
% 66.36/9.97 | |
% 66.36/9.97 | | BETA: splitting (21) gives:
% 66.36/9.97 | |
% 66.36/9.97 | | Case 1:
% 66.36/9.97 | | |
% 66.36/9.97 | | | (22) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.97 | | |
% 66.36/9.97 | | | REF_CLOSE: (9), (12), (22) are inconsistent by sub-proof #179.
% 66.36/9.97 | | |
% 66.36/9.97 | | Case 2:
% 66.36/9.97 | | |
% 66.36/9.97 | | | (23) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.97 | | |
% 66.36/9.97 | | | REF_CLOSE: (4), (5), (7), (10), (12), (13), (18), (19), (23) are
% 66.36/9.97 | | | inconsistent by sub-proof #109.
% 66.36/9.97 | | |
% 66.36/9.97 | | End of split
% 66.36/9.97 | |
% 66.36/9.97 | End of split
% 66.36/9.97 |
% 66.36/9.97 End of proof
% 66.36/9.97
% 66.36/9.97 Sub-proof #109 shows that the following formulas are inconsistent:
% 66.36/9.97 ----------------------------------------------------------------
% 66.36/9.97 (1) all_52_0 = e2
% 66.36/9.97 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.97 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.97 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (4) ~ (e1 = e0)
% 66.36/9.97 (5) ~ (e2 = e1)
% 66.36/9.97 (6) all_52_3 = all_6_2
% 66.36/9.97 (7) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.97 (8) all_52_1 = e2
% 66.36/9.97 (9) ~ (e3 = e2)
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | ALPHA: (7) implies:
% 66.36/9.97 | (10) all_52_2 = e0
% 66.36/9.97 | (11) ~ (all_52_3 = e3)
% 66.36/9.97 |
% 66.36/9.97 | REDUCE: (6), (11) imply:
% 66.36/9.97 | (12) ~ (all_6_2 = e3)
% 66.36/9.97 |
% 66.36/9.97 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12) are inconsistent
% 66.36/9.97 | by sub-proof #140.
% 66.36/9.97 |
% 66.36/9.97 End of proof
% 66.36/9.97
% 66.36/9.97 Sub-proof #110 shows that the following formulas are inconsistent:
% 66.36/9.97 ----------------------------------------------------------------
% 66.36/9.97 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.97 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.97 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.97 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (4) op(e2, e2) = all_10_2
% 66.36/9.97 (5) op(all_6_2, all_6_2) = e2
% 66.36/9.97 (6) all_52_1 = all_14_2
% 66.36/9.97 (7) ~ (e1 = e0)
% 66.36/9.97 (8) ~ (e2 = e1)
% 66.36/9.97 (9) all_52_3 = all_6_2
% 66.36/9.97 (10) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/9.97 (11) all_52_0 = all_10_2
% 66.36/9.97 (12) ~ (e3 = e2)
% 66.36/9.97 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.97 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | ALPHA: (10) implies:
% 66.36/9.97 | (14) all_52_3 = e2
% 66.36/9.97 | (15) ~ (all_52_0 = e0)
% 66.36/9.97 |
% 66.36/9.97 | COMBINE_EQS: (9), (14) imply:
% 66.36/9.97 | (16) all_6_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 66.36/9.97 | (15), (16) are inconsistent by sub-proof #150.
% 66.36/9.97 |
% 66.36/9.97 End of proof
% 66.36/9.97
% 66.36/9.97 Sub-proof #111 shows that the following formulas are inconsistent:
% 66.36/9.97 ----------------------------------------------------------------
% 66.36/9.97 (1) all_52_2 = all_4_2
% 66.36/9.97 (2) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.97 (4) ~ (all_4_0 = e0)
% 66.36/9.97 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (6) op(e2, e2) = all_10_2
% 66.36/9.97 (7) ~ (all_4_0 = e1)
% 66.36/9.97 (8) all_52_1 = all_14_2
% 66.36/9.97 (9) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.36/9.97 (10) ~ (e2 = e0)
% 66.36/9.97 (11) ~ (e2 = e1)
% 66.36/9.97 (12) all_52_0 = all_10_2
% 66.36/9.97 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.97 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | ALPHA: (9) implies:
% 66.36/9.97 | (14) all_52_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | COMBINE_EQS: (1), (14) imply:
% 66.36/9.97 | (15) all_4_2 = e2
% 66.36/9.97 |
% 66.36/9.97 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 66.36/9.97 | (15) are inconsistent by sub-proof #174.
% 66.36/9.97 |
% 66.36/9.97 End of proof
% 66.36/9.97
% 66.36/9.97 Sub-proof #112 shows that the following formulas are inconsistent:
% 66.36/9.97 ----------------------------------------------------------------
% 66.36/9.97 (1) ~ (all_54_4 = all_6_2)
% 66.36/9.97 (2) ~ (all_4_0 = e2)
% 66.36/9.97 (3) op(e1, e1) = e2
% 66.36/9.97 (4) ~ (all_54_9 = e2)
% 66.36/9.97 (5) all_52_2 = all_4_2
% 66.36/9.97 (6) all_58_9 = all_54_15
% 66.36/9.97 (7) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.97 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.97 (9) op(e1, e0) = all_54_4
% 66.36/9.97 (10) ~ (all_54_1 = all_54_3)
% 66.36/9.97 (11) ~ (all_54_4 = e2)
% 66.36/9.97 (12) all_38_2 = all_6_2
% 66.36/9.97 (13) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 66.36/9.97 (14) op(e0, e0) = all_6_2
% 66.36/9.97 (15) ~ (all_54_1 = all_54_9)
% 66.36/9.97 (16) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.97 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.97 (17) all_56_4 = all_54_4
% 66.36/9.97 (18) ~ (all_44_1 = e0) | ~ (all_44_2 = e2)
% 66.36/9.97 (19) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 66.36/9.97 (20) op(e2, e1) = all_14_1
% 66.36/9.97 (21) op(all_6_2, e0) = all_6_1
% 66.36/9.97 (22) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.97 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.97 (23) all_56_13 = all_54_13
% 66.36/9.97 (24) op(e2, e2) = all_10_2
% 66.36/9.97 (25) all_56_1 = all_54_1
% 66.36/9.97 (26) all_58_0 = all_6_2
% 66.36/9.97 (27) all_58_8 = all_54_3
% 66.36/9.97 (28) all_44_1 = all_14_1
% 66.36/9.97 (29) ~ (all_54_1 = all_54_13)
% 66.36/9.97 (30) all_56_9 = all_54_9
% 66.36/9.97 (31) ~ (e3 = e0)
% 66.36/9.97 (32) op(e2, e1) = all_54_9
% 66.36/9.97 (33) ~ (e1 = e0)
% 66.36/9.97 (34) all_58_7 = all_54_7
% 66.36/9.97 (35) all_44_2 = e2
% 66.36/9.97 (36) all_58_6 = all_10_2
% 66.36/9.97 (37) ~ (all_54_4 = all_54_7)
% 66.36/9.97 (38) op(e2, e2) = e3
% 66.36/9.97 (39) all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 66.36/9.97 (40) ~ (all_54_1 = e2)
% 66.36/9.97 (41) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 66.36/9.97 (42) ~ (all_54_15 = all_4_2)
% 66.36/9.97 (43) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0
% 66.36/9.97 (44) ~ (e2 = e0)
% 66.36/9.97 (45) all_58_1 = all_54_4
% 66.36/9.97 (46) ~ (all_54_9 = all_54_13)
% 66.36/9.97 (47) all_52_3 = all_6_2
% 66.36/9.97 (48) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 66.36/9.97 (49) all_52_0 = all_10_2
% 66.36/9.97 (50) all_38_1 = all_6_1
% 66.36/9.97 (51) ~ (all_54_13 = e2)
% 66.36/9.97 (52) all_52_1 = e2
% 66.36/9.97 (53) ~ (e3 = e2)
% 66.36/9.97 (54) ~ (all_54_9 = all_10_2)
% 66.36/9.97 (55) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/9.97 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/9.97 (56) ~ (all_54_13 = all_4_2)
% 66.36/9.97 (57) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 66.36/9.97 (58) ~ (all_10_2 = e1)
% 66.36/9.97
% 66.36/9.97 Begin of proof
% 66.36/9.97 |
% 66.36/9.97 | BETA: splitting (18) gives:
% 66.36/9.97 |
% 66.36/9.97 | Case 1:
% 66.36/9.97 | |
% 66.36/9.97 | | (59) ~ (all_44_1 = e0)
% 66.36/9.97 | |
% 66.36/9.97 | | REDUCE: (28), (59) imply:
% 66.36/9.98 | | (60) ~ (all_14_1 = e0)
% 66.36/9.98 | |
% 66.36/9.98 | | GROUND_INST: instantiating (8) with all_54_9, all_14_1, e1, e2, simplifying
% 66.36/9.98 | | with (20), (32) gives:
% 66.36/9.98 | | (61) all_54_9 = all_14_1
% 66.36/9.98 | |
% 66.36/9.98 | | GROUND_INST: instantiating (8) with all_10_2, e3, e2, e2, simplifying with
% 66.36/9.98 | | (24), (38) gives:
% 66.36/9.98 | | (62) all_10_2 = e3
% 66.36/9.98 | |
% 66.36/9.98 | | COMBINE_EQS: (49), (62) imply:
% 66.36/9.98 | | (63) all_52_0 = e3
% 66.36/9.98 | |
% 66.36/9.98 | | COMBINE_EQS: (30), (61) imply:
% 66.36/9.98 | | (64) all_56_9 = all_14_1
% 66.36/9.98 | |
% 66.36/9.98 | | COMBINE_EQS: (36), (62) imply:
% 66.36/9.98 | | (65) all_58_6 = e3
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (15), (61) imply:
% 66.36/9.98 | | (66) ~ (all_54_1 = all_14_1)
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (46), (61) imply:
% 66.36/9.98 | | (67) ~ (all_54_13 = all_14_1)
% 66.36/9.98 | |
% 66.36/9.98 | | SIMP: (67) implies:
% 66.36/9.98 | | (68) ~ (all_54_13 = all_14_1)
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (54), (61), (62) imply:
% 66.36/9.98 | | (69) ~ (all_14_1 = e3)
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (4), (61) imply:
% 66.36/9.98 | | (70) ~ (all_14_1 = e2)
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (58), (62) imply:
% 66.36/9.98 | | (71) ~ (e3 = e1)
% 66.36/9.98 | |
% 66.36/9.98 | | BETA: splitting (39) gives:
% 66.36/9.98 | |
% 66.36/9.98 | | Case 1:
% 66.36/9.98 | | |
% 66.36/9.98 | | | (72) all_56_9 = e3
% 66.36/9.98 | | |
% 66.36/9.98 | | | REF_CLOSE: (64), (69), (72) are inconsistent by sub-proof #119.
% 66.36/9.98 | | |
% 66.36/9.98 | | Case 2:
% 66.36/9.98 | | |
% 66.36/9.98 | | | (73) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 66.36/9.98 | | |
% 66.36/9.98 | | | BETA: splitting (55) gives:
% 66.36/9.98 | | |
% 66.36/9.98 | | | Case 1:
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | (74) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | ALPHA: (74) implies:
% 66.36/9.98 | | | | (75) all_52_0 = e0
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | REF_CLOSE: (2), (3), (5), (7), (8), (16), (22), (31), (33), (47), (52),
% 66.36/9.98 | | | | (53), (71), (75) are inconsistent by sub-proof #123.
% 66.36/9.98 | | | |
% 66.36/9.98 | | | Case 2:
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | (76) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.36/9.98 | | | | (all_52_3 = e3))
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | BETA: splitting (76) gives:
% 66.36/9.98 | | | |
% 66.36/9.98 | | | | Case 1:
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | (77) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | REF_CLOSE: (44), (52), (77) are inconsistent by sub-proof #179.
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | Case 2:
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | (78) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | ALPHA: (78) implies:
% 66.36/9.98 | | | | | (79) all_52_2 = e0
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | COMBINE_EQS: (5), (79) imply:
% 66.36/9.98 | | | | | (80) all_4_2 = e0
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | SIMP: (80) implies:
% 66.36/9.98 | | | | | (81) all_4_2 = e0
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | REDUCE: (56), (81) imply:
% 66.36/9.98 | | | | | (82) ~ (all_54_13 = e0)
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | REDUCE: (42), (81) imply:
% 66.36/9.98 | | | | | (83) ~ (all_54_15 = e0)
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | | REF_CLOSE: (1), (6), (8), (9), (10), (11), (12), (13), (14), (16),
% 66.36/9.98 | | | | | (17), (19), (21), (22), (23), (25), (26), (27), (29), (33),
% 66.36/9.98 | | | | | (34), (37), (40), (41), (43), (45), (47), (48), (50), (51),
% 66.36/9.98 | | | | | (52), (57), (60), (63), (64), (65), (66), (68), (70), (71),
% 66.36/9.98 | | | | | (73), (79), (82), (83) are inconsistent by sub-proof #113.
% 66.36/9.98 | | | | |
% 66.36/9.98 | | | | End of split
% 66.36/9.98 | | | |
% 66.36/9.98 | | | End of split
% 66.36/9.98 | | |
% 66.36/9.98 | | End of split
% 66.36/9.98 | |
% 66.36/9.98 | Case 2:
% 66.36/9.98 | |
% 66.36/9.98 | | (84) ~ (all_44_2 = e2)
% 66.36/9.98 | |
% 66.36/9.98 | | REDUCE: (35), (84) imply:
% 66.36/9.98 | | (85) $false
% 66.36/9.98 | |
% 66.36/9.98 | | CLOSE: (85) is inconsistent.
% 66.36/9.98 | |
% 66.36/9.98 | End of split
% 66.36/9.98 |
% 66.36/9.98 End of proof
% 66.36/9.98
% 66.36/9.98 Sub-proof #113 shows that the following formulas are inconsistent:
% 66.36/9.98 ----------------------------------------------------------------
% 66.36/9.98 (1) ~ (all_54_4 = all_6_2)
% 66.36/9.98 (2) ~ (all_14_1 = e0)
% 66.36/9.98 (3) all_58_9 = all_54_15
% 66.36/9.98 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.98 (5) op(e1, e0) = all_54_4
% 66.36/9.98 (6) all_52_0 = e3
% 66.36/9.98 (7) ~ (all_54_1 = all_54_3)
% 66.36/9.98 (8) ~ (all_54_4 = e2)
% 66.36/9.98 (9) all_38_2 = all_6_2
% 66.36/9.98 (10) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 66.36/9.98 (11) op(e0, e0) = all_6_2
% 66.36/9.98 (12) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.98 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.98 (13) all_56_4 = all_54_4
% 66.36/9.98 (14) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 66.36/9.98 (15) op(all_6_2, e0) = all_6_1
% 66.36/9.98 (16) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/9.98 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/9.98 (17) ~ (e3 = e1)
% 66.36/9.98 (18) all_56_13 = all_54_13
% 66.36/9.98 (19) ~ (all_54_15 = e0)
% 66.36/9.98 (20) all_56_1 = all_54_1
% 66.36/9.98 (21) all_58_0 = all_6_2
% 66.36/9.98 (22) all_58_8 = all_54_3
% 66.36/9.98 (23) ~ (all_54_1 = all_54_13)
% 66.36/9.98 (24) ~ (e1 = e0)
% 66.36/9.98 (25) ~ (all_14_1 = e2)
% 66.36/9.98 (26) all_58_7 = all_54_7
% 66.36/9.98 (27) ~ (all_54_13 = all_14_1)
% 66.36/9.98 (28) ~ (all_54_4 = all_54_7)
% 66.36/9.98 (29) all_52_2 = e0
% 66.36/9.98 (30) ~ (all_54_1 = e2)
% 66.36/9.98 (31) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 66.36/9.98 (32) ~ (all_54_13 = e0)
% 66.36/9.98 (33) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0
% 66.36/9.98 (34) ~ (all_54_1 = all_14_1)
% 66.36/9.98 (35) all_58_1 = all_54_4
% 66.36/9.98 (36) all_52_3 = all_6_2
% 66.36/9.98 (37) all_56_9 = all_14_1
% 66.36/9.98 (38) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 66.36/9.98 (39) all_38_1 = all_6_1
% 66.36/9.98 (40) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 66.36/9.98 (41) ~ (all_54_13 = e2)
% 66.36/9.98 (42) all_52_1 = e2
% 66.36/9.98 (43) all_58_6 = e3
% 66.36/9.98 (44) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 66.36/9.98
% 66.36/9.98 Begin of proof
% 66.36/9.98 |
% 66.36/9.98 | BETA: splitting (16) gives:
% 66.36/9.98 |
% 66.36/9.98 | Case 1:
% 66.36/9.98 | |
% 66.36/9.98 | | (45) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/9.98 | |
% 66.36/9.98 | | ALPHA: (45) implies:
% 66.36/9.98 | | (46) all_52_0 = e1
% 66.36/9.98 | |
% 66.36/9.98 | | REF_CLOSE: (6), (17), (46) are inconsistent by sub-proof #122.
% 66.36/9.98 | |
% 66.36/9.98 | Case 2:
% 66.36/9.98 | |
% 66.36/9.98 | | (47) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/9.98 | | = e0))
% 66.36/9.98 | |
% 66.36/9.98 | | BETA: splitting (47) gives:
% 66.36/9.98 | |
% 66.36/9.98 | | Case 1:
% 66.36/9.98 | | |
% 66.36/9.98 | | | (48) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/9.98 | | |
% 66.36/9.98 | | | REF_CLOSE: (24), (29), (48) are inconsistent by sub-proof #142.
% 66.36/9.98 | | |
% 66.36/9.98 | | Case 2:
% 66.36/9.98 | | |
% 66.36/9.98 | | | (49) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/9.98 | | |
% 66.36/9.98 | | | ALPHA: (49) implies:
% 66.36/9.98 | | | (50) all_52_3 = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | COMBINE_EQS: (36), (50) imply:
% 66.36/9.98 | | | (51) all_6_2 = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | SIMP: (51) implies:
% 66.36/9.98 | | | (52) all_6_2 = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | COMBINE_EQS: (9), (52) imply:
% 66.36/9.98 | | | (53) all_38_2 = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | COMBINE_EQS: (21), (52) imply:
% 66.36/9.98 | | | (54) all_58_0 = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | REDUCE: (1), (52) imply:
% 66.36/9.98 | | | (55) ~ (all_54_4 = e1)
% 66.36/9.98 | | |
% 66.36/9.98 | | | REDUCE: (15), (52) imply:
% 66.36/9.98 | | | (56) op(e1, e0) = all_6_1
% 66.36/9.98 | | |
% 66.36/9.98 | | | REDUCE: (11), (52) imply:
% 66.36/9.98 | | | (57) op(e0, e0) = e1
% 66.36/9.98 | | |
% 66.36/9.98 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 66.36/9.98 | | | (14), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 66.36/9.98 | | | (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 66.36/9.98 | | | (39), (40), (41), (42), (43), (44), (53), (54), (55), (56),
% 66.36/9.98 | | | (57) are inconsistent by sub-proof #114.
% 66.36/9.98 | | |
% 66.36/9.98 | | End of split
% 66.36/9.98 | |
% 66.36/9.98 | End of split
% 66.36/9.98 |
% 66.36/9.98 End of proof
% 66.36/9.98
% 66.36/9.98 Sub-proof #114 shows that the following formulas are inconsistent:
% 66.36/9.98 ----------------------------------------------------------------
% 66.36/9.98 (1) ~ (all_14_1 = e0)
% 66.36/9.98 (2) op(e0, e0) = e1
% 66.36/9.98 (3) all_58_0 = e1
% 66.36/9.98 (4) all_58_9 = all_54_15
% 66.36/9.98 (5) all_38_2 = e1
% 66.36/9.98 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/9.98 (7) op(e1, e0) = all_54_4
% 66.36/9.98 (8) all_52_0 = e3
% 66.36/9.98 (9) ~ (all_54_1 = all_54_3)
% 66.36/9.98 (10) ~ (all_54_4 = e2)
% 66.36/9.98 (11) all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 66.36/9.98 (12) op(e0, e0) = all_6_2
% 66.36/9.98 (13) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/9.98 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/9.98 (14) all_56_4 = all_54_4
% 66.36/9.98 (15) op(e1, e0) = all_6_1
% 66.36/9.98 (16) all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 66.36/9.99 (17) all_56_13 = all_54_13
% 66.36/9.99 (18) ~ (all_54_15 = e0)
% 66.36/9.99 (19) all_56_1 = all_54_1
% 66.36/9.99 (20) ~ (all_54_4 = e1)
% 66.36/9.99 (21) all_58_8 = all_54_3
% 66.36/9.99 (22) ~ (all_54_1 = all_54_13)
% 66.36/9.99 (23) ~ (e1 = e0)
% 66.36/9.99 (24) ~ (all_14_1 = e2)
% 66.36/9.99 (25) all_58_7 = all_54_7
% 66.36/9.99 (26) ~ (all_54_13 = all_14_1)
% 66.36/9.99 (27) ~ (all_54_4 = all_54_7)
% 66.36/9.99 (28) ~ (all_54_1 = e2)
% 66.36/9.99 (29) all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 66.36/9.99 (30) ~ (all_54_13 = e0)
% 66.36/9.99 (31) all_58_0 = e0 | all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0
% 66.36/9.99 (32) ~ (all_54_1 = all_14_1)
% 66.36/9.99 (33) all_58_1 = all_54_4
% 66.36/9.99 (34) all_52_3 = all_6_2
% 66.36/9.99 (35) all_56_9 = all_14_1
% 66.36/9.99 (36) ~ (all_38_1 = e3) | ~ (all_38_2 = e1)
% 66.36/9.99 (37) all_38_1 = all_6_1
% 66.36/9.99 (38) all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 66.36/9.99 (39) ~ (all_54_13 = e2)
% 66.36/9.99 (40) all_52_1 = e2
% 66.36/9.99 (41) all_58_6 = e3
% 66.36/9.99 (42) all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | BETA: splitting (31) gives:
% 66.36/9.99 |
% 66.36/9.99 | Case 1:
% 66.36/9.99 | |
% 66.36/9.99 | | (43) all_58_0 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (3), (43) imply:
% 66.36/9.99 | | (44) e1 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (23), (44) imply:
% 66.36/9.99 | | (45) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (45) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | Case 2:
% 66.36/9.99 | |
% 66.36/9.99 | | (46) all_58_1 = e0 | all_58_5 = e0 | all_58_11 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | BETA: splitting (46) gives:
% 66.36/9.99 | |
% 66.36/9.99 | | Case 1:
% 66.36/9.99 | | |
% 66.36/9.99 | | | (47) all_58_1 = e0
% 66.36/9.99 | | |
% 66.36/9.99 | | | COMBINE_EQS: (33), (47) imply:
% 66.36/9.99 | | | (48) all_54_4 = e0
% 66.36/9.99 | | |
% 66.36/9.99 | | | REDUCE: (27), (48) imply:
% 66.36/9.99 | | | (49) ~ (all_54_7 = e0)
% 66.36/9.99 | | |
% 66.36/9.99 | | | SIMP: (49) implies:
% 66.36/9.99 | | | (50) ~ (all_54_7 = e0)
% 66.36/9.99 | | |
% 66.36/9.99 | | | BETA: splitting (38) gives:
% 66.36/9.99 | | |
% 66.36/9.99 | | | Case 1:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | (51) all_56_9 = e2
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | COMBINE_EQS: (35), (51) imply:
% 66.36/9.99 | | | | (52) all_14_1 = e2
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | REDUCE: (24), (52) imply:
% 66.36/9.99 | | | | (53) $false
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | CLOSE: (53) is inconsistent.
% 66.36/9.99 | | | |
% 66.36/9.99 | | | Case 2:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | (54) all_56_9 = e1 | all_56_9 = e0
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | BETA: splitting (54) gives:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | Case 1:
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | (55) all_56_9 = e1
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | COMBINE_EQS: (35), (55) imply:
% 66.36/9.99 | | | | | (56) all_14_1 = e1
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REDUCE: (32), (56) imply:
% 66.36/9.99 | | | | | (57) ~ (all_54_1 = e1)
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REDUCE: (26), (56) imply:
% 66.36/9.99 | | | | | (58) ~ (all_54_13 = e1)
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | BETA: splitting (16) gives:
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | Case 1:
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | (59) all_56_13 = e3
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | COMBINE_EQS: (17), (59) imply:
% 66.36/9.99 | | | | | | (60) all_54_13 = e3
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | SIMP: (60) implies:
% 66.36/9.99 | | | | | | (61) all_54_13 = e3
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | REDUCE: (22), (61) imply:
% 66.36/9.99 | | | | | | (62) ~ (all_54_1 = e3)
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | REDUCE: (39), (61) imply:
% 66.36/9.99 | | | | | | (63) ~ (e3 = e2)
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | REDUCE: (58), (61) imply:
% 66.36/9.99 | | | | | | (64) ~ (e3 = e1)
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | REDUCE: (30), (61) imply:
% 66.36/9.99 | | | | | | (65) ~ (e3 = e0)
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | BETA: splitting (42) gives:
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | Case 1:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | (66) all_58_6 = e0
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | COMBINE_EQS: (41), (66) imply:
% 66.36/9.99 | | | | | | | (67) e3 = e0
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | COMBINE_EQS: (8), (67) imply:
% 66.36/9.99 | | | | | | | (68) all_52_0 = e0
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | REF_CLOSE: (2), (6), (12), (13), (34), (40), (63), (64), (65),
% 66.36/9.99 | | | | | | | (68) are inconsistent by sub-proof #137.
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | Case 2:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | (69) all_58_7 = e0 | all_58_8 = e0 | all_58_9 = e0
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | BETA: splitting (11) gives:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | Case 1:
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | (70) all_56_1 = e3
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | COMBINE_EQS: (19), (70) imply:
% 66.36/9.99 | | | | | | | | (71) all_54_1 = e3
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | REDUCE: (62), (71) imply:
% 66.36/9.99 | | | | | | | | (72) $false
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | CLOSE: (72) is inconsistent.
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | Case 2:
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | (73) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | BETA: splitting (69) gives:
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | Case 1:
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | (74) all_58_7 = e0
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | COMBINE_EQS: (25), (74) imply:
% 66.36/9.99 | | | | | | | | | (75) all_54_7 = e0
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | REDUCE: (50), (75) imply:
% 66.36/9.99 | | | | | | | | | (76) $false
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | CLOSE: (76) is inconsistent.
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | Case 2:
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | (77) all_58_8 = e0 | all_58_9 = e0
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | BETA: splitting (77) gives:
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | | Case 1:
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | (78) all_58_8 = e0
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | COMBINE_EQS: (21), (78) imply:
% 66.36/9.99 | | | | | | | | | | (79) all_54_3 = e0
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | REDUCE: (9), (79) imply:
% 66.36/9.99 | | | | | | | | | | (80) ~ (all_54_1 = e0)
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | REF_CLOSE: (19), (28), (57), (73), (80) are inconsistent by
% 66.36/9.99 | | | | | | | | | | sub-proof #117.
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | Case 2:
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | (81) all_58_9 = e0
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | COMBINE_EQS: (4), (81) imply:
% 66.36/9.99 | | | | | | | | | | (82) all_54_15 = e0
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | REDUCE: (18), (82) imply:
% 66.36/9.99 | | | | | | | | | | (83) $false
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | | CLOSE: (83) is inconsistent.
% 66.36/9.99 | | | | | | | | | |
% 66.36/9.99 | | | | | | | | | End of split
% 66.36/9.99 | | | | | | | | |
% 66.36/9.99 | | | | | | | | End of split
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | End of split
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | End of split
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | Case 2:
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | (84) all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | BETA: splitting (84) gives:
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | | Case 1:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | (85) all_56_13 = e2
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | COMBINE_EQS: (17), (85) imply:
% 66.36/9.99 | | | | | | | (86) all_54_13 = e2
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | SIMP: (86) implies:
% 66.36/9.99 | | | | | | | (87) all_54_13 = e2
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | REDUCE: (39), (87) imply:
% 66.36/9.99 | | | | | | | (88) $false
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | CLOSE: (88) is inconsistent.
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | Case 2:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | (89) all_56_13 = e1 | all_56_13 = e0
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | BETA: splitting (89) gives:
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | | Case 1:
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | (90) all_56_13 = e1
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | COMBINE_EQS: (17), (90) imply:
% 66.36/9.99 | | | | | | | | (91) all_54_13 = e1
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | SIMP: (91) implies:
% 66.36/9.99 | | | | | | | | (92) all_54_13 = e1
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | REDUCE: (58), (92) imply:
% 66.36/9.99 | | | | | | | | (93) $false
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | CLOSE: (93) is inconsistent.
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | Case 2:
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | (94) all_56_13 = e0
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | COMBINE_EQS: (17), (94) imply:
% 66.36/9.99 | | | | | | | | (95) all_54_13 = e0
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | SIMP: (95) implies:
% 66.36/9.99 | | | | | | | | (96) all_54_13 = e0
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | REDUCE: (30), (96) imply:
% 66.36/9.99 | | | | | | | | (97) $false
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | | CLOSE: (97) is inconsistent.
% 66.36/9.99 | | | | | | | |
% 66.36/9.99 | | | | | | | End of split
% 66.36/9.99 | | | | | | |
% 66.36/9.99 | | | | | | End of split
% 66.36/9.99 | | | | | |
% 66.36/9.99 | | | | | End of split
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | Case 2:
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | (98) all_56_9 = e0
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | COMBINE_EQS: (35), (98) imply:
% 66.36/9.99 | | | | | (99) all_14_1 = e0
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REDUCE: (1), (99) imply:
% 66.36/9.99 | | | | | (100) $false
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | CLOSE: (100) is inconsistent.
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | End of split
% 66.36/9.99 | | | |
% 66.36/9.99 | | | End of split
% 66.36/9.99 | | |
% 66.36/9.99 | | Case 2:
% 66.36/9.99 | | |
% 66.36/9.99 | | | (101) ~ (all_58_1 = e0)
% 66.36/9.99 | | |
% 66.36/9.99 | | | REDUCE: (33), (101) imply:
% 66.36/9.99 | | | (102) ~ (all_54_4 = e0)
% 66.36/9.99 | | |
% 66.36/9.99 | | | BETA: splitting (36) gives:
% 66.36/9.99 | | |
% 66.36/9.99 | | | Case 1:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | (103) ~ (all_38_1 = e3)
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | REDUCE: (37), (103) imply:
% 66.36/9.99 | | | | (104) ~ (all_6_1 = e3)
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | BETA: splitting (29) gives:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | Case 1:
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | (105) all_56_4 = e3
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | COMBINE_EQS: (14), (105) imply:
% 66.36/9.99 | | | | | (106) all_54_4 = e3
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REDUCE: (7), (106) imply:
% 66.36/9.99 | | | | | (107) op(e1, e0) = e3
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | GROUND_INST: instantiating (6) with e3, all_6_1, e0, e1, simplifying
% 66.36/9.99 | | | | | with (15), (107) gives:
% 66.36/9.99 | | | | | (108) all_6_1 = e3
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REDUCE: (104), (108) imply:
% 66.36/9.99 | | | | | (109) $false
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | CLOSE: (109) is inconsistent.
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | Case 2:
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | (110) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | | REF_CLOSE: (10), (14), (20), (102), (110) are inconsistent by
% 66.36/9.99 | | | | | sub-proof #115.
% 66.36/9.99 | | | | |
% 66.36/9.99 | | | | End of split
% 66.36/9.99 | | | |
% 66.36/9.99 | | | Case 2:
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | (111) ~ (all_38_2 = e1)
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | REDUCE: (5), (111) imply:
% 66.36/9.99 | | | | (112) $false
% 66.36/9.99 | | | |
% 66.36/9.99 | | | | CLOSE: (112) is inconsistent.
% 66.36/9.99 | | | |
% 66.36/9.99 | | | End of split
% 66.36/9.99 | | |
% 66.36/9.99 | | End of split
% 66.36/9.99 | |
% 66.36/9.99 | End of split
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #115 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) ~ (all_54_4 = e2)
% 66.36/9.99 (2) all_56_4 = all_54_4
% 66.36/9.99 (3) ~ (all_54_4 = e1)
% 66.36/9.99 (4) ~ (all_54_4 = e0)
% 66.36/9.99 (5) all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | BETA: splitting (5) gives:
% 66.36/9.99 |
% 66.36/9.99 | Case 1:
% 66.36/9.99 | |
% 66.36/9.99 | | (6) all_56_4 = e2
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (2), (6) imply:
% 66.36/9.99 | | (7) all_54_4 = e2
% 66.36/9.99 | |
% 66.36/9.99 | | SIMP: (7) implies:
% 66.36/9.99 | | (8) all_54_4 = e2
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (1), (8) imply:
% 66.36/9.99 | | (9) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (9) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | Case 2:
% 66.36/9.99 | |
% 66.36/9.99 | | (10) all_56_4 = e1 | all_56_4 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #116.
% 66.36/9.99 | |
% 66.36/9.99 | End of split
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #116 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) all_56_4 = e1 | all_56_4 = e0
% 66.36/9.99 (2) all_56_4 = all_54_4
% 66.36/9.99 (3) ~ (all_54_4 = e1)
% 66.36/9.99 (4) ~ (all_54_4 = e0)
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | BETA: splitting (1) gives:
% 66.36/9.99 |
% 66.36/9.99 | Case 1:
% 66.36/9.99 | |
% 66.36/9.99 | | (5) all_56_4 = e1
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (2), (5) imply:
% 66.36/9.99 | | (6) all_54_4 = e1
% 66.36/9.99 | |
% 66.36/9.99 | | SIMP: (6) implies:
% 66.36/9.99 | | (7) all_54_4 = e1
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (3), (7) imply:
% 66.36/9.99 | | (8) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (8) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | Case 2:
% 66.36/9.99 | |
% 66.36/9.99 | | (9) all_56_4 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (2), (9) imply:
% 66.36/9.99 | | (10) all_54_4 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | SIMP: (10) implies:
% 66.36/9.99 | | (11) all_54_4 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (4), (11) imply:
% 66.36/9.99 | | (12) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (12) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | End of split
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #117 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) all_56_1 = all_54_1
% 66.36/9.99 (2) all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 66.36/9.99 (3) ~ (all_54_1 = e2)
% 66.36/9.99 (4) ~ (all_54_1 = e1)
% 66.36/9.99 (5) ~ (all_54_1 = e0)
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | BETA: splitting (2) gives:
% 66.36/9.99 |
% 66.36/9.99 | Case 1:
% 66.36/9.99 | |
% 66.36/9.99 | | (6) all_56_1 = e2
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (1), (6) imply:
% 66.36/9.99 | | (7) all_54_1 = e2
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (3), (7) imply:
% 66.36/9.99 | | (8) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (8) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | Case 2:
% 66.36/9.99 | |
% 66.36/9.99 | | (9) all_56_1 = e1 | all_56_1 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #118.
% 66.36/9.99 | |
% 66.36/9.99 | End of split
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #118 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) all_56_1 = e1 | all_56_1 = e0
% 66.36/9.99 (2) all_56_1 = all_54_1
% 66.36/9.99 (3) ~ (all_54_1 = e1)
% 66.36/9.99 (4) ~ (all_54_1 = e0)
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | BETA: splitting (1) gives:
% 66.36/9.99 |
% 66.36/9.99 | Case 1:
% 66.36/9.99 | |
% 66.36/9.99 | | (5) all_56_1 = e1
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (2), (5) imply:
% 66.36/9.99 | | (6) all_54_1 = e1
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (3), (6) imply:
% 66.36/9.99 | | (7) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (7) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | Case 2:
% 66.36/9.99 | |
% 66.36/9.99 | | (8) all_56_1 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | COMBINE_EQS: (2), (8) imply:
% 66.36/9.99 | | (9) all_54_1 = e0
% 66.36/9.99 | |
% 66.36/9.99 | | REDUCE: (4), (9) imply:
% 66.36/9.99 | | (10) $false
% 66.36/9.99 | |
% 66.36/9.99 | | CLOSE: (10) is inconsistent.
% 66.36/9.99 | |
% 66.36/9.99 | End of split
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #119 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) all_56_9 = all_14_1
% 66.36/9.99 (2) all_56_9 = e3
% 66.36/9.99 (3) ~ (all_14_1 = e3)
% 66.36/9.99
% 66.36/9.99 Begin of proof
% 66.36/9.99 |
% 66.36/9.99 | COMBINE_EQS: (1), (2) imply:
% 66.36/9.99 | (4) all_14_1 = e3
% 66.36/9.99 |
% 66.36/9.99 | SIMP: (4) implies:
% 66.36/9.99 | (5) all_14_1 = e3
% 66.36/9.99 |
% 66.36/9.99 | REDUCE: (3), (5) imply:
% 66.36/9.99 | (6) $false
% 66.36/9.99 |
% 66.36/9.99 | CLOSE: (6) is inconsistent.
% 66.36/9.99 |
% 66.36/9.99 End of proof
% 66.36/9.99
% 66.36/9.99 Sub-proof #120 shows that the following formulas are inconsistent:
% 66.36/9.99 ----------------------------------------------------------------
% 66.36/9.99 (1) ~ (all_52_0 = e1)
% 66.36/9.99 (2) ~ (all_4_0 = e2)
% 66.36/9.99 (3) op(e1, e1) = all_14_2
% 66.36/9.99 (4) all_52_2 = all_4_2
% 66.36/9.99 (5) op(all_4_2, all_4_2) = all_4_0
% 66.36/9.99 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/9.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/10.00 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/10.00 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/10.00 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/10.00 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/10.00 (9) op(e2, e2) = all_10_2
% 66.36/10.00 (10) ~ (all_6_0 = e2)
% 66.36/10.00 (11) ~ (e3 = e0)
% 66.36/10.00 (12) ~ (e1 = e0)
% 66.36/10.00 (13) all_14_2 = e2
% 66.36/10.00 (14) op(all_6_2, all_6_2) = all_6_0
% 66.36/10.00 (15) ~ (e2 = e0)
% 66.36/10.00 (16) all_52_3 = all_6_2
% 66.36/10.00 (17) all_52_0 = all_10_2
% 66.36/10.00 (18) op(all_14_2, all_14_2) = e3
% 66.36/10.00 (19) all_52_1 = e2
% 66.36/10.00 (20) ~ (e3 = e2)
% 66.36/10.00 (21) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/10.00 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/10.00
% 66.36/10.00 Begin of proof
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (1), (17) imply:
% 66.36/10.00 | (22) ~ (all_10_2 = e1)
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (13), (18) imply:
% 66.36/10.00 | (23) op(e2, e2) = e3
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (3), (13) imply:
% 66.36/10.00 | (24) op(e1, e1) = e2
% 66.36/10.00 |
% 66.36/10.00 | GROUND_INST: instantiating (6) with all_10_2, e3, e2, e2, simplifying with
% 66.36/10.00 | (9), (23) gives:
% 66.36/10.00 | (25) all_10_2 = e3
% 66.36/10.00 |
% 66.36/10.00 | COMBINE_EQS: (17), (25) imply:
% 66.36/10.00 | (26) all_52_0 = e3
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (22), (25) imply:
% 66.36/10.00 | (27) ~ (e3 = e1)
% 66.36/10.00 |
% 66.36/10.00 | BETA: splitting (21) gives:
% 66.36/10.00 |
% 66.36/10.00 | Case 1:
% 66.36/10.00 | |
% 66.36/10.00 | | (28) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/10.00 | |
% 66.36/10.00 | | ALPHA: (28) implies:
% 66.36/10.00 | | (29) all_52_0 = e0
% 66.36/10.00 | |
% 66.36/10.00 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (11), (12), (16), (19), (20), (24),
% 66.36/10.00 | | (27), (29) are inconsistent by sub-proof #123.
% 66.36/10.00 | |
% 66.36/10.00 | Case 2:
% 66.36/10.00 | |
% 66.36/10.00 | | (30) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.36/10.00 | | = e3))
% 66.36/10.00 | |
% 66.36/10.00 | | BETA: splitting (30) gives:
% 66.36/10.00 | |
% 66.36/10.00 | | Case 1:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (31) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/10.00 | | |
% 66.36/10.00 | | | REF_CLOSE: (15), (19), (31) are inconsistent by sub-proof #179.
% 66.36/10.00 | | |
% 66.36/10.00 | | Case 2:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (32) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.36/10.00 | | |
% 66.36/10.00 | | | ALPHA: (32) implies:
% 66.36/10.00 | | | (33) all_52_2 = e0
% 66.36/10.00 | | |
% 66.36/10.00 | | | REF_CLOSE: (6), (8), (10), (12), (14), (16), (24), (26), (27), (33) are
% 66.36/10.00 | | | inconsistent by sub-proof #121.
% 66.36/10.00 | | |
% 66.36/10.00 | | End of split
% 66.36/10.00 | |
% 66.36/10.00 | End of split
% 66.36/10.00 |
% 66.36/10.00 End of proof
% 66.36/10.00
% 66.36/10.00 Sub-proof #121 shows that the following formulas are inconsistent:
% 66.36/10.00 ----------------------------------------------------------------
% 66.36/10.00 (1) op(e1, e1) = e2
% 66.36/10.00 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/10.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/10.00 (3) all_52_0 = e3
% 66.36/10.00 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/10.00 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/10.00 (5) ~ (e3 = e1)
% 66.36/10.00 (6) ~ (all_6_0 = e2)
% 66.36/10.00 (7) ~ (e1 = e0)
% 66.36/10.00 (8) op(all_6_2, all_6_2) = all_6_0
% 66.36/10.00 (9) all_52_2 = e0
% 66.36/10.00 (10) all_52_3 = all_6_2
% 66.36/10.00
% 66.36/10.00 Begin of proof
% 66.36/10.00 |
% 66.36/10.00 | BETA: splitting (4) gives:
% 66.36/10.00 |
% 66.36/10.00 | Case 1:
% 66.36/10.00 | |
% 66.36/10.00 | | (11) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/10.00 | |
% 66.36/10.00 | | ALPHA: (11) implies:
% 66.36/10.00 | | (12) all_52_0 = e1
% 66.36/10.00 | |
% 66.36/10.00 | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #122.
% 66.36/10.00 | |
% 66.36/10.00 | Case 2:
% 66.36/10.00 | |
% 66.36/10.00 | | (13) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.36/10.00 | | = e0))
% 66.36/10.00 | |
% 66.36/10.00 | | BETA: splitting (13) gives:
% 66.36/10.00 | |
% 66.36/10.00 | | Case 1:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (14) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/10.00 | | |
% 66.36/10.00 | | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #142.
% 66.36/10.00 | | |
% 66.36/10.00 | | Case 2:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (15) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/10.00 | | |
% 66.36/10.00 | | | ALPHA: (15) implies:
% 66.36/10.00 | | | (16) all_52_3 = e1
% 66.36/10.00 | | |
% 66.36/10.00 | | | COMBINE_EQS: (10), (16) imply:
% 66.36/10.00 | | | (17) all_6_2 = e1
% 66.36/10.00 | | |
% 66.36/10.00 | | | SIMP: (17) implies:
% 66.36/10.00 | | | (18) all_6_2 = e1
% 66.36/10.00 | | |
% 66.36/10.00 | | | REDUCE: (8), (18) imply:
% 66.36/10.00 | | | (19) op(e1, e1) = all_6_0
% 66.36/10.00 | | |
% 66.36/10.00 | | | GROUND_INST: instantiating (2) with e2, all_6_0, e1, e1, simplifying with
% 66.36/10.00 | | | (1), (19) gives:
% 66.36/10.00 | | | (20) all_6_0 = e2
% 66.36/10.00 | | |
% 66.36/10.00 | | | REDUCE: (6), (20) imply:
% 66.36/10.00 | | | (21) $false
% 66.36/10.00 | | |
% 66.36/10.00 | | | CLOSE: (21) is inconsistent.
% 66.36/10.00 | | |
% 66.36/10.00 | | End of split
% 66.36/10.00 | |
% 66.36/10.00 | End of split
% 66.36/10.00 |
% 66.36/10.00 End of proof
% 66.36/10.00
% 66.36/10.00 Sub-proof #122 shows that the following formulas are inconsistent:
% 66.36/10.00 ----------------------------------------------------------------
% 66.36/10.00 (1) all_52_0 = e3
% 66.36/10.00 (2) all_52_0 = e1
% 66.36/10.00 (3) ~ (e3 = e1)
% 66.36/10.00
% 66.36/10.00 Begin of proof
% 66.36/10.00 |
% 66.36/10.00 | COMBINE_EQS: (1), (2) imply:
% 66.36/10.00 | (4) e3 = e1
% 66.36/10.00 |
% 66.36/10.00 | SIMP: (4) implies:
% 66.36/10.00 | (5) e3 = e1
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (3), (5) imply:
% 66.36/10.00 | (6) $false
% 66.36/10.00 |
% 66.36/10.00 | CLOSE: (6) is inconsistent.
% 66.36/10.00 |
% 66.36/10.00 End of proof
% 66.36/10.00
% 66.36/10.00 Sub-proof #123 shows that the following formulas are inconsistent:
% 66.36/10.00 ----------------------------------------------------------------
% 66.36/10.00 (1) ~ (all_4_0 = e2)
% 66.36/10.00 (2) op(e1, e1) = e2
% 66.36/10.00 (3) all_52_2 = all_4_2
% 66.36/10.00 (4) op(all_4_2, all_4_2) = all_4_0
% 66.36/10.00 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/10.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/10.00 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/10.00 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/10.00 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/10.00 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/10.00 (8) ~ (e3 = e1)
% 66.36/10.00 (9) ~ (e3 = e0)
% 66.36/10.00 (10) ~ (e1 = e0)
% 66.36/10.00 (11) all_52_0 = e0
% 66.36/10.00 (12) all_52_3 = all_6_2
% 66.36/10.00 (13) all_52_1 = e2
% 66.36/10.00 (14) ~ (e3 = e2)
% 66.36/10.00
% 66.36/10.00 Begin of proof
% 66.36/10.00 |
% 66.36/10.00 | BETA: splitting (6) gives:
% 66.36/10.00 |
% 66.36/10.00 | Case 1:
% 66.36/10.00 | |
% 66.36/10.00 | | (15) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/10.00 | |
% 66.36/10.00 | | ALPHA: (15) implies:
% 66.36/10.00 | | (16) all_52_0 = e3
% 66.36/10.00 | |
% 66.36/10.00 | | REF_CLOSE: (9), (11), (16) are inconsistent by sub-proof #124.
% 66.36/10.00 | |
% 66.36/10.00 | Case 2:
% 66.36/10.00 | |
% 66.36/10.00 | | (17) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.36/10.00 | | = e0))
% 66.36/10.00 | |
% 66.36/10.00 | | BETA: splitting (17) gives:
% 66.36/10.00 | |
% 66.36/10.00 | | Case 1:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (18) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/10.00 | | |
% 66.36/10.00 | | | REF_CLOSE: (13), (14), (18) are inconsistent by sub-proof #180.
% 66.36/10.00 | | |
% 66.36/10.00 | | Case 2:
% 66.36/10.00 | | |
% 66.36/10.00 | | | (19) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/10.00 | | |
% 66.36/10.00 | | | ALPHA: (19) implies:
% 66.36/10.00 | | | (20) all_52_3 = e3
% 66.36/10.00 | | |
% 66.36/10.00 | | | COMBINE_EQS: (12), (20) imply:
% 66.36/10.00 | | | (21) all_6_2 = e3
% 66.36/10.00 | | |
% 66.36/10.00 | | | BETA: splitting (7) gives:
% 66.36/10.00 | | |
% 66.36/10.00 | | | Case 1:
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | (22) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | ALPHA: (22) implies:
% 66.36/10.00 | | | | (23) all_52_0 = e1
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | REF_CLOSE: (10), (11), (23) are inconsistent by sub-proof #133.
% 66.36/10.00 | | | |
% 66.36/10.00 | | | Case 2:
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | (24) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 66.36/10.00 | | | | (all_52_1 = e0))
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | BETA: splitting (24) gives:
% 66.36/10.00 | | | |
% 66.36/10.00 | | | | Case 1:
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | (25) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | ALPHA: (25) implies:
% 66.36/10.00 | | | | | (26) all_52_2 = e1
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | COMBINE_EQS: (3), (26) imply:
% 66.36/10.00 | | | | | (27) all_4_2 = e1
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | REDUCE: (4), (27) imply:
% 66.36/10.00 | | | | | (28) op(e1, e1) = all_4_0
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | GROUND_INST: instantiating (5) with e2, all_4_0, e1, e1, simplifying
% 66.36/10.00 | | | | | with (2), (28) gives:
% 66.36/10.00 | | | | | (29) all_4_0 = e2
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | REDUCE: (1), (29) imply:
% 66.36/10.00 | | | | | (30) $false
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | CLOSE: (30) is inconsistent.
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | Case 2:
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | (31) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | | REF_CLOSE: (8), (20), (31) are inconsistent by sub-proof #145.
% 66.36/10.00 | | | | |
% 66.36/10.00 | | | | End of split
% 66.36/10.00 | | | |
% 66.36/10.00 | | | End of split
% 66.36/10.00 | | |
% 66.36/10.00 | | End of split
% 66.36/10.00 | |
% 66.36/10.00 | End of split
% 66.36/10.00 |
% 66.36/10.00 End of proof
% 66.36/10.00
% 66.36/10.00 Sub-proof #124 shows that the following formulas are inconsistent:
% 66.36/10.00 ----------------------------------------------------------------
% 66.36/10.00 (1) all_52_0 = e3
% 66.36/10.00 (2) all_52_0 = e0
% 66.36/10.00 (3) ~ (e3 = e0)
% 66.36/10.00
% 66.36/10.00 Begin of proof
% 66.36/10.00 |
% 66.36/10.00 | COMBINE_EQS: (1), (2) imply:
% 66.36/10.00 | (4) e3 = e0
% 66.36/10.00 |
% 66.36/10.00 | SIMP: (4) implies:
% 66.36/10.00 | (5) e3 = e0
% 66.36/10.00 |
% 66.36/10.00 | REDUCE: (3), (5) imply:
% 66.36/10.00 | (6) $false
% 66.36/10.00 |
% 66.36/10.00 | CLOSE: (6) is inconsistent.
% 66.36/10.00 |
% 66.36/10.00 End of proof
% 66.36/10.00
% 66.36/10.00 Sub-proof #125 shows that the following formulas are inconsistent:
% 66.36/10.00 ----------------------------------------------------------------
% 66.36/10.00 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 66.36/10.00 e0))
% 66.36/10.00 (2) all_28_1 = all_6_1
% 66.36/10.00 (3) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 66.36/10.00 (4) all_52_2 = all_4_2
% 66.36/10.00 (5) op(all_4_2, all_4_2) = e1
% 66.36/10.00 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/10.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/10.00 (7) all_58_13 = all_54_10
% 66.36/10.00 (8) ~ (all_54_8 = all_54_12)
% 66.36/10.00 (9) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/10.00 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/10.00 (10) op(e3, e0) = all_54_12
% 66.36/10.00 (11) op(all_6_2, e0) = all_6_1
% 66.36/10.00 (12) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.36/10.00 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.36/10.00 (13) op(e2, e2) = all_10_2
% 66.36/10.00 (14) all_26_2 = all_4_2
% 66.36/10.00 (15) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 66.36/10.00 (16) op(all_6_2, all_6_2) = e2
% 66.36/10.00 (17) all_52_1 = all_14_2
% 66.36/10.00 (18) all_58_4 = all_54_9
% 66.36/10.00 (19) ~ (all_54_12 = all_4_2)
% 66.36/10.00 (20) ~ (e3 = e0)
% 66.36/10.00 (21) ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 66.36/10.00 (22) ~ (e1 = e0)
% 66.36/10.00 (23) op(e2, e3) = all_54_10
% 66.36/10.00 (24) all_58_6 = all_10_2
% 66.36/10.00 (25) ~ (all_54_9 = all_14_2)
% 66.36/10.00 (26) all_56_12 = all_54_12
% 66.36/10.00 (27) all_26_1 = all_4_1
% 66.36/10.00 (28) all_28_2 = all_6_2
% 66.36/10.00 (29) ~ (all_54_10 = all_4_2)
% 66.36/10.00 (30) ~ (e2 = e0)
% 66.36/10.00 (31) op(all_4_2, e3) = all_4_1
% 66.36/10.00 (32) ~ (e2 = e1)
% 66.36/10.00 (33) all_52_3 = all_6_2
% 66.36/10.00 (34) all_52_0 = all_10_2
% 66.36/10.00 (35) ~ (all_54_10 = all_10_2)
% 66.36/10.00 (36) all_56_11 = all_54_10
% 66.36/10.00 (37) ~ (e3 = e2)
% 66.36/10.00 (38) all_58_5 = all_54_8
% 66.36/10.00 (39) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/10.00 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/10.00 (40) ~ (all_54_12 = all_6_2)
% 66.36/10.01 (41) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 66.36/10.01 (42) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 66.36/10.01
% 66.36/10.01 Begin of proof
% 66.36/10.01 |
% 66.36/10.01 | BETA: splitting (1) gives:
% 66.36/10.01 |
% 66.36/10.01 | Case 1:
% 66.36/10.01 | |
% 66.36/10.01 | | (43) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.36/10.01 | |
% 66.36/10.01 | | ALPHA: (43) implies:
% 66.36/10.01 | | (44) all_52_2 = e2
% 66.36/10.01 | | (45) ~ (all_52_0 = e3)
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (4), (44) imply:
% 66.36/10.01 | | (46) all_4_2 = e2
% 66.36/10.01 | |
% 66.36/10.01 | | SIMP: (46) implies:
% 66.36/10.01 | | (47) all_4_2 = e2
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (14), (47) imply:
% 66.36/10.01 | | (48) all_26_2 = e2
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (29), (47) imply:
% 66.36/10.01 | | (49) ~ (all_54_10 = e2)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (19), (47) imply:
% 66.36/10.01 | | (50) ~ (all_54_12 = e2)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (34), (45) imply:
% 66.36/10.01 | | (51) ~ (all_10_2 = e3)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (5), (47) imply:
% 66.36/10.01 | | (52) op(e2, e2) = e1
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (31), (47) imply:
% 66.36/10.01 | | (53) op(e2, e3) = all_4_1
% 66.36/10.01 | |
% 66.36/10.01 | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (13), (15), (17), (18),
% 66.36/10.01 | | (20), (21), (22), (23), (24), (25), (26), (27), (28), (30), (33),
% 66.36/10.01 | | (34), (35), (36), (38), (39), (40), (41), (42), (44), (48), (49),
% 66.36/10.01 | | (50), (51), (52), (53) are inconsistent by sub-proof #126.
% 66.36/10.01 | |
% 66.36/10.01 | Case 2:
% 66.36/10.01 | |
% 66.36/10.01 | | (54) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.36/10.01 | |
% 66.36/10.01 | | REF_CLOSE: (6), (9), (12), (13), (16), (17), (22), (32), (33), (34), (37),
% 66.36/10.01 | | (39), (54) are inconsistent by sub-proof #149.
% 66.36/10.01 | |
% 66.36/10.01 | End of split
% 66.36/10.01 |
% 66.36/10.01 End of proof
% 66.36/10.01
% 66.36/10.01 Sub-proof #126 shows that the following formulas are inconsistent:
% 66.36/10.01 ----------------------------------------------------------------
% 66.36/10.01 (1) all_26_2 = e2
% 66.36/10.01 (2) all_28_1 = all_6_1
% 66.36/10.01 (3) all_58_4 = e0 | all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 66.36/10.01 (4) op(e2, e2) = e1
% 66.36/10.01 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.36/10.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.36/10.01 (6) all_58_13 = all_54_10
% 66.36/10.01 (7) ~ (all_54_8 = all_54_12)
% 66.36/10.01 (8) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.36/10.01 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.36/10.01 (9) op(e3, e0) = all_54_12
% 66.36/10.01 (10) op(all_6_2, e0) = all_6_1
% 66.36/10.01 (11) op(e2, e2) = all_10_2
% 66.36/10.01 (12) all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 66.36/10.01 (13) all_52_1 = all_14_2
% 66.36/10.01 (14) all_58_4 = all_54_9
% 66.36/10.01 (15) ~ (e3 = e0)
% 66.36/10.01 (16) ~ (all_28_1 = e1) | ~ (all_28_2 = e3)
% 66.36/10.01 (17) ~ (e1 = e0)
% 66.36/10.01 (18) ~ (all_54_12 = e2)
% 66.36/10.01 (19) op(e2, e3) = all_54_10
% 66.36/10.01 (20) all_58_6 = all_10_2
% 66.36/10.01 (21) ~ (all_54_9 = all_14_2)
% 66.36/10.01 (22) all_56_12 = all_54_12
% 66.36/10.01 (23) all_26_1 = all_4_1
% 66.36/10.01 (24) all_28_2 = all_6_2
% 66.36/10.01 (25) ~ (e2 = e0)
% 66.36/10.01 (26) all_52_3 = all_6_2
% 66.36/10.01 (27) ~ (all_54_10 = e2)
% 66.36/10.01 (28) all_52_0 = all_10_2
% 66.36/10.01 (29) ~ (all_54_10 = all_10_2)
% 66.36/10.01 (30) all_52_2 = e2
% 66.36/10.01 (31) all_56_11 = all_54_10
% 66.36/10.01 (32) ~ (all_10_2 = e3)
% 66.36/10.01 (33) all_58_5 = all_54_8
% 66.36/10.01 (34) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.36/10.01 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.36/10.01 (35) op(e2, e3) = all_4_1
% 66.36/10.01 (36) ~ (all_54_12 = all_6_2)
% 66.36/10.01 (37) all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 66.36/10.01 (38) ~ (all_26_1 = e0) | ~ (all_26_2 = e2)
% 66.36/10.01
% 66.36/10.01 Begin of proof
% 66.36/10.01 |
% 66.36/10.01 | BETA: splitting (38) gives:
% 66.36/10.01 |
% 66.36/10.01 | Case 1:
% 66.36/10.01 | |
% 66.36/10.01 | | (39) ~ (all_26_1 = e0)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (23), (39) imply:
% 66.36/10.01 | | (40) ~ (all_4_1 = e0)
% 66.36/10.01 | |
% 66.36/10.01 | | GROUND_INST: instantiating (5) with all_10_2, e1, e2, e2, simplifying with
% 66.36/10.01 | | (4), (11) gives:
% 66.36/10.01 | | (41) all_10_2 = e1
% 66.36/10.01 | |
% 66.36/10.01 | | GROUND_INST: instantiating (5) with all_54_10, all_4_1, e3, e2, simplifying
% 66.36/10.01 | | with (19), (35) gives:
% 66.36/10.01 | | (42) all_54_10 = all_4_1
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (28), (41) imply:
% 66.36/10.01 | | (43) all_52_0 = e1
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (31), (42) imply:
% 66.36/10.01 | | (44) all_56_11 = all_4_1
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (6), (42) imply:
% 66.36/10.01 | | (45) all_58_13 = all_4_1
% 66.36/10.01 | |
% 66.36/10.01 | | COMBINE_EQS: (20), (41) imply:
% 66.36/10.01 | | (46) all_58_6 = e1
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (29), (41), (42) imply:
% 66.36/10.01 | | (47) ~ (all_4_1 = e1)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (27), (42) imply:
% 66.36/10.01 | | (48) ~ (all_4_1 = e2)
% 66.36/10.01 | |
% 66.36/10.01 | | REDUCE: (32), (41) imply:
% 66.36/10.01 | | (49) ~ (e3 = e1)
% 66.36/10.01 | |
% 66.36/10.01 | | SIMP: (49) implies:
% 66.36/10.01 | | (50) ~ (e3 = e1)
% 66.36/10.01 | |
% 66.36/10.01 | | BETA: splitting (34) gives:
% 66.36/10.01 | |
% 66.36/10.01 | | Case 1:
% 66.36/10.01 | | |
% 66.36/10.01 | | | (51) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.36/10.01 | | |
% 66.36/10.01 | | | ALPHA: (51) implies:
% 66.36/10.01 | | | (52) all_52_0 = e0
% 66.36/10.01 | | |
% 66.36/10.01 | | | REF_CLOSE: (17), (43), (52) are inconsistent by sub-proof #133.
% 66.36/10.01 | | |
% 66.36/10.01 | | Case 2:
% 66.36/10.01 | | |
% 66.36/10.01 | | | (53) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.36/10.01 | | | (all_52_3 = e3))
% 66.36/10.01 | | |
% 66.36/10.01 | | | BETA: splitting (53) gives:
% 66.36/10.01 | | |
% 66.36/10.01 | | | Case 1:
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | (54) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | ALPHA: (54) implies:
% 66.36/10.01 | | | | (55) all_52_1 = e0
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | COMBINE_EQS: (13), (55) imply:
% 66.36/10.01 | | | | (56) all_14_2 = e0
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | SIMP: (56) implies:
% 66.36/10.01 | | | | (57) all_14_2 = e0
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | REDUCE: (21), (57) imply:
% 66.36/10.01 | | | | (58) ~ (all_54_9 = e0)
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | BETA: splitting (8) gives:
% 66.36/10.01 | | | |
% 66.36/10.01 | | | | Case 1:
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | | (59) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | | REF_CLOSE: (43), (50), (59) are inconsistent by sub-proof #132.
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | Case 2:
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | | (60) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.36/10.01 | | | | | (all_52_2 = e0))
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | | BETA: splitting (60) gives:
% 66.36/10.01 | | | | |
% 66.36/10.01 | | | | | Case 1:
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | (61) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | REF_CLOSE: (15), (55), (61) are inconsistent by sub-proof #154.
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | Case 2:
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | (62) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | ALPHA: (62) implies:
% 66.36/10.01 | | | | | | (63) all_52_3 = e3
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | COMBINE_EQS: (26), (63) imply:
% 66.36/10.01 | | | | | | (64) all_6_2 = e3
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | SIMP: (64) implies:
% 66.36/10.01 | | | | | | (65) all_6_2 = e3
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | COMBINE_EQS: (24), (65) imply:
% 66.36/10.01 | | | | | | (66) all_28_2 = e3
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | REDUCE: (36), (65) imply:
% 66.36/10.01 | | | | | | (67) ~ (all_54_12 = e3)
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | REDUCE: (10), (65) imply:
% 66.36/10.01 | | | | | | (68) op(e3, e0) = all_6_1
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | BETA: splitting (3) gives:
% 66.36/10.01 | | | | | |
% 66.36/10.01 | | | | | | Case 1:
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | (69) all_58_4 = e0
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | COMBINE_EQS: (14), (69) imply:
% 66.36/10.01 | | | | | | | (70) all_54_9 = e0
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | REDUCE: (58), (70) imply:
% 66.36/10.01 | | | | | | | (71) $false
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | CLOSE: (71) is inconsistent.
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | Case 2:
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | (72) all_58_5 = e0 | all_58_6 = e0 | all_58_13 = e0
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | BETA: splitting (16) gives:
% 66.36/10.01 | | | | | | |
% 66.36/10.01 | | | | | | | Case 1:
% 66.36/10.01 | | | | | | | |
% 66.36/10.01 | | | | | | | | (73) ~ (all_28_1 = e1)
% 66.36/10.01 | | | | | | | |
% 66.36/10.01 | | | | | | | | REDUCE: (2), (73) imply:
% 66.36/10.01 | | | | | | | | (74) ~ (all_6_1 = e1)
% 66.36/10.01 | | | | | | | |
% 66.36/10.01 | | | | | | | | BETA: splitting (12) gives:
% 66.36/10.01 | | | | | | | |
% 66.36/10.01 | | | | | | | | Case 1:
% 66.36/10.01 | | | | | | | | |
% 66.36/10.01 | | | | | | | | | (75) all_56_11 = e3
% 66.36/10.01 | | | | | | | | |
% 66.36/10.01 | | | | | | | | | COMBINE_EQS: (44), (75) imply:
% 66.36/10.01 | | | | | | | | | (76) all_4_1 = e3
% 66.36/10.01 | | | | | | | | |
% 66.36/10.01 | | | | | | | | | SIMP: (76) implies:
% 66.80/10.01 | | | | | | | | | (77) all_4_1 = e3
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | | COMBINE_EQS: (45), (77) imply:
% 66.80/10.01 | | | | | | | | | (78) all_58_13 = e3
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | | BETA: splitting (72) gives:
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | | Case 1:
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | (79) all_58_5 = e0
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | COMBINE_EQS: (33), (79) imply:
% 66.80/10.01 | | | | | | | | | | (80) all_54_8 = e0
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | REDUCE: (7), (80) imply:
% 66.80/10.01 | | | | | | | | | | (81) ~ (all_54_12 = e0)
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | SIMP: (81) implies:
% 66.80/10.01 | | | | | | | | | | (82) ~ (all_54_12 = e0)
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | BETA: splitting (37) gives:
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | Case 1:
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | (83) all_56_12 = e3
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | COMBINE_EQS: (22), (83) imply:
% 66.80/10.01 | | | | | | | | | | | (84) all_54_12 = e3
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | REDUCE: (67), (84) imply:
% 66.80/10.01 | | | | | | | | | | | (85) $false
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | CLOSE: (85) is inconsistent.
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | (86) all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | BETA: splitting (86) gives:
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | Case 1:
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | (87) all_56_12 = e2
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | COMBINE_EQS: (22), (87) imply:
% 66.80/10.01 | | | | | | | | | | | | (88) all_54_12 = e2
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | SIMP: (88) implies:
% 66.80/10.01 | | | | | | | | | | | | (89) all_54_12 = e2
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | REDUCE: (18), (89) imply:
% 66.80/10.01 | | | | | | | | | | | | (90) $false
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | CLOSE: (90) is inconsistent.
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | (91) all_56_12 = e1 | all_56_12 = e0
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | BETA: splitting (91) gives:
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | Case 1:
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | (92) all_56_12 = e1
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | COMBINE_EQS: (22), (92) imply:
% 66.80/10.01 | | | | | | | | | | | | | (93) all_54_12 = e1
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | SIMP: (93) implies:
% 66.80/10.01 | | | | | | | | | | | | | (94) all_54_12 = e1
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | REDUCE: (9), (94) imply:
% 66.80/10.01 | | | | | | | | | | | | | (95) op(e3, e0) = e1
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e1, all_6_1, e0, e3,
% 66.80/10.01 | | | | | | | | | | | | | simplifying with (68), (95) gives:
% 66.80/10.01 | | | | | | | | | | | | | (96) all_6_1 = e1
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | REDUCE: (74), (96) imply:
% 66.80/10.01 | | | | | | | | | | | | | (97) $false
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | CLOSE: (97) is inconsistent.
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | (98) all_56_12 = e0
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | COMBINE_EQS: (22), (98) imply:
% 66.80/10.01 | | | | | | | | | | | | | (99) all_54_12 = e0
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | SIMP: (99) implies:
% 66.80/10.01 | | | | | | | | | | | | | (100) all_54_12 = e0
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | REDUCE: (82), (100) imply:
% 66.80/10.01 | | | | | | | | | | | | | (101) $false
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | | CLOSE: (101) is inconsistent.
% 66.80/10.01 | | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | | End of split
% 66.80/10.01 | | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | End of split
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | End of split
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | (102) all_58_6 = e0 | all_58_13 = e0
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | BETA: splitting (102) gives:
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | Case 1:
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | (103) all_58_6 = e0
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | REF_CLOSE: (17), (46), (103) are inconsistent by sub-proof
% 66.80/10.01 | | | | | | | | | | | #128.
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | (104) all_58_13 = e0
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | COMBINE_EQS: (78), (104) imply:
% 66.80/10.01 | | | | | | | | | | | (105) e3 = e0
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | SIMP: (105) implies:
% 66.80/10.01 | | | | | | | | | | | (106) e3 = e0
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | REDUCE: (15), (106) imply:
% 66.80/10.01 | | | | | | | | | | | (107) $false
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 66.80/10.01 | | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | | End of split
% 66.80/10.01 | | | | | | | | | |
% 66.80/10.01 | | | | | | | | | End of split
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | | (108) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | | REF_CLOSE: (40), (44), (47), (48), (108) are inconsistent by
% 66.80/10.01 | | | | | | | | | sub-proof #127.
% 66.80/10.01 | | | | | | | | |
% 66.80/10.01 | | | | | | | | End of split
% 66.80/10.01 | | | | | | | |
% 66.80/10.01 | | | | | | | Case 2:
% 66.80/10.01 | | | | | | | |
% 66.80/10.01 | | | | | | | | (109) ~ (all_28_2 = e3)
% 66.80/10.01 | | | | | | | |
% 66.80/10.01 | | | | | | | | REDUCE: (66), (109) imply:
% 66.80/10.01 | | | | | | | | (110) $false
% 66.80/10.01 | | | | | | | |
% 66.80/10.01 | | | | | | | | CLOSE: (110) is inconsistent.
% 66.80/10.01 | | | | | | | |
% 66.80/10.01 | | | | | | | End of split
% 66.80/10.01 | | | | | | |
% 66.80/10.01 | | | | | | End of split
% 66.80/10.01 | | | | | |
% 66.80/10.01 | | | | | End of split
% 66.80/10.01 | | | | |
% 66.80/10.01 | | | | End of split
% 66.80/10.01 | | | |
% 66.80/10.01 | | | Case 2:
% 66.80/10.01 | | | |
% 66.80/10.02 | | | | (111) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | REF_CLOSE: (25), (30), (111) are inconsistent by sub-proof #131.
% 66.80/10.02 | | | |
% 66.80/10.02 | | | End of split
% 66.80/10.02 | | |
% 66.80/10.02 | | End of split
% 66.80/10.02 | |
% 66.80/10.02 | Case 2:
% 66.80/10.02 | |
% 66.80/10.02 | | (112) ~ (all_26_2 = e2)
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (1), (112) imply:
% 66.80/10.02 | | (113) $false
% 66.80/10.02 | |
% 66.80/10.02 | | CLOSE: (113) is inconsistent.
% 66.80/10.02 | |
% 66.80/10.02 | End of split
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #127 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) all_56_11 = all_4_1
% 66.80/10.02 (2) ~ (all_4_1 = e0)
% 66.80/10.02 (3) ~ (all_4_1 = e1)
% 66.80/10.02 (4) all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 66.80/10.02 (5) ~ (all_4_1 = e2)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | BETA: splitting (4) gives:
% 66.80/10.02 |
% 66.80/10.02 | Case 1:
% 66.80/10.02 | |
% 66.80/10.02 | | (6) all_56_11 = e2
% 66.80/10.02 | |
% 66.80/10.02 | | COMBINE_EQS: (1), (6) imply:
% 66.80/10.02 | | (7) all_4_1 = e2
% 66.80/10.02 | |
% 66.80/10.02 | | SIMP: (7) implies:
% 66.80/10.02 | | (8) all_4_1 = e2
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (5), (8) imply:
% 66.80/10.02 | | (9) $false
% 66.80/10.02 | |
% 66.80/10.02 | | CLOSE: (9) is inconsistent.
% 66.80/10.02 | |
% 66.80/10.02 | Case 2:
% 66.80/10.02 | |
% 66.80/10.02 | | (10) all_56_11 = e1 | all_56_11 = e0
% 66.80/10.02 | |
% 66.80/10.02 | | BETA: splitting (10) gives:
% 66.80/10.02 | |
% 66.80/10.02 | | Case 1:
% 66.80/10.02 | | |
% 66.80/10.02 | | | (11) all_56_11 = e1
% 66.80/10.02 | | |
% 66.80/10.02 | | | COMBINE_EQS: (1), (11) imply:
% 66.80/10.02 | | | (12) all_4_1 = e1
% 66.80/10.02 | | |
% 66.80/10.02 | | | SIMP: (12) implies:
% 66.80/10.02 | | | (13) all_4_1 = e1
% 66.80/10.02 | | |
% 66.80/10.02 | | | REDUCE: (3), (13) imply:
% 66.80/10.02 | | | (14) $false
% 66.80/10.02 | | |
% 66.80/10.02 | | | CLOSE: (14) is inconsistent.
% 66.80/10.02 | | |
% 66.80/10.02 | | Case 2:
% 66.80/10.02 | | |
% 66.80/10.02 | | | (15) all_56_11 = e0
% 66.80/10.02 | | |
% 66.80/10.02 | | | COMBINE_EQS: (1), (15) imply:
% 66.80/10.02 | | | (16) all_4_1 = e0
% 66.80/10.02 | | |
% 66.80/10.02 | | | SIMP: (16) implies:
% 66.80/10.02 | | | (17) all_4_1 = e0
% 66.80/10.02 | | |
% 66.80/10.02 | | | REDUCE: (2), (17) imply:
% 66.80/10.02 | | | (18) $false
% 66.80/10.02 | | |
% 66.80/10.02 | | | CLOSE: (18) is inconsistent.
% 66.80/10.02 | | |
% 66.80/10.02 | | End of split
% 66.80/10.02 | |
% 66.80/10.02 | End of split
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #128 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) all_58_6 = e1
% 66.80/10.02 (2) all_58_6 = e0
% 66.80/10.02 (3) ~ (e1 = e0)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | COMBINE_EQS: (1), (2) imply:
% 66.80/10.02 | (4) e1 = e0
% 66.80/10.02 |
% 66.80/10.02 | SIMP: (4) implies:
% 66.80/10.02 | (5) e1 = e0
% 66.80/10.02 |
% 66.80/10.02 | REDUCE: (3), (5) imply:
% 66.80/10.02 | (6) $false
% 66.80/10.02 |
% 66.80/10.02 | CLOSE: (6) is inconsistent.
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #129 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) op(e1, e1) = all_14_2
% 66.80/10.02 (2) all_52_2 = all_4_2
% 66.80/10.02 (3) op(all_4_2, all_4_2) = e1
% 66.80/10.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.02 (5) op(e0, e0) = all_6_2
% 66.80/10.02 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.02 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.02 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.02 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.02 (8) ~ (e3 = e1)
% 66.80/10.02 (9) op(e2, e2) = all_10_2
% 66.80/10.02 (10) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.02 (11) all_52_1 = all_14_2
% 66.80/10.02 (12) ~ (e3 = e0)
% 66.80/10.02 (13) ~ (e1 = e0)
% 66.80/10.02 (14) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.80/10.02 (15) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.02 (16) ~ (e2 = e0)
% 66.80/10.02 (17) ~ (e2 = e1)
% 66.80/10.02 (18) all_52_3 = all_6_2
% 66.80/10.02 (19) all_52_0 = all_10_2
% 66.80/10.02 (20) ~ (all_14_0 = e3)
% 66.80/10.02 (21) ~ (e3 = e2)
% 66.80/10.02 (22) all_56_10 = all_10_2
% 66.80/10.02 (23) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.02 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | ALPHA: (14) implies:
% 66.80/10.02 | (24) all_52_1 = e2
% 66.80/10.02 | (25) ~ (all_52_0 = e1)
% 66.80/10.02 |
% 66.80/10.02 | COMBINE_EQS: (11), (24) imply:
% 66.80/10.02 | (26) all_14_2 = e2
% 66.80/10.02 |
% 66.80/10.02 | SIMP: (26) implies:
% 66.80/10.02 | (27) all_14_2 = e2
% 66.80/10.02 |
% 66.80/10.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 66.80/10.02 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 66.80/10.02 | (27) are inconsistent by sub-proof #135.
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #130 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 66.80/10.02 e0))
% 66.80/10.02 (2) all_52_2 = all_4_2
% 66.80/10.02 (3) op(all_4_2, all_4_2) = e1
% 66.80/10.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.02 (5) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.02 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.02 (6) op(e2, e2) = all_10_2
% 66.80/10.02 (7) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.02 (8) ~ (all_6_0 = e2)
% 66.80/10.02 (9) ~ (e3 = e0)
% 66.80/10.02 (10) ~ (e1 = e0)
% 66.80/10.02 (11) op(e3, e3) = all_4_2
% 66.80/10.02 (12) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.02 (13) ~ (all_6_0 = e3)
% 66.80/10.02 (14) ~ (e2 = e0)
% 66.80/10.02 (15) all_52_3 = all_6_2
% 66.80/10.02 (16) all_52_0 = all_10_2
% 66.80/10.02 (17) all_56_10 = all_10_2
% 66.80/10.02 (18) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.02 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.02 (19) ~ (all_6_0 = e1)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | BETA: splitting (1) gives:
% 66.80/10.02 |
% 66.80/10.02 | Case 1:
% 66.80/10.02 | |
% 66.80/10.02 | | (20) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.02 | |
% 66.80/10.02 | | ALPHA: (20) implies:
% 66.80/10.02 | | (21) all_52_2 = e2
% 66.80/10.02 | | (22) ~ (all_52_0 = e3)
% 66.80/10.02 | |
% 66.80/10.02 | | COMBINE_EQS: (2), (21) imply:
% 66.80/10.02 | | (23) all_4_2 = e2
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (16), (22) imply:
% 66.80/10.02 | | (24) ~ (all_10_2 = e3)
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (3), (23) imply:
% 66.80/10.02 | | (25) op(e2, e2) = e1
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (11), (23) imply:
% 66.80/10.02 | | (26) op(e3, e3) = e2
% 66.80/10.02 | |
% 66.80/10.02 | | GROUND_INST: instantiating (4) with all_10_2, e1, e2, e2, simplifying with
% 66.80/10.02 | | (6), (25) gives:
% 66.80/10.02 | | (27) all_10_2 = e1
% 66.80/10.02 | |
% 66.80/10.02 | | COMBINE_EQS: (16), (27) imply:
% 66.80/10.02 | | (28) all_52_0 = e1
% 66.80/10.02 | |
% 66.80/10.02 | | REDUCE: (24), (27) imply:
% 66.80/10.02 | | (29) ~ (e3 = e1)
% 66.80/10.02 | |
% 66.80/10.02 | | SIMP: (29) implies:
% 66.80/10.02 | | (30) ~ (e3 = e1)
% 66.80/10.02 | |
% 66.80/10.02 | | BETA: splitting (18) gives:
% 66.80/10.02 | |
% 66.80/10.02 | | Case 1:
% 66.80/10.02 | | |
% 66.80/10.02 | | | (31) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.02 | | |
% 66.80/10.02 | | | ALPHA: (31) implies:
% 66.80/10.02 | | | (32) all_52_0 = e0
% 66.80/10.02 | | |
% 66.80/10.02 | | | REF_CLOSE: (10), (28), (32) are inconsistent by sub-proof #133.
% 66.80/10.02 | | |
% 66.80/10.02 | | Case 2:
% 66.80/10.02 | | |
% 66.80/10.02 | | | (33) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.80/10.02 | | | (all_52_3 = e3))
% 66.80/10.02 | | |
% 66.80/10.02 | | | BETA: splitting (33) gives:
% 66.80/10.02 | | |
% 66.80/10.02 | | | Case 1:
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | (34) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | ALPHA: (34) implies:
% 66.80/10.02 | | | | (35) all_52_1 = e0
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | BETA: splitting (5) gives:
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | Case 1:
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | | (36) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | | REF_CLOSE: (28), (30), (36) are inconsistent by sub-proof #132.
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | Case 2:
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | | (37) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.80/10.02 | | | | | (all_52_2 = e0))
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | | BETA: splitting (37) gives:
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | | Case 1:
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | (38) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | REF_CLOSE: (9), (35), (38) are inconsistent by sub-proof #154.
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | Case 2:
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | (39) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | ALPHA: (39) implies:
% 66.80/10.02 | | | | | | (40) all_52_3 = e3
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | COMBINE_EQS: (15), (40) imply:
% 66.80/10.02 | | | | | | (41) all_6_2 = e3
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | SIMP: (41) implies:
% 66.80/10.02 | | | | | | (42) all_6_2 = e3
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | REDUCE: (12), (42) imply:
% 66.80/10.02 | | | | | | (43) op(e3, e3) = all_6_0
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | GROUND_INST: instantiating (4) with e2, all_6_0, e3, e3, simplifying
% 66.80/10.02 | | | | | | with (26), (43) gives:
% 66.80/10.02 | | | | | | (44) all_6_0 = e2
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | REDUCE: (8), (44) imply:
% 66.80/10.02 | | | | | | (45) $false
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | | CLOSE: (45) is inconsistent.
% 66.80/10.02 | | | | | |
% 66.80/10.02 | | | | | End of split
% 66.80/10.02 | | | | |
% 66.80/10.02 | | | | End of split
% 66.80/10.02 | | | |
% 66.80/10.02 | | | Case 2:
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | (46) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.02 | | | |
% 66.80/10.02 | | | | REF_CLOSE: (14), (21), (46) are inconsistent by sub-proof #131.
% 66.80/10.02 | | | |
% 66.80/10.02 | | | End of split
% 66.80/10.02 | | |
% 66.80/10.02 | | End of split
% 66.80/10.02 | |
% 66.80/10.02 | Case 2:
% 66.80/10.02 | |
% 66.80/10.02 | | (47) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.80/10.02 | |
% 66.80/10.02 | | ALPHA: (47) implies:
% 66.80/10.02 | | (48) all_52_3 = e2
% 66.80/10.02 | | (49) ~ (all_52_0 = e0)
% 66.80/10.02 | |
% 66.80/10.02 | | COMBINE_EQS: (15), (48) imply:
% 66.80/10.02 | | (50) all_6_2 = e2
% 66.80/10.02 | |
% 66.80/10.02 | | REF_CLOSE: (4), (6), (7), (8), (12), (13), (16), (17), (19), (49), (50) are
% 66.80/10.02 | | inconsistent by sub-proof #161.
% 66.80/10.02 | |
% 66.80/10.02 | End of split
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #131 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.02 (2) all_52_2 = e2
% 66.80/10.02 (3) ~ (e2 = e0)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | ALPHA: (1) implies:
% 66.80/10.02 | (4) all_52_2 = e0
% 66.80/10.02 |
% 66.80/10.02 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.02 | (5) e2 = e0
% 66.80/10.02 |
% 66.80/10.02 | SIMP: (5) implies:
% 66.80/10.02 | (6) e2 = e0
% 66.80/10.02 |
% 66.80/10.02 | REDUCE: (3), (6) imply:
% 66.80/10.02 | (7) $false
% 66.80/10.02 |
% 66.80/10.02 | CLOSE: (7) is inconsistent.
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #132 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.02 (2) all_52_0 = e1
% 66.80/10.02 (3) ~ (e3 = e1)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.02 |
% 66.80/10.02 | ALPHA: (1) implies:
% 66.80/10.02 | (4) all_52_0 = e3
% 66.80/10.02 |
% 66.80/10.02 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.02 | (5) e3 = e1
% 66.80/10.02 |
% 66.80/10.02 | REDUCE: (3), (5) imply:
% 66.80/10.02 | (6) $false
% 66.80/10.02 |
% 66.80/10.02 | CLOSE: (6) is inconsistent.
% 66.80/10.02 |
% 66.80/10.02 End of proof
% 66.80/10.02
% 66.80/10.02 Sub-proof #133 shows that the following formulas are inconsistent:
% 66.80/10.02 ----------------------------------------------------------------
% 66.80/10.02 (1) all_52_0 = e1
% 66.80/10.02 (2) all_52_0 = e0
% 66.80/10.02 (3) ~ (e1 = e0)
% 66.80/10.02
% 66.80/10.02 Begin of proof
% 66.80/10.03 |
% 66.80/10.03 | COMBINE_EQS: (1), (2) imply:
% 66.80/10.03 | (4) e1 = e0
% 66.80/10.03 |
% 66.80/10.03 | SIMP: (4) implies:
% 66.80/10.03 | (5) e1 = e0
% 66.80/10.03 |
% 66.80/10.03 | REDUCE: (3), (5) imply:
% 66.80/10.03 | (6) $false
% 66.80/10.03 |
% 66.80/10.03 | CLOSE: (6) is inconsistent.
% 66.80/10.03 |
% 66.80/10.03 End of proof
% 66.80/10.03
% 66.80/10.03 Sub-proof #134 shows that the following formulas are inconsistent:
% 66.80/10.03 ----------------------------------------------------------------
% 66.80/10.03 (1) op(e1, e1) = all_14_2
% 66.80/10.03 (2) all_52_2 = all_4_2
% 66.80/10.03 (3) op(all_4_2, all_4_2) = e1
% 66.80/10.03 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.03 (5) op(e0, e0) = all_6_2
% 66.80/10.03 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.03 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.03 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.03 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.03 (8) ~ (e3 = e1)
% 66.80/10.03 (9) op(e2, e2) = all_10_2
% 66.80/10.03 (10) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.03 (11) all_52_1 = all_14_2
% 66.80/10.03 (12) ~ (e3 = e0)
% 66.80/10.03 (13) ~ (e1 = e0)
% 66.80/10.03 (14) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.80/10.03 (15) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.03 (16) ~ (e2 = e0)
% 66.80/10.03 (17) ~ (e2 = e1)
% 66.80/10.03 (18) all_52_3 = all_6_2
% 66.80/10.03 (19) all_52_0 = all_10_2
% 66.80/10.03 (20) ~ (all_14_0 = e3)
% 66.80/10.03 (21) ~ (e3 = e2)
% 66.80/10.03 (22) all_56_10 = all_10_2
% 66.80/10.03 (23) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.03 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.03
% 66.80/10.03 Begin of proof
% 66.80/10.03 |
% 66.80/10.03 | ALPHA: (14) implies:
% 66.80/10.03 | (24) all_52_1 = e2
% 66.80/10.03 | (25) ~ (all_52_0 = e1)
% 66.80/10.03 |
% 66.80/10.03 | COMBINE_EQS: (11), (24) imply:
% 66.80/10.03 | (26) all_14_2 = e2
% 66.80/10.03 |
% 66.80/10.03 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 66.80/10.03 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 66.80/10.03 | (26) are inconsistent by sub-proof #135.
% 66.80/10.03 |
% 66.80/10.03 End of proof
% 66.80/10.03
% 66.80/10.03 Sub-proof #135 shows that the following formulas are inconsistent:
% 66.80/10.03 ----------------------------------------------------------------
% 66.80/10.03 (1) ~ (all_52_0 = e1)
% 66.80/10.03 (2) op(e1, e1) = all_14_2
% 66.80/10.03 (3) all_52_2 = all_4_2
% 66.80/10.03 (4) op(all_4_2, all_4_2) = e1
% 66.80/10.03 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.03 (6) op(e0, e0) = all_6_2
% 66.80/10.03 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.03 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.03 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.03 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.03 (9) ~ (e3 = e1)
% 66.80/10.03 (10) op(e2, e2) = all_10_2
% 66.80/10.03 (11) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.03 (12) ~ (e3 = e0)
% 66.80/10.03 (13) ~ (e1 = e0)
% 66.80/10.03 (14) all_14_2 = e2
% 66.80/10.03 (15) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.03 (16) ~ (e2 = e0)
% 66.80/10.03 (17) ~ (e2 = e1)
% 66.80/10.03 (18) all_52_3 = all_6_2
% 66.80/10.03 (19) all_52_0 = all_10_2
% 66.80/10.03 (20) ~ (all_14_0 = e3)
% 66.80/10.03 (21) all_52_1 = e2
% 66.80/10.03 (22) ~ (e3 = e2)
% 66.80/10.03 (23) all_56_10 = all_10_2
% 66.80/10.03 (24) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.03 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.03
% 66.80/10.03 Begin of proof
% 66.80/10.03 |
% 66.80/10.03 | REDUCE: (1), (19) imply:
% 66.80/10.03 | (25) ~ (all_10_2 = e1)
% 66.80/10.03 |
% 66.80/10.03 | REDUCE: (14), (15) imply:
% 66.80/10.03 | (26) op(e2, e2) = all_14_0
% 66.80/10.03 |
% 66.80/10.03 | REDUCE: (2), (14) imply:
% 66.80/10.03 | (27) op(e1, e1) = e2
% 66.80/10.03 |
% 66.80/10.03 | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (16),
% 66.80/10.03 | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27)
% 66.80/10.03 | are inconsistent by sub-proof #136.
% 66.80/10.03 |
% 66.80/10.03 End of proof
% 66.80/10.03
% 66.80/10.03 Sub-proof #136 shows that the following formulas are inconsistent:
% 66.80/10.03 ----------------------------------------------------------------
% 66.80/10.03 (1) op(e1, e1) = e2
% 66.80/10.03 (2) all_52_2 = all_4_2
% 66.80/10.03 (3) op(all_4_2, all_4_2) = e1
% 66.80/10.03 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.03 (5) op(e0, e0) = all_6_2
% 66.80/10.03 (6) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.03 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.03 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.03 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.03 (8) ~ (e3 = e1)
% 66.80/10.03 (9) op(e2, e2) = all_10_2
% 66.80/10.03 (10) op(e2, e2) = all_14_0
% 66.80/10.03 (11) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.03 (12) ~ (e3 = e0)
% 66.80/10.03 (13) ~ (e1 = e0)
% 66.80/10.03 (14) ~ (e2 = e0)
% 66.80/10.03 (15) ~ (e2 = e1)
% 66.80/10.03 (16) all_52_3 = all_6_2
% 66.80/10.03 (17) all_52_0 = all_10_2
% 66.80/10.03 (18) ~ (all_14_0 = e3)
% 66.80/10.03 (19) all_52_1 = e2
% 66.80/10.03 (20) ~ (e3 = e2)
% 66.80/10.03 (21) all_56_10 = all_10_2
% 66.80/10.03 (22) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.03 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.03 (23) ~ (all_10_2 = e1)
% 66.80/10.03
% 66.80/10.03 Begin of proof
% 66.80/10.03 |
% 66.80/10.03 | GROUND_INST: instantiating (4) with all_10_2, all_14_0, e2, e2, simplifying
% 66.80/10.03 | with (9), (10) gives:
% 66.80/10.03 | (24) all_14_0 = all_10_2
% 66.80/10.03 |
% 66.80/10.03 | REDUCE: (18), (24) imply:
% 66.80/10.03 | (25) ~ (all_10_2 = e3)
% 66.80/10.03 |
% 66.80/10.03 | BETA: splitting (22) gives:
% 66.80/10.03 |
% 66.80/10.03 | Case 1:
% 66.80/10.03 | |
% 66.80/10.03 | | (26) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.03 | |
% 66.80/10.03 | | ALPHA: (26) implies:
% 66.80/10.03 | | (27) all_52_0 = e0
% 66.80/10.03 | |
% 66.80/10.03 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (12), (13), (15), (19), (20),
% 66.80/10.03 | | (27) are inconsistent by sub-proof #144.
% 66.80/10.03 | |
% 66.80/10.03 | Case 2:
% 66.80/10.03 | |
% 66.80/10.03 | | (28) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~ (all_52_3
% 66.80/10.03 | | = e3))
% 66.80/10.03 | |
% 66.80/10.03 | | BETA: splitting (28) gives:
% 66.80/10.03 | |
% 66.80/10.03 | | Case 1:
% 66.80/10.03 | | |
% 66.80/10.03 | | | (29) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.03 | | |
% 66.80/10.03 | | | REF_CLOSE: (14), (19), (29) are inconsistent by sub-proof #179.
% 66.80/10.03 | | |
% 66.80/10.03 | | Case 2:
% 66.80/10.03 | | |
% 66.80/10.03 | | | (30) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.03 | | |
% 66.80/10.03 | | | ALPHA: (30) implies:
% 66.80/10.03 | | | (31) all_52_2 = e0
% 66.80/10.03 | | | (32) ~ (all_52_3 = e3)
% 66.80/10.03 | | |
% 66.80/10.03 | | | COMBINE_EQS: (2), (31) imply:
% 66.80/10.03 | | | (33) all_4_2 = e0
% 66.80/10.03 | | |
% 66.80/10.03 | | | SIMP: (33) implies:
% 66.80/10.03 | | | (34) all_4_2 = e0
% 66.80/10.03 | | |
% 66.80/10.03 | | | REDUCE: (16), (32) imply:
% 66.80/10.03 | | | (35) ~ (all_6_2 = e3)
% 66.80/10.03 | | |
% 66.80/10.03 | | | REDUCE: (3), (34) imply:
% 66.80/10.03 | | | (36) op(e0, e0) = e1
% 66.80/10.03 | | |
% 66.80/10.03 | | | BETA: splitting (11) gives:
% 66.80/10.03 | | |
% 66.80/10.03 | | | Case 1:
% 66.80/10.03 | | | |
% 66.80/10.03 | | | | (37) all_56_10 = e3
% 66.80/10.03 | | | |
% 66.80/10.03 | | | | REF_CLOSE: (21), (25), (37) are inconsistent by sub-proof #143.
% 66.80/10.03 | | | |
% 66.80/10.03 | | | Case 2:
% 66.80/10.03 | | | |
% 66.80/10.03 | | | | (38) all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.03 | | | |
% 66.80/10.03 | | | | BETA: splitting (38) gives:
% 66.80/10.03 | | | |
% 66.80/10.03 | | | | Case 1:
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | | (39) all_56_10 = e2
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | | REF_CLOSE: (6), (7), (13), (15), (16), (17), (19), (20), (21), (31),
% 66.80/10.03 | | | | | (35), (39) are inconsistent by sub-proof #139.
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | Case 2:
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | | (40) all_56_10 = e1 | all_56_10 = e0
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | | BETA: splitting (40) gives:
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | | Case 1:
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | (41) all_56_10 = e1
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | REF_CLOSE: (21), (23), (41) are inconsistent by sub-proof #138.
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | Case 2:
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | (42) all_56_10 = e0
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | COMBINE_EQS: (21), (42) imply:
% 66.80/10.03 | | | | | | (43) all_10_2 = e0
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | SIMP: (43) implies:
% 66.80/10.03 | | | | | | (44) all_10_2 = e0
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | COMBINE_EQS: (17), (44) imply:
% 66.80/10.03 | | | | | | (45) all_52_0 = e0
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | | REF_CLOSE: (4), (5), (6), (8), (12), (16), (19), (20), (36), (45)
% 66.80/10.03 | | | | | | are inconsistent by sub-proof #137.
% 66.80/10.03 | | | | | |
% 66.80/10.03 | | | | | End of split
% 66.80/10.03 | | | | |
% 66.80/10.03 | | | | End of split
% 66.80/10.03 | | | |
% 66.80/10.03 | | | End of split
% 66.80/10.03 | | |
% 66.80/10.03 | | End of split
% 66.80/10.03 | |
% 66.80/10.03 | End of split
% 66.80/10.03 |
% 66.80/10.03 End of proof
% 66.80/10.03
% 66.80/10.03 Sub-proof #137 shows that the following formulas are inconsistent:
% 66.80/10.03 ----------------------------------------------------------------
% 66.80/10.03 (1) op(e0, e0) = e1
% 66.80/10.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.03 (3) op(e0, e0) = all_6_2
% 66.80/10.03 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.03 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.03 (5) ~ (e3 = e1)
% 66.80/10.03 (6) ~ (e3 = e0)
% 66.80/10.03 (7) all_52_0 = e0
% 66.80/10.03 (8) all_52_3 = all_6_2
% 66.80/10.03 (9) all_52_1 = e2
% 66.80/10.03 (10) ~ (e3 = e2)
% 66.80/10.03
% 66.80/10.03 Begin of proof
% 66.80/10.03 |
% 66.80/10.03 | BETA: splitting (4) gives:
% 66.80/10.03 |
% 66.80/10.03 | Case 1:
% 66.80/10.03 | |
% 66.80/10.04 | | (11) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.04 | |
% 66.80/10.04 | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #148.
% 66.80/10.04 | |
% 66.80/10.04 | Case 2:
% 66.80/10.04 | |
% 66.80/10.04 | | (12) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.80/10.04 | | = e0))
% 66.80/10.04 | |
% 66.80/10.04 | | BETA: splitting (12) gives:
% 66.80/10.04 | |
% 66.80/10.04 | | Case 1:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (13) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.04 | | |
% 66.80/10.04 | | | REF_CLOSE: (9), (10), (13) are inconsistent by sub-proof #147.
% 66.80/10.04 | | |
% 66.80/10.04 | | Case 2:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (14) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.04 | | |
% 66.80/10.04 | | | ALPHA: (14) implies:
% 66.80/10.04 | | | (15) all_52_3 = e3
% 66.80/10.04 | | |
% 66.80/10.04 | | | COMBINE_EQS: (8), (15) imply:
% 66.80/10.04 | | | (16) all_6_2 = e3
% 66.80/10.04 | | |
% 66.80/10.04 | | | SIMP: (16) implies:
% 66.80/10.04 | | | (17) all_6_2 = e3
% 66.80/10.04 | | |
% 66.80/10.04 | | | REDUCE: (3), (17) imply:
% 66.80/10.04 | | | (18) op(e0, e0) = e3
% 66.80/10.04 | | |
% 66.80/10.04 | | | GROUND_INST: instantiating (2) with e1, e3, e0, e0, simplifying with (1),
% 66.80/10.04 | | | (18) gives:
% 66.80/10.04 | | | (19) e3 = e1
% 66.80/10.04 | | |
% 66.80/10.04 | | | REDUCE: (5), (19) imply:
% 66.80/10.04 | | | (20) $false
% 66.80/10.04 | | |
% 66.80/10.04 | | | CLOSE: (20) is inconsistent.
% 66.80/10.04 | | |
% 66.80/10.04 | | End of split
% 66.80/10.04 | |
% 66.80/10.04 | End of split
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #138 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_56_10 = all_10_2
% 66.80/10.04 (2) all_56_10 = e1
% 66.80/10.04 (3) ~ (all_10_2 = e1)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (1), (2) imply:
% 66.80/10.04 | (4) all_10_2 = e1
% 66.80/10.04 |
% 66.80/10.04 | SIMP: (4) implies:
% 66.80/10.04 | (5) all_10_2 = e1
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #139 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.04 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.04 (2) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.04 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.04 (3) ~ (e1 = e0)
% 66.80/10.04 (4) all_52_2 = e0
% 66.80/10.04 (5) ~ (e2 = e1)
% 66.80/10.04 (6) all_52_3 = all_6_2
% 66.80/10.04 (7) all_52_0 = all_10_2
% 66.80/10.04 (8) ~ (all_6_2 = e3)
% 66.80/10.04 (9) all_52_1 = e2
% 66.80/10.04 (10) ~ (e3 = e2)
% 66.80/10.04 (11) all_56_10 = e2
% 66.80/10.04 (12) all_56_10 = all_10_2
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (11), (12) imply:
% 66.80/10.04 | (13) all_10_2 = e2
% 66.80/10.04 |
% 66.80/10.04 | SIMP: (13) implies:
% 66.80/10.04 | (14) all_10_2 = e2
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (7), (14) imply:
% 66.80/10.04 | (15) all_52_0 = e2
% 66.80/10.04 |
% 66.80/10.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (15) are inconsistent
% 66.80/10.04 | by sub-proof #140.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #140 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_52_0 = e2
% 66.80/10.04 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.04 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.04 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.04 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.04 (4) ~ (e1 = e0)
% 66.80/10.04 (5) all_52_2 = e0
% 66.80/10.04 (6) ~ (e2 = e1)
% 66.80/10.04 (7) all_52_3 = all_6_2
% 66.80/10.04 (8) ~ (all_6_2 = e3)
% 66.80/10.04 (9) all_52_1 = e2
% 66.80/10.04 (10) ~ (e3 = e2)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | BETA: splitting (3) gives:
% 66.80/10.04 |
% 66.80/10.04 | Case 1:
% 66.80/10.04 | |
% 66.80/10.04 | | (11) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.04 | |
% 66.80/10.04 | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #157.
% 66.80/10.04 | |
% 66.80/10.04 | Case 2:
% 66.80/10.04 | |
% 66.80/10.04 | | (12) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.80/10.04 | | = e0))
% 66.80/10.04 | |
% 66.80/10.04 | | BETA: splitting (12) gives:
% 66.80/10.04 | |
% 66.80/10.04 | | Case 1:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (13) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.04 | | |
% 66.80/10.04 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #142.
% 66.80/10.04 | | |
% 66.80/10.04 | | Case 2:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (14) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.04 | | |
% 66.80/10.04 | | | ALPHA: (14) implies:
% 66.80/10.04 | | | (15) all_52_3 = e1
% 66.80/10.04 | | |
% 66.80/10.04 | | | COMBINE_EQS: (7), (15) imply:
% 66.80/10.04 | | | (16) all_6_2 = e1
% 66.80/10.04 | | |
% 66.80/10.04 | | | SIMP: (16) implies:
% 66.80/10.04 | | | (17) all_6_2 = e1
% 66.80/10.04 | | |
% 66.80/10.04 | | | REDUCE: (8), (17) imply:
% 66.80/10.04 | | | (18) ~ (e3 = e1)
% 66.80/10.04 | | |
% 66.80/10.04 | | | SIMP: (18) implies:
% 66.80/10.04 | | | (19) ~ (e3 = e1)
% 66.80/10.04 | | |
% 66.80/10.04 | | | BETA: splitting (2) gives:
% 66.80/10.04 | | |
% 66.80/10.04 | | | Case 1:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | (20) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | REF_CLOSE: (1), (10), (20) are inconsistent by sub-proof #155.
% 66.80/10.04 | | | |
% 66.80/10.04 | | | Case 2:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | (21) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.80/10.04 | | | | (all_52_2 = e0))
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | BETA: splitting (21) gives:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | Case 1:
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | (22) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | REF_CLOSE: (9), (10), (22) are inconsistent by sub-proof #147.
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | Case 2:
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | (23) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | REF_CLOSE: (15), (19), (23) are inconsistent by sub-proof #141.
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | End of split
% 66.80/10.04 | | | |
% 66.80/10.04 | | | End of split
% 66.80/10.04 | | |
% 66.80/10.04 | | End of split
% 66.80/10.04 | |
% 66.80/10.04 | End of split
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #141 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.04 (2) all_52_3 = e1
% 66.80/10.04 (3) ~ (e3 = e1)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | ALPHA: (1) implies:
% 66.80/10.04 | (4) all_52_3 = e3
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.04 | (5) e3 = e1
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #142 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.04 (2) all_52_2 = e0
% 66.80/10.04 (3) ~ (e1 = e0)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | ALPHA: (1) implies:
% 66.80/10.04 | (4) all_52_2 = e1
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.04 | (5) e1 = e0
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #143 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_56_10 = all_10_2
% 66.80/10.04 (2) all_56_10 = e3
% 66.80/10.04 (3) ~ (all_10_2 = e3)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (1), (2) imply:
% 66.80/10.04 | (4) all_10_2 = e3
% 66.80/10.04 |
% 66.80/10.04 | SIMP: (4) implies:
% 66.80/10.04 | (5) all_10_2 = e3
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #144 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) op(e1, e1) = e2
% 66.80/10.04 (2) all_52_2 = all_4_2
% 66.80/10.04 (3) op(all_4_2, all_4_2) = e1
% 66.80/10.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.04 (5) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.04 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.04 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.04 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.04 (7) ~ (e3 = e1)
% 66.80/10.04 (8) ~ (e3 = e0)
% 66.80/10.04 (9) ~ (e1 = e0)
% 66.80/10.04 (10) all_52_0 = e0
% 66.80/10.04 (11) ~ (e2 = e1)
% 66.80/10.04 (12) all_52_1 = e2
% 66.80/10.04 (13) ~ (e3 = e2)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | BETA: splitting (5) gives:
% 66.80/10.04 |
% 66.80/10.04 | Case 1:
% 66.80/10.04 | |
% 66.80/10.04 | | (14) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.04 | |
% 66.80/10.04 | | REF_CLOSE: (8), (10), (14) are inconsistent by sub-proof #148.
% 66.80/10.04 | |
% 66.80/10.04 | Case 2:
% 66.80/10.04 | |
% 66.80/10.04 | | (15) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.80/10.04 | | = e0))
% 66.80/10.04 | |
% 66.80/10.04 | | BETA: splitting (15) gives:
% 66.80/10.04 | |
% 66.80/10.04 | | Case 1:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (16) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.04 | | |
% 66.80/10.04 | | | REF_CLOSE: (12), (13), (16) are inconsistent by sub-proof #147.
% 66.80/10.04 | | |
% 66.80/10.04 | | Case 2:
% 66.80/10.04 | | |
% 66.80/10.04 | | | (17) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.04 | | |
% 66.80/10.04 | | | ALPHA: (17) implies:
% 66.80/10.04 | | | (18) all_52_3 = e3
% 66.80/10.04 | | |
% 66.80/10.04 | | | BETA: splitting (6) gives:
% 66.80/10.04 | | |
% 66.80/10.04 | | | Case 1:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | (19) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #164.
% 66.80/10.04 | | | |
% 66.80/10.04 | | | Case 2:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | (20) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 66.80/10.04 | | | | (all_52_1 = e0))
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | BETA: splitting (20) gives:
% 66.80/10.04 | | | |
% 66.80/10.04 | | | | Case 1:
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | (21) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | ALPHA: (21) implies:
% 66.80/10.04 | | | | | (22) all_52_2 = e1
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | COMBINE_EQS: (2), (22) imply:
% 66.80/10.04 | | | | | (23) all_4_2 = e1
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | SIMP: (23) implies:
% 66.80/10.04 | | | | | (24) all_4_2 = e1
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | REDUCE: (3), (24) imply:
% 66.80/10.04 | | | | | (25) op(e1, e1) = e1
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | REF_CLOSE: (1), (4), (11), (25) are inconsistent by sub-proof #146.
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | Case 2:
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | (26) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | | REF_CLOSE: (7), (18), (26) are inconsistent by sub-proof #145.
% 66.80/10.04 | | | | |
% 66.80/10.04 | | | | End of split
% 66.80/10.04 | | | |
% 66.80/10.04 | | | End of split
% 66.80/10.04 | | |
% 66.80/10.04 | | End of split
% 66.80/10.04 | |
% 66.80/10.04 | End of split
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #145 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.04 (2) all_52_3 = e3
% 66.80/10.04 (3) ~ (e3 = e1)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | ALPHA: (1) implies:
% 66.80/10.04 | (4) all_52_3 = e1
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.04 | (5) e3 = e1
% 66.80/10.04 |
% 66.80/10.04 | SIMP: (5) implies:
% 66.80/10.04 | (6) e3 = e1
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (6) imply:
% 66.80/10.04 | (7) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (7) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #146 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.04 (2) op(e1, e1) = e2
% 66.80/10.04 (3) op(e1, e1) = e1
% 66.80/10.04 (4) ~ (e2 = e1)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | GROUND_INST: instantiating (1) with e2, e1, e1, e1, simplifying with (2), (3)
% 66.80/10.04 | gives:
% 66.80/10.04 | (5) e2 = e1
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (4), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #147 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.04 (1) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.04 (2) all_52_1 = e2
% 66.80/10.04 (3) ~ (e3 = e2)
% 66.80/10.04
% 66.80/10.04 Begin of proof
% 66.80/10.04 |
% 66.80/10.04 | ALPHA: (1) implies:
% 66.80/10.04 | (4) all_52_1 = e3
% 66.80/10.04 |
% 66.80/10.04 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.04 | (5) e3 = e2
% 66.80/10.04 |
% 66.80/10.04 | REDUCE: (3), (5) imply:
% 66.80/10.04 | (6) $false
% 66.80/10.04 |
% 66.80/10.04 | CLOSE: (6) is inconsistent.
% 66.80/10.04 |
% 66.80/10.04 End of proof
% 66.80/10.04
% 66.80/10.04 Sub-proof #148 shows that the following formulas are inconsistent:
% 66.80/10.04 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.05 (2) all_52_0 = e0
% 66.80/10.05 (3) ~ (e3 = e0)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_0 = e3
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e3 = e0
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (5) imply:
% 66.80/10.05 | (6) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (6) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #149 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.05 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.05 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.05 (3) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.05 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.05 (4) op(e2, e2) = all_10_2
% 66.80/10.05 (5) op(all_6_2, all_6_2) = e2
% 66.80/10.05 (6) all_52_1 = all_14_2
% 66.80/10.05 (7) ~ (e1 = e0)
% 66.80/10.05 (8) ~ (e2 = e1)
% 66.80/10.05 (9) all_52_3 = all_6_2
% 66.80/10.05 (10) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.80/10.05 (11) all_52_0 = all_10_2
% 66.80/10.05 (12) ~ (e3 = e2)
% 66.80/10.05 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.05 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (10) implies:
% 66.80/10.05 | (14) all_52_3 = e2
% 66.80/10.05 | (15) ~ (all_52_0 = e0)
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (9), (14) imply:
% 66.80/10.05 | (16) all_6_2 = e2
% 66.80/10.05 |
% 66.80/10.05 | SIMP: (16) implies:
% 66.80/10.05 | (17) all_6_2 = e2
% 66.80/10.05 |
% 66.80/10.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 66.80/10.05 | (15), (17) are inconsistent by sub-proof #150.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #150 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.05 (2) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.05 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.05 (3) all_6_2 = e2
% 66.80/10.05 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.05 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.05 (5) op(e2, e2) = all_10_2
% 66.80/10.05 (6) op(all_6_2, all_6_2) = e2
% 66.80/10.05 (7) all_52_1 = all_14_2
% 66.80/10.05 (8) ~ (e1 = e0)
% 66.80/10.05 (9) ~ (all_52_0 = e0)
% 66.80/10.05 (10) all_52_3 = e2
% 66.80/10.05 (11) ~ (e2 = e1)
% 66.80/10.05 (12) all_52_0 = all_10_2
% 66.80/10.05 (13) ~ (e3 = e2)
% 66.80/10.05 (14) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.05 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (9), (12) imply:
% 66.80/10.05 | (15) ~ (all_10_2 = e0)
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (6) imply:
% 66.80/10.05 | (16) op(e2, e2) = e2
% 66.80/10.05 |
% 66.80/10.05 | GROUND_INST: instantiating (1) with all_10_2, e2, e2, e2, simplifying with
% 66.80/10.05 | (5), (16) gives:
% 66.80/10.05 | (17) all_10_2 = e2
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (12), (17) imply:
% 66.80/10.05 | (18) all_52_0 = e2
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (15), (17) imply:
% 66.80/10.05 | (19) ~ (e2 = e0)
% 66.80/10.05 |
% 66.80/10.05 | BETA: splitting (4) gives:
% 66.80/10.05 |
% 66.80/10.05 | Case 1:
% 66.80/10.05 | |
% 66.80/10.05 | | (20) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.05 | |
% 66.80/10.05 | | REF_CLOSE: (11), (18), (20) are inconsistent by sub-proof #157.
% 66.80/10.05 | |
% 66.80/10.05 | Case 2:
% 66.80/10.05 | |
% 66.80/10.05 | | (21) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.80/10.05 | | = e0))
% 66.80/10.05 | |
% 66.80/10.05 | | BETA: splitting (21) gives:
% 66.80/10.05 | |
% 66.80/10.05 | | Case 1:
% 66.80/10.05 | | |
% 66.80/10.05 | | | (22) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.05 | | |
% 66.80/10.05 | | | ALPHA: (22) implies:
% 66.80/10.05 | | | (23) all_52_2 = e1
% 66.80/10.05 | | | (24) ~ (all_52_1 = e3)
% 66.80/10.05 | | |
% 66.80/10.05 | | | REDUCE: (7), (24) imply:
% 66.80/10.05 | | | (25) ~ (all_14_2 = e3)
% 66.80/10.05 | | |
% 66.80/10.05 | | | BETA: splitting (14) gives:
% 66.80/10.05 | | |
% 66.80/10.05 | | | Case 1:
% 66.80/10.05 | | | |
% 66.80/10.05 | | | | (26) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.05 | | | |
% 66.80/10.05 | | | | REF_CLOSE: (18), (19), (26) are inconsistent by sub-proof #156.
% 66.80/10.05 | | | |
% 66.80/10.05 | | | Case 2:
% 66.80/10.05 | | | |
% 66.80/10.05 | | | | (27) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.80/10.05 | | | | (all_52_3 = e3))
% 66.80/10.05 | | | |
% 66.80/10.05 | | | | BETA: splitting (27) gives:
% 66.80/10.05 | | | |
% 66.80/10.05 | | | | Case 1:
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | (28) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | ALPHA: (28) implies:
% 66.80/10.05 | | | | | (29) all_52_1 = e0
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | COMBINE_EQS: (7), (29) imply:
% 66.80/10.05 | | | | | (30) all_14_2 = e0
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | SIMP: (30) implies:
% 66.80/10.05 | | | | | (31) all_14_2 = e0
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | REDUCE: (25), (31) imply:
% 66.80/10.05 | | | | | (32) ~ (e3 = e0)
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | SIMP: (32) implies:
% 66.80/10.05 | | | | | (33) ~ (e3 = e0)
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | BETA: splitting (2) gives:
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | Case 1:
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | | (34) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | | REF_CLOSE: (13), (18), (34) are inconsistent by sub-proof #155.
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | Case 2:
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | | (35) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~
% 66.80/10.05 | | | | | | (all_52_2 = e0))
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | | BETA: splitting (35) gives:
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | | Case 1:
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | | (36) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | | REF_CLOSE: (29), (33), (36) are inconsistent by sub-proof #154.
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | Case 2:
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | | (37) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | | REF_CLOSE: (10), (13), (37) are inconsistent by sub-proof #153.
% 66.80/10.05 | | | | | | |
% 66.80/10.05 | | | | | | End of split
% 66.80/10.05 | | | | | |
% 66.80/10.05 | | | | | End of split
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | Case 2:
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | (38) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | ALPHA: (38) implies:
% 66.80/10.05 | | | | | (39) all_52_2 = e0
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | | REF_CLOSE: (8), (23), (39) are inconsistent by sub-proof #152.
% 66.80/10.05 | | | | |
% 66.80/10.05 | | | | End of split
% 66.80/10.05 | | | |
% 66.80/10.05 | | | End of split
% 66.80/10.05 | | |
% 66.80/10.05 | | Case 2:
% 66.80/10.05 | | |
% 66.80/10.05 | | | (40) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.05 | | |
% 66.80/10.05 | | | REF_CLOSE: (10), (11), (40) are inconsistent by sub-proof #151.
% 66.80/10.05 | | |
% 66.80/10.05 | | End of split
% 66.80/10.05 | |
% 66.80/10.05 | End of split
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #151 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.05 (2) all_52_3 = e2
% 66.80/10.05 (3) ~ (e2 = e1)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_3 = e1
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e2 = e1
% 66.80/10.05 |
% 66.80/10.05 | SIMP: (5) implies:
% 66.80/10.05 | (6) e2 = e1
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (6) imply:
% 66.80/10.05 | (7) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (7) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #152 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_2 = e1
% 66.80/10.05 (2) all_52_2 = e0
% 66.80/10.05 (3) ~ (e1 = e0)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (1), (2) imply:
% 66.80/10.05 | (4) e1 = e0
% 66.80/10.05 |
% 66.80/10.05 | SIMP: (4) implies:
% 66.80/10.05 | (5) e1 = e0
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (5) imply:
% 66.80/10.05 | (6) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (6) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #153 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.05 (2) all_52_3 = e2
% 66.80/10.05 (3) ~ (e3 = e2)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_3 = e3
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e3 = e2
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (5) imply:
% 66.80/10.05 | (6) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (6) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #154 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.05 (2) all_52_1 = e0
% 66.80/10.05 (3) ~ (e3 = e0)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_1 = e3
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e3 = e0
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (5) imply:
% 66.80/10.05 | (6) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (6) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #155 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.05 (2) all_52_0 = e2
% 66.80/10.05 (3) ~ (e3 = e2)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_0 = e3
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e3 = e2
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (5) imply:
% 66.80/10.05 | (6) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (6) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #156 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.05 (2) all_52_0 = e2
% 66.80/10.05 (3) ~ (e2 = e0)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_0 = e0
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e2 = e0
% 66.80/10.05 |
% 66.80/10.05 | SIMP: (5) implies:
% 66.80/10.05 | (6) e2 = e0
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (6) imply:
% 66.80/10.05 | (7) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (7) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #157 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.05 (2) all_52_0 = e2
% 66.80/10.05 (3) ~ (e2 = e1)
% 66.80/10.05
% 66.80/10.05 Begin of proof
% 66.80/10.05 |
% 66.80/10.05 | ALPHA: (1) implies:
% 66.80/10.05 | (4) all_52_0 = e1
% 66.80/10.05 |
% 66.80/10.05 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.05 | (5) e2 = e1
% 66.80/10.05 |
% 66.80/10.05 | SIMP: (5) implies:
% 66.80/10.05 | (6) e2 = e1
% 66.80/10.05 |
% 66.80/10.05 | REDUCE: (3), (6) imply:
% 66.80/10.05 | (7) $false
% 66.80/10.05 |
% 66.80/10.05 | CLOSE: (7) is inconsistent.
% 66.80/10.05 |
% 66.80/10.05 End of proof
% 66.80/10.05
% 66.80/10.05 Sub-proof #158 shows that the following formulas are inconsistent:
% 66.80/10.05 ----------------------------------------------------------------
% 66.80/10.05 (1) all_52_2 = all_4_2
% 66.80/10.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.05 (3) op(e0, e0) = all_6_2
% 66.80/10.05 (4) ~ (all_10_0 = e1)
% 66.80/10.05 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.05 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.05 (6) op(e2, e2) = all_10_2
% 66.80/10.05 (7) ~ (e1 = e0)
% 66.80/10.05 (8) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.06 (9) ~ (e2 = e1)
% 66.80/10.06 (10) op(all_4_2, all_4_2) = e0
% 66.80/10.06 (11) all_52_3 = all_6_2
% 66.80/10.06 (12) op(all_10_2, all_10_2) = all_10_0
% 66.80/10.06 (13) all_52_0 = all_10_2
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | ALPHA: (8) implies:
% 66.80/10.06 | (14) all_52_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | COMBINE_EQS: (1), (14) imply:
% 66.80/10.06 | (15) all_4_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | SIMP: (15) implies:
% 66.80/10.06 | (16) all_4_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 66.80/10.06 | (16) are inconsistent by sub-proof #163.
% 66.80/10.06 |
% 66.80/10.06 End of proof
% 66.80/10.06
% 66.80/10.06 Sub-proof #159 shows that the following formulas are inconsistent:
% 66.80/10.06 ----------------------------------------------------------------
% 66.80/10.06 (1) all_52_2 = all_4_2
% 66.80/10.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.06 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.06 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.06 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.06 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.06 (5) ~ (e3 = e1)
% 66.80/10.06 (6) op(e2, e2) = all_10_2
% 66.80/10.06 (7) all_52_1 = all_14_2
% 66.80/10.06 (8) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.80/10.06 (9) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.06 (10) ~ (e2 = e0)
% 66.80/10.06 (11) all_52_0 = all_10_2
% 66.80/10.06 (12) ~ (all_14_0 = e3)
% 66.80/10.06 (13) ~ (e3 = e2)
% 66.80/10.06 (14) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.06 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.06 (15) ~ (all_14_0 = e0)
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | ALPHA: (8) implies:
% 66.80/10.06 | (16) all_52_1 = e2
% 66.80/10.06 | (17) ~ (all_52_0 = e1)
% 66.80/10.06 |
% 66.80/10.06 | COMBINE_EQS: (7), (16) imply:
% 66.80/10.06 | (18) all_14_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | SIMP: (18) implies:
% 66.80/10.06 | (19) all_14_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 66.80/10.06 | (15), (16), (17), (19) are inconsistent by sub-proof #166.
% 66.80/10.06 |
% 66.80/10.06 End of proof
% 66.80/10.06
% 66.80/10.06 Sub-proof #160 shows that the following formulas are inconsistent:
% 66.80/10.06 ----------------------------------------------------------------
% 66.80/10.06 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 66.80/10.06 e0))
% 66.80/10.06 (2) all_52_2 = all_4_2
% 66.80/10.06 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.06 (4) op(e0, e0) = all_6_2
% 66.80/10.06 (5) ~ (all_10_0 = e1)
% 66.80/10.06 (6) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.06 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.06 (7) op(e2, e2) = all_10_2
% 66.80/10.06 (8) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.06 (9) ~ (all_6_0 = e2)
% 66.80/10.06 (10) ~ (e1 = e0)
% 66.80/10.06 (11) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.06 (12) ~ (all_6_0 = e3)
% 66.80/10.06 (13) ~ (e2 = e1)
% 66.80/10.06 (14) op(all_4_2, all_4_2) = e0
% 66.80/10.06 (15) all_52_3 = all_6_2
% 66.80/10.06 (16) op(all_10_2, all_10_2) = all_10_0
% 66.80/10.06 (17) all_52_0 = all_10_2
% 66.80/10.06 (18) all_56_10 = all_10_2
% 66.80/10.06 (19) ~ (all_6_0 = e1)
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | BETA: splitting (1) gives:
% 66.80/10.06 |
% 66.80/10.06 | Case 1:
% 66.80/10.06 | |
% 66.80/10.06 | | (20) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.06 | |
% 66.80/10.06 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (13), (14), (15), (16), (17),
% 66.80/10.06 | | (20) are inconsistent by sub-proof #162.
% 66.80/10.06 | |
% 66.80/10.06 | Case 2:
% 66.80/10.06 | |
% 66.80/10.06 | | (21) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.80/10.06 | |
% 66.80/10.06 | | ALPHA: (21) implies:
% 66.80/10.06 | | (22) all_52_3 = e2
% 66.80/10.06 | | (23) ~ (all_52_0 = e0)
% 66.80/10.06 | |
% 66.80/10.06 | | COMBINE_EQS: (15), (22) imply:
% 66.80/10.06 | | (24) all_6_2 = e2
% 66.80/10.06 | |
% 66.80/10.06 | | REF_CLOSE: (3), (7), (8), (9), (11), (12), (17), (18), (19), (23), (24) are
% 66.80/10.06 | | inconsistent by sub-proof #161.
% 66.80/10.06 | |
% 66.80/10.06 | End of split
% 66.80/10.06 |
% 66.80/10.06 End of proof
% 66.80/10.06
% 66.80/10.06 Sub-proof #161 shows that the following formulas are inconsistent:
% 66.80/10.06 ----------------------------------------------------------------
% 66.80/10.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.06 (2) all_6_2 = e2
% 66.80/10.06 (3) op(e2, e2) = all_10_2
% 66.80/10.06 (4) all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.06 (5) ~ (all_6_0 = e2)
% 66.80/10.06 (6) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.06 (7) ~ (all_52_0 = e0)
% 66.80/10.06 (8) ~ (all_6_0 = e3)
% 66.80/10.06 (9) all_52_0 = all_10_2
% 66.80/10.06 (10) all_56_10 = all_10_2
% 66.80/10.06 (11) ~ (all_6_0 = e1)
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | REDUCE: (7), (9) imply:
% 66.80/10.06 | (12) ~ (all_10_2 = e0)
% 66.80/10.06 |
% 66.80/10.06 | REDUCE: (2), (6) imply:
% 66.80/10.06 | (13) op(e2, e2) = all_6_0
% 66.80/10.06 |
% 66.80/10.06 | GROUND_INST: instantiating (1) with all_10_2, all_6_0, e2, e2, simplifying
% 66.80/10.06 | with (3), (13) gives:
% 66.80/10.06 | (14) all_10_2 = all_6_0
% 66.80/10.06 |
% 66.80/10.06 | COMBINE_EQS: (10), (14) imply:
% 66.80/10.06 | (15) all_56_10 = all_6_0
% 66.80/10.06 |
% 66.80/10.06 | REDUCE: (12), (14) imply:
% 66.80/10.06 | (16) ~ (all_6_0 = e0)
% 66.80/10.06 |
% 66.80/10.06 | BETA: splitting (4) gives:
% 66.80/10.06 |
% 66.80/10.06 | Case 1:
% 66.80/10.06 | |
% 66.80/10.06 | | (17) all_56_10 = e3
% 66.80/10.06 | |
% 66.80/10.06 | | COMBINE_EQS: (15), (17) imply:
% 66.80/10.06 | | (18) all_6_0 = e3
% 66.80/10.06 | |
% 66.80/10.06 | | SIMP: (18) implies:
% 66.80/10.06 | | (19) all_6_0 = e3
% 66.80/10.06 | |
% 66.80/10.06 | | REDUCE: (8), (19) imply:
% 66.80/10.06 | | (20) $false
% 66.80/10.06 | |
% 66.80/10.06 | | CLOSE: (20) is inconsistent.
% 66.80/10.06 | |
% 66.80/10.06 | Case 2:
% 66.80/10.06 | |
% 66.80/10.06 | | (21) all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 66.80/10.06 | |
% 66.80/10.06 | | BETA: splitting (21) gives:
% 66.80/10.06 | |
% 66.80/10.06 | | Case 1:
% 66.80/10.06 | | |
% 66.80/10.06 | | | (22) all_56_10 = e2
% 66.80/10.06 | | |
% 66.80/10.06 | | | COMBINE_EQS: (15), (22) imply:
% 66.80/10.06 | | | (23) all_6_0 = e2
% 66.80/10.06 | | |
% 66.80/10.06 | | | SIMP: (23) implies:
% 66.80/10.06 | | | (24) all_6_0 = e2
% 66.80/10.06 | | |
% 66.80/10.06 | | | REDUCE: (5), (24) imply:
% 66.80/10.06 | | | (25) $false
% 66.80/10.06 | | |
% 66.80/10.06 | | | CLOSE: (25) is inconsistent.
% 66.80/10.06 | | |
% 66.80/10.06 | | Case 2:
% 66.80/10.06 | | |
% 66.80/10.06 | | | (26) all_56_10 = e1 | all_56_10 = e0
% 66.80/10.06 | | |
% 66.80/10.06 | | | BETA: splitting (26) gives:
% 66.80/10.06 | | |
% 66.80/10.06 | | | Case 1:
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | (27) all_56_10 = e1
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | COMBINE_EQS: (15), (27) imply:
% 66.80/10.06 | | | | (28) all_6_0 = e1
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | SIMP: (28) implies:
% 66.80/10.06 | | | | (29) all_6_0 = e1
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | REDUCE: (11), (29) imply:
% 66.80/10.06 | | | | (30) $false
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | CLOSE: (30) is inconsistent.
% 66.80/10.06 | | | |
% 66.80/10.06 | | | Case 2:
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | (31) all_56_10 = e0
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | COMBINE_EQS: (15), (31) imply:
% 66.80/10.06 | | | | (32) all_6_0 = e0
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | SIMP: (32) implies:
% 66.80/10.06 | | | | (33) all_6_0 = e0
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | REDUCE: (16), (33) imply:
% 66.80/10.06 | | | | (34) $false
% 66.80/10.06 | | | |
% 66.80/10.06 | | | | CLOSE: (34) is inconsistent.
% 66.80/10.06 | | | |
% 66.80/10.06 | | | End of split
% 66.80/10.06 | | |
% 66.80/10.06 | | End of split
% 66.80/10.06 | |
% 66.80/10.06 | End of split
% 66.80/10.06 |
% 66.80/10.06 End of proof
% 66.80/10.06
% 66.80/10.06 Sub-proof #162 shows that the following formulas are inconsistent:
% 66.80/10.06 ----------------------------------------------------------------
% 66.80/10.06 (1) all_52_2 = all_4_2
% 66.80/10.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.06 (3) op(e0, e0) = all_6_2
% 66.80/10.06 (4) ~ (all_10_0 = e1)
% 66.80/10.06 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.06 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.06 (6) op(e2, e2) = all_10_2
% 66.80/10.06 (7) ~ (e1 = e0)
% 66.80/10.06 (8) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.06 (9) ~ (e2 = e1)
% 66.80/10.06 (10) op(all_4_2, all_4_2) = e0
% 66.80/10.06 (11) all_52_3 = all_6_2
% 66.80/10.06 (12) op(all_10_2, all_10_2) = all_10_0
% 66.80/10.06 (13) all_52_0 = all_10_2
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | ALPHA: (8) implies:
% 66.80/10.06 | (14) all_52_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | COMBINE_EQS: (1), (14) imply:
% 66.80/10.06 | (15) all_4_2 = e2
% 66.80/10.06 |
% 66.80/10.06 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 66.80/10.06 | (15) are inconsistent by sub-proof #163.
% 66.80/10.06 |
% 66.80/10.06 End of proof
% 66.80/10.06
% 66.80/10.06 Sub-proof #163 shows that the following formulas are inconsistent:
% 66.80/10.06 ----------------------------------------------------------------
% 66.80/10.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.06 (2) op(e0, e0) = all_6_2
% 66.80/10.06 (3) ~ (all_10_0 = e1)
% 66.80/10.06 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.06 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.06 (5) op(e2, e2) = all_10_2
% 66.80/10.06 (6) ~ (e1 = e0)
% 66.80/10.06 (7) all_4_2 = e2
% 66.80/10.06 (8) ~ (e2 = e1)
% 66.80/10.06 (9) op(all_4_2, all_4_2) = e0
% 66.80/10.06 (10) all_52_3 = all_6_2
% 66.80/10.06 (11) op(all_10_2, all_10_2) = all_10_0
% 66.80/10.06 (12) all_52_0 = all_10_2
% 66.80/10.06 (13) all_52_2 = e2
% 66.80/10.06
% 66.80/10.06 Begin of proof
% 66.80/10.06 |
% 66.80/10.06 | REDUCE: (7), (9) imply:
% 66.80/10.06 | (14) op(e2, e2) = e0
% 66.80/10.06 |
% 66.80/10.06 | GROUND_INST: instantiating (1) with all_10_2, e0, e2, e2, simplifying with
% 66.80/10.06 | (5), (14) gives:
% 66.80/10.06 | (15) all_10_2 = e0
% 66.80/10.06 |
% 66.80/10.06 | COMBINE_EQS: (12), (15) imply:
% 66.80/10.06 | (16) all_52_0 = e0
% 66.80/10.06 |
% 66.80/10.06 | REDUCE: (11), (15) imply:
% 66.80/10.06 | (17) op(e0, e0) = all_10_0
% 66.80/10.06 |
% 66.80/10.06 | BETA: splitting (4) gives:
% 66.80/10.06 |
% 66.80/10.06 | Case 1:
% 66.80/10.06 | |
% 66.80/10.06 | | (18) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.06 | |
% 66.80/10.06 | | REF_CLOSE: (6), (16), (18) are inconsistent by sub-proof #164.
% 66.80/10.06 | |
% 66.80/10.06 | Case 2:
% 66.80/10.06 | |
% 66.80/10.06 | | (19) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.80/10.06 | | = e0))
% 66.80/10.06 | |
% 66.80/10.06 | | BETA: splitting (19) gives:
% 66.80/10.06 | |
% 66.80/10.06 | | Case 1:
% 66.80/10.06 | | |
% 66.80/10.06 | | | (20) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.06 | | |
% 66.80/10.06 | | | REF_CLOSE: (8), (13), (20) are inconsistent by sub-proof #175.
% 66.80/10.06 | | |
% 66.80/10.06 | | Case 2:
% 66.80/10.06 | | |
% 66.80/10.06 | | | (21) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.06 | | |
% 66.80/10.06 | | | ALPHA: (21) implies:
% 66.80/10.07 | | | (22) all_52_3 = e1
% 66.80/10.07 | | |
% 66.80/10.07 | | | COMBINE_EQS: (10), (22) imply:
% 66.80/10.07 | | | (23) all_6_2 = e1
% 66.80/10.07 | | |
% 66.80/10.07 | | | SIMP: (23) implies:
% 66.80/10.07 | | | (24) all_6_2 = e1
% 66.80/10.07 | | |
% 66.80/10.07 | | | REDUCE: (2), (24) imply:
% 66.80/10.07 | | | (25) op(e0, e0) = e1
% 66.80/10.07 | | |
% 66.80/10.07 | | | GROUND_INST: instantiating (1) with e1, all_10_0, e0, e0, simplifying with
% 66.80/10.07 | | | (17), (25) gives:
% 66.80/10.07 | | | (26) all_10_0 = e1
% 66.80/10.07 | | |
% 66.80/10.07 | | | REDUCE: (3), (26) imply:
% 66.80/10.07 | | | (27) $false
% 66.80/10.07 | | |
% 66.80/10.07 | | | CLOSE: (27) is inconsistent.
% 66.80/10.07 | | |
% 66.80/10.07 | | End of split
% 66.80/10.07 | |
% 66.80/10.07 | End of split
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #164 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.07 (2) all_52_0 = e0
% 66.80/10.07 (3) ~ (e1 = e0)
% 66.80/10.07
% 66.80/10.07 Begin of proof
% 66.80/10.07 |
% 66.80/10.07 | ALPHA: (1) implies:
% 66.80/10.07 | (4) all_52_0 = e1
% 66.80/10.07 |
% 66.80/10.07 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.07 | (5) e1 = e0
% 66.80/10.07 |
% 66.80/10.07 | REDUCE: (3), (5) imply:
% 66.80/10.07 | (6) $false
% 66.80/10.07 |
% 66.80/10.07 | CLOSE: (6) is inconsistent.
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #165 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) all_52_2 = all_4_2
% 66.80/10.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.07 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.07 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.07 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.07 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.07 (5) ~ (e3 = e1)
% 66.80/10.07 (6) op(e2, e2) = all_10_2
% 66.80/10.07 (7) all_52_1 = all_14_2
% 66.80/10.07 (8) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.80/10.07 (9) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.07 (10) ~ (e2 = e0)
% 66.80/10.07 (11) all_52_0 = all_10_2
% 66.80/10.07 (12) ~ (all_14_0 = e3)
% 66.80/10.07 (13) ~ (e3 = e2)
% 66.80/10.07 (14) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.07 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.07 (15) ~ (all_14_0 = e0)
% 66.80/10.07
% 66.80/10.07 Begin of proof
% 66.80/10.07 |
% 66.80/10.07 | ALPHA: (8) implies:
% 66.80/10.07 | (16) all_52_1 = e2
% 66.80/10.07 | (17) ~ (all_52_0 = e1)
% 66.80/10.07 |
% 66.80/10.07 | COMBINE_EQS: (7), (16) imply:
% 66.80/10.07 | (18) all_14_2 = e2
% 66.80/10.07 |
% 66.80/10.07 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 66.80/10.07 | (15), (16), (17), (18) are inconsistent by sub-proof #166.
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #166 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) ~ (all_52_0 = e1)
% 66.80/10.07 (2) all_52_2 = all_4_2
% 66.80/10.07 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.07 (4) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.07 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.07 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.07 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.07 (6) ~ (e3 = e1)
% 66.80/10.07 (7) op(e2, e2) = all_10_2
% 66.80/10.07 (8) all_14_2 = e2
% 66.80/10.07 (9) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.07 (10) ~ (e2 = e0)
% 66.80/10.07 (11) all_52_0 = all_10_2
% 66.80/10.07 (12) ~ (all_14_0 = e3)
% 66.80/10.07 (13) all_52_1 = e2
% 66.80/10.07 (14) ~ (e3 = e2)
% 66.80/10.07 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.07 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.07 (16) ~ (all_14_0 = e0)
% 66.80/10.07
% 66.80/10.07 Begin of proof
% 66.80/10.07 |
% 66.80/10.07 | REDUCE: (1), (11) imply:
% 66.80/10.07 | (17) ~ (all_10_2 = e1)
% 66.80/10.07 |
% 66.80/10.07 | REDUCE: (8), (9) imply:
% 66.80/10.07 | (18) op(e2, e2) = all_14_0
% 66.80/10.07 |
% 66.80/10.07 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 66.80/10.07 | (16), (17), (18) are inconsistent by sub-proof #177.
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #167 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) (all_52_1 = e2 & ~ (all_52_0 = e1)) | (all_52_2 = e2 & ~ (all_52_0 =
% 66.80/10.07 e3)) | (all_52_3 = e2 & ~ (all_52_0 = e0))
% 66.80/10.07 (2) op(e1, e1) = all_14_2
% 66.80/10.07 (3) all_52_2 = all_4_2
% 66.80/10.07 (4) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.07 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.07 (6) ~ (all_4_0 = e0)
% 66.80/10.07 (7) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.07 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.07 (8) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.07 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.07 (9) ~ (e3 = e1)
% 66.80/10.07 (10) op(e2, e2) = all_10_2
% 66.80/10.07 (11) ~ (all_4_0 = e1)
% 66.80/10.07 (12) all_52_1 = all_14_2
% 66.80/10.07 (13) ~ (e1 = e0)
% 66.80/10.07 (14) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.07 (15) op(all_14_2, all_14_2) = all_14_0
% 66.80/10.07 (16) ~ (e2 = e0)
% 66.80/10.07 (17) ~ (e2 = e1)
% 66.80/10.07 (18) all_52_3 = all_6_2
% 66.80/10.07 (19) all_52_0 = all_10_2
% 66.80/10.07 (20) ~ (all_14_0 = e3)
% 66.80/10.07 (21) ~ (e3 = e2)
% 66.80/10.07 (22) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.07 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.07 (23) ~ (all_14_0 = e0)
% 66.80/10.07 (24) ~ (all_6_0 = e1)
% 66.80/10.07
% 66.80/10.07 Begin of proof
% 66.80/10.07 |
% 66.80/10.07 | BETA: splitting (1) gives:
% 66.80/10.07 |
% 66.80/10.07 | Case 1:
% 66.80/10.07 | |
% 66.80/10.07 | | (25) all_52_1 = e2 & ~ (all_52_0 = e1)
% 66.80/10.07 | |
% 66.80/10.07 | | ALPHA: (25) implies:
% 66.80/10.07 | | (26) all_52_1 = e2
% 66.80/10.07 | | (27) ~ (all_52_0 = e1)
% 66.80/10.07 | |
% 66.80/10.07 | | COMBINE_EQS: (12), (26) imply:
% 66.80/10.07 | | (28) all_14_2 = e2
% 66.80/10.07 | |
% 66.80/10.07 | | REDUCE: (19), (27) imply:
% 66.80/10.07 | | (29) ~ (all_10_2 = e1)
% 66.80/10.07 | |
% 66.80/10.07 | | REDUCE: (15), (28) imply:
% 66.80/10.07 | | (30) op(e2, e2) = all_14_0
% 66.80/10.07 | |
% 66.80/10.07 | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (16), (19), (20), (21), (22),
% 66.80/10.07 | | (23), (26), (29), (30) are inconsistent by sub-proof #177.
% 66.80/10.07 | |
% 66.80/10.07 | Case 2:
% 66.80/10.07 | |
% 66.80/10.07 | | (31) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0
% 66.80/10.07 | | = e0))
% 66.80/10.07 | |
% 66.80/10.07 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (16),
% 66.80/10.07 | | (17), (18), (19), (22), (24), (31) are inconsistent by sub-proof
% 66.80/10.07 | | #168.
% 66.80/10.07 | |
% 66.80/10.07 | End of split
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #168 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) (all_52_2 = e2 & ~ (all_52_0 = e3)) | (all_52_3 = e2 & ~ (all_52_0 =
% 66.80/10.07 e0))
% 66.80/10.07 (2) op(e1, e1) = all_14_2
% 66.80/10.07 (3) all_52_2 = all_4_2
% 66.80/10.07 (4) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.07 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.07 (6) ~ (all_4_0 = e0)
% 66.80/10.07 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.07 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.07 (8) op(e2, e2) = all_10_2
% 66.80/10.07 (9) ~ (all_4_0 = e1)
% 66.80/10.07 (10) all_52_1 = all_14_2
% 66.80/10.07 (11) ~ (e1 = e0)
% 66.80/10.07 (12) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.07 (13) ~ (e2 = e0)
% 66.80/10.07 (14) ~ (e2 = e1)
% 66.80/10.07 (15) all_52_3 = all_6_2
% 66.80/10.07 (16) all_52_0 = all_10_2
% 66.80/10.07 (17) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.07 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.07 (18) ~ (all_6_0 = e1)
% 66.80/10.07
% 66.80/10.07 Begin of proof
% 66.80/10.07 |
% 66.80/10.07 | BETA: splitting (1) gives:
% 66.80/10.07 |
% 66.80/10.07 | Case 1:
% 66.80/10.07 | |
% 66.80/10.07 | | (19) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.07 | |
% 66.80/10.07 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (16), (17),
% 66.80/10.07 | | (19) are inconsistent by sub-proof #173.
% 66.80/10.07 | |
% 66.80/10.07 | Case 2:
% 66.80/10.07 | |
% 66.80/10.07 | | (20) all_52_3 = e2 & ~ (all_52_0 = e0)
% 66.80/10.07 | |
% 66.80/10.07 | | ALPHA: (20) implies:
% 66.80/10.07 | | (21) all_52_3 = e2
% 66.80/10.07 | | (22) ~ (all_52_0 = e0)
% 66.80/10.07 | |
% 66.80/10.07 | | COMBINE_EQS: (15), (21) imply:
% 66.80/10.07 | | (23) all_6_2 = e2
% 66.80/10.07 | |
% 66.80/10.07 | | SIMP: (23) implies:
% 66.80/10.07 | | (24) all_6_2 = e2
% 66.80/10.07 | |
% 66.80/10.07 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (16),
% 66.80/10.07 | | (17), (18), (21), (22), (24) are inconsistent by sub-proof #169.
% 66.80/10.07 | |
% 66.80/10.07 | End of split
% 66.80/10.07 |
% 66.80/10.07 End of proof
% 66.80/10.07
% 66.80/10.07 Sub-proof #169 shows that the following formulas are inconsistent:
% 66.80/10.07 ----------------------------------------------------------------
% 66.80/10.07 (1) op(e1, e1) = all_14_2
% 66.80/10.07 (2) all_52_2 = all_4_2
% 66.80/10.07 (3) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.07 (5) ~ (all_4_0 = e0)
% 66.80/10.07 (6) all_6_2 = e2
% 66.80/10.07 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.07 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.07 (8) op(e2, e2) = all_10_2
% 66.80/10.07 (9) all_52_1 = all_14_2
% 66.80/10.07 (10) ~ (e1 = e0)
% 66.80/10.07 (11) op(all_6_2, all_6_2) = all_6_0
% 66.80/10.07 (12) ~ (all_52_0 = e0)
% 66.80/10.07 (13) all_52_3 = e2
% 66.80/10.07 (14) ~ (e2 = e1)
% 66.80/10.07 (15) all_52_0 = all_10_2
% 66.80/10.08 (16) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.08 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.08 (17) ~ (all_6_0 = e1)
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (12), (15) imply:
% 66.80/10.08 | (18) ~ (all_10_2 = e0)
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (6), (11) imply:
% 66.80/10.08 | (19) op(e2, e2) = all_6_0
% 66.80/10.08 |
% 66.80/10.08 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (13), (14), (15),
% 66.80/10.08 | (16), (17), (18), (19) are inconsistent by sub-proof #170.
% 66.80/10.08 |
% 66.80/10.08 End of proof
% 66.80/10.08
% 66.80/10.08 Sub-proof #170 shows that the following formulas are inconsistent:
% 66.80/10.08 ----------------------------------------------------------------
% 66.80/10.08 (1) ~ (all_10_2 = e0)
% 66.80/10.08 (2) op(e1, e1) = all_14_2
% 66.80/10.08 (3) all_52_2 = all_4_2
% 66.80/10.08 (4) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.08 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.08 (6) ~ (all_4_0 = e0)
% 66.80/10.08 (7) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.08 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.08 (8) op(e2, e2) = all_10_2
% 66.80/10.08 (9) all_52_1 = all_14_2
% 66.80/10.08 (10) op(e2, e2) = all_6_0
% 66.80/10.08 (11) ~ (e1 = e0)
% 66.80/10.08 (12) all_52_3 = e2
% 66.80/10.08 (13) ~ (e2 = e1)
% 66.80/10.08 (14) all_52_0 = all_10_2
% 66.80/10.08 (15) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.08 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.08 (16) ~ (all_6_0 = e1)
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | GROUND_INST: instantiating (5) with all_10_2, all_6_0, e2, e2, simplifying
% 66.80/10.08 | with (8), (10) gives:
% 66.80/10.08 | (17) all_10_2 = all_6_0
% 66.80/10.08 |
% 66.80/10.08 | COMBINE_EQS: (14), (17) imply:
% 66.80/10.08 | (18) all_52_0 = all_6_0
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (1), (17) imply:
% 66.80/10.08 | (19) ~ (all_6_0 = e0)
% 66.80/10.08 |
% 66.80/10.08 | BETA: splitting (7) gives:
% 66.80/10.08 |
% 66.80/10.08 | Case 1:
% 66.80/10.08 | |
% 66.80/10.08 | | (20) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.08 | |
% 66.80/10.08 | | ALPHA: (20) implies:
% 66.80/10.08 | | (21) all_52_0 = e1
% 66.80/10.08 | |
% 66.80/10.08 | | COMBINE_EQS: (18), (21) imply:
% 66.80/10.08 | | (22) all_6_0 = e1
% 66.80/10.08 | |
% 66.80/10.08 | | REDUCE: (16), (22) imply:
% 66.80/10.08 | | (23) $false
% 66.80/10.08 | |
% 66.80/10.08 | | CLOSE: (23) is inconsistent.
% 66.80/10.08 | |
% 66.80/10.08 | Case 2:
% 66.80/10.08 | |
% 66.80/10.08 | | (24) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.80/10.08 | | = e0))
% 66.80/10.08 | |
% 66.80/10.08 | | BETA: splitting (24) gives:
% 66.80/10.08 | |
% 66.80/10.08 | | Case 1:
% 66.80/10.08 | | |
% 66.80/10.08 | | | (25) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.08 | | |
% 66.80/10.08 | | | ALPHA: (25) implies:
% 66.80/10.08 | | | (26) all_52_2 = e1
% 66.80/10.08 | | |
% 66.80/10.08 | | | COMBINE_EQS: (3), (26) imply:
% 66.80/10.08 | | | (27) all_4_2 = e1
% 66.80/10.08 | | |
% 66.80/10.08 | | | REDUCE: (4), (27) imply:
% 66.80/10.08 | | | (28) op(e1, e1) = all_4_0
% 66.80/10.08 | | |
% 66.80/10.08 | | | BETA: splitting (15) gives:
% 66.80/10.08 | | |
% 66.80/10.08 | | | Case 1:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | (29) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | ALPHA: (29) implies:
% 66.80/10.08 | | | | (30) all_52_0 = e0
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | COMBINE_EQS: (18), (30) imply:
% 66.80/10.08 | | | | (31) all_6_0 = e0
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | REDUCE: (19), (31) imply:
% 66.80/10.08 | | | | (32) $false
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | CLOSE: (32) is inconsistent.
% 66.80/10.08 | | | |
% 66.80/10.08 | | | Case 2:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | (33) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.80/10.08 | | | | (all_52_3 = e3))
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | BETA: splitting (33) gives:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | Case 1:
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | (34) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | ALPHA: (34) implies:
% 66.80/10.08 | | | | | (35) all_52_1 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | COMBINE_EQS: (9), (35) imply:
% 66.80/10.08 | | | | | (36) all_14_2 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | REF_CLOSE: (2), (5), (6), (28), (36) are inconsistent by sub-proof
% 66.80/10.08 | | | | | #172.
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | Case 2:
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | (37) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | REF_CLOSE: (11), (26), (37) are inconsistent by sub-proof #178.
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | End of split
% 66.80/10.08 | | | |
% 66.80/10.08 | | | End of split
% 66.80/10.08 | | |
% 66.80/10.08 | | Case 2:
% 66.80/10.08 | | |
% 66.80/10.08 | | | (38) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.08 | | |
% 66.80/10.08 | | | REF_CLOSE: (12), (13), (38) are inconsistent by sub-proof #171.
% 66.80/10.08 | | |
% 66.80/10.08 | | End of split
% 66.80/10.08 | |
% 66.80/10.08 | End of split
% 66.80/10.08 |
% 66.80/10.08 End of proof
% 66.80/10.08
% 66.80/10.08 Sub-proof #171 shows that the following formulas are inconsistent:
% 66.80/10.08 ----------------------------------------------------------------
% 66.80/10.08 (1) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.08 (2) all_52_3 = e2
% 66.80/10.08 (3) ~ (e2 = e1)
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | ALPHA: (1) implies:
% 66.80/10.08 | (4) all_52_3 = e1
% 66.80/10.08 |
% 66.80/10.08 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.08 | (5) e2 = e1
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (3), (5) imply:
% 66.80/10.08 | (6) $false
% 66.80/10.08 |
% 66.80/10.08 | CLOSE: (6) is inconsistent.
% 66.80/10.08 |
% 66.80/10.08 End of proof
% 66.80/10.08
% 66.80/10.08 Sub-proof #172 shows that the following formulas are inconsistent:
% 66.80/10.08 ----------------------------------------------------------------
% 66.80/10.08 (1) op(e1, e1) = all_14_2
% 66.80/10.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.08 (3) ~ (all_4_0 = e0)
% 66.80/10.08 (4) all_14_2 = e0
% 66.80/10.08 (5) op(e1, e1) = all_4_0
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (1), (4) imply:
% 66.80/10.08 | (6) op(e1, e1) = e0
% 66.80/10.08 |
% 66.80/10.08 | GROUND_INST: instantiating (2) with e0, all_4_0, e1, e1, simplifying with (5),
% 66.80/10.08 | (6) gives:
% 66.80/10.08 | (7) all_4_0 = e0
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (3), (7) imply:
% 66.80/10.08 | (8) $false
% 66.80/10.08 |
% 66.80/10.08 | CLOSE: (8) is inconsistent.
% 66.80/10.08 |
% 66.80/10.08 End of proof
% 66.80/10.08
% 66.80/10.08 Sub-proof #173 shows that the following formulas are inconsistent:
% 66.80/10.08 ----------------------------------------------------------------
% 66.80/10.08 (1) all_52_2 = all_4_2
% 66.80/10.08 (2) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.08 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.08 (4) ~ (all_4_0 = e0)
% 66.80/10.08 (5) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.08 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.08 (6) op(e2, e2) = all_10_2
% 66.80/10.08 (7) ~ (all_4_0 = e1)
% 66.80/10.08 (8) all_52_1 = all_14_2
% 66.80/10.08 (9) all_52_2 = e2 & ~ (all_52_0 = e3)
% 66.80/10.08 (10) ~ (e2 = e0)
% 66.80/10.08 (11) ~ (e2 = e1)
% 66.80/10.08 (12) all_52_0 = all_10_2
% 66.80/10.08 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.08 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | ALPHA: (9) implies:
% 66.80/10.08 | (14) all_52_2 = e2
% 66.80/10.08 |
% 66.80/10.08 | COMBINE_EQS: (1), (14) imply:
% 66.80/10.08 | (15) all_4_2 = e2
% 66.80/10.08 |
% 66.80/10.08 | SIMP: (15) implies:
% 66.80/10.08 | (16) all_4_2 = e2
% 66.80/10.08 |
% 66.80/10.08 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 66.80/10.08 | (16) are inconsistent by sub-proof #174.
% 66.80/10.08 |
% 66.80/10.08 End of proof
% 66.80/10.08
% 66.80/10.08 Sub-proof #174 shows that the following formulas are inconsistent:
% 66.80/10.08 ----------------------------------------------------------------
% 66.80/10.08 (1) op(all_4_2, all_4_2) = all_4_0
% 66.80/10.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.08 (3) ~ (all_4_0 = e0)
% 66.80/10.08 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.08 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.08 (5) op(e2, e2) = all_10_2
% 66.80/10.08 (6) ~ (all_4_0 = e1)
% 66.80/10.08 (7) all_52_1 = all_14_2
% 66.80/10.08 (8) all_4_2 = e2
% 66.80/10.08 (9) ~ (e2 = e0)
% 66.80/10.08 (10) ~ (e2 = e1)
% 66.80/10.08 (11) all_52_0 = all_10_2
% 66.80/10.08 (12) all_52_2 = e2
% 66.80/10.08 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.08 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.08
% 66.80/10.08 Begin of proof
% 66.80/10.08 |
% 66.80/10.08 | REDUCE: (1), (8) imply:
% 66.80/10.08 | (14) op(e2, e2) = all_4_0
% 66.80/10.08 |
% 66.80/10.08 | GROUND_INST: instantiating (2) with all_10_2, all_4_0, e2, e2, simplifying
% 66.80/10.08 | with (5), (14) gives:
% 66.80/10.08 | (15) all_10_2 = all_4_0
% 66.80/10.08 |
% 66.80/10.08 | COMBINE_EQS: (11), (15) imply:
% 66.80/10.08 | (16) all_52_0 = all_4_0
% 66.80/10.08 |
% 66.80/10.08 | BETA: splitting (4) gives:
% 66.80/10.08 |
% 66.80/10.08 | Case 1:
% 66.80/10.08 | |
% 66.80/10.08 | | (17) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.08 | |
% 66.80/10.08 | | REF_CLOSE: (6), (16), (17) are inconsistent by sub-proof #176.
% 66.80/10.08 | |
% 66.80/10.08 | Case 2:
% 66.80/10.08 | |
% 66.80/10.08 | | (18) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~ (all_52_1
% 66.80/10.08 | | = e0))
% 66.80/10.08 | |
% 66.80/10.08 | | BETA: splitting (18) gives:
% 66.80/10.08 | |
% 66.80/10.08 | | Case 1:
% 66.80/10.08 | | |
% 66.80/10.08 | | | (19) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.08 | | |
% 66.80/10.08 | | | REF_CLOSE: (10), (12), (19) are inconsistent by sub-proof #175.
% 66.80/10.08 | | |
% 66.80/10.08 | | Case 2:
% 66.80/10.08 | | |
% 66.80/10.08 | | | (20) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.08 | | |
% 66.80/10.08 | | | ALPHA: (20) implies:
% 66.80/10.08 | | | (21) ~ (all_52_1 = e0)
% 66.80/10.08 | | |
% 66.80/10.08 | | | REDUCE: (7), (21) imply:
% 66.80/10.08 | | | (22) ~ (all_14_2 = e0)
% 66.80/10.08 | | |
% 66.80/10.08 | | | BETA: splitting (13) gives:
% 66.80/10.08 | | |
% 66.80/10.08 | | | Case 1:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | (23) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | ALPHA: (23) implies:
% 66.80/10.08 | | | | (24) all_52_0 = e0
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | COMBINE_EQS: (16), (24) imply:
% 66.80/10.08 | | | | (25) all_4_0 = e0
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | SIMP: (25) implies:
% 66.80/10.08 | | | | (26) all_4_0 = e0
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | REDUCE: (3), (26) imply:
% 66.80/10.08 | | | | (27) $false
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | CLOSE: (27) is inconsistent.
% 66.80/10.08 | | | |
% 66.80/10.08 | | | Case 2:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | (28) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.80/10.08 | | | | (all_52_3 = e3))
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | BETA: splitting (28) gives:
% 66.80/10.08 | | | |
% 66.80/10.08 | | | | Case 1:
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | (29) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | ALPHA: (29) implies:
% 66.80/10.08 | | | | | (30) all_52_1 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | COMBINE_EQS: (7), (30) imply:
% 66.80/10.08 | | | | | (31) all_14_2 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | REDUCE: (22), (31) imply:
% 66.80/10.08 | | | | | (32) $false
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | CLOSE: (32) is inconsistent.
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | Case 2:
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | (33) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | ALPHA: (33) implies:
% 66.80/10.08 | | | | | (34) all_52_2 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | COMBINE_EQS: (12), (34) imply:
% 66.80/10.08 | | | | | (35) e2 = e0
% 66.80/10.08 | | | | |
% 66.80/10.08 | | | | | REDUCE: (9), (35) imply:
% 66.80/10.08 | | | | | (36) $false
% 66.80/10.08 | | | | |
% 66.80/10.09 | | | | | CLOSE: (36) is inconsistent.
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | End of split
% 66.80/10.09 | | | |
% 66.80/10.09 | | | End of split
% 66.80/10.09 | | |
% 66.80/10.09 | | End of split
% 66.80/10.09 | |
% 66.80/10.09 | End of split
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #175 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.09 (2) all_52_2 = e2
% 66.80/10.09 (3) ~ (e2 = e1)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | ALPHA: (1) implies:
% 66.80/10.09 | (4) all_52_2 = e1
% 66.80/10.09 |
% 66.80/10.09 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.09 | (5) e2 = e1
% 66.80/10.09 |
% 66.80/10.09 | SIMP: (5) implies:
% 66.80/10.09 | (6) e2 = e1
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (3), (6) imply:
% 66.80/10.09 | (7) $false
% 66.80/10.09 |
% 66.80/10.09 | CLOSE: (7) is inconsistent.
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #176 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.09 (2) all_52_0 = all_4_0
% 66.80/10.09 (3) ~ (all_4_0 = e1)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | ALPHA: (1) implies:
% 66.80/10.09 | (4) all_52_0 = e1
% 66.80/10.09 |
% 66.80/10.09 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.09 | (5) all_4_0 = e1
% 66.80/10.09 |
% 66.80/10.09 | SIMP: (5) implies:
% 66.80/10.09 | (6) all_4_0 = e1
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (3), (6) imply:
% 66.80/10.09 | (7) $false
% 66.80/10.09 |
% 66.80/10.09 | CLOSE: (7) is inconsistent.
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #177 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_2 = all_4_2
% 66.80/10.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 66.80/10.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 66.80/10.09 (3) (all_52_0 = e3 & ~ (all_52_2 = e2)) | (all_52_1 = e3 & ~ (all_52_2 =
% 66.80/10.09 e1)) | (all_52_3 = e3 & ~ (all_52_2 = e0))
% 66.80/10.09 (4) (all_52_0 = e1 & ~ (all_52_1 = e2)) | (all_52_2 = e1 & ~ (all_52_1 =
% 66.80/10.09 e3)) | (all_52_3 = e1 & ~ (all_52_1 = e0))
% 66.80/10.09 (5) ~ (e3 = e1)
% 66.80/10.09 (6) op(e2, e2) = all_10_2
% 66.80/10.09 (7) op(e2, e2) = all_14_0
% 66.80/10.09 (8) ~ (e2 = e0)
% 66.80/10.09 (9) all_52_0 = all_10_2
% 66.80/10.09 (10) ~ (all_14_0 = e3)
% 66.80/10.09 (11) all_52_1 = e2
% 66.80/10.09 (12) ~ (e3 = e2)
% 66.80/10.09 (13) (all_52_0 = e0 & ~ (all_52_3 = e2)) | (all_52_1 = e0 & ~ (all_52_3 =
% 66.80/10.09 e1)) | (all_52_2 = e0 & ~ (all_52_3 = e3))
% 66.80/10.09 (14) ~ (all_14_0 = e0)
% 66.80/10.09 (15) ~ (all_10_2 = e1)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | GROUND_INST: instantiating (2) with all_10_2, all_14_0, e2, e2, simplifying
% 66.80/10.09 | with (6), (7) gives:
% 66.80/10.09 | (16) all_14_0 = all_10_2
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (10), (16) imply:
% 66.80/10.09 | (17) ~ (all_10_2 = e3)
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (14), (16) imply:
% 66.80/10.09 | (18) ~ (all_10_2 = e0)
% 66.80/10.09 |
% 66.80/10.09 | BETA: splitting (3) gives:
% 66.80/10.09 |
% 66.80/10.09 | Case 1:
% 66.80/10.09 | |
% 66.80/10.09 | | (19) all_52_0 = e3 & ~ (all_52_2 = e2)
% 66.80/10.09 | |
% 66.80/10.09 | | ALPHA: (19) implies:
% 66.80/10.09 | | (20) all_52_0 = e3
% 66.80/10.09 | |
% 66.80/10.09 | | COMBINE_EQS: (9), (20) imply:
% 66.80/10.09 | | (21) all_10_2 = e3
% 66.80/10.09 | |
% 66.80/10.09 | | REDUCE: (17), (21) imply:
% 66.80/10.09 | | (22) $false
% 66.80/10.09 | |
% 66.80/10.09 | | CLOSE: (22) is inconsistent.
% 66.80/10.09 | |
% 66.80/10.09 | Case 2:
% 66.80/10.09 | |
% 66.80/10.09 | | (23) (all_52_1 = e3 & ~ (all_52_2 = e1)) | (all_52_3 = e3 & ~ (all_52_2
% 66.80/10.09 | | = e0))
% 66.80/10.09 | |
% 66.80/10.09 | | BETA: splitting (23) gives:
% 66.80/10.09 | |
% 66.80/10.09 | | Case 1:
% 66.80/10.09 | | |
% 66.80/10.09 | | | (24) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.09 | | |
% 66.80/10.09 | | | REF_CLOSE: (11), (12), (24) are inconsistent by sub-proof #180.
% 66.80/10.09 | | |
% 66.80/10.09 | | Case 2:
% 66.80/10.09 | | |
% 66.80/10.09 | | | (25) all_52_3 = e3 & ~ (all_52_2 = e0)
% 66.80/10.09 | | |
% 66.80/10.09 | | | ALPHA: (25) implies:
% 66.80/10.09 | | | (26) all_52_3 = e3
% 66.80/10.09 | | | (27) ~ (all_52_2 = e0)
% 66.80/10.09 | | |
% 66.80/10.09 | | | REDUCE: (1), (27) imply:
% 66.80/10.09 | | | (28) ~ (all_4_2 = e0)
% 66.80/10.09 | | |
% 66.80/10.09 | | | BETA: splitting (4) gives:
% 66.80/10.09 | | |
% 66.80/10.09 | | | Case 1:
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | (29) all_52_0 = e1 & ~ (all_52_1 = e2)
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | ALPHA: (29) implies:
% 66.80/10.09 | | | | (30) all_52_0 = e1
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | COMBINE_EQS: (9), (30) imply:
% 66.80/10.09 | | | | (31) all_10_2 = e1
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | SIMP: (31) implies:
% 66.80/10.09 | | | | (32) all_10_2 = e1
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | REDUCE: (15), (32) imply:
% 66.80/10.09 | | | | (33) $false
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | CLOSE: (33) is inconsistent.
% 66.80/10.09 | | | |
% 66.80/10.09 | | | Case 2:
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | (34) (all_52_2 = e1 & ~ (all_52_1 = e3)) | (all_52_3 = e1 & ~
% 66.80/10.09 | | | | (all_52_1 = e0))
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | BETA: splitting (34) gives:
% 66.80/10.09 | | | |
% 66.80/10.09 | | | | Case 1:
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | (35) all_52_2 = e1 & ~ (all_52_1 = e3)
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | ALPHA: (35) implies:
% 66.80/10.09 | | | | | (36) all_52_2 = e1
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | COMBINE_EQS: (1), (36) imply:
% 66.80/10.09 | | | | | (37) all_4_2 = e1
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | REDUCE: (28), (37) imply:
% 66.80/10.09 | | | | | (38) ~ (e1 = e0)
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | BETA: splitting (13) gives:
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | Case 1:
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | (39) all_52_0 = e0 & ~ (all_52_3 = e2)
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | ALPHA: (39) implies:
% 66.80/10.09 | | | | | | (40) all_52_0 = e0
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | COMBINE_EQS: (9), (40) imply:
% 66.80/10.09 | | | | | | (41) all_10_2 = e0
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | REDUCE: (18), (41) imply:
% 66.80/10.09 | | | | | | (42) $false
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | CLOSE: (42) is inconsistent.
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | Case 2:
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | (43) (all_52_1 = e0 & ~ (all_52_3 = e1)) | (all_52_2 = e0 & ~
% 66.80/10.09 | | | | | | (all_52_3 = e3))
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | BETA: splitting (43) gives:
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | | Case 1:
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | | (44) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | | REF_CLOSE: (8), (11), (44) are inconsistent by sub-proof #179.
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | Case 2:
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | | (45) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | | REF_CLOSE: (36), (38), (45) are inconsistent by sub-proof #178.
% 66.80/10.09 | | | | | | |
% 66.80/10.09 | | | | | | End of split
% 66.80/10.09 | | | | | |
% 66.80/10.09 | | | | | End of split
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | Case 2:
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | (46) all_52_3 = e1 & ~ (all_52_1 = e0)
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | ALPHA: (46) implies:
% 66.80/10.09 | | | | | (47) all_52_3 = e1
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | COMBINE_EQS: (26), (47) imply:
% 66.80/10.09 | | | | | (48) e3 = e1
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | REDUCE: (5), (48) imply:
% 66.80/10.09 | | | | | (49) $false
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | | CLOSE: (49) is inconsistent.
% 66.80/10.09 | | | | |
% 66.80/10.09 | | | | End of split
% 66.80/10.09 | | | |
% 66.80/10.09 | | | End of split
% 66.80/10.09 | | |
% 66.80/10.09 | | End of split
% 66.80/10.09 | |
% 66.80/10.09 | End of split
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #178 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_2 = e0 & ~ (all_52_3 = e3)
% 66.80/10.09 (2) all_52_2 = e1
% 66.80/10.09 (3) ~ (e1 = e0)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | ALPHA: (1) implies:
% 66.80/10.09 | (4) all_52_2 = e0
% 66.80/10.09 |
% 66.80/10.09 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.09 | (5) e1 = e0
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (3), (5) imply:
% 66.80/10.09 | (6) $false
% 66.80/10.09 |
% 66.80/10.09 | CLOSE: (6) is inconsistent.
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #179 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_1 = e0 & ~ (all_52_3 = e1)
% 66.80/10.09 (2) all_52_1 = e2
% 66.80/10.09 (3) ~ (e2 = e0)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | ALPHA: (1) implies:
% 66.80/10.09 | (4) all_52_1 = e0
% 66.80/10.09 |
% 66.80/10.09 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.09 | (5) e2 = e0
% 66.80/10.09 |
% 66.80/10.09 | SIMP: (5) implies:
% 66.80/10.09 | (6) e2 = e0
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (3), (6) imply:
% 66.80/10.09 | (7) $false
% 66.80/10.09 |
% 66.80/10.09 | CLOSE: (7) is inconsistent.
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09
% 66.80/10.09 Sub-proof #180 shows that the following formulas are inconsistent:
% 66.80/10.09 ----------------------------------------------------------------
% 66.80/10.09 (1) all_52_1 = e3 & ~ (all_52_2 = e1)
% 66.80/10.09 (2) all_52_1 = e2
% 66.80/10.09 (3) ~ (e3 = e2)
% 66.80/10.09
% 66.80/10.09 Begin of proof
% 66.80/10.09 |
% 66.80/10.09 | ALPHA: (1) implies:
% 66.80/10.09 | (4) all_52_1 = e3
% 66.80/10.09 |
% 66.80/10.09 | COMBINE_EQS: (2), (4) imply:
% 66.80/10.09 | (5) e3 = e2
% 66.80/10.09 |
% 66.80/10.09 | SIMP: (5) implies:
% 66.80/10.09 | (6) e3 = e2
% 66.80/10.09 |
% 66.80/10.09 | REDUCE: (3), (6) imply:
% 66.80/10.09 | (7) $false
% 66.80/10.09 |
% 66.80/10.09 | CLOSE: (7) is inconsistent.
% 66.80/10.09 |
% 66.80/10.09 End of proof
% 66.80/10.09 % SZS output end Proof for theBenchmark
% 66.80/10.09
% 66.80/10.09 9485ms
%------------------------------------------------------------------------------